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3.2 Incompressible Navier-Stokes equations

As in the whetting the appetite demo we consider the unsteady Navier Stokes equations

Find \((u,p):[0,T] \to (H_{0,D}^1)^d \times L^2\), s.t.

\begin{align*} \int_{\Omega} \partial_t u \cdot v + \int_{\Omega} \nu \nabla u \nabla v + u \cdot \nabla u v - \int_{\Omega} \operatorname{div}(v) p &= \int f v && \forall v \in (H_{0,D}^1)^d, \\ - \int_{\Omega} \operatorname{div}(u) q &= 0 && \forall q \in L^2, \\ \quad u(t=0) & = u_0 \end{align*}

Schäfer-Turek benchmark

We consider the benchmark setup of from http://www.featflow.de/en/benchmarks/cfdbenchmarking/flow/dfg_benchmark2_re100.html . The geometry is a 2D channel with a circular obstacle which is positioned (only slightly) off the center of the channel. The geometry:

title

The viscosity is set to \(\nu = 10^{-3}\).

[1]:
# import libarries, define geometry and generate mesh
from ngsolve import *
from ngsolve.webgui import Draw
from netgen.occ import *
from netgen.webgui import Draw as DrawGeo
shape = Rectangle(2,0.41).Circle(0.2,0.2,0.05).Reverse().Face()
shape.edges.name="cyl"
shape.edges.Min(X).name="inlet"
shape.edges.Max(X).name="outlet"
shape.edges.Min(Y).name="wall"
shape.edges.Max(Y).name="wall"
mesh = Mesh(OCCGeometry(shape, dim=2).GenerateMesh(maxh=0.07)).Curve(3)
[2]:
DrawGeo (shape)
Draw (mesh)
[2]:
BaseWebGuiScene

Viscosity:

[3]:
# viscosity
nu = 0.001

Taylor-Hood velocity-pressure pair

We use a Taylor-Hood discretization of degree \(k\). The finite element space for the (vectorial) velocity \(\mathbf{u}\) and the pressure \(p\) are:

\begin{align} \mathbf{u} \in \mathbf{V} &= \{ v \in H^1(\Omega) | v|_T \in \mathcal{P}^k(T) \}^2 \\ p \in Q &= \{ q \in H^1(\Omega) | q|_T \in \mathcal{P}^{k-1}(T) \} \end{align}

[4]:
k = 3
V = VectorH1(mesh,order=k, dirichlet="wall|cyl|inlet")
Q = H1(mesh,order=k-1)
X = V*Q

The VectorH1 is the product space of two H1 spaces with convenience operators for identity, grad(Grad) and div.

Stokes problem for initial values

Find \(\mathbf{u} \in \mathbf{V}\), \(p \in Q\) so that

\begin{align} \int_{\Omega} \nu \nabla \mathbf{u} : \nabla \mathbf{v} - \int_{\Omega} \operatorname{div}(\mathbf{v}) p &= \int \mathbf{f} \cdot \mathbf{v} && \forall \mathbf{v} \in \mathbf{V}, \\- \int_{\Omega} \operatorname{div}(\mathbf{u}) q &= 0 && \forall q \in Q, \end{align}

with boundary conditions:

  • the inflow boundary data ('inlet') with mean value \(1\)

\begin{align} u_x(0,y) &= 6 y(0.41-y)/(0.41)^2, \quad \int_{0}^{0.41} u_x(0,y) dy = 1 \\ u_y(0,y) &= 0 \end{align}

  • "do-nothing" boundary conditions on the ouflow ('outlet') and

  • homogeneous Dirichlet conditions on all other boundaries ('wall').

[5]:
gfu = GridFunction(X)
velocity, pressure = gfu.components
# parabolic inflow at bc=1:
uin = CoefficientFunction((1.5*4*y*(0.41-y)/(0.41*0.41),0))
velocity.Set(uin, definedon=mesh.Boundaries("inlet"))

Draw(velocity,mesh,"u")
Draw(pressure,mesh,"p")
[5]:
BaseWebGuiScene

inflow profile plot:

[6]:
import matplotlib; import numpy as np; import matplotlib.pyplot as plt;
%matplotlib inline
s = np.arange(0.0, 0.42, 0.01)
bvs = 6*s*(0.41-s)/(0.41)**2
plt.plot(s, bvs)
plt.xlabel('y'); plt.ylabel('$u_x(0,y)$'); plt.title('inflow profile')
plt.grid(True)
plt.show()
../../_images/i-tutorials_unit-3.2-navierstokes_navierstokes_12_0.png

To solve the Stokes (and later the Navier-Stokes) problem, we introduce the bilinear form:

\[a((u,p),(v,q)) := \int_{\Omega} \nu \nabla u : \nabla v - \operatorname{div}(v) p - \operatorname{div}(u) q\]

and directly use it to solve the Stokes problem for suitable initial values:

[7]:
(u,p), (v,q) = X.TnT()

a = BilinearForm(X)
stokes = (nu*InnerProduct(grad(u),grad(v))-div(u)*q-div(v)*p)*dx
a += stokes
a.Assemble()

f = LinearForm(X)
f.Assemble()

res = f.vec - a.mat*gfu.vec
inv_stokes = a.mat.Inverse(X.FreeDofs())
gfu.vec.data += inv_stokes * res
[8]:
sceneu = Draw(velocity,mesh,"u")
scenep = Draw(pressure,mesh,"p")

IMEX time discretization

For the time integration we consider an semi-implicit Euler method (IMEX) where the convection is treated only explicitly and the remaining part implicitly:

Find \((\mathbf{u}^{n+1},p^{n+1}) \in X = \mathbf{V} \times Q\), s.t. for all \((\mathbf{v},q) \in X = \mathbf{V} \times Q\)

\begin{align} \underbrace{m(\mathbf{u}^{n+1},\mathbf{v}) + \Delta t ~\cdot~a((\mathbf{u}^{n+1},p^{n+1}),(\mathbf{v},q))}_{ \to M^\ast} ~=~m(\mathbf{u}^{n},\mathbf{v}) - \Delta t ~\cdot~c(\mathbf{u}^{n}; \mathbf{u}^{n},\mathbf{v}) \end{align}

with \begin{align} m(\mathbf{u},\mathbf{v}) = \int \mathbf{u} \cdot \mathbf{v} \end{align}

and \begin{align} c(\mathbf{w},\mathbf{u},\mathbf{v}) = \int \mathbf{w} \cdot \nabla \mathbf{u} \cdot \mathbf{v} \end{align}

We prefer the incremental form (as it homogenizes the boundary conditions): \begin{align} m(\delta \mathbf{u}^{n+1},\mathbf{v}) + \Delta t ~\cdot~a((\delta \mathbf{u}^{n+1},\delta p^{n+1}),(\mathbf{v},q)) ~=~ \Delta t (-a((\mathbf{u}^{n},p^n),(\mathbf{v},q)) -c(\mathbf{u}^{n}; \mathbf{u}^{n},\mathbf{v})) \end{align}

[9]:
dt = 0.001
# matrix for implicit part of IMEX(1) scheme:
mstar = BilinearForm(X)
mstar += InnerProduct(u,v)*dx + dt*stokes
mstar.Assemble()
inv = mstar.mat.Inverse(X.FreeDofs())

Next, we want to evaluate the convection term \(c(u^n;u^n,v)\) for given \(u^n\), i.e. a linear form. We can do this by setting up a LinearForm

fc = LinearForm(X)
fc += (Grad(gfu) * gfu) * v * dx

Then, for \(u^n =\)gfu a call fc.Assemble() yields a vector fc.vecrepresenting the linear form.

Alternatively, we can use the semi-linear form structure of the convection form and put it into a BilinearForm (which indeed is able to represent non-bilinear forms as we will discuss in more detail in unit-3.3). We will not need the assembly (or the storage of a sparse matrix) though:

[10]:
conv = BilinearForm(X, nonassemble = True)
conv += (Grad(u) * u) * v * dx

Instead of assembling a LinearForm in every time step, we use an operator application of a BilinearForm, see unit-2.11 or the next units for more details.

The BilinearForm(which indeed is rather a semi-linear form) can compute the linear form at a given state u:

  • either by a call conv.Apply(gfu.vec,res) where the result ends up in the vector res

  • alternatively we can use the notation of an operator application conv.mat * gfu.vec yielding the same.

Below, we will use the latter.

[11]:
tend = 0
gfut = GridFunction(gfu.space,multidim=0)
[12]:
# implicit Euler/explicit Euler splitting method:
tend += 1
gfut.AddMultiDimComponent(gfu.vec)
t = 0; cnt = 0
while t < tend-0.5*dt:
    print ("\rt=", t, end="")

    conv.Assemble()
    res = (a.mat + conv.mat)* gfu.vec
    gfu.vec.data -= dt * inv * res

    t = t + dt; cnt += 1
    sceneu.Redraw()
    scenep.Redraw()
    if cnt % 50 == 0:
        gfut.AddMultiDimComponent(gfu.vec)

t= 0 t= 0.001 t= 0.002 t= 0.003 t= 0.004craete bilinearformapplication

t= 0.005 t= 0.006 t= 0.007 t= 0.008 t= 0.009000000000000001 t= 0.010000000000000002 t= 0.011000000000000003 t= 0.012000000000000004 t= 0.013000000000000005 t= 0.014000000000000005 t= 0.015000000000000006 t= 0.016000000000000007 t= 0.017000000000000008 t= 0.01800000000000001 t= 0.01900000000000001 t= 0.02000000000000001 t= 0.02100000000000001 t= 0.022000000000000013 t= 0.023000000000000013 t= 0.024000000000000014 t= 0.025000000000000015 t= 0.026000000000000016 t= 0.027000000000000017 t= 0.028000000000000018 t= 0.02900000000000002 t= 0.03000000000000002 t= 0.03100000000000002 t= 0.03200000000000002 t= 0.03300000000000002 t= 0.03400000000000002 t= 0.035000000000000024 t= 0.036000000000000025 t= 0.037000000000000026 t= 0.03800000000000003 t= 0.03900000000000003 t= 0.04000000000000003 t= 0.04100000000000003 t= 0.04200000000000003 t= 0.04300000000000003 t= 0.04400000000000003 t= 0.04500000000000003 t= 0.046000000000000034 t= 0.047000000000000035 t= 0.048000000000000036 t= 0.04900000000000004 t= 0.05000000000000004 t= 0.05100000000000004 t= 0.05200000000000004 t= 0.05300000000000004 t= 0.05400000000000004 t= 0.05500000000000004 t= 0.05600000000000004 t= 0.057000000000000044 t= 0.058000000000000045 t= 0.059000000000000045 t= 0.060000000000000046 t= 0.06100000000000005 t= 0.06200000000000005 t= 0.06300000000000004 t= 0.06400000000000004 t= 0.06500000000000004 t= 0.06600000000000004 t= 0.06700000000000005 t= 0.06800000000000005 t= 0.06900000000000005 t= 0.07000000000000005 t= 0.07100000000000005 t= 0.07200000000000005 t= 0.07300000000000005 t= 0.07400000000000005 t= 0.07500000000000005 t= 0.07600000000000005 t= 0.07700000000000005 t= 0.07800000000000006 t= 0.07900000000000006 t= 0.08000000000000006 t= 0.08100000000000006 t= 0.08200000000000006 t= 0.08300000000000006 t= 0.08400000000000006 t= 0.08500000000000006 t= 0.08600000000000006 t= 0.08700000000000006 t= 0.08800000000000006 t= 0.08900000000000007 t= 0.09000000000000007 t= 0.09100000000000007 t= 0.09200000000000007 t= 0.09300000000000007 t= 0.09400000000000007 t= 0.09500000000000007 t= 0.09600000000000007 t= 0.09700000000000007 t= 0.09800000000000007 t= 0.09900000000000007 t= 0.10000000000000007 t= 0.10100000000000008 t= 0.10200000000000008 t= 0.10300000000000008 t= 0.10400000000000008 t= 0.10500000000000008 t= 0.10600000000000008 t= 0.10700000000000008 t= 0.10800000000000008 t= 0.10900000000000008 t= 0.11000000000000008 t= 0.11100000000000008 t= 0.11200000000000009 t= 0.11300000000000009 t= 0.11400000000000009 t= 0.11500000000000009 t= 0.11600000000000009 t= 0.11700000000000009 t= 0.11800000000000009 t= 0.11900000000000009 t= 0.12000000000000009 t= 0.1210000000000001 t= 0.1220000000000001 t= 0.1230000000000001 t= 0.1240000000000001 t= 0.12500000000000008 t= 0.12600000000000008 t= 0.12700000000000009 t= 0.12800000000000009 t= 0.1290000000000001 t= 0.1300000000000001 t= 0.1310000000000001 t= 0.1320000000000001 t= 0.1330000000000001 t= 0.1340000000000001 t= 0.1350000000000001 t= 0.1360000000000001 t= 0.1370000000000001 t= 0.1380000000000001 t= 0.1390000000000001 t= 0.1400000000000001 t= 0.1410000000000001 t= 0.1420000000000001 t= 0.1430000000000001 t= 0.1440000000000001 t= 0.1450000000000001 t= 0.1460000000000001 t= 0.1470000000000001 t= 0.1480000000000001 t= 0.1490000000000001 t= 0.1500000000000001 t= 0.1510000000000001 t= 0.1520000000000001 t= 0.1530000000000001 t= 0.1540000000000001 t= 0.1550000000000001 t= 0.1560000000000001 t= 0.1570000000000001 t= 0.1580000000000001 t= 0.1590000000000001 t= 0.16000000000000011 t= 0.16100000000000012 t= 0.16200000000000012 t= 0.16300000000000012 t= 0.16400000000000012 t= 0.16500000000000012 t= 0.16600000000000012 t= 0.16700000000000012 t= 0.16800000000000012 t= 0.16900000000000012 t= 0.17000000000000012 t= 0.17100000000000012 t= 0.17200000000000013 t= 0.17300000000000013 t= 0.17400000000000013 t= 0.17500000000000013 t= 0.17600000000000013 t= 0.17700000000000013 t= 0.17800000000000013 t= 0.17900000000000013 t= 0.18000000000000013 t= 0.18100000000000013 t= 0.18200000000000013 t= 0.18300000000000013 t= 0.18400000000000014 t= 0.18500000000000014 t= 0.18600000000000014 t= 0.18700000000000014 t= 0.18800000000000014 t= 0.18900000000000014 t= 0.19000000000000014 t= 0.19100000000000014 t= 0.19200000000000014 t= 0.19300000000000014 t= 0.19400000000000014 t= 0.19500000000000015 t= 0.19600000000000015 t= 0.19700000000000015 t= 0.19800000000000015 t= 0.19900000000000015 t= 0.20000000000000015 t= 0.20100000000000015 t= 0.20200000000000015 t= 0.20300000000000015 t= 0.20400000000000015 t= 0.20500000000000015 t= 0.20600000000000016 t= 0.20700000000000016 t= 0.20800000000000016 t= 0.20900000000000016 t= 0.21000000000000016 t= 0.21100000000000016 t= 0.21200000000000016 t= 0.21300000000000016 t= 0.21400000000000016 t= 0.21500000000000016 t= 0.21600000000000016 t= 0.21700000000000016 t= 0.21800000000000017 t= 0.21900000000000017 t= 0.22000000000000017 t= 0.22100000000000017 t= 0.22200000000000017 t= 0.22300000000000017 t= 0.22400000000000017 t= 0.22500000000000017 t= 0.22600000000000017 t= 0.22700000000000017 t= 0.22800000000000017 t= 0.22900000000000018 t= 0.23000000000000018 t= 0.23100000000000018 t= 0.23200000000000018 t= 0.23300000000000018 t= 0.23400000000000018 t= 0.23500000000000018 t= 0.23600000000000018 t= 0.23700000000000018 t= 0.23800000000000018 t= 0.23900000000000018 t= 0.24000000000000019 t= 0.2410000000000002 t= 0.2420000000000002 t= 0.2430000000000002 t= 0.2440000000000002 t= 0.2450000000000002 t= 0.2460000000000002 t= 0.2470000000000002 t= 0.2480000000000002 t= 0.2490000000000002 t= 0.25000000000000017 t= 0.25100000000000017 t= 0.25200000000000017 t= 0.25300000000000017 t= 0.25400000000000017 t= 0.25500000000000017 t= 0.25600000000000017 t= 0.2570000000000002 t= 0.2580000000000002 t= 0.2590000000000002 t= 0.2600000000000002 t= 0.2610000000000002 t= 0.2620000000000002 t= 0.2630000000000002 t= 0.2640000000000002 t= 0.2650000000000002 t= 0.2660000000000002 t= 0.2670000000000002 t= 0.2680000000000002 t= 0.2690000000000002 t= 0.2700000000000002 t= 0.2710000000000002 t= 0.2720000000000002 t= 0.2730000000000002 t= 0.2740000000000002 t= 0.2750000000000002 t= 0.2760000000000002 t= 0.2770000000000002 t= 0.2780000000000002 t= 0.2790000000000002 t= 0.2800000000000002 t= 0.2810000000000002 t= 0.2820000000000002 t= 0.2830000000000002 t= 0.2840000000000002 t= 0.2850000000000002 t= 0.2860000000000002 t= 0.2870000000000002 t= 0.2880000000000002 t= 0.2890000000000002 t= 0.2900000000000002 t= 0.2910000000000002 t= 0.2920000000000002 t= 0.2930000000000002 t= 0.2940000000000002 t= 0.2950000000000002 t= 0.2960000000000002 t= 0.2970000000000002 t= 0.2980000000000002 t= 0.2990000000000002 t= 0.3000000000000002 t= 0.3010000000000002 t= 0.3020000000000002 t= 0.3030000000000002 t= 0.3040000000000002 t= 0.3050000000000002 t= 0.3060000000000002 t= 0.3070000000000002 t= 0.3080000000000002 t= 0.3090000000000002 t= 0.3100000000000002 t= 0.3110000000000002 t= 0.3120000000000002 t= 0.3130000000000002 t= 0.3140000000000002 t= 0.3150000000000002 t= 0.3160000000000002 t= 0.3170000000000002 t= 0.3180000000000002 t= 0.31900000000000023 t= 0.32000000000000023 t= 0.32100000000000023 t= 0.32200000000000023 t= 0.32300000000000023 t= 0.32400000000000023 t= 0.32500000000000023 t= 0.32600000000000023 t= 0.32700000000000023 t= 0.32800000000000024 t= 0.32900000000000024 t= 0.33000000000000024 t= 0.33100000000000024 t= 0.33200000000000024 t= 0.33300000000000024 t= 0.33400000000000024 t= 0.33500000000000024 t= 0.33600000000000024 t= 0.33700000000000024 t= 0.33800000000000024 t= 0.33900000000000025 t= 0.34000000000000025 t= 0.34100000000000025 t= 0.34200000000000025 t= 0.34300000000000025 t= 0.34400000000000025 t= 0.34500000000000025 t= 0.34600000000000025 t= 0.34700000000000025 t= 0.34800000000000025 t= 0.34900000000000025 t= 0.35000000000000026 t= 0.35100000000000026 t= 0.35200000000000026 t= 0.35300000000000026 t= 0.35400000000000026 t= 0.35500000000000026 t= 0.35600000000000026 t= 0.35700000000000026 t= 0.35800000000000026 t= 0.35900000000000026 t= 0.36000000000000026 t= 0.36100000000000027 t= 0.36200000000000027 t= 0.36300000000000027 t= 0.36400000000000027 t= 0.36500000000000027 t= 0.36600000000000027 t= 0.36700000000000027 t= 0.36800000000000027 t= 0.36900000000000027 t= 0.3700000000000003 t= 0.3710000000000003 t= 0.3720000000000003 t= 0.3730000000000003 t= 0.3740000000000003 t= 0.3750000000000003 t= 0.3760000000000003 t= 0.3770000000000003 t= 0.3780000000000003 t= 0.3790000000000003 t= 0.3800000000000003 t= 0.3810000000000003 t= 0.3820000000000003 t= 0.3830000000000003 t= 0.3840000000000003 t= 0.3850000000000003 t= 0.3860000000000003 t= 0.3870000000000003 t= 0.3880000000000003 t= 0.3890000000000003 t= 0.3900000000000003 t= 0.3910000000000003 t= 0.3920000000000003 t= 0.3930000000000003 t= 0.3940000000000003 t= 0.3950000000000003 t= 0.3960000000000003 t= 0.3970000000000003 t= 0.3980000000000003 t= 0.3990000000000003 t= 0.4000000000000003 t= 0.4010000000000003 t= 0.4020000000000003 t= 0.4030000000000003 t= 0.4040000000000003 t= 0.4050000000000003 t= 0.4060000000000003 t= 0.4070000000000003 t= 0.4080000000000003 t= 0.4090000000000003 t= 0.4100000000000003 t= 0.4110000000000003 t= 0.4120000000000003 t= 0.4130000000000003 t= 0.4140000000000003 t= 0.4150000000000003 t= 0.4160000000000003 t= 0.4170000000000003 t= 0.4180000000000003 t= 0.4190000000000003 t= 0.4200000000000003 t= 0.4210000000000003 t= 0.4220000000000003 t= 0.4230000000000003 t= 0.4240000000000003 t= 0.4250000000000003 t= 0.4260000000000003 t= 0.4270000000000003 t= 0.4280000000000003 t= 0.4290000000000003 t= 0.4300000000000003 t= 0.4310000000000003 t= 0.43200000000000033 t= 0.43300000000000033 t= 0.43400000000000033 t= 0.43500000000000033 t= 0.43600000000000033 t= 0.43700000000000033 t= 0.43800000000000033 t= 0.43900000000000033 t= 0.44000000000000034 t= 0.44100000000000034 t= 0.44200000000000034 t= 0.44300000000000034 t= 0.44400000000000034 t= 0.44500000000000034 t= 0.44600000000000034 t= 0.44700000000000034 t= 0.44800000000000034 t= 0.44900000000000034 t= 0.45000000000000034 t= 0.45100000000000035 t= 0.45200000000000035 t= 0.45300000000000035 t= 0.45400000000000035 t= 0.45500000000000035 t= 0.45600000000000035 t= 0.45700000000000035 t= 0.45800000000000035 t= 0.45900000000000035 t= 0.46000000000000035 t= 0.46100000000000035 t= 0.46200000000000035 t= 0.46300000000000036 t= 0.46400000000000036 t= 0.46500000000000036 t= 0.46600000000000036 t= 0.46700000000000036 t= 0.46800000000000036 t= 0.46900000000000036 t= 0.47000000000000036 t= 0.47100000000000036 t= 0.47200000000000036 t= 0.47300000000000036 t= 0.47400000000000037 t= 0.47500000000000037 t= 0.47600000000000037 t= 0.47700000000000037 t= 0.47800000000000037 t= 0.47900000000000037 t= 0.48000000000000037 t= 0.48100000000000037 t= 0.4820000000000004 t= 0.4830000000000004 t= 0.4840000000000004 t= 0.4850000000000004 t= 0.4860000000000004 t= 0.4870000000000004 t= 0.4880000000000004 t= 0.4890000000000004 t= 0.4900000000000004 t= 0.4910000000000004 t= 0.4920000000000004 t= 0.4930000000000004 t= 0.4940000000000004 t= 0.4950000000000004 t= 0.4960000000000004 t= 0.4970000000000004 t= 0.4980000000000004 t= 0.4990000000000004 t= 0.5000000000000003 t= 0.5010000000000003 t= 0.5020000000000003 t= 0.5030000000000003 t= 0.5040000000000003 t= 0.5050000000000003 t= 0.5060000000000003 t= 0.5070000000000003 t= 0.5080000000000003 t= 0.5090000000000003 t= 0.5100000000000003 t= 0.5110000000000003 t= 0.5120000000000003 t= 0.5130000000000003 t= 0.5140000000000003 t= 0.5150000000000003 t= 0.5160000000000003 t= 0.5170000000000003 t= 0.5180000000000003 t= 0.5190000000000003 t= 0.5200000000000004 t= 0.5210000000000004 t= 0.5220000000000004 t= 0.5230000000000004 t= 0.5240000000000004 t= 0.5250000000000004 t= 0.5260000000000004 t= 0.5270000000000004 t= 0.5280000000000004 t= 0.5290000000000004 t= 0.5300000000000004 t= 0.5310000000000004 t= 0.5320000000000004 t= 0.5330000000000004 t= 0.5340000000000004 t= 0.5350000000000004 t= 0.5360000000000004 t= 0.5370000000000004 t= 0.5380000000000004 t= 0.5390000000000004 t= 0.5400000000000004 t= 0.5410000000000004 t= 0.5420000000000004 t= 0.5430000000000004 t= 0.5440000000000004 t= 0.5450000000000004 t= 0.5460000000000004 t= 0.5470000000000004 t= 0.5480000000000004 t= 0.5490000000000004 t= 0.5500000000000004 t= 0.5510000000000004 t= 0.5520000000000004 t= 0.5530000000000004 t= 0.5540000000000004 t= 0.5550000000000004 t= 0.5560000000000004 t= 0.5570000000000004 t= 0.5580000000000004 t= 0.5590000000000004 t= 0.5600000000000004 t= 0.5610000000000004 t= 0.5620000000000004 t= 0.5630000000000004 t= 0.5640000000000004 t= 0.5650000000000004 t= 0.5660000000000004 t= 0.5670000000000004 t= 0.5680000000000004 t= 0.5690000000000004 t= 0.5700000000000004 t= 0.5710000000000004 t= 0.5720000000000004 t= 0.5730000000000004 t= 0.5740000000000004 t= 0.5750000000000004 t= 0.5760000000000004 t= 0.5770000000000004 t= 0.5780000000000004 t= 0.5790000000000004 t= 0.5800000000000004 t= 0.5810000000000004 t= 0.5820000000000004 t= 0.5830000000000004 t= 0.5840000000000004 t= 0.5850000000000004 t= 0.5860000000000004 t= 0.5870000000000004 t= 0.5880000000000004 t= 0.5890000000000004 t= 0.5900000000000004 t= 0.5910000000000004 t= 0.5920000000000004 t= 0.5930000000000004 t= 0.5940000000000004 t= 0.5950000000000004 t= 0.5960000000000004 t= 0.5970000000000004 t= 0.5980000000000004 t= 0.5990000000000004 t= 0.6000000000000004 t= 0.6010000000000004 t= 0.6020000000000004 t= 0.6030000000000004 t= 0.6040000000000004 t= 0.6050000000000004 t= 0.6060000000000004 t= 0.6070000000000004 t= 0.6080000000000004 t= 0.6090000000000004 t= 0.6100000000000004 t= 0.6110000000000004 t= 0.6120000000000004 t= 0.6130000000000004 t= 0.6140000000000004 t= 0.6150000000000004 t= 0.6160000000000004 t= 0.6170000000000004 t= 0.6180000000000004 t= 0.6190000000000004 t= 0.6200000000000004 t= 0.6210000000000004 t= 0.6220000000000004 t= 0.6230000000000004 t= 0.6240000000000004 t= 0.6250000000000004 t= 0.6260000000000004 t= 0.6270000000000004 t= 0.6280000000000004 t= 0.6290000000000004 t= 0.6300000000000004 t= 0.6310000000000004 t= 0.6320000000000005 t= 0.6330000000000005 t= 0.6340000000000005 t= 0.6350000000000005 t= 0.6360000000000005 t= 0.6370000000000005 t= 0.6380000000000005 t= 0.6390000000000005 t= 0.6400000000000005 t= 0.6410000000000005 t= 0.6420000000000005 t= 0.6430000000000005 t= 0.6440000000000005 t= 0.6450000000000005 t= 0.6460000000000005 t= 0.6470000000000005 t= 0.6480000000000005 t= 0.6490000000000005 t= 0.6500000000000005 t= 0.6510000000000005 t= 0.6520000000000005 t= 0.6530000000000005 t= 0.6540000000000005 t= 0.6550000000000005 t= 0.6560000000000005 t= 0.6570000000000005 t= 0.6580000000000005 t= 0.6590000000000005 t= 0.6600000000000005 t= 0.6610000000000005 t= 0.6620000000000005 t= 0.6630000000000005 t= 0.6640000000000005 t= 0.6650000000000005 t= 0.6660000000000005 t= 0.6670000000000005 t= 0.6680000000000005 t= 0.6690000000000005 t= 0.6700000000000005 t= 0.6710000000000005 t= 0.6720000000000005 t= 0.6730000000000005 t= 0.6740000000000005 t= 0.6750000000000005 t= 0.6760000000000005 t= 0.6770000000000005 t= 0.6780000000000005 t= 0.6790000000000005 t= 0.6800000000000005 t= 0.6810000000000005 t= 0.6820000000000005 t= 0.6830000000000005 t= 0.6840000000000005 t= 0.6850000000000005 t= 0.6860000000000005 t= 0.6870000000000005 t= 0.6880000000000005 t= 0.6890000000000005 t= 0.6900000000000005 t= 0.6910000000000005 t= 0.6920000000000005 t= 0.6930000000000005 t= 0.6940000000000005 t= 0.6950000000000005 t= 0.6960000000000005 t= 0.6970000000000005 t= 0.6980000000000005 t= 0.6990000000000005 t= 0.7000000000000005 t= 0.7010000000000005 t= 0.7020000000000005 t= 0.7030000000000005 t= 0.7040000000000005 t= 0.7050000000000005 t= 0.7060000000000005 t= 0.7070000000000005 t= 0.7080000000000005 t= 0.7090000000000005 t= 0.7100000000000005 t= 0.7110000000000005 t= 0.7120000000000005 t= 0.7130000000000005 t= 0.7140000000000005 t= 0.7150000000000005 t= 0.7160000000000005 t= 0.7170000000000005 t= 0.7180000000000005 t= 0.7190000000000005 t= 0.7200000000000005 t= 0.7210000000000005 t= 0.7220000000000005 t= 0.7230000000000005 t= 0.7240000000000005 t= 0.7250000000000005 t= 0.7260000000000005 t= 0.7270000000000005 t= 0.7280000000000005 t= 0.7290000000000005 t= 0.7300000000000005 t= 0.7310000000000005 t= 0.7320000000000005 t= 0.7330000000000005 t= 0.7340000000000005 t= 0.7350000000000005 t= 0.7360000000000005 t= 0.7370000000000005 t= 0.7380000000000005 t= 0.7390000000000005 t= 0.7400000000000005 t= 0.7410000000000005 t= 0.7420000000000005 t= 0.7430000000000005 t= 0.7440000000000005 t= 0.7450000000000006 t= 0.7460000000000006 t= 0.7470000000000006 t= 0.7480000000000006 t= 0.7490000000000006 t= 0.7500000000000006 t= 0.7510000000000006 t= 0.7520000000000006 t= 0.7530000000000006 t= 0.7540000000000006 t= 0.7550000000000006 t= 0.7560000000000006 t= 0.7570000000000006 t= 0.7580000000000006 t= 0.7590000000000006 t= 0.7600000000000006 t= 0.7610000000000006 t= 0.7620000000000006 t= 0.7630000000000006 t= 0.7640000000000006 t= 0.7650000000000006 t= 0.7660000000000006 t= 0.7670000000000006 t= 0.7680000000000006 t= 0.7690000000000006 t= 0.7700000000000006 t= 0.7710000000000006 t= 0.7720000000000006 t= 0.7730000000000006 t= 0.7740000000000006 t= 0.7750000000000006 t= 0.7760000000000006 t= 0.7770000000000006 t= 0.7780000000000006 t= 0.7790000000000006 t= 0.7800000000000006 t= 0.7810000000000006 t= 0.7820000000000006 t= 0.7830000000000006 t= 0.7840000000000006 t= 0.7850000000000006 t= 0.7860000000000006 t= 0.7870000000000006 t= 0.7880000000000006 t= 0.7890000000000006 t= 0.7900000000000006 t= 0.7910000000000006 t= 0.7920000000000006 t= 0.7930000000000006 t= 0.7940000000000006 t= 0.7950000000000006 t= 0.7960000000000006 t= 0.7970000000000006 t= 0.7980000000000006 t= 0.7990000000000006 t= 0.8000000000000006 t= 0.8010000000000006 t= 0.8020000000000006 t= 0.8030000000000006 t= 0.8040000000000006 t= 0.8050000000000006 t= 0.8060000000000006 t= 0.8070000000000006 t= 0.8080000000000006 t= 0.8090000000000006 t= 0.8100000000000006 t= 0.8110000000000006 t= 0.8120000000000006 t= 0.8130000000000006 t= 0.8140000000000006 t= 0.8150000000000006 t= 0.8160000000000006 t= 0.8170000000000006 t= 0.8180000000000006 t= 0.8190000000000006 t= 0.8200000000000006 t= 0.8210000000000006 t= 0.8220000000000006 t= 0.8230000000000006 t= 0.8240000000000006 t= 0.8250000000000006 t= 0.8260000000000006 t= 0.8270000000000006 t= 0.8280000000000006 t= 0.8290000000000006 t= 0.8300000000000006 t= 0.8310000000000006 t= 0.8320000000000006 t= 0.8330000000000006 t= 0.8340000000000006 t= 0.8350000000000006 t= 0.8360000000000006 t= 0.8370000000000006 t= 0.8380000000000006 t= 0.8390000000000006 t= 0.8400000000000006 t= 0.8410000000000006 t= 0.8420000000000006 t= 0.8430000000000006 t= 0.8440000000000006 t= 0.8450000000000006 t= 0.8460000000000006 t= 0.8470000000000006 t= 0.8480000000000006 t= 0.8490000000000006 t= 0.8500000000000006 t= 0.8510000000000006 t= 0.8520000000000006 t= 0.8530000000000006 t= 0.8540000000000006 t= 0.8550000000000006 t= 0.8560000000000006 t= 0.8570000000000007 t= 0.8580000000000007 t= 0.8590000000000007 t= 0.8600000000000007 t= 0.8610000000000007 t= 0.8620000000000007 t= 0.8630000000000007 t= 0.8640000000000007 t= 0.8650000000000007 t= 0.8660000000000007 t= 0.8670000000000007 t= 0.8680000000000007 t= 0.8690000000000007 t= 0.8700000000000007 t= 0.8710000000000007 t= 0.8720000000000007 t= 0.8730000000000007 t= 0.8740000000000007 t= 0.8750000000000007 t= 0.8760000000000007 t= 0.8770000000000007 t= 0.8780000000000007 t= 0.8790000000000007 t= 0.8800000000000007 t= 0.8810000000000007 t= 0.8820000000000007 t= 0.8830000000000007 t= 0.8840000000000007 t= 0.8850000000000007 t= 0.8860000000000007 t= 0.8870000000000007 t= 0.8880000000000007 t= 0.8890000000000007 t= 0.8900000000000007 t= 0.8910000000000007 t= 0.8920000000000007 t= 0.8930000000000007 t= 0.8940000000000007 t= 0.8950000000000007 t= 0.8960000000000007 t= 0.8970000000000007 t= 0.8980000000000007 t= 0.8990000000000007 t= 0.9000000000000007 t= 0.9010000000000007 t= 0.9020000000000007 t= 0.9030000000000007 t= 0.9040000000000007 t= 0.9050000000000007 t= 0.9060000000000007 t= 0.9070000000000007 t= 0.9080000000000007 t= 0.9090000000000007 t= 0.9100000000000007 t= 0.9110000000000007 t= 0.9120000000000007 t= 0.9130000000000007 t= 0.9140000000000007 t= 0.9150000000000007 t= 0.9160000000000007 t= 0.9170000000000007 t= 0.9180000000000007 t= 0.9190000000000007 t= 0.9200000000000007 t= 0.9210000000000007 t= 0.9220000000000007 t= 0.9230000000000007 t= 0.9240000000000007 t= 0.9250000000000007 t= 0.9260000000000007 t= 0.9270000000000007 t= 0.9280000000000007 t= 0.9290000000000007 t= 0.9300000000000007 t= 0.9310000000000007 t= 0.9320000000000007 t= 0.9330000000000007 t= 0.9340000000000007 t= 0.9350000000000007 t= 0.9360000000000007 t= 0.9370000000000007 t= 0.9380000000000007 t= 0.9390000000000007 t= 0.9400000000000007 t= 0.9410000000000007 t= 0.9420000000000007 t= 0.9430000000000007 t= 0.9440000000000007 t= 0.9450000000000007 t= 0.9460000000000007 t= 0.9470000000000007 t= 0.9480000000000007 t= 0.9490000000000007 t= 0.9500000000000007 t= 0.9510000000000007 t= 0.9520000000000007 t= 0.9530000000000007 t= 0.9540000000000007 t= 0.9550000000000007 t= 0.9560000000000007 t= 0.9570000000000007 t= 0.9580000000000007 t= 0.9590000000000007 t= 0.9600000000000007 t= 0.9610000000000007 t= 0.9620000000000007 t= 0.9630000000000007 t= 0.9640000000000007 t= 0.9650000000000007 t= 0.9660000000000007 t= 0.9670000000000007 t= 0.9680000000000007 t= 0.9690000000000007 t= 0.9700000000000008 t= 0.9710000000000008 t= 0.9720000000000008 t= 0.9730000000000008 t= 0.9740000000000008 t= 0.9750000000000008 t= 0.9760000000000008 t= 0.9770000000000008 t= 0.9780000000000008 t= 0.9790000000000008 t= 0.9800000000000008 t= 0.9810000000000008 t= 0.9820000000000008 t= 0.9830000000000008 t= 0.9840000000000008 t= 0.9850000000000008 t= 0.9860000000000008 t= 0.9870000000000008 t= 0.9880000000000008 t= 0.9890000000000008 t= 0.9900000000000008 t= 0.9910000000000008 t= 0.9920000000000008 t= 0.9930000000000008 t= 0.9940000000000008 t= 0.9950000000000008 t= 0.9960000000000008 t= 0.9970000000000008 t= 0.9980000000000008 t= 0.9990000000000008

</pre>

t= 0 t= 0.001 t= 0.002 t= 0.003 t= 0.004craete bilinearformapplication

t= 0.005 t= 0.006 t= 0.007 t= 0.008 t= 0.009000000000000001 t= 0.010000000000000002 t= 0.011000000000000003 t= 0.012000000000000004 t= 0.013000000000000005 t= 0.014000000000000005 t= 0.015000000000000006 t= 0.016000000000000007 t= 0.017000000000000008 t= 0.01800000000000001 t= 0.01900000000000001 t= 0.02000000000000001 t= 0.02100000000000001 t= 0.022000000000000013 t= 0.023000000000000013 t= 0.024000000000000014 t= 0.025000000000000015 t= 0.026000000000000016 t= 0.027000000000000017 t= 0.028000000000000018 t= 0.02900000000000002 t= 0.03000000000000002 t= 0.03100000000000002 t= 0.03200000000000002 t= 0.03300000000000002 t= 0.03400000000000002 t= 0.035000000000000024 t= 0.036000000000000025 t= 0.037000000000000026 t= 0.03800000000000003 t= 0.03900000000000003 t= 0.04000000000000003 t= 0.04100000000000003 t= 0.04200000000000003 t= 0.04300000000000003 t= 0.04400000000000003 t= 0.04500000000000003 t= 0.046000000000000034 t= 0.047000000000000035 t= 0.048000000000000036 t= 0.04900000000000004 t= 0.05000000000000004 t= 0.05100000000000004 t= 0.05200000000000004 t= 0.05300000000000004 t= 0.05400000000000004 t= 0.05500000000000004 t= 0.05600000000000004 t= 0.057000000000000044 t= 0.058000000000000045 t= 0.059000000000000045 t= 0.060000000000000046 t= 0.06100000000000005 t= 0.06200000000000005 t= 0.06300000000000004 t= 0.06400000000000004 t= 0.06500000000000004 t= 0.06600000000000004 t= 0.06700000000000005 t= 0.06800000000000005 t= 0.06900000000000005 t= 0.07000000000000005 t= 0.07100000000000005 t= 0.07200000000000005 t= 0.07300000000000005 t= 0.07400000000000005 t= 0.07500000000000005 t= 0.07600000000000005 t= 0.07700000000000005 t= 0.07800000000000006 t= 0.07900000000000006 t= 0.08000000000000006 t= 0.08100000000000006 t= 0.08200000000000006 t= 0.08300000000000006 t= 0.08400000000000006 t= 0.08500000000000006 t= 0.08600000000000006 t= 0.08700000000000006 t= 0.08800000000000006 t= 0.08900000000000007 t= 0.09000000000000007 t= 0.09100000000000007 t= 0.09200000000000007 t= 0.09300000000000007 t= 0.09400000000000007 t= 0.09500000000000007 t= 0.09600000000000007 t= 0.09700000000000007 t= 0.09800000000000007 t= 0.09900000000000007 t= 0.10000000000000007 t= 0.10100000000000008 t= 0.10200000000000008 t= 0.10300000000000008 t= 0.10400000000000008 t= 0.10500000000000008 t= 0.10600000000000008 t= 0.10700000000000008 t= 0.10800000000000008 t= 0.10900000000000008 t= 0.11000000000000008 t= 0.11100000000000008 t= 0.11200000000000009 t= 0.11300000000000009 t= 0.11400000000000009 t= 0.11500000000000009 t= 0.11600000000000009 t= 0.11700000000000009 t= 0.11800000000000009 t= 0.11900000000000009 t= 0.12000000000000009 t= 0.1210000000000001 t= 0.1220000000000001 t= 0.1230000000000001 t= 0.1240000000000001 t= 0.12500000000000008 t= 0.12600000000000008 t= 0.12700000000000009 t= 0.12800000000000009 t= 0.1290000000000001 t= 0.1300000000000001 t= 0.1310000000000001 t= 0.1320000000000001 t= 0.1330000000000001 t= 0.1340000000000001 t= 0.1350000000000001 t= 0.1360000000000001 t= 0.1370000000000001 t= 0.1380000000000001 t= 0.1390000000000001 t= 0.1400000000000001 t= 0.1410000000000001 t= 0.1420000000000001 t= 0.1430000000000001 t= 0.1440000000000001 t= 0.1450000000000001 t= 0.1460000000000001 t= 0.1470000000000001 t= 0.1480000000000001 t= 0.1490000000000001 t= 0.1500000000000001 t= 0.1510000000000001 t= 0.1520000000000001 t= 0.1530000000000001 t= 0.1540000000000001 t= 0.1550000000000001 t= 0.1560000000000001 t= 0.1570000000000001 t= 0.1580000000000001 t= 0.1590000000000001 t= 0.16000000000000011 t= 0.16100000000000012 t= 0.16200000000000012 t= 0.16300000000000012 t= 0.16400000000000012 t= 0.16500000000000012 t= 0.16600000000000012 t= 0.16700000000000012 t= 0.16800000000000012 t= 0.16900000000000012 t= 0.17000000000000012 t= 0.17100000000000012 t= 0.17200000000000013 t= 0.17300000000000013 t= 0.17400000000000013 t= 0.17500000000000013 t= 0.17600000000000013 t= 0.17700000000000013 t= 0.17800000000000013 t= 0.17900000000000013 t= 0.18000000000000013 t= 0.18100000000000013 t= 0.18200000000000013 t= 0.18300000000000013 t= 0.18400000000000014 t= 0.18500000000000014 t= 0.18600000000000014 t= 0.18700000000000014 t= 0.18800000000000014 t= 0.18900000000000014 t= 0.19000000000000014 t= 0.19100000000000014 t= 0.19200000000000014 t= 0.19300000000000014 t= 0.19400000000000014 t= 0.19500000000000015 t= 0.19600000000000015 t= 0.19700000000000015 t= 0.19800000000000015 t= 0.19900000000000015 t= 0.20000000000000015 t= 0.20100000000000015 t= 0.20200000000000015 t= 0.20300000000000015 t= 0.20400000000000015 t= 0.20500000000000015 t= 0.20600000000000016 t= 0.20700000000000016 t= 0.20800000000000016 t= 0.20900000000000016 t= 0.21000000000000016 t= 0.21100000000000016 t= 0.21200000000000016 t= 0.21300000000000016 t= 0.21400000000000016 t= 0.21500000000000016 t= 0.21600000000000016 t= 0.21700000000000016 t= 0.21800000000000017 t= 0.21900000000000017 t= 0.22000000000000017 t= 0.22100000000000017 t= 0.22200000000000017 t= 0.22300000000000017 t= 0.22400000000000017 t= 0.22500000000000017 t= 0.22600000000000017 t= 0.22700000000000017 t= 0.22800000000000017 t= 0.22900000000000018 t= 0.23000000000000018 t= 0.23100000000000018 t= 0.23200000000000018 t= 0.23300000000000018 t= 0.23400000000000018 t= 0.23500000000000018 t= 0.23600000000000018 t= 0.23700000000000018 t= 0.23800000000000018 t= 0.23900000000000018 t= 0.24000000000000019 t= 0.2410000000000002 t= 0.2420000000000002 t= 0.2430000000000002 t= 0.2440000000000002 t= 0.2450000000000002 t= 0.2460000000000002 t= 0.2470000000000002 t= 0.2480000000000002 t= 0.2490000000000002 t= 0.25000000000000017 t= 0.25100000000000017 t= 0.25200000000000017 t= 0.25300000000000017 t= 0.25400000000000017 t= 0.25500000000000017 t= 0.25600000000000017 t= 0.2570000000000002 t= 0.2580000000000002 t= 0.2590000000000002 t= 0.2600000000000002 t= 0.2610000000000002 t= 0.2620000000000002 t= 0.2630000000000002 t= 0.2640000000000002 t= 0.2650000000000002 t= 0.2660000000000002 t= 0.2670000000000002 t= 0.2680000000000002 t= 0.2690000000000002 t= 0.2700000000000002 t= 0.2710000000000002 t= 0.2720000000000002 t= 0.2730000000000002 t= 0.2740000000000002 t= 0.2750000000000002 t= 0.2760000000000002 t= 0.2770000000000002 t= 0.2780000000000002 t= 0.2790000000000002 t= 0.2800000000000002 t= 0.2810000000000002 t= 0.2820000000000002 t= 0.2830000000000002 t= 0.2840000000000002 t= 0.2850000000000002 t= 0.2860000000000002 t= 0.2870000000000002 t= 0.2880000000000002 t= 0.2890000000000002 t= 0.2900000000000002 t= 0.2910000000000002 t= 0.2920000000000002 t= 0.2930000000000002 t= 0.2940000000000002 t= 0.2950000000000002 t= 0.2960000000000002 t= 0.2970000000000002 t= 0.2980000000000002 t= 0.2990000000000002 t= 0.3000000000000002 t= 0.3010000000000002 t= 0.3020000000000002 t= 0.3030000000000002 t= 0.3040000000000002 t= 0.3050000000000002 t= 0.3060000000000002 t= 0.3070000000000002 t= 0.3080000000000002 t= 0.3090000000000002 t= 0.3100000000000002 t= 0.3110000000000002 t= 0.3120000000000002 t= 0.3130000000000002 t= 0.3140000000000002 t= 0.3150000000000002 t= 0.3160000000000002 t= 0.3170000000000002 t= 0.3180000000000002 t= 0.31900000000000023 t= 0.32000000000000023 t= 0.32100000000000023 t= 0.32200000000000023 t= 0.32300000000000023 t= 0.32400000000000023 t= 0.32500000000000023 t= 0.32600000000000023 t= 0.32700000000000023 t= 0.32800000000000024 t= 0.32900000000000024 t= 0.33000000000000024 t= 0.33100000000000024 t= 0.33200000000000024 t= 0.33300000000000024 t= 0.33400000000000024 t= 0.33500000000000024 t= 0.33600000000000024 t= 0.33700000000000024 t= 0.33800000000000024 t= 0.33900000000000025 t= 0.34000000000000025 t= 0.34100000000000025 t= 0.34200000000000025 t= 0.34300000000000025 t= 0.34400000000000025 t= 0.34500000000000025 t= 0.34600000000000025 t= 0.34700000000000025 t= 0.34800000000000025 t= 0.34900000000000025 t= 0.35000000000000026 t= 0.35100000000000026 t= 0.35200000000000026 t= 0.35300000000000026 t= 0.35400000000000026 t= 0.35500000000000026 t= 0.35600000000000026 t= 0.35700000000000026 t= 0.35800000000000026 t= 0.35900000000000026 t= 0.36000000000000026 t= 0.36100000000000027 t= 0.36200000000000027 t= 0.36300000000000027 t= 0.36400000000000027 t= 0.36500000000000027 t= 0.36600000000000027 t= 0.36700000000000027 t= 0.36800000000000027 t= 0.36900000000000027 t= 0.3700000000000003 t= 0.3710000000000003 t= 0.3720000000000003 t= 0.3730000000000003 t= 0.3740000000000003 t= 0.3750000000000003 t= 0.3760000000000003 t= 0.3770000000000003 t= 0.3780000000000003 t= 0.3790000000000003 t= 0.3800000000000003 t= 0.3810000000000003 t= 0.3820000000000003 t= 0.3830000000000003 t= 0.3840000000000003 t= 0.3850000000000003 t= 0.3860000000000003 t= 0.3870000000000003 t= 0.3880000000000003 t= 0.3890000000000003 t= 0.3900000000000003 t= 0.3910000000000003 t= 0.3920000000000003 t= 0.3930000000000003 t= 0.3940000000000003 t= 0.3950000000000003 t= 0.3960000000000003 t= 0.3970000000000003 t= 0.3980000000000003 t= 0.3990000000000003 t= 0.4000000000000003 t= 0.4010000000000003 t= 0.4020000000000003 t= 0.4030000000000003 t= 0.4040000000000003 t= 0.4050000000000003 t= 0.4060000000000003 t= 0.4070000000000003 t= 0.4080000000000003 t= 0.4090000000000003 t= 0.4100000000000003 t= 0.4110000000000003 t= 0.4120000000000003 t= 0.4130000000000003 t= 0.4140000000000003 t= 0.4150000000000003 t= 0.4160000000000003 t= 0.4170000000000003 t= 0.4180000000000003 t= 0.4190000000000003 t= 0.4200000000000003 t= 0.4210000000000003 t= 0.4220000000000003 t= 0.4230000000000003 t= 0.4240000000000003 t= 0.4250000000000003 t= 0.4260000000000003 t= 0.4270000000000003 t= 0.4280000000000003 t= 0.4290000000000003 t= 0.4300000000000003 t= 0.4310000000000003 t= 0.43200000000000033 t= 0.43300000000000033 t= 0.43400000000000033 t= 0.43500000000000033 t= 0.43600000000000033 t= 0.43700000000000033 t= 0.43800000000000033 t= 0.43900000000000033 t= 0.44000000000000034 t= 0.44100000000000034 t= 0.44200000000000034 t= 0.44300000000000034 t= 0.44400000000000034 t= 0.44500000000000034 t= 0.44600000000000034 t= 0.44700000000000034 t= 0.44800000000000034 t= 0.44900000000000034 t= 0.45000000000000034 t= 0.45100000000000035 t= 0.45200000000000035 t= 0.45300000000000035 t= 0.45400000000000035 t= 0.45500000000000035 t= 0.45600000000000035 t= 0.45700000000000035 t= 0.45800000000000035 t= 0.45900000000000035 t= 0.46000000000000035 t= 0.46100000000000035 t= 0.46200000000000035 t= 0.46300000000000036 t= 0.46400000000000036 t= 0.46500000000000036 t= 0.46600000000000036 t= 0.46700000000000036 t= 0.46800000000000036 t= 0.46900000000000036 t= 0.47000000000000036 t= 0.47100000000000036 t= 0.47200000000000036 t= 0.47300000000000036 t= 0.47400000000000037 t= 0.47500000000000037 t= 0.47600000000000037 t= 0.47700000000000037 t= 0.47800000000000037 t= 0.47900000000000037 t= 0.48000000000000037 t= 0.48100000000000037 t= 0.4820000000000004 t= 0.4830000000000004 t= 0.4840000000000004 t= 0.4850000000000004 t= 0.4860000000000004 t= 0.4870000000000004 t= 0.4880000000000004 t= 0.4890000000000004 t= 0.4900000000000004 t= 0.4910000000000004 t= 0.4920000000000004 t= 0.4930000000000004 t= 0.4940000000000004 t= 0.4950000000000004 t= 0.4960000000000004 t= 0.4970000000000004 t= 0.4980000000000004 t= 0.4990000000000004 t= 0.5000000000000003 t= 0.5010000000000003 t= 0.5020000000000003 t= 0.5030000000000003 t= 0.5040000000000003 t= 0.5050000000000003 t= 0.5060000000000003 t= 0.5070000000000003 t= 0.5080000000000003 t= 0.5090000000000003 t= 0.5100000000000003 t= 0.5110000000000003 t= 0.5120000000000003 t= 0.5130000000000003 t= 0.5140000000000003 t= 0.5150000000000003 t= 0.5160000000000003 t= 0.5170000000000003 t= 0.5180000000000003 t= 0.5190000000000003 t= 0.5200000000000004 t= 0.5210000000000004 t= 0.5220000000000004 t= 0.5230000000000004 t= 0.5240000000000004 t= 0.5250000000000004 t= 0.5260000000000004 t= 0.5270000000000004 t= 0.5280000000000004 t= 0.5290000000000004 t= 0.5300000000000004 t= 0.5310000000000004 t= 0.5320000000000004 t= 0.5330000000000004 t= 0.5340000000000004 t= 0.5350000000000004 t= 0.5360000000000004 t= 0.5370000000000004 t= 0.5380000000000004 t= 0.5390000000000004 t= 0.5400000000000004 t= 0.5410000000000004 t= 0.5420000000000004 t= 0.5430000000000004 t= 0.5440000000000004 t= 0.5450000000000004 t= 0.5460000000000004 t= 0.5470000000000004 t= 0.5480000000000004 t= 0.5490000000000004 t= 0.5500000000000004 t= 0.5510000000000004 t= 0.5520000000000004 t= 0.5530000000000004 t= 0.5540000000000004 t= 0.5550000000000004 t= 0.5560000000000004 t= 0.5570000000000004 t= 0.5580000000000004 t= 0.5590000000000004 t= 0.5600000000000004 t= 0.5610000000000004 t= 0.5620000000000004 t= 0.5630000000000004 t= 0.5640000000000004 t= 0.5650000000000004 t= 0.5660000000000004 t= 0.5670000000000004 t= 0.5680000000000004 t= 0.5690000000000004 t= 0.5700000000000004 t= 0.5710000000000004 t= 0.5720000000000004 t= 0.5730000000000004 t= 0.5740000000000004 t= 0.5750000000000004 t= 0.5760000000000004 t= 0.5770000000000004 t= 0.5780000000000004 t= 0.5790000000000004 t= 0.5800000000000004 t= 0.5810000000000004 t= 0.5820000000000004 t= 0.5830000000000004 t= 0.5840000000000004 t= 0.5850000000000004 t= 0.5860000000000004 t= 0.5870000000000004 t= 0.5880000000000004 t= 0.5890000000000004 t= 0.5900000000000004 t= 0.5910000000000004 t= 0.5920000000000004 t= 0.5930000000000004 t= 0.5940000000000004 t= 0.5950000000000004 t= 0.5960000000000004 t= 0.5970000000000004 t= 0.5980000000000004 t= 0.5990000000000004 t= 0.6000000000000004 t= 0.6010000000000004 t= 0.6020000000000004 t= 0.6030000000000004 t= 0.6040000000000004 t= 0.6050000000000004 t= 0.6060000000000004 t= 0.6070000000000004 t= 0.6080000000000004 t= 0.6090000000000004 t= 0.6100000000000004 t= 0.6110000000000004 t= 0.6120000000000004 t= 0.6130000000000004 t= 0.6140000000000004 t= 0.6150000000000004 t= 0.6160000000000004 t= 0.6170000000000004 t= 0.6180000000000004 t= 0.6190000000000004 t= 0.6200000000000004 t= 0.6210000000000004 t= 0.6220000000000004 t= 0.6230000000000004 t= 0.6240000000000004 t= 0.6250000000000004 t= 0.6260000000000004 t= 0.6270000000000004 t= 0.6280000000000004 t= 0.6290000000000004 t= 0.6300000000000004 t= 0.6310000000000004 t= 0.6320000000000005 t= 0.6330000000000005 t= 0.6340000000000005 t= 0.6350000000000005 t= 0.6360000000000005 t= 0.6370000000000005 t= 0.6380000000000005 t= 0.6390000000000005 t= 0.6400000000000005 t= 0.6410000000000005 t= 0.6420000000000005 t= 0.6430000000000005 t= 0.6440000000000005 t= 0.6450000000000005 t= 0.6460000000000005 t= 0.6470000000000005 t= 0.6480000000000005 t= 0.6490000000000005 t= 0.6500000000000005 t= 0.6510000000000005 t= 0.6520000000000005 t= 0.6530000000000005 t= 0.6540000000000005 t= 0.6550000000000005 t= 0.6560000000000005 t= 0.6570000000000005 t= 0.6580000000000005 t= 0.6590000000000005 t= 0.6600000000000005 t= 0.6610000000000005 t= 0.6620000000000005 t= 0.6630000000000005 t= 0.6640000000000005 t= 0.6650000000000005 t= 0.6660000000000005 t= 0.6670000000000005 t= 0.6680000000000005 t= 0.6690000000000005 t= 0.6700000000000005 t= 0.6710000000000005 t= 0.6720000000000005 t= 0.6730000000000005 t= 0.6740000000000005 t= 0.6750000000000005 t= 0.6760000000000005 t= 0.6770000000000005 t= 0.6780000000000005 t= 0.6790000000000005 t= 0.6800000000000005 t= 0.6810000000000005 t= 0.6820000000000005 t= 0.6830000000000005 t= 0.6840000000000005 t= 0.6850000000000005 t= 0.6860000000000005 t= 0.6870000000000005 t= 0.6880000000000005 t= 0.6890000000000005 t= 0.6900000000000005 t= 0.6910000000000005 t= 0.6920000000000005 t= 0.6930000000000005 t= 0.6940000000000005 t= 0.6950000000000005 t= 0.6960000000000005 t= 0.6970000000000005 t= 0.6980000000000005 t= 0.6990000000000005 t= 0.7000000000000005 t= 0.7010000000000005 t= 0.7020000000000005 t= 0.7030000000000005 t= 0.7040000000000005 t= 0.7050000000000005 t= 0.7060000000000005 t= 0.7070000000000005 t= 0.7080000000000005 t= 0.7090000000000005 t= 0.7100000000000005 t= 0.7110000000000005 t= 0.7120000000000005 t= 0.7130000000000005 t= 0.7140000000000005 t= 0.7150000000000005 t= 0.7160000000000005 t= 0.7170000000000005 t= 0.7180000000000005 t= 0.7190000000000005 t= 0.7200000000000005 t= 0.7210000000000005 t= 0.7220000000000005 t= 0.7230000000000005 t= 0.7240000000000005 t= 0.7250000000000005 t= 0.7260000000000005 t= 0.7270000000000005 t= 0.7280000000000005 t= 0.7290000000000005 t= 0.7300000000000005 t= 0.7310000000000005 t= 0.7320000000000005 t= 0.7330000000000005 t= 0.7340000000000005 t= 0.7350000000000005 t= 0.7360000000000005 t= 0.7370000000000005 t= 0.7380000000000005 t= 0.7390000000000005 t= 0.7400000000000005 t= 0.7410000000000005 t= 0.7420000000000005 t= 0.7430000000000005 t= 0.7440000000000005 t= 0.7450000000000006 t= 0.7460000000000006 t= 0.7470000000000006 t= 0.7480000000000006 t= 0.7490000000000006 t= 0.7500000000000006 t= 0.7510000000000006 t= 0.7520000000000006 t= 0.7530000000000006 t= 0.7540000000000006 t= 0.7550000000000006 t= 0.7560000000000006 t= 0.7570000000000006 t= 0.7580000000000006 t= 0.7590000000000006 t= 0.7600000000000006 t= 0.7610000000000006 t= 0.7620000000000006 t= 0.7630000000000006 t= 0.7640000000000006 t= 0.7650000000000006 t= 0.7660000000000006 t= 0.7670000000000006 t= 0.7680000000000006 t= 0.7690000000000006 t= 0.7700000000000006 t= 0.7710000000000006 t= 0.7720000000000006 t= 0.7730000000000006 t= 0.7740000000000006 t= 0.7750000000000006 t= 0.7760000000000006 t= 0.7770000000000006 t= 0.7780000000000006 t= 0.7790000000000006 t= 0.7800000000000006 t= 0.7810000000000006 t= 0.7820000000000006 t= 0.7830000000000006 t= 0.7840000000000006 t= 0.7850000000000006 t= 0.7860000000000006 t= 0.7870000000000006 t= 0.7880000000000006 t= 0.7890000000000006 t= 0.7900000000000006 t= 0.7910000000000006 t= 0.7920000000000006 t= 0.7930000000000006 t= 0.7940000000000006 t= 0.7950000000000006 t= 0.7960000000000006 t= 0.7970000000000006 t= 0.7980000000000006 t= 0.7990000000000006 t= 0.8000000000000006 t= 0.8010000000000006 t= 0.8020000000000006 t= 0.8030000000000006 t= 0.8040000000000006 t= 0.8050000000000006 t= 0.8060000000000006 t= 0.8070000000000006 t= 0.8080000000000006 t= 0.8090000000000006 t= 0.8100000000000006 t= 0.8110000000000006 t= 0.8120000000000006 t= 0.8130000000000006 t= 0.8140000000000006 t= 0.8150000000000006 t= 0.8160000000000006 t= 0.8170000000000006 t= 0.8180000000000006 t= 0.8190000000000006 t= 0.8200000000000006 t= 0.8210000000000006 t= 0.8220000000000006 t= 0.8230000000000006 t= 0.8240000000000006 t= 0.8250000000000006 t= 0.8260000000000006 t= 0.8270000000000006 t= 0.8280000000000006 t= 0.8290000000000006 t= 0.8300000000000006 t= 0.8310000000000006 t= 0.8320000000000006 t= 0.8330000000000006 t= 0.8340000000000006 t= 0.8350000000000006 t= 0.8360000000000006 t= 0.8370000000000006 t= 0.8380000000000006 t= 0.8390000000000006 t= 0.8400000000000006 t= 0.8410000000000006 t= 0.8420000000000006 t= 0.8430000000000006 t= 0.8440000000000006 t= 0.8450000000000006 t= 0.8460000000000006 t= 0.8470000000000006 t= 0.8480000000000006 t= 0.8490000000000006 t= 0.8500000000000006 t= 0.8510000000000006 t= 0.8520000000000006 t= 0.8530000000000006 t= 0.8540000000000006 t= 0.8550000000000006 t= 0.8560000000000006 t= 0.8570000000000007 t= 0.8580000000000007 t= 0.8590000000000007 t= 0.8600000000000007 t= 0.8610000000000007 t= 0.8620000000000007 t= 0.8630000000000007 t= 0.8640000000000007 t= 0.8650000000000007 t= 0.8660000000000007 t= 0.8670000000000007 t= 0.8680000000000007 t= 0.8690000000000007 t= 0.8700000000000007 t= 0.8710000000000007 t= 0.8720000000000007 t= 0.8730000000000007 t= 0.8740000000000007 t= 0.8750000000000007 t= 0.8760000000000007 t= 0.8770000000000007 t= 0.8780000000000007 t= 0.8790000000000007 t= 0.8800000000000007 t= 0.8810000000000007 t= 0.8820000000000007 t= 0.8830000000000007 t= 0.8840000000000007 t= 0.8850000000000007 t= 0.8860000000000007 t= 0.8870000000000007 t= 0.8880000000000007 t= 0.8890000000000007 t= 0.8900000000000007 t= 0.8910000000000007 t= 0.8920000000000007 t= 0.8930000000000007 t= 0.8940000000000007 t= 0.8950000000000007 t= 0.8960000000000007 t= 0.8970000000000007 t= 0.8980000000000007 t= 0.8990000000000007 t= 0.9000000000000007 t= 0.9010000000000007 t= 0.9020000000000007 t= 0.9030000000000007 t= 0.9040000000000007 t= 0.9050000000000007 t= 0.9060000000000007 t= 0.9070000000000007 t= 0.9080000000000007 t= 0.9090000000000007 t= 0.9100000000000007 t= 0.9110000000000007 t= 0.9120000000000007 t= 0.9130000000000007 t= 0.9140000000000007 t= 0.9150000000000007 t= 0.9160000000000007 t= 0.9170000000000007 t= 0.9180000000000007 t= 0.9190000000000007 t= 0.9200000000000007 t= 0.9210000000000007 t= 0.9220000000000007 t= 0.9230000000000007 t= 0.9240000000000007 t= 0.9250000000000007 t= 0.9260000000000007 t= 0.9270000000000007 t= 0.9280000000000007 t= 0.9290000000000007 t= 0.9300000000000007 t= 0.9310000000000007 t= 0.9320000000000007 t= 0.9330000000000007 t= 0.9340000000000007 t= 0.9350000000000007 t= 0.9360000000000007 t= 0.9370000000000007 t= 0.9380000000000007 t= 0.9390000000000007 t= 0.9400000000000007 t= 0.9410000000000007 t= 0.9420000000000007 t= 0.9430000000000007 t= 0.9440000000000007 t= 0.9450000000000007 t= 0.9460000000000007 t= 0.9470000000000007 t= 0.9480000000000007 t= 0.9490000000000007 t= 0.9500000000000007 t= 0.9510000000000007 t= 0.9520000000000007 t= 0.9530000000000007 t= 0.9540000000000007 t= 0.9550000000000007 t= 0.9560000000000007 t= 0.9570000000000007 t= 0.9580000000000007 t= 0.9590000000000007 t= 0.9600000000000007 t= 0.9610000000000007 t= 0.9620000000000007 t= 0.9630000000000007 t= 0.9640000000000007 t= 0.9650000000000007 t= 0.9660000000000007 t= 0.9670000000000007 t= 0.9680000000000007 t= 0.9690000000000007 t= 0.9700000000000008 t= 0.9710000000000008 t= 0.9720000000000008 t= 0.9730000000000008 t= 0.9740000000000008 t= 0.9750000000000008 t= 0.9760000000000008 t= 0.9770000000000008 t= 0.9780000000000008 t= 0.9790000000000008 t= 0.9800000000000008 t= 0.9810000000000008 t= 0.9820000000000008 t= 0.9830000000000008 t= 0.9840000000000008 t= 0.9850000000000008 t= 0.9860000000000008 t= 0.9870000000000008 t= 0.9880000000000008 t= 0.9890000000000008 t= 0.9900000000000008 t= 0.9910000000000008 t= 0.9920000000000008 t= 0.9930000000000008 t= 0.9940000000000008 t= 0.9950000000000008 t= 0.9960000000000008 t= 0.9970000000000008 t= 0.9980000000000008 t= 0.9990000000000008

end{sphinxVerbatim}

t= 0 t= 0.001 t= 0.002 t= 0.003 t= 0.004craete bilinearformapplication

t= 0.005 t= 0.006 t= 0.007 t= 0.008 t= 0.009000000000000001 t= 0.010000000000000002 t= 0.011000000000000003 t= 0.012000000000000004 t= 0.013000000000000005 t= 0.014000000000000005 t= 0.015000000000000006 t= 0.016000000000000007 t= 0.017000000000000008 t= 0.01800000000000001 t= 0.01900000000000001 t= 0.02000000000000001 t= 0.02100000000000001 t= 0.022000000000000013 t= 0.023000000000000013 t= 0.024000000000000014 t= 0.025000000000000015 t= 0.026000000000000016 t= 0.027000000000000017 t= 0.028000000000000018 t= 0.02900000000000002 t= 0.03000000000000002 t= 0.03100000000000002 t= 0.03200000000000002 t= 0.03300000000000002 t= 0.03400000000000002 t= 0.035000000000000024 t= 0.036000000000000025 t= 0.037000000000000026 t= 0.03800000000000003 t= 0.03900000000000003 t= 0.04000000000000003 t= 0.04100000000000003 t= 0.04200000000000003 t= 0.04300000000000003 t= 0.04400000000000003 t= 0.04500000000000003 t= 0.046000000000000034 t= 0.047000000000000035 t= 0.048000000000000036 t= 0.04900000000000004 t= 0.05000000000000004 t= 0.05100000000000004 t= 0.05200000000000004 t= 0.05300000000000004 t= 0.05400000000000004 t= 0.05500000000000004 t= 0.05600000000000004 t= 0.057000000000000044 t= 0.058000000000000045 t= 0.059000000000000045 t= 0.060000000000000046 t= 0.06100000000000005 t= 0.06200000000000005 t= 0.06300000000000004 t= 0.06400000000000004 t= 0.06500000000000004 t= 0.06600000000000004 t= 0.06700000000000005 t= 0.06800000000000005 t= 0.06900000000000005 t= 0.07000000000000005 t= 0.07100000000000005 t= 0.07200000000000005 t= 0.07300000000000005 t= 0.07400000000000005 t= 0.07500000000000005 t= 0.07600000000000005 t= 0.07700000000000005 t= 0.07800000000000006 t= 0.07900000000000006 t= 0.08000000000000006 t= 0.08100000000000006 t= 0.08200000000000006 t= 0.08300000000000006 t= 0.08400000000000006 t= 0.08500000000000006 t= 0.08600000000000006 t= 0.08700000000000006 t= 0.08800000000000006 t= 0.08900000000000007 t= 0.09000000000000007 t= 0.09100000000000007 t= 0.09200000000000007 t= 0.09300000000000007 t= 0.09400000000000007 t= 0.09500000000000007 t= 0.09600000000000007 t= 0.09700000000000007 t= 0.09800000000000007 t= 0.09900000000000007 t= 0.10000000000000007 t= 0.10100000000000008 t= 0.10200000000000008 t= 0.10300000000000008 t= 0.10400000000000008 t= 0.10500000000000008 t= 0.10600000000000008 t= 0.10700000000000008 t= 0.10800000000000008 t= 0.10900000000000008 t= 0.11000000000000008 t= 0.11100000000000008 t= 0.11200000000000009 t= 0.11300000000000009 t= 0.11400000000000009 t= 0.11500000000000009 t= 0.11600000000000009 t= 0.11700000000000009 t= 0.11800000000000009 t= 0.11900000000000009 t= 0.12000000000000009 t= 0.1210000000000001 t= 0.1220000000000001 t= 0.1230000000000001 t= 0.1240000000000001 t= 0.12500000000000008 t= 0.12600000000000008 t= 0.12700000000000009 t= 0.12800000000000009 t= 0.1290000000000001 t= 0.1300000000000001 t= 0.1310000000000001 t= 0.1320000000000001 t= 0.1330000000000001 t= 0.1340000000000001 t= 0.1350000000000001 t= 0.1360000000000001 t= 0.1370000000000001 t= 0.1380000000000001 t= 0.1390000000000001 t= 0.1400000000000001 t= 0.1410000000000001 t= 0.1420000000000001 t= 0.1430000000000001 t= 0.1440000000000001 t= 0.1450000000000001 t= 0.1460000000000001 t= 0.1470000000000001 t= 0.1480000000000001 t= 0.1490000000000001 t= 0.1500000000000001 t= 0.1510000000000001 t= 0.1520000000000001 t= 0.1530000000000001 t= 0.1540000000000001 t= 0.1550000000000001 t= 0.1560000000000001 t= 0.1570000000000001 t= 0.1580000000000001 t= 0.1590000000000001 t= 0.16000000000000011 t= 0.16100000000000012 t= 0.16200000000000012 t= 0.16300000000000012 t= 0.16400000000000012 t= 0.16500000000000012 t= 0.16600000000000012 t= 0.16700000000000012 t= 0.16800000000000012 t= 0.16900000000000012 t= 0.17000000000000012 t= 0.17100000000000012 t= 0.17200000000000013 t= 0.17300000000000013 t= 0.17400000000000013 t= 0.17500000000000013 t= 0.17600000000000013 t= 0.17700000000000013 t= 0.17800000000000013 t= 0.17900000000000013 t= 0.18000000000000013 t= 0.18100000000000013 t= 0.18200000000000013 t= 0.18300000000000013 t= 0.18400000000000014 t= 0.18500000000000014 t= 0.18600000000000014 t= 0.18700000000000014 t= 0.18800000000000014 t= 0.18900000000000014 t= 0.19000000000000014 t= 0.19100000000000014 t= 0.19200000000000014 t= 0.19300000000000014 t= 0.19400000000000014 t= 0.19500000000000015 t= 0.19600000000000015 t= 0.19700000000000015 t= 0.19800000000000015 t= 0.19900000000000015 t= 0.20000000000000015 t= 0.20100000000000015 t= 0.20200000000000015 t= 0.20300000000000015 t= 0.20400000000000015 t= 0.20500000000000015 t= 0.20600000000000016 t= 0.20700000000000016 t= 0.20800000000000016 t= 0.20900000000000016 t= 0.21000000000000016 t= 0.21100000000000016 t= 0.21200000000000016 t= 0.21300000000000016 t= 0.21400000000000016 t= 0.21500000000000016 t= 0.21600000000000016 t= 0.21700000000000016 t= 0.21800000000000017 t= 0.21900000000000017 t= 0.22000000000000017 t= 0.22100000000000017 t= 0.22200000000000017 t= 0.22300000000000017 t= 0.22400000000000017 t= 0.22500000000000017 t= 0.22600000000000017 t= 0.22700000000000017 t= 0.22800000000000017 t= 0.22900000000000018 t= 0.23000000000000018 t= 0.23100000000000018 t= 0.23200000000000018 t= 0.23300000000000018 t= 0.23400000000000018 t= 0.23500000000000018 t= 0.23600000000000018 t= 0.23700000000000018 t= 0.23800000000000018 t= 0.23900000000000018 t= 0.24000000000000019 t= 0.2410000000000002 t= 0.2420000000000002 t= 0.2430000000000002 t= 0.2440000000000002 t= 0.2450000000000002 t= 0.2460000000000002 t= 0.2470000000000002 t= 0.2480000000000002 t= 0.2490000000000002 t= 0.25000000000000017 t= 0.25100000000000017 t= 0.25200000000000017 t= 0.25300000000000017 t= 0.25400000000000017 t= 0.25500000000000017 t= 0.25600000000000017 t= 0.2570000000000002 t= 0.2580000000000002 t= 0.2590000000000002 t= 0.2600000000000002 t= 0.2610000000000002 t= 0.2620000000000002 t= 0.2630000000000002 t= 0.2640000000000002 t= 0.2650000000000002 t= 0.2660000000000002 t= 0.2670000000000002 t= 0.2680000000000002 t= 0.2690000000000002 t= 0.2700000000000002 t= 0.2710000000000002 t= 0.2720000000000002 t= 0.2730000000000002 t= 0.2740000000000002 t= 0.2750000000000002 t= 0.2760000000000002 t= 0.2770000000000002 t= 0.2780000000000002 t= 0.2790000000000002 t= 0.2800000000000002 t= 0.2810000000000002 t= 0.2820000000000002 t= 0.2830000000000002 t= 0.2840000000000002 t= 0.2850000000000002 t= 0.2860000000000002 t= 0.2870000000000002 t= 0.2880000000000002 t= 0.2890000000000002 t= 0.2900000000000002 t= 0.2910000000000002 t= 0.2920000000000002 t= 0.2930000000000002 t= 0.2940000000000002 t= 0.2950000000000002 t= 0.2960000000000002 t= 0.2970000000000002 t= 0.2980000000000002 t= 0.2990000000000002 t= 0.3000000000000002 t= 0.3010000000000002 t= 0.3020000000000002 t= 0.3030000000000002 t= 0.3040000000000002 t= 0.3050000000000002 t= 0.3060000000000002 t= 0.3070000000000002 t= 0.3080000000000002 t= 0.3090000000000002 t= 0.3100000000000002 t= 0.3110000000000002 t= 0.3120000000000002 t= 0.3130000000000002 t= 0.3140000000000002 t= 0.3150000000000002 t= 0.3160000000000002 t= 0.3170000000000002 t= 0.3180000000000002 t= 0.31900000000000023 t= 0.32000000000000023 t= 0.32100000000000023 t= 0.32200000000000023 t= 0.32300000000000023 t= 0.32400000000000023 t= 0.32500000000000023 t= 0.32600000000000023 t= 0.32700000000000023 t= 0.32800000000000024 t= 0.32900000000000024 t= 0.33000000000000024 t= 0.33100000000000024 t= 0.33200000000000024 t= 0.33300000000000024 t= 0.33400000000000024 t= 0.33500000000000024 t= 0.33600000000000024 t= 0.33700000000000024 t= 0.33800000000000024 t= 0.33900000000000025 t= 0.34000000000000025 t= 0.34100000000000025 t= 0.34200000000000025 t= 0.34300000000000025 t= 0.34400000000000025 t= 0.34500000000000025 t= 0.34600000000000025 t= 0.34700000000000025 t= 0.34800000000000025 t= 0.34900000000000025 t= 0.35000000000000026 t= 0.35100000000000026 t= 0.35200000000000026 t= 0.35300000000000026 t= 0.35400000000000026 t= 0.35500000000000026 t= 0.35600000000000026 t= 0.35700000000000026 t= 0.35800000000000026 t= 0.35900000000000026 t= 0.36000000000000026 t= 0.36100000000000027 t= 0.36200000000000027 t= 0.36300000000000027 t= 0.36400000000000027 t= 0.36500000000000027 t= 0.36600000000000027 t= 0.36700000000000027 t= 0.36800000000000027 t= 0.36900000000000027 t= 0.3700000000000003 t= 0.3710000000000003 t= 0.3720000000000003 t= 0.3730000000000003 t= 0.3740000000000003 t= 0.3750000000000003 t= 0.3760000000000003 t= 0.3770000000000003 t= 0.3780000000000003 t= 0.3790000000000003 t= 0.3800000000000003 t= 0.3810000000000003 t= 0.3820000000000003 t= 0.3830000000000003 t= 0.3840000000000003 t= 0.3850000000000003 t= 0.3860000000000003 t= 0.3870000000000003 t= 0.3880000000000003 t= 0.3890000000000003 t= 0.3900000000000003 t= 0.3910000000000003 t= 0.3920000000000003 t= 0.3930000000000003 t= 0.3940000000000003 t= 0.3950000000000003 t= 0.3960000000000003 t= 0.3970000000000003 t= 0.3980000000000003 t= 0.3990000000000003 t= 0.4000000000000003 t= 0.4010000000000003 t= 0.4020000000000003 t= 0.4030000000000003 t= 0.4040000000000003 t= 0.4050000000000003 t= 0.4060000000000003 t= 0.4070000000000003 t= 0.4080000000000003 t= 0.4090000000000003 t= 0.4100000000000003 t= 0.4110000000000003 t= 0.4120000000000003 t= 0.4130000000000003 t= 0.4140000000000003 t= 0.4150000000000003 t= 0.4160000000000003 t= 0.4170000000000003 t= 0.4180000000000003 t= 0.4190000000000003 t= 0.4200000000000003 t= 0.4210000000000003 t= 0.4220000000000003 t= 0.4230000000000003 t= 0.4240000000000003 t= 0.4250000000000003 t= 0.4260000000000003 t= 0.4270000000000003 t= 0.4280000000000003 t= 0.4290000000000003 t= 0.4300000000000003 t= 0.4310000000000003 t= 0.43200000000000033 t= 0.43300000000000033 t= 0.43400000000000033 t= 0.43500000000000033 t= 0.43600000000000033 t= 0.43700000000000033 t= 0.43800000000000033 t= 0.43900000000000033 t= 0.44000000000000034 t= 0.44100000000000034 t= 0.44200000000000034 t= 0.44300000000000034 t= 0.44400000000000034 t= 0.44500000000000034 t= 0.44600000000000034 t= 0.44700000000000034 t= 0.44800000000000034 t= 0.44900000000000034 t= 0.45000000000000034 t= 0.45100000000000035 t= 0.45200000000000035 t= 0.45300000000000035 t= 0.45400000000000035 t= 0.45500000000000035 t= 0.45600000000000035 t= 0.45700000000000035 t= 0.45800000000000035 t= 0.45900000000000035 t= 0.46000000000000035 t= 0.46100000000000035 t= 0.46200000000000035 t= 0.46300000000000036 t= 0.46400000000000036 t= 0.46500000000000036 t= 0.46600000000000036 t= 0.46700000000000036 t= 0.46800000000000036 t= 0.46900000000000036 t= 0.47000000000000036 t= 0.47100000000000036 t= 0.47200000000000036 t= 0.47300000000000036 t= 0.47400000000000037 t= 0.47500000000000037 t= 0.47600000000000037 t= 0.47700000000000037 t= 0.47800000000000037 t= 0.47900000000000037 t= 0.48000000000000037 t= 0.48100000000000037 t= 0.4820000000000004 t= 0.4830000000000004 t= 0.4840000000000004 t= 0.4850000000000004 t= 0.4860000000000004 t= 0.4870000000000004 t= 0.4880000000000004 t= 0.4890000000000004 t= 0.4900000000000004 t= 0.4910000000000004 t= 0.4920000000000004 t= 0.4930000000000004 t= 0.4940000000000004 t= 0.4950000000000004 t= 0.4960000000000004 t= 0.4970000000000004 t= 0.4980000000000004 t= 0.4990000000000004 t= 0.5000000000000003 t= 0.5010000000000003 t= 0.5020000000000003 t= 0.5030000000000003 t= 0.5040000000000003 t= 0.5050000000000003 t= 0.5060000000000003 t= 0.5070000000000003 t= 0.5080000000000003 t= 0.5090000000000003 t= 0.5100000000000003 t= 0.5110000000000003 t= 0.5120000000000003 t= 0.5130000000000003 t= 0.5140000000000003 t= 0.5150000000000003 t= 0.5160000000000003 t= 0.5170000000000003 t= 0.5180000000000003 t= 0.5190000000000003 t= 0.5200000000000004 t= 0.5210000000000004 t= 0.5220000000000004 t= 0.5230000000000004 t= 0.5240000000000004 t= 0.5250000000000004 t= 0.5260000000000004 t= 0.5270000000000004 t= 0.5280000000000004 t= 0.5290000000000004 t= 0.5300000000000004 t= 0.5310000000000004 t= 0.5320000000000004 t= 0.5330000000000004 t= 0.5340000000000004 t= 0.5350000000000004 t= 0.5360000000000004 t= 0.5370000000000004 t= 0.5380000000000004 t= 0.5390000000000004 t= 0.5400000000000004 t= 0.5410000000000004 t= 0.5420000000000004 t= 0.5430000000000004 t= 0.5440000000000004 t= 0.5450000000000004 t= 0.5460000000000004 t= 0.5470000000000004 t= 0.5480000000000004 t= 0.5490000000000004 t= 0.5500000000000004 t= 0.5510000000000004 t= 0.5520000000000004 t= 0.5530000000000004 t= 0.5540000000000004 t= 0.5550000000000004 t= 0.5560000000000004 t= 0.5570000000000004 t= 0.5580000000000004 t= 0.5590000000000004 t= 0.5600000000000004 t= 0.5610000000000004 t= 0.5620000000000004 t= 0.5630000000000004 t= 0.5640000000000004 t= 0.5650000000000004 t= 0.5660000000000004 t= 0.5670000000000004 t= 0.5680000000000004 t= 0.5690000000000004 t= 0.5700000000000004 t= 0.5710000000000004 t= 0.5720000000000004 t= 0.5730000000000004 t= 0.5740000000000004 t= 0.5750000000000004 t= 0.5760000000000004 t= 0.5770000000000004 t= 0.5780000000000004 t= 0.5790000000000004 t= 0.5800000000000004 t= 0.5810000000000004 t= 0.5820000000000004 t= 0.5830000000000004 t= 0.5840000000000004 t= 0.5850000000000004 t= 0.5860000000000004 t= 0.5870000000000004 t= 0.5880000000000004 t= 0.5890000000000004 t= 0.5900000000000004 t= 0.5910000000000004 t= 0.5920000000000004 t= 0.5930000000000004 t= 0.5940000000000004 t= 0.5950000000000004 t= 0.5960000000000004 t= 0.5970000000000004 t= 0.5980000000000004 t= 0.5990000000000004 t= 0.6000000000000004 t= 0.6010000000000004 t= 0.6020000000000004 t= 0.6030000000000004 t= 0.6040000000000004 t= 0.6050000000000004 t= 0.6060000000000004 t= 0.6070000000000004 t= 0.6080000000000004 t= 0.6090000000000004 t= 0.6100000000000004 t= 0.6110000000000004 t= 0.6120000000000004 t= 0.6130000000000004 t= 0.6140000000000004 t= 0.6150000000000004 t= 0.6160000000000004 t= 0.6170000000000004 t= 0.6180000000000004 t= 0.6190000000000004 t= 0.6200000000000004 t= 0.6210000000000004 t= 0.6220000000000004 t= 0.6230000000000004 t= 0.6240000000000004 t= 0.6250000000000004 t= 0.6260000000000004 t= 0.6270000000000004 t= 0.6280000000000004 t= 0.6290000000000004 t= 0.6300000000000004 t= 0.6310000000000004 t= 0.6320000000000005 t= 0.6330000000000005 t= 0.6340000000000005 t= 0.6350000000000005 t= 0.6360000000000005 t= 0.6370000000000005 t= 0.6380000000000005 t= 0.6390000000000005 t= 0.6400000000000005 t= 0.6410000000000005 t= 0.6420000000000005 t= 0.6430000000000005 t= 0.6440000000000005 t= 0.6450000000000005 t= 0.6460000000000005 t= 0.6470000000000005 t= 0.6480000000000005 t= 0.6490000000000005 t= 0.6500000000000005 t= 0.6510000000000005 t= 0.6520000000000005 t= 0.6530000000000005 t= 0.6540000000000005 t= 0.6550000000000005 t= 0.6560000000000005 t= 0.6570000000000005 t= 0.6580000000000005 t= 0.6590000000000005 t= 0.6600000000000005 t= 0.6610000000000005 t= 0.6620000000000005 t= 0.6630000000000005 t= 0.6640000000000005 t= 0.6650000000000005 t= 0.6660000000000005 t= 0.6670000000000005 t= 0.6680000000000005 t= 0.6690000000000005 t= 0.6700000000000005 t= 0.6710000000000005 t= 0.6720000000000005 t= 0.6730000000000005 t= 0.6740000000000005 t= 0.6750000000000005 t= 0.6760000000000005 t= 0.6770000000000005 t= 0.6780000000000005 t= 0.6790000000000005 t= 0.6800000000000005 t= 0.6810000000000005 t= 0.6820000000000005 t= 0.6830000000000005 t= 0.6840000000000005 t= 0.6850000000000005 t= 0.6860000000000005 t= 0.6870000000000005 t= 0.6880000000000005 t= 0.6890000000000005 t= 0.6900000000000005 t= 0.6910000000000005 t= 0.6920000000000005 t= 0.6930000000000005 t= 0.6940000000000005 t= 0.6950000000000005 t= 0.6960000000000005 t= 0.6970000000000005 t= 0.6980000000000005 t= 0.6990000000000005 t= 0.7000000000000005 t= 0.7010000000000005 t= 0.7020000000000005 t= 0.7030000000000005 t= 0.7040000000000005 t= 0.7050000000000005 t= 0.7060000000000005 t= 0.7070000000000005 t= 0.7080000000000005 t= 0.7090000000000005 t= 0.7100000000000005 t= 0.7110000000000005 t= 0.7120000000000005 t= 0.7130000000000005 t= 0.7140000000000005 t= 0.7150000000000005 t= 0.7160000000000005 t= 0.7170000000000005 t= 0.7180000000000005 t= 0.7190000000000005 t= 0.7200000000000005 t= 0.7210000000000005 t= 0.7220000000000005 t= 0.7230000000000005 t= 0.7240000000000005 t= 0.7250000000000005 t= 0.7260000000000005 t= 0.7270000000000005 t= 0.7280000000000005 t= 0.7290000000000005 t= 0.7300000000000005 t= 0.7310000000000005 t= 0.7320000000000005 t= 0.7330000000000005 t= 0.7340000000000005 t= 0.7350000000000005 t= 0.7360000000000005 t= 0.7370000000000005 t= 0.7380000000000005 t= 0.7390000000000005 t= 0.7400000000000005 t= 0.7410000000000005 t= 0.7420000000000005 t= 0.7430000000000005 t= 0.7440000000000005 t= 0.7450000000000006 t= 0.7460000000000006 t= 0.7470000000000006 t= 0.7480000000000006 t= 0.7490000000000006 t= 0.7500000000000006 t= 0.7510000000000006 t= 0.7520000000000006 t= 0.7530000000000006 t= 0.7540000000000006 t= 0.7550000000000006 t= 0.7560000000000006 t= 0.7570000000000006 t= 0.7580000000000006 t= 0.7590000000000006 t= 0.7600000000000006 t= 0.7610000000000006 t= 0.7620000000000006 t= 0.7630000000000006 t= 0.7640000000000006 t= 0.7650000000000006 t= 0.7660000000000006 t= 0.7670000000000006 t= 0.7680000000000006 t= 0.7690000000000006 t= 0.7700000000000006 t= 0.7710000000000006 t= 0.7720000000000006 t= 0.7730000000000006 t= 0.7740000000000006 t= 0.7750000000000006 t= 0.7760000000000006 t= 0.7770000000000006 t= 0.7780000000000006 t= 0.7790000000000006 t= 0.7800000000000006 t= 0.7810000000000006 t= 0.7820000000000006 t= 0.7830000000000006 t= 0.7840000000000006 t= 0.7850000000000006 t= 0.7860000000000006 t= 0.7870000000000006 t= 0.7880000000000006 t= 0.7890000000000006 t= 0.7900000000000006 t= 0.7910000000000006 t= 0.7920000000000006 t= 0.7930000000000006 t= 0.7940000000000006 t= 0.7950000000000006 t= 0.7960000000000006 t= 0.7970000000000006 t= 0.7980000000000006 t= 0.7990000000000006 t= 0.8000000000000006 t= 0.8010000000000006 t= 0.8020000000000006 t= 0.8030000000000006 t= 0.8040000000000006 t= 0.8050000000000006 t= 0.8060000000000006 t= 0.8070000000000006 t= 0.8080000000000006 t= 0.8090000000000006 t= 0.8100000000000006 t= 0.8110000000000006 t= 0.8120000000000006 t= 0.8130000000000006 t= 0.8140000000000006 t= 0.8150000000000006 t= 0.8160000000000006 t= 0.8170000000000006 t= 0.8180000000000006 t= 0.8190000000000006 t= 0.8200000000000006 t= 0.8210000000000006 t= 0.8220000000000006 t= 0.8230000000000006 t= 0.8240000000000006 t= 0.8250000000000006 t= 0.8260000000000006 t= 0.8270000000000006 t= 0.8280000000000006 t= 0.8290000000000006 t= 0.8300000000000006 t= 0.8310000000000006 t= 0.8320000000000006 t= 0.8330000000000006 t= 0.8340000000000006 t= 0.8350000000000006 t= 0.8360000000000006 t= 0.8370000000000006 t= 0.8380000000000006 t= 0.8390000000000006 t= 0.8400000000000006 t= 0.8410000000000006 t= 0.8420000000000006 t= 0.8430000000000006 t= 0.8440000000000006 t= 0.8450000000000006 t= 0.8460000000000006 t= 0.8470000000000006 t= 0.8480000000000006 t= 0.8490000000000006 t= 0.8500000000000006 t= 0.8510000000000006 t= 0.8520000000000006 t= 0.8530000000000006 t= 0.8540000000000006 t= 0.8550000000000006 t= 0.8560000000000006 t= 0.8570000000000007 t= 0.8580000000000007 t= 0.8590000000000007 t= 0.8600000000000007 t= 0.8610000000000007 t= 0.8620000000000007 t= 0.8630000000000007 t= 0.8640000000000007 t= 0.8650000000000007 t= 0.8660000000000007 t= 0.8670000000000007 t= 0.8680000000000007 t= 0.8690000000000007 t= 0.8700000000000007 t= 0.8710000000000007 t= 0.8720000000000007 t= 0.8730000000000007 t= 0.8740000000000007 t= 0.8750000000000007 t= 0.8760000000000007 t= 0.8770000000000007 t= 0.8780000000000007 t= 0.8790000000000007 t= 0.8800000000000007 t= 0.8810000000000007 t= 0.8820000000000007 t= 0.8830000000000007 t= 0.8840000000000007 t= 0.8850000000000007 t= 0.8860000000000007 t= 0.8870000000000007 t= 0.8880000000000007 t= 0.8890000000000007 t= 0.8900000000000007 t= 0.8910000000000007 t= 0.8920000000000007 t= 0.8930000000000007 t= 0.8940000000000007 t= 0.8950000000000007 t= 0.8960000000000007 t= 0.8970000000000007 t= 0.8980000000000007 t= 0.8990000000000007 t= 0.9000000000000007 t= 0.9010000000000007 t= 0.9020000000000007 t= 0.9030000000000007 t= 0.9040000000000007 t= 0.9050000000000007 t= 0.9060000000000007 t= 0.9070000000000007 t= 0.9080000000000007 t= 0.9090000000000007 t= 0.9100000000000007 t= 0.9110000000000007 t= 0.9120000000000007 t= 0.9130000000000007 t= 0.9140000000000007 t= 0.9150000000000007 t= 0.9160000000000007 t= 0.9170000000000007 t= 0.9180000000000007 t= 0.9190000000000007 t= 0.9200000000000007 t= 0.9210000000000007 t= 0.9220000000000007 t= 0.9230000000000007 t= 0.9240000000000007 t= 0.9250000000000007 t= 0.9260000000000007 t= 0.9270000000000007 t= 0.9280000000000007 t= 0.9290000000000007 t= 0.9300000000000007 t= 0.9310000000000007 t= 0.9320000000000007 t= 0.9330000000000007 t= 0.9340000000000007 t= 0.9350000000000007 t= 0.9360000000000007 t= 0.9370000000000007 t= 0.9380000000000007 t= 0.9390000000000007 t= 0.9400000000000007 t= 0.9410000000000007 t= 0.9420000000000007 t= 0.9430000000000007 t= 0.9440000000000007 t= 0.9450000000000007 t= 0.9460000000000007 t= 0.9470000000000007 t= 0.9480000000000007 t= 0.9490000000000007 t= 0.9500000000000007 t= 0.9510000000000007 t= 0.9520000000000007 t= 0.9530000000000007 t= 0.9540000000000007 t= 0.9550000000000007 t= 0.9560000000000007 t= 0.9570000000000007 t= 0.9580000000000007 t= 0.9590000000000007 t= 0.9600000000000007 t= 0.9610000000000007 t= 0.9620000000000007 t= 0.9630000000000007 t= 0.9640000000000007 t= 0.9650000000000007 t= 0.9660000000000007 t= 0.9670000000000007 t= 0.9680000000000007 t= 0.9690000000000007 t= 0.9700000000000008 t= 0.9710000000000008 t= 0.9720000000000008 t= 0.9730000000000008 t= 0.9740000000000008 t= 0.9750000000000008 t= 0.9760000000000008 t= 0.9770000000000008 t= 0.9780000000000008 t= 0.9790000000000008 t= 0.9800000000000008 t= 0.9810000000000008 t= 0.9820000000000008 t= 0.9830000000000008 t= 0.9840000000000008 t= 0.9850000000000008 t= 0.9860000000000008 t= 0.9870000000000008 t= 0.9880000000000008 t= 0.9890000000000008 t= 0.9900000000000008 t= 0.9910000000000008 t= 0.9920000000000008 t= 0.9930000000000008 t= 0.9940000000000008 t= 0.9950000000000008 t= 0.9960000000000008 t= 0.9970000000000008 t= 0.9980000000000008 t= 0.9990000000000008

[13]:
Draw (gfut.components[0], mesh, interpolate_multidim=True, animate=True,
      min=0, max=1.9, autoscale=False, vectors = True)
Draw (gfut.components[1], mesh, interpolate_multidim=True, animate=True,
      min=-0.5, max=1, autoscale=False)
[13]:
BaseWebGuiScene

In this benchmark scenario of specific interests are the forces acting on the disk (cylinder). We will discuss how to compute them next.

Supplementary 1: Computing stresses

In the previously used benchmark the stresses on the obstacle are evaluated, the so-called drag and lift coefficients.

The force acting on the obstacle is

\[F_{\circ} = (F_D,F_L) = \int_{\Gamma_{cyl}} \sigma_n = \int_{\Gamma_{cyl}} (-\nu \frac{\partial u}{\partial n} + p I) \cdot n\]

The drag/lift coefficients are

\[c_D = \frac{2 }{\bar{u} L} F_D, \quad c_L = \frac{2 }{\bar{u} L} F_L.\]

where \(\bar{u} = 1\) is the mean inflow velocity and \(L = 0.41\) is the channel width.

We use the residual of our discretization to compute the forces. On the boundary degrees of freedoms of the disk we overwrote the equation by prescribing the (homogeneous) boundary conditions. The equations related to these dofs describe the force (im)balance at this boundary.

Testing the residual (functional) with the characteristic function on that boundary (in the x- or y-direction) we obtain the integrated stresses (in the x- or y-direction):

We define the functions which are characteristic functions (in terms of boundary evaluations)

[14]:
drag_x_test = GridFunction(X)
drag_x_test.components[0].Set(CoefficientFunction((-20.0,0)), definedon=mesh.Boundaries("cyl"))
drag_y_test = GridFunction(X)
drag_y_test.components[0].Set(CoefficientFunction((0,-20.0)), definedon=mesh.Boundaries("cyl"))

We will collect drag and lift forces over time and therefore create empty arrays

and reset initial data (and time)

[15]:
time_vals, drag_x_vals, drag_y_vals = [],[],[]
[16]:
# restoring initial data
res = f.vec - a.mat*gfu.vec
gfu.vec.data += inv_stokes * res

With the same discretization as before.

Remarks: * you can call the following block several times to continue a simulation and collect more data * note that you can reset the array without rerunning the simulation

[17]:
t = 0
tend = 0
[18]:
tend += 1
while t < tend-0.5*dt:
    print ("\rt=", t, end="")
    res = (a.mat + conv.mat) * gfu.vec
    gfu.vec.data -= dt * inv * res
    t += dt
    time_vals.append( t )
    drag_x_vals.append(InnerProduct(res, drag_x_test.vec) )
    drag_y_vals.append(InnerProduct(res, drag_y_test.vec) )

t= 0 t= 0.001 t= 0.002 t= 0.003 t= 0.004 t= 0.005 t= 0.006 t= 0.007 t= 0.008 t= 0.009000000000000001 t= 0.010000000000000002 t= 0.011000000000000003 t= 0.012000000000000004 t= 0.013000000000000005 t= 0.014000000000000005 t= 0.015000000000000006 t= 0.016000000000000007 t= 0.017000000000000008 t= 0.01800000000000001 t= 0.01900000000000001 t= 0.02000000000000001 t= 0.02100000000000001 t= 0.022000000000000013 t= 0.023000000000000013 t= 0.024000000000000014 t= 0.025000000000000015 t= 0.026000000000000016 t= 0.027000000000000017 t= 0.028000000000000018 t= 0.02900000000000002 t= 0.03000000000000002 t= 0.03100000000000002 t= 0.03200000000000002 t= 0.03300000000000002 t= 0.03400000000000002 t= 0.035000000000000024 t= 0.036000000000000025 t= 0.037000000000000026 t= 0.03800000000000003 t= 0.03900000000000003

</pre>

t= 0 t= 0.001 t= 0.002 t= 0.003 t= 0.004 t= 0.005 t= 0.006 t= 0.007 t= 0.008 t= 0.009000000000000001 t= 0.010000000000000002 t= 0.011000000000000003 t= 0.012000000000000004 t= 0.013000000000000005 t= 0.014000000000000005 t= 0.015000000000000006 t= 0.016000000000000007 t= 0.017000000000000008 t= 0.01800000000000001 t= 0.01900000000000001 t= 0.02000000000000001 t= 0.02100000000000001 t= 0.022000000000000013 t= 0.023000000000000013 t= 0.024000000000000014 t= 0.025000000000000015 t= 0.026000000000000016 t= 0.027000000000000017 t= 0.028000000000000018 t= 0.02900000000000002 t= 0.03000000000000002 t= 0.03100000000000002 t= 0.03200000000000002 t= 0.03300000000000002 t= 0.03400000000000002 t= 0.035000000000000024 t= 0.036000000000000025 t= 0.037000000000000026 t= 0.03800000000000003 t= 0.03900000000000003

end{sphinxVerbatim}

t= 0 t= 0.001 t= 0.002 t= 0.003 t= 0.004 t= 0.005 t= 0.006 t= 0.007 t= 0.008 t= 0.009000000000000001 t= 0.010000000000000002 t= 0.011000000000000003 t= 0.012000000000000004 t= 0.013000000000000005 t= 0.014000000000000005 t= 0.015000000000000006 t= 0.016000000000000007 t= 0.017000000000000008 t= 0.01800000000000001 t= 0.01900000000000001 t= 0.02000000000000001 t= 0.02100000000000001 t= 0.022000000000000013 t= 0.023000000000000013 t= 0.024000000000000014 t= 0.025000000000000015 t= 0.026000000000000016 t= 0.027000000000000017 t= 0.028000000000000018 t= 0.02900000000000002 t= 0.03000000000000002 t= 0.03100000000000002 t= 0.03200000000000002 t= 0.03300000000000002 t= 0.03400000000000002 t= 0.035000000000000024 t= 0.036000000000000025 t= 0.037000000000000026 t= 0.03800000000000003 t= 0.03900000000000003

t= 0.04000000000000003 t= 0.04100000000000003 t= 0.04200000000000003 t= 0.04300000000000003 t= 0.04400000000000003 t= 0.04500000000000003 t= 0.046000000000000034 t= 0.047000000000000035 t= 0.048000000000000036 t= 0.04900000000000004 t= 0.05000000000000004 t= 0.05100000000000004 t= 0.05200000000000004 t= 0.05300000000000004 t= 0.05400000000000004 t= 0.05500000000000004 t= 0.05600000000000004 t= 0.057000000000000044 t= 0.058000000000000045 t= 0.059000000000000045 t= 0.060000000000000046 t= 0.06100000000000005 t= 0.06200000000000005 t= 0.06300000000000004 t= 0.06400000000000004 t= 0.06500000000000004 t= 0.06600000000000004 t= 0.06700000000000005

</pre>

t= 0.04000000000000003 t= 0.04100000000000003 t= 0.04200000000000003 t= 0.04300000000000003 t= 0.04400000000000003 t= 0.04500000000000003 t= 0.046000000000000034 t= 0.047000000000000035 t= 0.048000000000000036 t= 0.04900000000000004 t= 0.05000000000000004 t= 0.05100000000000004 t= 0.05200000000000004 t= 0.05300000000000004 t= 0.05400000000000004 t= 0.05500000000000004 t= 0.05600000000000004 t= 0.057000000000000044 t= 0.058000000000000045 t= 0.059000000000000045 t= 0.060000000000000046 t= 0.06100000000000005 t= 0.06200000000000005 t= 0.06300000000000004 t= 0.06400000000000004 t= 0.06500000000000004 t= 0.06600000000000004 t= 0.06700000000000005

end{sphinxVerbatim}

t= 0.04000000000000003 t= 0.04100000000000003 t= 0.04200000000000003 t= 0.04300000000000003 t= 0.04400000000000003 t= 0.04500000000000003 t= 0.046000000000000034 t= 0.047000000000000035 t= 0.048000000000000036 t= 0.04900000000000004 t= 0.05000000000000004 t= 0.05100000000000004 t= 0.05200000000000004 t= 0.05300000000000004 t= 0.05400000000000004 t= 0.05500000000000004 t= 0.05600000000000004 t= 0.057000000000000044 t= 0.058000000000000045 t= 0.059000000000000045 t= 0.060000000000000046 t= 0.06100000000000005 t= 0.06200000000000005 t= 0.06300000000000004 t= 0.06400000000000004 t= 0.06500000000000004 t= 0.06600000000000004 t= 0.06700000000000005

t= 0.06800000000000005 t= 0.06900000000000005 t= 0.07000000000000005 t= 0.07100000000000005 t= 0.07200000000000005 t= 0.07300000000000005 t= 0.07400000000000005 t= 0.07500000000000005 t= 0.07600000000000005 t= 0.07700000000000005 t= 0.07800000000000006 t= 0.07900000000000006 t= 0.08000000000000006 t= 0.08100000000000006 t= 0.08200000000000006 t= 0.08300000000000006 t= 0.08400000000000006 t= 0.08500000000000006 t= 0.08600000000000006 t= 0.08700000000000006 t= 0.08800000000000006 t= 0.08900000000000007 t= 0.09000000000000007 t= 0.09100000000000007 t= 0.09200000000000007 t= 0.09300000000000007 t= 0.09400000000000007 t= 0.09500000000000007 t= 0.09600000000000007 t= 0.09700000000000007 t= 0.09800000000000007 t= 0.09900000000000007 t= 0.10000000000000007 t= 0.10100000000000008 t= 0.10200000000000008 t= 0.10300000000000008 t= 0.10400000000000008 t= 0.10500000000000008 t= 0.10600000000000008 t= 0.10700000000000008

</pre>

t= 0.06800000000000005 t= 0.06900000000000005 t= 0.07000000000000005 t= 0.07100000000000005 t= 0.07200000000000005 t= 0.07300000000000005 t= 0.07400000000000005 t= 0.07500000000000005 t= 0.07600000000000005 t= 0.07700000000000005 t= 0.07800000000000006 t= 0.07900000000000006 t= 0.08000000000000006 t= 0.08100000000000006 t= 0.08200000000000006 t= 0.08300000000000006 t= 0.08400000000000006 t= 0.08500000000000006 t= 0.08600000000000006 t= 0.08700000000000006 t= 0.08800000000000006 t= 0.08900000000000007 t= 0.09000000000000007 t= 0.09100000000000007 t= 0.09200000000000007 t= 0.09300000000000007 t= 0.09400000000000007 t= 0.09500000000000007 t= 0.09600000000000007 t= 0.09700000000000007 t= 0.09800000000000007 t= 0.09900000000000007 t= 0.10000000000000007 t= 0.10100000000000008 t= 0.10200000000000008 t= 0.10300000000000008 t= 0.10400000000000008 t= 0.10500000000000008 t= 0.10600000000000008 t= 0.10700000000000008

end{sphinxVerbatim}

t= 0.06800000000000005 t= 0.06900000000000005 t= 0.07000000000000005 t= 0.07100000000000005 t= 0.07200000000000005 t= 0.07300000000000005 t= 0.07400000000000005 t= 0.07500000000000005 t= 0.07600000000000005 t= 0.07700000000000005 t= 0.07800000000000006 t= 0.07900000000000006 t= 0.08000000000000006 t= 0.08100000000000006 t= 0.08200000000000006 t= 0.08300000000000006 t= 0.08400000000000006 t= 0.08500000000000006 t= 0.08600000000000006 t= 0.08700000000000006 t= 0.08800000000000006 t= 0.08900000000000007 t= 0.09000000000000007 t= 0.09100000000000007 t= 0.09200000000000007 t= 0.09300000000000007 t= 0.09400000000000007 t= 0.09500000000000007 t= 0.09600000000000007 t= 0.09700000000000007 t= 0.09800000000000007 t= 0.09900000000000007 t= 0.10000000000000007 t= 0.10100000000000008 t= 0.10200000000000008 t= 0.10300000000000008 t= 0.10400000000000008 t= 0.10500000000000008 t= 0.10600000000000008 t= 0.10700000000000008

t= 0.10800000000000008 t= 0.10900000000000008 t= 0.11000000000000008 t= 0.11100000000000008 t= 0.11200000000000009 t= 0.11300000000000009 t= 0.11400000000000009 t= 0.11500000000000009 t= 0.11600000000000009 t= 0.11700000000000009 t= 0.11800000000000009 t= 0.11900000000000009 t= 0.12000000000000009 t= 0.1210000000000001 t= 0.1220000000000001 t= 0.1230000000000001 t= 0.1240000000000001 t= 0.12500000000000008 t= 0.12600000000000008 t= 0.12700000000000009 t= 0.12800000000000009 t= 0.1290000000000001 t= 0.1300000000000001 t= 0.1310000000000001 t= 0.1320000000000001 t= 0.1330000000000001 t= 0.1340000000000001 t= 0.1350000000000001 t= 0.1360000000000001 t= 0.1370000000000001 t= 0.1380000000000001 t= 0.1390000000000001 t= 0.1400000000000001 t= 0.1410000000000001 t= 0.1420000000000001 t= 0.1430000000000001 t= 0.1440000000000001 t= 0.1450000000000001 t= 0.1460000000000001 t= 0.1470000000000001 t= 0.1480000000000001 t= 0.1490000000000001

</pre>

t= 0.10800000000000008 t= 0.10900000000000008 t= 0.11000000000000008 t= 0.11100000000000008 t= 0.11200000000000009 t= 0.11300000000000009 t= 0.11400000000000009 t= 0.11500000000000009 t= 0.11600000000000009 t= 0.11700000000000009 t= 0.11800000000000009 t= 0.11900000000000009 t= 0.12000000000000009 t= 0.1210000000000001 t= 0.1220000000000001 t= 0.1230000000000001 t= 0.1240000000000001 t= 0.12500000000000008 t= 0.12600000000000008 t= 0.12700000000000009 t= 0.12800000000000009 t= 0.1290000000000001 t= 0.1300000000000001 t= 0.1310000000000001 t= 0.1320000000000001 t= 0.1330000000000001 t= 0.1340000000000001 t= 0.1350000000000001 t= 0.1360000000000001 t= 0.1370000000000001 t= 0.1380000000000001 t= 0.1390000000000001 t= 0.1400000000000001 t= 0.1410000000000001 t= 0.1420000000000001 t= 0.1430000000000001 t= 0.1440000000000001 t= 0.1450000000000001 t= 0.1460000000000001 t= 0.1470000000000001 t= 0.1480000000000001 t= 0.1490000000000001

end{sphinxVerbatim}

t= 0.10800000000000008 t= 0.10900000000000008 t= 0.11000000000000008 t= 0.11100000000000008 t= 0.11200000000000009 t= 0.11300000000000009 t= 0.11400000000000009 t= 0.11500000000000009 t= 0.11600000000000009 t= 0.11700000000000009 t= 0.11800000000000009 t= 0.11900000000000009 t= 0.12000000000000009 t= 0.1210000000000001 t= 0.1220000000000001 t= 0.1230000000000001 t= 0.1240000000000001 t= 0.12500000000000008 t= 0.12600000000000008 t= 0.12700000000000009 t= 0.12800000000000009 t= 0.1290000000000001 t= 0.1300000000000001 t= 0.1310000000000001 t= 0.1320000000000001 t= 0.1330000000000001 t= 0.1340000000000001 t= 0.1350000000000001 t= 0.1360000000000001 t= 0.1370000000000001 t= 0.1380000000000001 t= 0.1390000000000001 t= 0.1400000000000001 t= 0.1410000000000001 t= 0.1420000000000001 t= 0.1430000000000001 t= 0.1440000000000001 t= 0.1450000000000001 t= 0.1460000000000001 t= 0.1470000000000001 t= 0.1480000000000001 t= 0.1490000000000001

t= 0.1500000000000001 t= 0.1510000000000001 t= 0.1520000000000001 t= 0.1530000000000001 t= 0.1540000000000001 t= 0.1550000000000001 t= 0.1560000000000001 t= 0.1570000000000001 t= 0.1580000000000001 t= 0.1590000000000001 t= 0.16000000000000011 t= 0.16100000000000012 t= 0.16200000000000012 t= 0.16300000000000012 t= 0.16400000000000012 t= 0.16500000000000012 t= 0.16600000000000012 t= 0.16700000000000012 t= 0.16800000000000012 t= 0.16900000000000012 t= 0.17000000000000012 t= 0.17100000000000012 t= 0.17200000000000013 t= 0.17300000000000013 t= 0.17400000000000013 t= 0.17500000000000013 t= 0.17600000000000013 t= 0.17700000000000013 t= 0.17800000000000013 t= 0.17900000000000013 t= 0.18000000000000013 t= 0.18100000000000013 t= 0.18200000000000013 t= 0.18300000000000013 t= 0.18400000000000014 t= 0.18500000000000014 t= 0.18600000000000014 t= 0.18700000000000014 t= 0.18800000000000014 t= 0.18900000000000014

</pre>

t= 0.1500000000000001 t= 0.1510000000000001 t= 0.1520000000000001 t= 0.1530000000000001 t= 0.1540000000000001 t= 0.1550000000000001 t= 0.1560000000000001 t= 0.1570000000000001 t= 0.1580000000000001 t= 0.1590000000000001 t= 0.16000000000000011 t= 0.16100000000000012 t= 0.16200000000000012 t= 0.16300000000000012 t= 0.16400000000000012 t= 0.16500000000000012 t= 0.16600000000000012 t= 0.16700000000000012 t= 0.16800000000000012 t= 0.16900000000000012 t= 0.17000000000000012 t= 0.17100000000000012 t= 0.17200000000000013 t= 0.17300000000000013 t= 0.17400000000000013 t= 0.17500000000000013 t= 0.17600000000000013 t= 0.17700000000000013 t= 0.17800000000000013 t= 0.17900000000000013 t= 0.18000000000000013 t= 0.18100000000000013 t= 0.18200000000000013 t= 0.18300000000000013 t= 0.18400000000000014 t= 0.18500000000000014 t= 0.18600000000000014 t= 0.18700000000000014 t= 0.18800000000000014 t= 0.18900000000000014

end{sphinxVerbatim}

t= 0.1500000000000001 t= 0.1510000000000001 t= 0.1520000000000001 t= 0.1530000000000001 t= 0.1540000000000001 t= 0.1550000000000001 t= 0.1560000000000001 t= 0.1570000000000001 t= 0.1580000000000001 t= 0.1590000000000001 t= 0.16000000000000011 t= 0.16100000000000012 t= 0.16200000000000012 t= 0.16300000000000012 t= 0.16400000000000012 t= 0.16500000000000012 t= 0.16600000000000012 t= 0.16700000000000012 t= 0.16800000000000012 t= 0.16900000000000012 t= 0.17000000000000012 t= 0.17100000000000012 t= 0.17200000000000013 t= 0.17300000000000013 t= 0.17400000000000013 t= 0.17500000000000013 t= 0.17600000000000013 t= 0.17700000000000013 t= 0.17800000000000013 t= 0.17900000000000013 t= 0.18000000000000013 t= 0.18100000000000013 t= 0.18200000000000013 t= 0.18300000000000013 t= 0.18400000000000014 t= 0.18500000000000014 t= 0.18600000000000014 t= 0.18700000000000014 t= 0.18800000000000014 t= 0.18900000000000014

t= 0.19000000000000014 t= 0.19100000000000014 t= 0.19200000000000014 t= 0.19300000000000014 t= 0.19400000000000014 t= 0.19500000000000015 t= 0.19600000000000015 t= 0.19700000000000015 t= 0.19800000000000015 t= 0.19900000000000015 t= 0.20000000000000015 t= 0.20100000000000015 t= 0.20200000000000015 t= 0.20300000000000015 t= 0.20400000000000015 t= 0.20500000000000015 t= 0.20600000000000016 t= 0.20700000000000016 t= 0.20800000000000016 t= 0.20900000000000016 t= 0.21000000000000016 t= 0.21100000000000016 t= 0.21200000000000016 t= 0.21300000000000016 t= 0.21400000000000016 t= 0.21500000000000016 t= 0.21600000000000016 t= 0.21700000000000016 t= 0.21800000000000017 t= 0.21900000000000017 t= 0.22000000000000017 t= 0.22100000000000017 t= 0.22200000000000017 t= 0.22300000000000017 t= 0.22400000000000017 t= 0.22500000000000017 t= 0.22600000000000017 t= 0.22700000000000017 t= 0.22800000000000017 t= 0.22900000000000018 t= 0.23000000000000018 t= 0.23100000000000018

</pre>

t= 0.19000000000000014 t= 0.19100000000000014 t= 0.19200000000000014 t= 0.19300000000000014 t= 0.19400000000000014 t= 0.19500000000000015 t= 0.19600000000000015 t= 0.19700000000000015 t= 0.19800000000000015 t= 0.19900000000000015 t= 0.20000000000000015 t= 0.20100000000000015 t= 0.20200000000000015 t= 0.20300000000000015 t= 0.20400000000000015 t= 0.20500000000000015 t= 0.20600000000000016 t= 0.20700000000000016 t= 0.20800000000000016 t= 0.20900000000000016 t= 0.21000000000000016 t= 0.21100000000000016 t= 0.21200000000000016 t= 0.21300000000000016 t= 0.21400000000000016 t= 0.21500000000000016 t= 0.21600000000000016 t= 0.21700000000000016 t= 0.21800000000000017 t= 0.21900000000000017 t= 0.22000000000000017 t= 0.22100000000000017 t= 0.22200000000000017 t= 0.22300000000000017 t= 0.22400000000000017 t= 0.22500000000000017 t= 0.22600000000000017 t= 0.22700000000000017 t= 0.22800000000000017 t= 0.22900000000000018 t= 0.23000000000000018 t= 0.23100000000000018

end{sphinxVerbatim}

t= 0.19000000000000014 t= 0.19100000000000014 t= 0.19200000000000014 t= 0.19300000000000014 t= 0.19400000000000014 t= 0.19500000000000015 t= 0.19600000000000015 t= 0.19700000000000015 t= 0.19800000000000015 t= 0.19900000000000015 t= 0.20000000000000015 t= 0.20100000000000015 t= 0.20200000000000015 t= 0.20300000000000015 t= 0.20400000000000015 t= 0.20500000000000015 t= 0.20600000000000016 t= 0.20700000000000016 t= 0.20800000000000016 t= 0.20900000000000016 t= 0.21000000000000016 t= 0.21100000000000016 t= 0.21200000000000016 t= 0.21300000000000016 t= 0.21400000000000016 t= 0.21500000000000016 t= 0.21600000000000016 t= 0.21700000000000016 t= 0.21800000000000017 t= 0.21900000000000017 t= 0.22000000000000017 t= 0.22100000000000017 t= 0.22200000000000017 t= 0.22300000000000017 t= 0.22400000000000017 t= 0.22500000000000017 t= 0.22600000000000017 t= 0.22700000000000017 t= 0.22800000000000017 t= 0.22900000000000018 t= 0.23000000000000018 t= 0.23100000000000018

t= 0.23200000000000018 t= 0.23300000000000018 t= 0.23400000000000018 t= 0.23500000000000018 t= 0.23600000000000018 t= 0.23700000000000018 t= 0.23800000000000018 t= 0.23900000000000018 t= 0.24000000000000019 t= 0.2410000000000002 t= 0.2420000000000002 t= 0.2430000000000002 t= 0.2440000000000002 t= 0.2450000000000002 t= 0.2460000000000002 t= 0.2470000000000002 t= 0.2480000000000002 t= 0.2490000000000002 t= 0.25000000000000017 t= 0.25100000000000017 t= 0.25200000000000017 t= 0.25300000000000017 t= 0.25400000000000017 t= 0.25500000000000017 t= 0.25600000000000017 t= 0.2570000000000002 t= 0.2580000000000002 t= 0.2590000000000002 t= 0.2600000000000002 t= 0.2610000000000002 t= 0.2620000000000002 t= 0.2630000000000002 t= 0.2640000000000002 t= 0.2650000000000002 t= 0.2660000000000002 t= 0.2670000000000002 t= 0.2680000000000002 t= 0.2690000000000002 t= 0.2700000000000002 t= 0.2710000000000002 t= 0.2720000000000002 t= 0.2730000000000002

</pre>

t= 0.23200000000000018 t= 0.23300000000000018 t= 0.23400000000000018 t= 0.23500000000000018 t= 0.23600000000000018 t= 0.23700000000000018 t= 0.23800000000000018 t= 0.23900000000000018 t= 0.24000000000000019 t= 0.2410000000000002 t= 0.2420000000000002 t= 0.2430000000000002 t= 0.2440000000000002 t= 0.2450000000000002 t= 0.2460000000000002 t= 0.2470000000000002 t= 0.2480000000000002 t= 0.2490000000000002 t= 0.25000000000000017 t= 0.25100000000000017 t= 0.25200000000000017 t= 0.25300000000000017 t= 0.25400000000000017 t= 0.25500000000000017 t= 0.25600000000000017 t= 0.2570000000000002 t= 0.2580000000000002 t= 0.2590000000000002 t= 0.2600000000000002 t= 0.2610000000000002 t= 0.2620000000000002 t= 0.2630000000000002 t= 0.2640000000000002 t= 0.2650000000000002 t= 0.2660000000000002 t= 0.2670000000000002 t= 0.2680000000000002 t= 0.2690000000000002 t= 0.2700000000000002 t= 0.2710000000000002 t= 0.2720000000000002 t= 0.2730000000000002

end{sphinxVerbatim}

t= 0.23200000000000018 t= 0.23300000000000018 t= 0.23400000000000018 t= 0.23500000000000018 t= 0.23600000000000018 t= 0.23700000000000018 t= 0.23800000000000018 t= 0.23900000000000018 t= 0.24000000000000019 t= 0.2410000000000002 t= 0.2420000000000002 t= 0.2430000000000002 t= 0.2440000000000002 t= 0.2450000000000002 t= 0.2460000000000002 t= 0.2470000000000002 t= 0.2480000000000002 t= 0.2490000000000002 t= 0.25000000000000017 t= 0.25100000000000017 t= 0.25200000000000017 t= 0.25300000000000017 t= 0.25400000000000017 t= 0.25500000000000017 t= 0.25600000000000017 t= 0.2570000000000002 t= 0.2580000000000002 t= 0.2590000000000002 t= 0.2600000000000002 t= 0.2610000000000002 t= 0.2620000000000002 t= 0.2630000000000002 t= 0.2640000000000002 t= 0.2650000000000002 t= 0.2660000000000002 t= 0.2670000000000002 t= 0.2680000000000002 t= 0.2690000000000002 t= 0.2700000000000002 t= 0.2710000000000002 t= 0.2720000000000002 t= 0.2730000000000002

t= 0.2740000000000002 t= 0.2750000000000002 t= 0.2760000000000002 t= 0.2770000000000002 t= 0.2780000000000002 t= 0.2790000000000002 t= 0.2800000000000002 t= 0.2810000000000002 t= 0.2820000000000002 t= 0.2830000000000002 t= 0.2840000000000002 t= 0.2850000000000002 t= 0.2860000000000002 t= 0.2870000000000002 t= 0.2880000000000002 t= 0.2890000000000002 t= 0.2900000000000002 t= 0.2910000000000002 t= 0.2920000000000002 t= 0.2930000000000002 t= 0.2940000000000002 t= 0.2950000000000002 t= 0.2960000000000002 t= 0.2970000000000002 t= 0.2980000000000002 t= 0.2990000000000002 t= 0.3000000000000002 t= 0.3010000000000002 t= 0.3020000000000002 t= 0.3030000000000002 t= 0.3040000000000002 t= 0.3050000000000002 t= 0.3060000000000002 t= 0.3070000000000002 t= 0.3080000000000002 t= 0.3090000000000002 t= 0.3100000000000002 t= 0.3110000000000002 t= 0.3120000000000002 t= 0.3130000000000002 t= 0.3140000000000002 t= 0.3150000000000002 t= 0.3160000000000002

</pre>

t= 0.2740000000000002 t= 0.2750000000000002 t= 0.2760000000000002 t= 0.2770000000000002 t= 0.2780000000000002 t= 0.2790000000000002 t= 0.2800000000000002 t= 0.2810000000000002 t= 0.2820000000000002 t= 0.2830000000000002 t= 0.2840000000000002 t= 0.2850000000000002 t= 0.2860000000000002 t= 0.2870000000000002 t= 0.2880000000000002 t= 0.2890000000000002 t= 0.2900000000000002 t= 0.2910000000000002 t= 0.2920000000000002 t= 0.2930000000000002 t= 0.2940000000000002 t= 0.2950000000000002 t= 0.2960000000000002 t= 0.2970000000000002 t= 0.2980000000000002 t= 0.2990000000000002 t= 0.3000000000000002 t= 0.3010000000000002 t= 0.3020000000000002 t= 0.3030000000000002 t= 0.3040000000000002 t= 0.3050000000000002 t= 0.3060000000000002 t= 0.3070000000000002 t= 0.3080000000000002 t= 0.3090000000000002 t= 0.3100000000000002 t= 0.3110000000000002 t= 0.3120000000000002 t= 0.3130000000000002 t= 0.3140000000000002 t= 0.3150000000000002 t= 0.3160000000000002

end{sphinxVerbatim}

t= 0.2740000000000002 t= 0.2750000000000002 t= 0.2760000000000002 t= 0.2770000000000002 t= 0.2780000000000002 t= 0.2790000000000002 t= 0.2800000000000002 t= 0.2810000000000002 t= 0.2820000000000002 t= 0.2830000000000002 t= 0.2840000000000002 t= 0.2850000000000002 t= 0.2860000000000002 t= 0.2870000000000002 t= 0.2880000000000002 t= 0.2890000000000002 t= 0.2900000000000002 t= 0.2910000000000002 t= 0.2920000000000002 t= 0.2930000000000002 t= 0.2940000000000002 t= 0.2950000000000002 t= 0.2960000000000002 t= 0.2970000000000002 t= 0.2980000000000002 t= 0.2990000000000002 t= 0.3000000000000002 t= 0.3010000000000002 t= 0.3020000000000002 t= 0.3030000000000002 t= 0.3040000000000002 t= 0.3050000000000002 t= 0.3060000000000002 t= 0.3070000000000002 t= 0.3080000000000002 t= 0.3090000000000002 t= 0.3100000000000002 t= 0.3110000000000002 t= 0.3120000000000002 t= 0.3130000000000002 t= 0.3140000000000002 t= 0.3150000000000002 t= 0.3160000000000002

t= 0.3170000000000002 t= 0.3180000000000002 t= 0.31900000000000023 t= 0.32000000000000023 t= 0.32100000000000023 t= 0.32200000000000023 t= 0.32300000000000023 t= 0.32400000000000023 t= 0.32500000000000023 t= 0.32600000000000023 t= 0.32700000000000023 t= 0.32800000000000024 t= 0.32900000000000024 t= 0.33000000000000024 t= 0.33100000000000024 t= 0.33200000000000024 t= 0.33300000000000024 t= 0.33400000000000024 t= 0.33500000000000024 t= 0.33600000000000024 t= 0.33700000000000024 t= 0.33800000000000024 t= 0.33900000000000025 t= 0.34000000000000025 t= 0.34100000000000025 t= 0.34200000000000025 t= 0.34300000000000025 t= 0.34400000000000025 t= 0.34500000000000025 t= 0.34600000000000025 t= 0.34700000000000025 t= 0.34800000000000025 t= 0.34900000000000025 t= 0.35000000000000026 t= 0.35100000000000026

</pre>

t= 0.3170000000000002 t= 0.3180000000000002 t= 0.31900000000000023 t= 0.32000000000000023 t= 0.32100000000000023 t= 0.32200000000000023 t= 0.32300000000000023 t= 0.32400000000000023 t= 0.32500000000000023 t= 0.32600000000000023 t= 0.32700000000000023 t= 0.32800000000000024 t= 0.32900000000000024 t= 0.33000000000000024 t= 0.33100000000000024 t= 0.33200000000000024 t= 0.33300000000000024 t= 0.33400000000000024 t= 0.33500000000000024 t= 0.33600000000000024 t= 0.33700000000000024 t= 0.33800000000000024 t= 0.33900000000000025 t= 0.34000000000000025 t= 0.34100000000000025 t= 0.34200000000000025 t= 0.34300000000000025 t= 0.34400000000000025 t= 0.34500000000000025 t= 0.34600000000000025 t= 0.34700000000000025 t= 0.34800000000000025 t= 0.34900000000000025 t= 0.35000000000000026 t= 0.35100000000000026

end{sphinxVerbatim}

t= 0.3170000000000002 t= 0.3180000000000002 t= 0.31900000000000023 t= 0.32000000000000023 t= 0.32100000000000023 t= 0.32200000000000023 t= 0.32300000000000023 t= 0.32400000000000023 t= 0.32500000000000023 t= 0.32600000000000023 t= 0.32700000000000023 t= 0.32800000000000024 t= 0.32900000000000024 t= 0.33000000000000024 t= 0.33100000000000024 t= 0.33200000000000024 t= 0.33300000000000024 t= 0.33400000000000024 t= 0.33500000000000024 t= 0.33600000000000024 t= 0.33700000000000024 t= 0.33800000000000024 t= 0.33900000000000025 t= 0.34000000000000025 t= 0.34100000000000025 t= 0.34200000000000025 t= 0.34300000000000025 t= 0.34400000000000025 t= 0.34500000000000025 t= 0.34600000000000025 t= 0.34700000000000025 t= 0.34800000000000025 t= 0.34900000000000025 t= 0.35000000000000026 t= 0.35100000000000026

t= 0.35200000000000026 t= 0.35300000000000026 t= 0.35400000000000026 t= 0.35500000000000026 t= 0.35600000000000026 t= 0.35700000000000026 t= 0.35800000000000026 t= 0.35900000000000026 t= 0.36000000000000026 t= 0.36100000000000027 t= 0.36200000000000027 t= 0.36300000000000027 t= 0.36400000000000027 t= 0.36500000000000027 t= 0.36600000000000027 t= 0.36700000000000027 t= 0.36800000000000027 t= 0.36900000000000027 t= 0.3700000000000003 t= 0.3710000000000003 t= 0.3720000000000003 t= 0.3730000000000003 t= 0.3740000000000003 t= 0.3750000000000003 t= 0.3760000000000003 t= 0.3770000000000003 t= 0.3780000000000003 t= 0.3790000000000003 t= 0.3800000000000003 t= 0.3810000000000003 t= 0.3820000000000003 t= 0.3830000000000003 t= 0.3840000000000003 t= 0.3850000000000003 t= 0.3860000000000003 t= 0.3870000000000003

</pre>

t= 0.35200000000000026 t= 0.35300000000000026 t= 0.35400000000000026 t= 0.35500000000000026 t= 0.35600000000000026 t= 0.35700000000000026 t= 0.35800000000000026 t= 0.35900000000000026 t= 0.36000000000000026 t= 0.36100000000000027 t= 0.36200000000000027 t= 0.36300000000000027 t= 0.36400000000000027 t= 0.36500000000000027 t= 0.36600000000000027 t= 0.36700000000000027 t= 0.36800000000000027 t= 0.36900000000000027 t= 0.3700000000000003 t= 0.3710000000000003 t= 0.3720000000000003 t= 0.3730000000000003 t= 0.3740000000000003 t= 0.3750000000000003 t= 0.3760000000000003 t= 0.3770000000000003 t= 0.3780000000000003 t= 0.3790000000000003 t= 0.3800000000000003 t= 0.3810000000000003 t= 0.3820000000000003 t= 0.3830000000000003 t= 0.3840000000000003 t= 0.3850000000000003 t= 0.3860000000000003 t= 0.3870000000000003

end{sphinxVerbatim}

t= 0.35200000000000026 t= 0.35300000000000026 t= 0.35400000000000026 t= 0.35500000000000026 t= 0.35600000000000026 t= 0.35700000000000026 t= 0.35800000000000026 t= 0.35900000000000026 t= 0.36000000000000026 t= 0.36100000000000027 t= 0.36200000000000027 t= 0.36300000000000027 t= 0.36400000000000027 t= 0.36500000000000027 t= 0.36600000000000027 t= 0.36700000000000027 t= 0.36800000000000027 t= 0.36900000000000027 t= 0.3700000000000003 t= 0.3710000000000003 t= 0.3720000000000003 t= 0.3730000000000003 t= 0.3740000000000003 t= 0.3750000000000003 t= 0.3760000000000003 t= 0.3770000000000003 t= 0.3780000000000003 t= 0.3790000000000003 t= 0.3800000000000003 t= 0.3810000000000003 t= 0.3820000000000003 t= 0.3830000000000003 t= 0.3840000000000003 t= 0.3850000000000003 t= 0.3860000000000003 t= 0.3870000000000003

t= 0.3880000000000003 t= 0.3890000000000003 t= 0.3900000000000003 t= 0.3910000000000003 t= 0.3920000000000003 t= 0.3930000000000003 t= 0.3940000000000003 t= 0.3950000000000003 t= 0.3960000000000003 t= 0.3970000000000003 t= 0.3980000000000003 t= 0.3990000000000003 t= 0.4000000000000003 t= 0.4010000000000003 t= 0.4020000000000003 t= 0.4030000000000003 t= 0.4040000000000003 t= 0.4050000000000003 t= 0.4060000000000003 t= 0.4070000000000003 t= 0.4080000000000003 t= 0.4090000000000003 t= 0.4100000000000003 t= 0.4110000000000003 t= 0.4120000000000003 t= 0.4130000000000003 t= 0.4140000000000003 t= 0.4150000000000003 t= 0.4160000000000003 t= 0.4170000000000003 t= 0.4180000000000003 t= 0.4190000000000003 t= 0.4200000000000003 t= 0.4210000000000003 t= 0.4220000000000003 t= 0.4230000000000003 t= 0.4240000000000003 t= 0.4250000000000003 t= 0.4260000000000003 t= 0.4270000000000003 t= 0.4280000000000003 t= 0.4290000000000003

</pre>

t= 0.3880000000000003 t= 0.3890000000000003 t= 0.3900000000000003 t= 0.3910000000000003 t= 0.3920000000000003 t= 0.3930000000000003 t= 0.3940000000000003 t= 0.3950000000000003 t= 0.3960000000000003 t= 0.3970000000000003 t= 0.3980000000000003 t= 0.3990000000000003 t= 0.4000000000000003 t= 0.4010000000000003 t= 0.4020000000000003 t= 0.4030000000000003 t= 0.4040000000000003 t= 0.4050000000000003 t= 0.4060000000000003 t= 0.4070000000000003 t= 0.4080000000000003 t= 0.4090000000000003 t= 0.4100000000000003 t= 0.4110000000000003 t= 0.4120000000000003 t= 0.4130000000000003 t= 0.4140000000000003 t= 0.4150000000000003 t= 0.4160000000000003 t= 0.4170000000000003 t= 0.4180000000000003 t= 0.4190000000000003 t= 0.4200000000000003 t= 0.4210000000000003 t= 0.4220000000000003 t= 0.4230000000000003 t= 0.4240000000000003 t= 0.4250000000000003 t= 0.4260000000000003 t= 0.4270000000000003 t= 0.4280000000000003 t= 0.4290000000000003

end{sphinxVerbatim}

t= 0.3880000000000003 t= 0.3890000000000003 t= 0.3900000000000003 t= 0.3910000000000003 t= 0.3920000000000003 t= 0.3930000000000003 t= 0.3940000000000003 t= 0.3950000000000003 t= 0.3960000000000003 t= 0.3970000000000003 t= 0.3980000000000003 t= 0.3990000000000003 t= 0.4000000000000003 t= 0.4010000000000003 t= 0.4020000000000003 t= 0.4030000000000003 t= 0.4040000000000003 t= 0.4050000000000003 t= 0.4060000000000003 t= 0.4070000000000003 t= 0.4080000000000003 t= 0.4090000000000003 t= 0.4100000000000003 t= 0.4110000000000003 t= 0.4120000000000003 t= 0.4130000000000003 t= 0.4140000000000003 t= 0.4150000000000003 t= 0.4160000000000003 t= 0.4170000000000003 t= 0.4180000000000003 t= 0.4190000000000003 t= 0.4200000000000003 t= 0.4210000000000003 t= 0.4220000000000003 t= 0.4230000000000003 t= 0.4240000000000003 t= 0.4250000000000003 t= 0.4260000000000003 t= 0.4270000000000003 t= 0.4280000000000003 t= 0.4290000000000003

t= 0.4300000000000003 t= 0.4310000000000003 t= 0.43200000000000033 t= 0.43300000000000033 t= 0.43400000000000033 t= 0.43500000000000033 t= 0.43600000000000033 t= 0.43700000000000033 t= 0.43800000000000033 t= 0.43900000000000033 t= 0.44000000000000034 t= 0.44100000000000034 t= 0.44200000000000034 t= 0.44300000000000034 t= 0.44400000000000034 t= 0.44500000000000034 t= 0.44600000000000034 t= 0.44700000000000034 t= 0.44800000000000034 t= 0.44900000000000034 t= 0.45000000000000034 t= 0.45100000000000035 t= 0.45200000000000035 t= 0.45300000000000035 t= 0.45400000000000035 t= 0.45500000000000035 t= 0.45600000000000035 t= 0.45700000000000035 t= 0.45800000000000035 t= 0.45900000000000035 t= 0.46000000000000035 t= 0.46100000000000035 t= 0.46200000000000035 t= 0.46300000000000036 t= 0.46400000000000036 t= 0.46500000000000036 t= 0.46600000000000036

</pre>

t= 0.4300000000000003 t= 0.4310000000000003 t= 0.43200000000000033 t= 0.43300000000000033 t= 0.43400000000000033 t= 0.43500000000000033 t= 0.43600000000000033 t= 0.43700000000000033 t= 0.43800000000000033 t= 0.43900000000000033 t= 0.44000000000000034 t= 0.44100000000000034 t= 0.44200000000000034 t= 0.44300000000000034 t= 0.44400000000000034 t= 0.44500000000000034 t= 0.44600000000000034 t= 0.44700000000000034 t= 0.44800000000000034 t= 0.44900000000000034 t= 0.45000000000000034 t= 0.45100000000000035 t= 0.45200000000000035 t= 0.45300000000000035 t= 0.45400000000000035 t= 0.45500000000000035 t= 0.45600000000000035 t= 0.45700000000000035 t= 0.45800000000000035 t= 0.45900000000000035 t= 0.46000000000000035 t= 0.46100000000000035 t= 0.46200000000000035 t= 0.46300000000000036 t= 0.46400000000000036 t= 0.46500000000000036 t= 0.46600000000000036

end{sphinxVerbatim}

t= 0.4300000000000003 t= 0.4310000000000003 t= 0.43200000000000033 t= 0.43300000000000033 t= 0.43400000000000033 t= 0.43500000000000033 t= 0.43600000000000033 t= 0.43700000000000033 t= 0.43800000000000033 t= 0.43900000000000033 t= 0.44000000000000034 t= 0.44100000000000034 t= 0.44200000000000034 t= 0.44300000000000034 t= 0.44400000000000034 t= 0.44500000000000034 t= 0.44600000000000034 t= 0.44700000000000034 t= 0.44800000000000034 t= 0.44900000000000034 t= 0.45000000000000034 t= 0.45100000000000035 t= 0.45200000000000035 t= 0.45300000000000035 t= 0.45400000000000035 t= 0.45500000000000035 t= 0.45600000000000035 t= 0.45700000000000035 t= 0.45800000000000035 t= 0.45900000000000035 t= 0.46000000000000035 t= 0.46100000000000035 t= 0.46200000000000035 t= 0.46300000000000036 t= 0.46400000000000036 t= 0.46500000000000036 t= 0.46600000000000036

t= 0.46700000000000036 t= 0.46800000000000036 t= 0.46900000000000036 t= 0.47000000000000036 t= 0.47100000000000036 t= 0.47200000000000036 t= 0.47300000000000036 t= 0.47400000000000037 t= 0.47500000000000037 t= 0.47600000000000037 t= 0.47700000000000037 t= 0.47800000000000037 t= 0.47900000000000037 t= 0.48000000000000037 t= 0.48100000000000037 t= 0.4820000000000004 t= 0.4830000000000004 t= 0.4840000000000004 t= 0.4850000000000004 t= 0.4860000000000004 t= 0.4870000000000004 t= 0.4880000000000004 t= 0.4890000000000004 t= 0.4900000000000004 t= 0.4910000000000004 t= 0.4920000000000004 t= 0.4930000000000004 t= 0.4940000000000004 t= 0.4950000000000004 t= 0.4960000000000004 t= 0.4970000000000004 t= 0.4980000000000004 t= 0.4990000000000004 t= 0.5000000000000003 t= 0.5010000000000003 t= 0.5020000000000003 t= 0.5030000000000003 t= 0.5040000000000003 t= 0.5050000000000003 t= 0.5060000000000003 t= 0.5070000000000003

</pre>

t= 0.46700000000000036 t= 0.46800000000000036 t= 0.46900000000000036 t= 0.47000000000000036 t= 0.47100000000000036 t= 0.47200000000000036 t= 0.47300000000000036 t= 0.47400000000000037 t= 0.47500000000000037 t= 0.47600000000000037 t= 0.47700000000000037 t= 0.47800000000000037 t= 0.47900000000000037 t= 0.48000000000000037 t= 0.48100000000000037 t= 0.4820000000000004 t= 0.4830000000000004 t= 0.4840000000000004 t= 0.4850000000000004 t= 0.4860000000000004 t= 0.4870000000000004 t= 0.4880000000000004 t= 0.4890000000000004 t= 0.4900000000000004 t= 0.4910000000000004 t= 0.4920000000000004 t= 0.4930000000000004 t= 0.4940000000000004 t= 0.4950000000000004 t= 0.4960000000000004 t= 0.4970000000000004 t= 0.4980000000000004 t= 0.4990000000000004 t= 0.5000000000000003 t= 0.5010000000000003 t= 0.5020000000000003 t= 0.5030000000000003 t= 0.5040000000000003 t= 0.5050000000000003 t= 0.5060000000000003 t= 0.5070000000000003

end{sphinxVerbatim}

t= 0.46700000000000036 t= 0.46800000000000036 t= 0.46900000000000036 t= 0.47000000000000036 t= 0.47100000000000036 t= 0.47200000000000036 t= 0.47300000000000036 t= 0.47400000000000037 t= 0.47500000000000037 t= 0.47600000000000037 t= 0.47700000000000037 t= 0.47800000000000037 t= 0.47900000000000037 t= 0.48000000000000037 t= 0.48100000000000037 t= 0.4820000000000004 t= 0.4830000000000004 t= 0.4840000000000004 t= 0.4850000000000004 t= 0.4860000000000004 t= 0.4870000000000004 t= 0.4880000000000004 t= 0.4890000000000004 t= 0.4900000000000004 t= 0.4910000000000004 t= 0.4920000000000004 t= 0.4930000000000004 t= 0.4940000000000004 t= 0.4950000000000004 t= 0.4960000000000004 t= 0.4970000000000004 t= 0.4980000000000004 t= 0.4990000000000004 t= 0.5000000000000003 t= 0.5010000000000003 t= 0.5020000000000003 t= 0.5030000000000003 t= 0.5040000000000003 t= 0.5050000000000003 t= 0.5060000000000003 t= 0.5070000000000003

t= 0.5080000000000003 t= 0.5090000000000003 t= 0.5100000000000003 t= 0.5110000000000003 t= 0.5120000000000003 t= 0.5130000000000003 t= 0.5140000000000003 t= 0.5150000000000003 t= 0.5160000000000003 t= 0.5170000000000003 t= 0.5180000000000003 t= 0.5190000000000003 t= 0.5200000000000004 t= 0.5210000000000004 t= 0.5220000000000004 t= 0.5230000000000004 t= 0.5240000000000004 t= 0.5250000000000004 t= 0.5260000000000004 t= 0.5270000000000004 t= 0.5280000000000004 t= 0.5290000000000004 t= 0.5300000000000004 t= 0.5310000000000004 t= 0.5320000000000004 t= 0.5330000000000004 t= 0.5340000000000004 t= 0.5350000000000004 t= 0.5360000000000004 t= 0.5370000000000004 t= 0.5380000000000004 t= 0.5390000000000004 t= 0.5400000000000004 t= 0.5410000000000004 t= 0.5420000000000004 t= 0.5430000000000004 t= 0.5440000000000004

</pre>

t= 0.5080000000000003 t= 0.5090000000000003 t= 0.5100000000000003 t= 0.5110000000000003 t= 0.5120000000000003 t= 0.5130000000000003 t= 0.5140000000000003 t= 0.5150000000000003 t= 0.5160000000000003 t= 0.5170000000000003 t= 0.5180000000000003 t= 0.5190000000000003 t= 0.5200000000000004 t= 0.5210000000000004 t= 0.5220000000000004 t= 0.5230000000000004 t= 0.5240000000000004 t= 0.5250000000000004 t= 0.5260000000000004 t= 0.5270000000000004 t= 0.5280000000000004 t= 0.5290000000000004 t= 0.5300000000000004 t= 0.5310000000000004 t= 0.5320000000000004 t= 0.5330000000000004 t= 0.5340000000000004 t= 0.5350000000000004 t= 0.5360000000000004 t= 0.5370000000000004 t= 0.5380000000000004 t= 0.5390000000000004 t= 0.5400000000000004 t= 0.5410000000000004 t= 0.5420000000000004 t= 0.5430000000000004 t= 0.5440000000000004

end{sphinxVerbatim}

t= 0.5080000000000003 t= 0.5090000000000003 t= 0.5100000000000003 t= 0.5110000000000003 t= 0.5120000000000003 t= 0.5130000000000003 t= 0.5140000000000003 t= 0.5150000000000003 t= 0.5160000000000003 t= 0.5170000000000003 t= 0.5180000000000003 t= 0.5190000000000003 t= 0.5200000000000004 t= 0.5210000000000004 t= 0.5220000000000004 t= 0.5230000000000004 t= 0.5240000000000004 t= 0.5250000000000004 t= 0.5260000000000004 t= 0.5270000000000004 t= 0.5280000000000004 t= 0.5290000000000004 t= 0.5300000000000004 t= 0.5310000000000004 t= 0.5320000000000004 t= 0.5330000000000004 t= 0.5340000000000004 t= 0.5350000000000004 t= 0.5360000000000004 t= 0.5370000000000004 t= 0.5380000000000004 t= 0.5390000000000004 t= 0.5400000000000004 t= 0.5410000000000004 t= 0.5420000000000004 t= 0.5430000000000004 t= 0.5440000000000004

t= 0.5450000000000004 t= 0.5460000000000004 t= 0.5470000000000004 t= 0.5480000000000004 t= 0.5490000000000004 t= 0.5500000000000004 t= 0.5510000000000004 t= 0.5520000000000004 t= 0.5530000000000004 t= 0.5540000000000004 t= 0.5550000000000004 t= 0.5560000000000004 t= 0.5570000000000004 t= 0.5580000000000004 t= 0.5590000000000004 t= 0.5600000000000004 t= 0.5610000000000004 t= 0.5620000000000004 t= 0.5630000000000004 t= 0.5640000000000004 t= 0.5650000000000004 t= 0.5660000000000004 t= 0.5670000000000004 t= 0.5680000000000004 t= 0.5690000000000004 t= 0.5700000000000004 t= 0.5710000000000004 t= 0.5720000000000004 t= 0.5730000000000004 t= 0.5740000000000004 t= 0.5750000000000004 t= 0.5760000000000004 t= 0.5770000000000004 t= 0.5780000000000004 t= 0.5790000000000004 t= 0.5800000000000004 t= 0.5810000000000004 t= 0.5820000000000004 t= 0.5830000000000004 t= 0.5840000000000004 t= 0.5850000000000004 t= 0.5860000000000004

</pre>

t= 0.5450000000000004 t= 0.5460000000000004 t= 0.5470000000000004 t= 0.5480000000000004 t= 0.5490000000000004 t= 0.5500000000000004 t= 0.5510000000000004 t= 0.5520000000000004 t= 0.5530000000000004 t= 0.5540000000000004 t= 0.5550000000000004 t= 0.5560000000000004 t= 0.5570000000000004 t= 0.5580000000000004 t= 0.5590000000000004 t= 0.5600000000000004 t= 0.5610000000000004 t= 0.5620000000000004 t= 0.5630000000000004 t= 0.5640000000000004 t= 0.5650000000000004 t= 0.5660000000000004 t= 0.5670000000000004 t= 0.5680000000000004 t= 0.5690000000000004 t= 0.5700000000000004 t= 0.5710000000000004 t= 0.5720000000000004 t= 0.5730000000000004 t= 0.5740000000000004 t= 0.5750000000000004 t= 0.5760000000000004 t= 0.5770000000000004 t= 0.5780000000000004 t= 0.5790000000000004 t= 0.5800000000000004 t= 0.5810000000000004 t= 0.5820000000000004 t= 0.5830000000000004 t= 0.5840000000000004 t= 0.5850000000000004 t= 0.5860000000000004

end{sphinxVerbatim}

t= 0.5450000000000004 t= 0.5460000000000004 t= 0.5470000000000004 t= 0.5480000000000004 t= 0.5490000000000004 t= 0.5500000000000004 t= 0.5510000000000004 t= 0.5520000000000004 t= 0.5530000000000004 t= 0.5540000000000004 t= 0.5550000000000004 t= 0.5560000000000004 t= 0.5570000000000004 t= 0.5580000000000004 t= 0.5590000000000004 t= 0.5600000000000004 t= 0.5610000000000004 t= 0.5620000000000004 t= 0.5630000000000004 t= 0.5640000000000004 t= 0.5650000000000004 t= 0.5660000000000004 t= 0.5670000000000004 t= 0.5680000000000004 t= 0.5690000000000004 t= 0.5700000000000004 t= 0.5710000000000004 t= 0.5720000000000004 t= 0.5730000000000004 t= 0.5740000000000004 t= 0.5750000000000004 t= 0.5760000000000004 t= 0.5770000000000004 t= 0.5780000000000004 t= 0.5790000000000004 t= 0.5800000000000004 t= 0.5810000000000004 t= 0.5820000000000004 t= 0.5830000000000004 t= 0.5840000000000004 t= 0.5850000000000004 t= 0.5860000000000004

t= 0.5870000000000004 t= 0.5880000000000004 t= 0.5890000000000004 t= 0.5900000000000004 t= 0.5910000000000004 t= 0.5920000000000004 t= 0.5930000000000004 t= 0.5940000000000004 t= 0.5950000000000004 t= 0.5960000000000004 t= 0.5970000000000004 t= 0.5980000000000004 t= 0.5990000000000004 t= 0.6000000000000004 t= 0.6010000000000004 t= 0.6020000000000004 t= 0.6030000000000004 t= 0.6040000000000004 t= 0.6050000000000004 t= 0.6060000000000004 t= 0.6070000000000004 t= 0.6080000000000004 t= 0.6090000000000004 t= 0.6100000000000004 t= 0.6110000000000004 t= 0.6120000000000004 t= 0.6130000000000004 t= 0.6140000000000004 t= 0.6150000000000004 t= 0.6160000000000004 t= 0.6170000000000004 t= 0.6180000000000004 t= 0.6190000000000004 t= 0.6200000000000004 t= 0.6210000000000004

</pre>

t= 0.5870000000000004 t= 0.5880000000000004 t= 0.5890000000000004 t= 0.5900000000000004 t= 0.5910000000000004 t= 0.5920000000000004 t= 0.5930000000000004 t= 0.5940000000000004 t= 0.5950000000000004 t= 0.5960000000000004 t= 0.5970000000000004 t= 0.5980000000000004 t= 0.5990000000000004 t= 0.6000000000000004 t= 0.6010000000000004 t= 0.6020000000000004 t= 0.6030000000000004 t= 0.6040000000000004 t= 0.6050000000000004 t= 0.6060000000000004 t= 0.6070000000000004 t= 0.6080000000000004 t= 0.6090000000000004 t= 0.6100000000000004 t= 0.6110000000000004 t= 0.6120000000000004 t= 0.6130000000000004 t= 0.6140000000000004 t= 0.6150000000000004 t= 0.6160000000000004 t= 0.6170000000000004 t= 0.6180000000000004 t= 0.6190000000000004 t= 0.6200000000000004 t= 0.6210000000000004

end{sphinxVerbatim}

t= 0.5870000000000004 t= 0.5880000000000004 t= 0.5890000000000004 t= 0.5900000000000004 t= 0.5910000000000004 t= 0.5920000000000004 t= 0.5930000000000004 t= 0.5940000000000004 t= 0.5950000000000004 t= 0.5960000000000004 t= 0.5970000000000004 t= 0.5980000000000004 t= 0.5990000000000004 t= 0.6000000000000004 t= 0.6010000000000004 t= 0.6020000000000004 t= 0.6030000000000004 t= 0.6040000000000004 t= 0.6050000000000004 t= 0.6060000000000004 t= 0.6070000000000004 t= 0.6080000000000004 t= 0.6090000000000004 t= 0.6100000000000004 t= 0.6110000000000004 t= 0.6120000000000004 t= 0.6130000000000004 t= 0.6140000000000004 t= 0.6150000000000004 t= 0.6160000000000004 t= 0.6170000000000004 t= 0.6180000000000004 t= 0.6190000000000004 t= 0.6200000000000004 t= 0.6210000000000004

t= 0.6220000000000004 t= 0.6230000000000004 t= 0.6240000000000004 t= 0.6250000000000004 t= 0.6260000000000004 t= 0.6270000000000004 t= 0.6280000000000004 t= 0.6290000000000004 t= 0.6300000000000004 t= 0.6310000000000004 t= 0.6320000000000005 t= 0.6330000000000005 t= 0.6340000000000005 t= 0.6350000000000005 t= 0.6360000000000005 t= 0.6370000000000005 t= 0.6380000000000005 t= 0.6390000000000005 t= 0.6400000000000005 t= 0.6410000000000005 t= 0.6420000000000005 t= 0.6430000000000005 t= 0.6440000000000005 t= 0.6450000000000005 t= 0.6460000000000005 t= 0.6470000000000005 t= 0.6480000000000005 t= 0.6490000000000005 t= 0.6500000000000005 t= 0.6510000000000005 t= 0.6520000000000005 t= 0.6530000000000005 t= 0.6540000000000005 t= 0.6550000000000005 t= 0.6560000000000005 t= 0.6570000000000005 t= 0.6580000000000005 t= 0.6590000000000005

</pre>

t= 0.6220000000000004 t= 0.6230000000000004 t= 0.6240000000000004 t= 0.6250000000000004 t= 0.6260000000000004 t= 0.6270000000000004 t= 0.6280000000000004 t= 0.6290000000000004 t= 0.6300000000000004 t= 0.6310000000000004 t= 0.6320000000000005 t= 0.6330000000000005 t= 0.6340000000000005 t= 0.6350000000000005 t= 0.6360000000000005 t= 0.6370000000000005 t= 0.6380000000000005 t= 0.6390000000000005 t= 0.6400000000000005 t= 0.6410000000000005 t= 0.6420000000000005 t= 0.6430000000000005 t= 0.6440000000000005 t= 0.6450000000000005 t= 0.6460000000000005 t= 0.6470000000000005 t= 0.6480000000000005 t= 0.6490000000000005 t= 0.6500000000000005 t= 0.6510000000000005 t= 0.6520000000000005 t= 0.6530000000000005 t= 0.6540000000000005 t= 0.6550000000000005 t= 0.6560000000000005 t= 0.6570000000000005 t= 0.6580000000000005 t= 0.6590000000000005

end{sphinxVerbatim}

t= 0.6220000000000004 t= 0.6230000000000004 t= 0.6240000000000004 t= 0.6250000000000004 t= 0.6260000000000004 t= 0.6270000000000004 t= 0.6280000000000004 t= 0.6290000000000004 t= 0.6300000000000004 t= 0.6310000000000004 t= 0.6320000000000005 t= 0.6330000000000005 t= 0.6340000000000005 t= 0.6350000000000005 t= 0.6360000000000005 t= 0.6370000000000005 t= 0.6380000000000005 t= 0.6390000000000005 t= 0.6400000000000005 t= 0.6410000000000005 t= 0.6420000000000005 t= 0.6430000000000005 t= 0.6440000000000005 t= 0.6450000000000005 t= 0.6460000000000005 t= 0.6470000000000005 t= 0.6480000000000005 t= 0.6490000000000005 t= 0.6500000000000005 t= 0.6510000000000005 t= 0.6520000000000005 t= 0.6530000000000005 t= 0.6540000000000005 t= 0.6550000000000005 t= 0.6560000000000005 t= 0.6570000000000005 t= 0.6580000000000005 t= 0.6590000000000005

t= 0.6600000000000005 t= 0.6610000000000005 t= 0.6620000000000005 t= 0.6630000000000005 t= 0.6640000000000005 t= 0.6650000000000005 t= 0.6660000000000005 t= 0.6670000000000005 t= 0.6680000000000005 t= 0.6690000000000005 t= 0.6700000000000005 t= 0.6710000000000005 t= 0.6720000000000005 t= 0.6730000000000005 t= 0.6740000000000005 t= 0.6750000000000005 t= 0.6760000000000005 t= 0.6770000000000005 t= 0.6780000000000005 t= 0.6790000000000005 t= 0.6800000000000005 t= 0.6810000000000005 t= 0.6820000000000005 t= 0.6830000000000005 t= 0.6840000000000005 t= 0.6850000000000005 t= 0.6860000000000005 t= 0.6870000000000005 t= 0.6880000000000005 t= 0.6890000000000005 t= 0.6900000000000005 t= 0.6910000000000005 t= 0.6920000000000005 t= 0.6930000000000005 t= 0.6940000000000005 t= 0.6950000000000005 t= 0.6960000000000005 t= 0.6970000000000005 t= 0.6980000000000005

</pre>

t= 0.6600000000000005 t= 0.6610000000000005 t= 0.6620000000000005 t= 0.6630000000000005 t= 0.6640000000000005 t= 0.6650000000000005 t= 0.6660000000000005 t= 0.6670000000000005 t= 0.6680000000000005 t= 0.6690000000000005 t= 0.6700000000000005 t= 0.6710000000000005 t= 0.6720000000000005 t= 0.6730000000000005 t= 0.6740000000000005 t= 0.6750000000000005 t= 0.6760000000000005 t= 0.6770000000000005 t= 0.6780000000000005 t= 0.6790000000000005 t= 0.6800000000000005 t= 0.6810000000000005 t= 0.6820000000000005 t= 0.6830000000000005 t= 0.6840000000000005 t= 0.6850000000000005 t= 0.6860000000000005 t= 0.6870000000000005 t= 0.6880000000000005 t= 0.6890000000000005 t= 0.6900000000000005 t= 0.6910000000000005 t= 0.6920000000000005 t= 0.6930000000000005 t= 0.6940000000000005 t= 0.6950000000000005 t= 0.6960000000000005 t= 0.6970000000000005 t= 0.6980000000000005

end{sphinxVerbatim}

t= 0.6600000000000005 t= 0.6610000000000005 t= 0.6620000000000005 t= 0.6630000000000005 t= 0.6640000000000005 t= 0.6650000000000005 t= 0.6660000000000005 t= 0.6670000000000005 t= 0.6680000000000005 t= 0.6690000000000005 t= 0.6700000000000005 t= 0.6710000000000005 t= 0.6720000000000005 t= 0.6730000000000005 t= 0.6740000000000005 t= 0.6750000000000005 t= 0.6760000000000005 t= 0.6770000000000005 t= 0.6780000000000005 t= 0.6790000000000005 t= 0.6800000000000005 t= 0.6810000000000005 t= 0.6820000000000005 t= 0.6830000000000005 t= 0.6840000000000005 t= 0.6850000000000005 t= 0.6860000000000005 t= 0.6870000000000005 t= 0.6880000000000005 t= 0.6890000000000005 t= 0.6900000000000005 t= 0.6910000000000005 t= 0.6920000000000005 t= 0.6930000000000005 t= 0.6940000000000005 t= 0.6950000000000005 t= 0.6960000000000005 t= 0.6970000000000005 t= 0.6980000000000005

t= 0.6990000000000005 t= 0.7000000000000005 t= 0.7010000000000005 t= 0.7020000000000005 t= 0.7030000000000005 t= 0.7040000000000005 t= 0.7050000000000005 t= 0.7060000000000005 t= 0.7070000000000005 t= 0.7080000000000005 t= 0.7090000000000005 t= 0.7100000000000005 t= 0.7110000000000005 t= 0.7120000000000005 t= 0.7130000000000005 t= 0.7140000000000005 t= 0.7150000000000005 t= 0.7160000000000005 t= 0.7170000000000005 t= 0.7180000000000005 t= 0.7190000000000005 t= 0.7200000000000005 t= 0.7210000000000005 t= 0.7220000000000005 t= 0.7230000000000005 t= 0.7240000000000005 t= 0.7250000000000005 t= 0.7260000000000005 t= 0.7270000000000005 t= 0.7280000000000005 t= 0.7290000000000005 t= 0.7300000000000005 t= 0.7310000000000005 t= 0.7320000000000005 t= 0.7330000000000005 t= 0.7340000000000005 t= 0.7350000000000005 t= 0.7360000000000005 t= 0.7370000000000005 t= 0.7380000000000005 t= 0.7390000000000005 t= 0.7400000000000005

</pre>

t= 0.6990000000000005 t= 0.7000000000000005 t= 0.7010000000000005 t= 0.7020000000000005 t= 0.7030000000000005 t= 0.7040000000000005 t= 0.7050000000000005 t= 0.7060000000000005 t= 0.7070000000000005 t= 0.7080000000000005 t= 0.7090000000000005 t= 0.7100000000000005 t= 0.7110000000000005 t= 0.7120000000000005 t= 0.7130000000000005 t= 0.7140000000000005 t= 0.7150000000000005 t= 0.7160000000000005 t= 0.7170000000000005 t= 0.7180000000000005 t= 0.7190000000000005 t= 0.7200000000000005 t= 0.7210000000000005 t= 0.7220000000000005 t= 0.7230000000000005 t= 0.7240000000000005 t= 0.7250000000000005 t= 0.7260000000000005 t= 0.7270000000000005 t= 0.7280000000000005 t= 0.7290000000000005 t= 0.7300000000000005 t= 0.7310000000000005 t= 0.7320000000000005 t= 0.7330000000000005 t= 0.7340000000000005 t= 0.7350000000000005 t= 0.7360000000000005 t= 0.7370000000000005 t= 0.7380000000000005 t= 0.7390000000000005 t= 0.7400000000000005

end{sphinxVerbatim}

t= 0.6990000000000005 t= 0.7000000000000005 t= 0.7010000000000005 t= 0.7020000000000005 t= 0.7030000000000005 t= 0.7040000000000005 t= 0.7050000000000005 t= 0.7060000000000005 t= 0.7070000000000005 t= 0.7080000000000005 t= 0.7090000000000005 t= 0.7100000000000005 t= 0.7110000000000005 t= 0.7120000000000005 t= 0.7130000000000005 t= 0.7140000000000005 t= 0.7150000000000005 t= 0.7160000000000005 t= 0.7170000000000005 t= 0.7180000000000005 t= 0.7190000000000005 t= 0.7200000000000005 t= 0.7210000000000005 t= 0.7220000000000005 t= 0.7230000000000005 t= 0.7240000000000005 t= 0.7250000000000005 t= 0.7260000000000005 t= 0.7270000000000005 t= 0.7280000000000005 t= 0.7290000000000005 t= 0.7300000000000005 t= 0.7310000000000005 t= 0.7320000000000005 t= 0.7330000000000005 t= 0.7340000000000005 t= 0.7350000000000005 t= 0.7360000000000005 t= 0.7370000000000005 t= 0.7380000000000005 t= 0.7390000000000005 t= 0.7400000000000005

t= 0.7410000000000005 t= 0.7420000000000005 t= 0.7430000000000005 t= 0.7440000000000005 t= 0.7450000000000006 t= 0.7460000000000006 t= 0.7470000000000006 t= 0.7480000000000006 t= 0.7490000000000006 t= 0.7500000000000006 t= 0.7510000000000006 t= 0.7520000000000006 t= 0.7530000000000006 t= 0.7540000000000006 t= 0.7550000000000006 t= 0.7560000000000006 t= 0.7570000000000006 t= 0.7580000000000006 t= 0.7590000000000006 t= 0.7600000000000006 t= 0.7610000000000006 t= 0.7620000000000006 t= 0.7630000000000006 t= 0.7640000000000006 t= 0.7650000000000006 t= 0.7660000000000006 t= 0.7670000000000006 t= 0.7680000000000006 t= 0.7690000000000006 t= 0.7700000000000006 t= 0.7710000000000006 t= 0.7720000000000006 t= 0.7730000000000006 t= 0.7740000000000006 t= 0.7750000000000006 t= 0.7760000000000006 t= 0.7770000000000006

</pre>

t= 0.7410000000000005 t= 0.7420000000000005 t= 0.7430000000000005 t= 0.7440000000000005 t= 0.7450000000000006 t= 0.7460000000000006 t= 0.7470000000000006 t= 0.7480000000000006 t= 0.7490000000000006 t= 0.7500000000000006 t= 0.7510000000000006 t= 0.7520000000000006 t= 0.7530000000000006 t= 0.7540000000000006 t= 0.7550000000000006 t= 0.7560000000000006 t= 0.7570000000000006 t= 0.7580000000000006 t= 0.7590000000000006 t= 0.7600000000000006 t= 0.7610000000000006 t= 0.7620000000000006 t= 0.7630000000000006 t= 0.7640000000000006 t= 0.7650000000000006 t= 0.7660000000000006 t= 0.7670000000000006 t= 0.7680000000000006 t= 0.7690000000000006 t= 0.7700000000000006 t= 0.7710000000000006 t= 0.7720000000000006 t= 0.7730000000000006 t= 0.7740000000000006 t= 0.7750000000000006 t= 0.7760000000000006 t= 0.7770000000000006

end{sphinxVerbatim}

t= 0.7410000000000005 t= 0.7420000000000005 t= 0.7430000000000005 t= 0.7440000000000005 t= 0.7450000000000006 t= 0.7460000000000006 t= 0.7470000000000006 t= 0.7480000000000006 t= 0.7490000000000006 t= 0.7500000000000006 t= 0.7510000000000006 t= 0.7520000000000006 t= 0.7530000000000006 t= 0.7540000000000006 t= 0.7550000000000006 t= 0.7560000000000006 t= 0.7570000000000006 t= 0.7580000000000006 t= 0.7590000000000006 t= 0.7600000000000006 t= 0.7610000000000006 t= 0.7620000000000006 t= 0.7630000000000006 t= 0.7640000000000006 t= 0.7650000000000006 t= 0.7660000000000006 t= 0.7670000000000006 t= 0.7680000000000006 t= 0.7690000000000006 t= 0.7700000000000006 t= 0.7710000000000006 t= 0.7720000000000006 t= 0.7730000000000006 t= 0.7740000000000006 t= 0.7750000000000006 t= 0.7760000000000006 t= 0.7770000000000006

t= 0.7780000000000006 t= 0.7790000000000006 t= 0.7800000000000006 t= 0.7810000000000006 t= 0.7820000000000006 t= 0.7830000000000006 t= 0.7840000000000006 t= 0.7850000000000006 t= 0.7860000000000006 t= 0.7870000000000006 t= 0.7880000000000006 t= 0.7890000000000006 t= 0.7900000000000006 t= 0.7910000000000006 t= 0.7920000000000006 t= 0.7930000000000006 t= 0.7940000000000006 t= 0.7950000000000006 t= 0.7960000000000006 t= 0.7970000000000006 t= 0.7980000000000006 t= 0.7990000000000006 t= 0.8000000000000006 t= 0.8010000000000006 t= 0.8020000000000006 t= 0.8030000000000006 t= 0.8040000000000006 t= 0.8050000000000006 t= 0.8060000000000006 t= 0.8070000000000006 t= 0.8080000000000006 t= 0.8090000000000006 t= 0.8100000000000006 t= 0.8110000000000006 t= 0.8120000000000006 t= 0.8130000000000006 t= 0.8140000000000006 t= 0.8150000000000006 t= 0.8160000000000006

</pre>

t= 0.7780000000000006 t= 0.7790000000000006 t= 0.7800000000000006 t= 0.7810000000000006 t= 0.7820000000000006 t= 0.7830000000000006 t= 0.7840000000000006 t= 0.7850000000000006 t= 0.7860000000000006 t= 0.7870000000000006 t= 0.7880000000000006 t= 0.7890000000000006 t= 0.7900000000000006 t= 0.7910000000000006 t= 0.7920000000000006 t= 0.7930000000000006 t= 0.7940000000000006 t= 0.7950000000000006 t= 0.7960000000000006 t= 0.7970000000000006 t= 0.7980000000000006 t= 0.7990000000000006 t= 0.8000000000000006 t= 0.8010000000000006 t= 0.8020000000000006 t= 0.8030000000000006 t= 0.8040000000000006 t= 0.8050000000000006 t= 0.8060000000000006 t= 0.8070000000000006 t= 0.8080000000000006 t= 0.8090000000000006 t= 0.8100000000000006 t= 0.8110000000000006 t= 0.8120000000000006 t= 0.8130000000000006 t= 0.8140000000000006 t= 0.8150000000000006 t= 0.8160000000000006

end{sphinxVerbatim}

t= 0.7780000000000006 t= 0.7790000000000006 t= 0.7800000000000006 t= 0.7810000000000006 t= 0.7820000000000006 t= 0.7830000000000006 t= 0.7840000000000006 t= 0.7850000000000006 t= 0.7860000000000006 t= 0.7870000000000006 t= 0.7880000000000006 t= 0.7890000000000006 t= 0.7900000000000006 t= 0.7910000000000006 t= 0.7920000000000006 t= 0.7930000000000006 t= 0.7940000000000006 t= 0.7950000000000006 t= 0.7960000000000006 t= 0.7970000000000006 t= 0.7980000000000006 t= 0.7990000000000006 t= 0.8000000000000006 t= 0.8010000000000006 t= 0.8020000000000006 t= 0.8030000000000006 t= 0.8040000000000006 t= 0.8050000000000006 t= 0.8060000000000006 t= 0.8070000000000006 t= 0.8080000000000006 t= 0.8090000000000006 t= 0.8100000000000006 t= 0.8110000000000006 t= 0.8120000000000006 t= 0.8130000000000006 t= 0.8140000000000006 t= 0.8150000000000006 t= 0.8160000000000006

t= 0.8170000000000006 t= 0.8180000000000006 t= 0.8190000000000006 t= 0.8200000000000006 t= 0.8210000000000006 t= 0.8220000000000006 t= 0.8230000000000006 t= 0.8240000000000006 t= 0.8250000000000006 t= 0.8260000000000006 t= 0.8270000000000006 t= 0.8280000000000006 t= 0.8290000000000006 t= 0.8300000000000006 t= 0.8310000000000006 t= 0.8320000000000006 t= 0.8330000000000006 t= 0.8340000000000006 t= 0.8350000000000006 t= 0.8360000000000006 t= 0.8370000000000006 t= 0.8380000000000006 t= 0.8390000000000006 t= 0.8400000000000006 t= 0.8410000000000006 t= 0.8420000000000006 t= 0.8430000000000006 t= 0.8440000000000006 t= 0.8450000000000006 t= 0.8460000000000006 t= 0.8470000000000006 t= 0.8480000000000006 t= 0.8490000000000006 t= 0.8500000000000006 t= 0.8510000000000006 t= 0.8520000000000006 t= 0.8530000000000006

</pre>

t= 0.8170000000000006 t= 0.8180000000000006 t= 0.8190000000000006 t= 0.8200000000000006 t= 0.8210000000000006 t= 0.8220000000000006 t= 0.8230000000000006 t= 0.8240000000000006 t= 0.8250000000000006 t= 0.8260000000000006 t= 0.8270000000000006 t= 0.8280000000000006 t= 0.8290000000000006 t= 0.8300000000000006 t= 0.8310000000000006 t= 0.8320000000000006 t= 0.8330000000000006 t= 0.8340000000000006 t= 0.8350000000000006 t= 0.8360000000000006 t= 0.8370000000000006 t= 0.8380000000000006 t= 0.8390000000000006 t= 0.8400000000000006 t= 0.8410000000000006 t= 0.8420000000000006 t= 0.8430000000000006 t= 0.8440000000000006 t= 0.8450000000000006 t= 0.8460000000000006 t= 0.8470000000000006 t= 0.8480000000000006 t= 0.8490000000000006 t= 0.8500000000000006 t= 0.8510000000000006 t= 0.8520000000000006 t= 0.8530000000000006

end{sphinxVerbatim}

t= 0.8170000000000006 t= 0.8180000000000006 t= 0.8190000000000006 t= 0.8200000000000006 t= 0.8210000000000006 t= 0.8220000000000006 t= 0.8230000000000006 t= 0.8240000000000006 t= 0.8250000000000006 t= 0.8260000000000006 t= 0.8270000000000006 t= 0.8280000000000006 t= 0.8290000000000006 t= 0.8300000000000006 t= 0.8310000000000006 t= 0.8320000000000006 t= 0.8330000000000006 t= 0.8340000000000006 t= 0.8350000000000006 t= 0.8360000000000006 t= 0.8370000000000006 t= 0.8380000000000006 t= 0.8390000000000006 t= 0.8400000000000006 t= 0.8410000000000006 t= 0.8420000000000006 t= 0.8430000000000006 t= 0.8440000000000006 t= 0.8450000000000006 t= 0.8460000000000006 t= 0.8470000000000006 t= 0.8480000000000006 t= 0.8490000000000006 t= 0.8500000000000006 t= 0.8510000000000006 t= 0.8520000000000006 t= 0.8530000000000006

t= 0.8540000000000006 t= 0.8550000000000006 t= 0.8560000000000006 t= 0.8570000000000007 t= 0.8580000000000007 t= 0.8590000000000007 t= 0.8600000000000007 t= 0.8610000000000007 t= 0.8620000000000007 t= 0.8630000000000007 t= 0.8640000000000007 t= 0.8650000000000007 t= 0.8660000000000007 t= 0.8670000000000007 t= 0.8680000000000007 t= 0.8690000000000007 t= 0.8700000000000007 t= 0.8710000000000007 t= 0.8720000000000007 t= 0.8730000000000007 t= 0.8740000000000007 t= 0.8750000000000007 t= 0.8760000000000007 t= 0.8770000000000007 t= 0.8780000000000007 t= 0.8790000000000007 t= 0.8800000000000007 t= 0.8810000000000007 t= 0.8820000000000007 t= 0.8830000000000007 t= 0.8840000000000007 t= 0.8850000000000007 t= 0.8860000000000007 t= 0.8870000000000007 t= 0.8880000000000007 t= 0.8890000000000007 t= 0.8900000000000007 t= 0.8910000000000007 t= 0.8920000000000007 t= 0.8930000000000007 t= 0.8940000000000007 t= 0.8950000000000007

</pre>

t= 0.8540000000000006 t= 0.8550000000000006 t= 0.8560000000000006 t= 0.8570000000000007 t= 0.8580000000000007 t= 0.8590000000000007 t= 0.8600000000000007 t= 0.8610000000000007 t= 0.8620000000000007 t= 0.8630000000000007 t= 0.8640000000000007 t= 0.8650000000000007 t= 0.8660000000000007 t= 0.8670000000000007 t= 0.8680000000000007 t= 0.8690000000000007 t= 0.8700000000000007 t= 0.8710000000000007 t= 0.8720000000000007 t= 0.8730000000000007 t= 0.8740000000000007 t= 0.8750000000000007 t= 0.8760000000000007 t= 0.8770000000000007 t= 0.8780000000000007 t= 0.8790000000000007 t= 0.8800000000000007 t= 0.8810000000000007 t= 0.8820000000000007 t= 0.8830000000000007 t= 0.8840000000000007 t= 0.8850000000000007 t= 0.8860000000000007 t= 0.8870000000000007 t= 0.8880000000000007 t= 0.8890000000000007 t= 0.8900000000000007 t= 0.8910000000000007 t= 0.8920000000000007 t= 0.8930000000000007 t= 0.8940000000000007 t= 0.8950000000000007

end{sphinxVerbatim}

t= 0.8540000000000006 t= 0.8550000000000006 t= 0.8560000000000006 t= 0.8570000000000007 t= 0.8580000000000007 t= 0.8590000000000007 t= 0.8600000000000007 t= 0.8610000000000007 t= 0.8620000000000007 t= 0.8630000000000007 t= 0.8640000000000007 t= 0.8650000000000007 t= 0.8660000000000007 t= 0.8670000000000007 t= 0.8680000000000007 t= 0.8690000000000007 t= 0.8700000000000007 t= 0.8710000000000007 t= 0.8720000000000007 t= 0.8730000000000007 t= 0.8740000000000007 t= 0.8750000000000007 t= 0.8760000000000007 t= 0.8770000000000007 t= 0.8780000000000007 t= 0.8790000000000007 t= 0.8800000000000007 t= 0.8810000000000007 t= 0.8820000000000007 t= 0.8830000000000007 t= 0.8840000000000007 t= 0.8850000000000007 t= 0.8860000000000007 t= 0.8870000000000007 t= 0.8880000000000007 t= 0.8890000000000007 t= 0.8900000000000007 t= 0.8910000000000007 t= 0.8920000000000007 t= 0.8930000000000007 t= 0.8940000000000007 t= 0.8950000000000007

t= 0.8960000000000007 t= 0.8970000000000007 t= 0.8980000000000007 t= 0.8990000000000007 t= 0.9000000000000007 t= 0.9010000000000007 t= 0.9020000000000007 t= 0.9030000000000007 t= 0.9040000000000007 t= 0.9050000000000007 t= 0.9060000000000007 t= 0.9070000000000007 t= 0.9080000000000007 t= 0.9090000000000007 t= 0.9100000000000007 t= 0.9110000000000007 t= 0.9120000000000007 t= 0.9130000000000007 t= 0.9140000000000007 t= 0.9150000000000007 t= 0.9160000000000007 t= 0.9170000000000007 t= 0.9180000000000007 t= 0.9190000000000007 t= 0.9200000000000007 t= 0.9210000000000007 t= 0.9220000000000007 t= 0.9230000000000007 t= 0.9240000000000007 t= 0.9250000000000007 t= 0.9260000000000007 t= 0.9270000000000007 t= 0.9280000000000007 t= 0.9290000000000007 t= 0.9300000000000007 t= 0.9310000000000007 t= 0.9320000000000007 t= 0.9330000000000007 t= 0.9340000000000007 t= 0.9350000000000007 t= 0.9360000000000007 t= 0.9370000000000007

</pre>

t= 0.8960000000000007 t= 0.8970000000000007 t= 0.8980000000000007 t= 0.8990000000000007 t= 0.9000000000000007 t= 0.9010000000000007 t= 0.9020000000000007 t= 0.9030000000000007 t= 0.9040000000000007 t= 0.9050000000000007 t= 0.9060000000000007 t= 0.9070000000000007 t= 0.9080000000000007 t= 0.9090000000000007 t= 0.9100000000000007 t= 0.9110000000000007 t= 0.9120000000000007 t= 0.9130000000000007 t= 0.9140000000000007 t= 0.9150000000000007 t= 0.9160000000000007 t= 0.9170000000000007 t= 0.9180000000000007 t= 0.9190000000000007 t= 0.9200000000000007 t= 0.9210000000000007 t= 0.9220000000000007 t= 0.9230000000000007 t= 0.9240000000000007 t= 0.9250000000000007 t= 0.9260000000000007 t= 0.9270000000000007 t= 0.9280000000000007 t= 0.9290000000000007 t= 0.9300000000000007 t= 0.9310000000000007 t= 0.9320000000000007 t= 0.9330000000000007 t= 0.9340000000000007 t= 0.9350000000000007 t= 0.9360000000000007 t= 0.9370000000000007

end{sphinxVerbatim}

t= 0.8960000000000007 t= 0.8970000000000007 t= 0.8980000000000007 t= 0.8990000000000007 t= 0.9000000000000007 t= 0.9010000000000007 t= 0.9020000000000007 t= 0.9030000000000007 t= 0.9040000000000007 t= 0.9050000000000007 t= 0.9060000000000007 t= 0.9070000000000007 t= 0.9080000000000007 t= 0.9090000000000007 t= 0.9100000000000007 t= 0.9110000000000007 t= 0.9120000000000007 t= 0.9130000000000007 t= 0.9140000000000007 t= 0.9150000000000007 t= 0.9160000000000007 t= 0.9170000000000007 t= 0.9180000000000007 t= 0.9190000000000007 t= 0.9200000000000007 t= 0.9210000000000007 t= 0.9220000000000007 t= 0.9230000000000007 t= 0.9240000000000007 t= 0.9250000000000007 t= 0.9260000000000007 t= 0.9270000000000007 t= 0.9280000000000007 t= 0.9290000000000007 t= 0.9300000000000007 t= 0.9310000000000007 t= 0.9320000000000007 t= 0.9330000000000007 t= 0.9340000000000007 t= 0.9350000000000007 t= 0.9360000000000007 t= 0.9370000000000007

t= 0.9380000000000007 t= 0.9390000000000007 t= 0.9400000000000007 t= 0.9410000000000007 t= 0.9420000000000007 t= 0.9430000000000007 t= 0.9440000000000007 t= 0.9450000000000007 t= 0.9460000000000007 t= 0.9470000000000007 t= 0.9480000000000007 t= 0.9490000000000007 t= 0.9500000000000007 t= 0.9510000000000007 t= 0.9520000000000007 t= 0.9530000000000007 t= 0.9540000000000007 t= 0.9550000000000007 t= 0.9560000000000007 t= 0.9570000000000007 t= 0.9580000000000007 t= 0.9590000000000007 t= 0.9600000000000007 t= 0.9610000000000007 t= 0.9620000000000007 t= 0.9630000000000007 t= 0.9640000000000007 t= 0.9650000000000007 t= 0.9660000000000007 t= 0.9670000000000007 t= 0.9680000000000007 t= 0.9690000000000007 t= 0.9700000000000008 t= 0.9710000000000008 t= 0.9720000000000008 t= 0.9730000000000008 t= 0.9740000000000008 t= 0.9750000000000008 t= 0.9760000000000008 t= 0.9770000000000008 t= 0.9780000000000008 t= 0.9790000000000008

</pre>

t= 0.9380000000000007 t= 0.9390000000000007 t= 0.9400000000000007 t= 0.9410000000000007 t= 0.9420000000000007 t= 0.9430000000000007 t= 0.9440000000000007 t= 0.9450000000000007 t= 0.9460000000000007 t= 0.9470000000000007 t= 0.9480000000000007 t= 0.9490000000000007 t= 0.9500000000000007 t= 0.9510000000000007 t= 0.9520000000000007 t= 0.9530000000000007 t= 0.9540000000000007 t= 0.9550000000000007 t= 0.9560000000000007 t= 0.9570000000000007 t= 0.9580000000000007 t= 0.9590000000000007 t= 0.9600000000000007 t= 0.9610000000000007 t= 0.9620000000000007 t= 0.9630000000000007 t= 0.9640000000000007 t= 0.9650000000000007 t= 0.9660000000000007 t= 0.9670000000000007 t= 0.9680000000000007 t= 0.9690000000000007 t= 0.9700000000000008 t= 0.9710000000000008 t= 0.9720000000000008 t= 0.9730000000000008 t= 0.9740000000000008 t= 0.9750000000000008 t= 0.9760000000000008 t= 0.9770000000000008 t= 0.9780000000000008 t= 0.9790000000000008

end{sphinxVerbatim}

t= 0.9380000000000007 t= 0.9390000000000007 t= 0.9400000000000007 t= 0.9410000000000007 t= 0.9420000000000007 t= 0.9430000000000007 t= 0.9440000000000007 t= 0.9450000000000007 t= 0.9460000000000007 t= 0.9470000000000007 t= 0.9480000000000007 t= 0.9490000000000007 t= 0.9500000000000007 t= 0.9510000000000007 t= 0.9520000000000007 t= 0.9530000000000007 t= 0.9540000000000007 t= 0.9550000000000007 t= 0.9560000000000007 t= 0.9570000000000007 t= 0.9580000000000007 t= 0.9590000000000007 t= 0.9600000000000007 t= 0.9610000000000007 t= 0.9620000000000007 t= 0.9630000000000007 t= 0.9640000000000007 t= 0.9650000000000007 t= 0.9660000000000007 t= 0.9670000000000007 t= 0.9680000000000007 t= 0.9690000000000007 t= 0.9700000000000008 t= 0.9710000000000008 t= 0.9720000000000008 t= 0.9730000000000008 t= 0.9740000000000008 t= 0.9750000000000008 t= 0.9760000000000008 t= 0.9770000000000008 t= 0.9780000000000008 t= 0.9790000000000008

t= 0.9800000000000008 t= 0.9810000000000008 t= 0.9820000000000008 t= 0.9830000000000008 t= 0.9840000000000008 t= 0.9850000000000008 t= 0.9860000000000008 t= 0.9870000000000008 t= 0.9880000000000008 t= 0.9890000000000008 t= 0.9900000000000008 t= 0.9910000000000008 t= 0.9920000000000008 t= 0.9930000000000008 t= 0.9940000000000008 t= 0.9950000000000008 t= 0.9960000000000008 t= 0.9970000000000008 t= 0.9980000000000008 t= 0.9990000000000008

</pre>

t= 0.9800000000000008 t= 0.9810000000000008 t= 0.9820000000000008 t= 0.9830000000000008 t= 0.9840000000000008 t= 0.9850000000000008 t= 0.9860000000000008 t= 0.9870000000000008 t= 0.9880000000000008 t= 0.9890000000000008 t= 0.9900000000000008 t= 0.9910000000000008 t= 0.9920000000000008 t= 0.9930000000000008 t= 0.9940000000000008 t= 0.9950000000000008 t= 0.9960000000000008 t= 0.9970000000000008 t= 0.9980000000000008 t= 0.9990000000000008

end{sphinxVerbatim}

t= 0.9800000000000008 t= 0.9810000000000008 t= 0.9820000000000008 t= 0.9830000000000008 t= 0.9840000000000008 t= 0.9850000000000008 t= 0.9860000000000008 t= 0.9870000000000008 t= 0.9880000000000008 t= 0.9890000000000008 t= 0.9900000000000008 t= 0.9910000000000008 t= 0.9920000000000008 t= 0.9930000000000008 t= 0.9940000000000008 t= 0.9950000000000008 t= 0.9960000000000008 t= 0.9970000000000008 t= 0.9980000000000008 t= 0.9990000000000008

Below you can plot the gathered drag and lift values:

[19]:
# Plot drag force over time
plt.plot(time_vals, drag_x_vals)
plt.xlabel('time'); plt.ylabel('drag'); plt.title('drag'); plt.grid(True)
plt.show()
../../_images/i-tutorials_unit-3.2-navierstokes_navierstokes_38_0.png
[20]:
# Plot lift force over time
plt.plot(time_vals, drag_y_vals)
plt.xlabel('time'); plt.ylabel('lift'); plt.title('lift'); plt.grid(True)
plt.show()
../../_images/i-tutorials_unit-3.2-navierstokes_navierstokes_39_0.png

Tasks

If you understood the tutorial so far, you may want to play around with it further. Here are some suggestions on what you could do:

  • Compute drag and lift forces directly through the surface integrals and compare to the residual based evaluation

  • Change the geometry and solve a driven cavity example

  • Use a fully implicit time integration scheme

  • Use a higher order implict or IMEX scheme for time integration