Re: need your help!
- To: mathgroup at smc.vnet.net
- Subject: [mg109802] Re: need your help!
- From: dh <dh at metrohm.com>
- Date: Tue, 18 May 2010 02:14:06 -0400 (EDT)
- References: <hsgnhg$d3r$1@smc.vnet.net>
Hi,
I would guess that the problem is not with Plot but with your function.
Try if you function returns numeric values for some specific input.
Probably you will then see what is wrong.
cheers, Daniel
Am 13.05.2010 13:24, schrieb Ben:
> In[1]:= s[\[Omega]_, t_] =
> FullSimplify[
> Integrate[
> Sin[\[Omega] \[Tau]] Sin[\[Omega]0 \[Tau]], {\[Tau], 0, t}]]
>
> Out[1]= (\[Omega]0 Cos[t \[Omega]0] Sin[t \[Omega]] - \[Omega] Cos[
> t \[Omega]] Sin[t \[Omega]0])/(\[Omega]^2 - \[Omega]0^2)
>
> In[2]:= c[\[Omega]_, t_] =
> FullSimplify[
> Integrate[
> Cos[\[Omega] \[Tau]] Cos[\[Omega]0 \[Tau]], {\[Tau], 0, t}]]
> d[\[Omega]_, t_] =
> FullSimplify[
> Integrate[
> Cos[\[Omega] \[Tau]] Sin[\[Omega]0 \[Tau]], {\[Tau], 0, t}]]
>
> Out[2]= (\[Omega] Cos[t \[Omega]0] Sin[t \[Omega]] - \[Omega]0 Cos[
> t \[Omega]] Sin[t \[Omega]0])/(\[Omega]^2 - \[Omega]0^2)
>
> Out[3]= (-\[Omega]0 + \[Omega]0 Cos[t \[Omega]] Cos[
> t \[Omega]0] + \[Omega] Sin[t \[Omega]] Sin[
> t \[Omega]0])/(\[Omega]^2 - \[Omega]0^2)
>
> Jpbg[\[Omega]_] = If[\[Omega]> 0, 1/Sqrt[\[Omega]], 0];
>
> J1[\[Alpha]_, \[Omega]0_, t_] =
> FullSimplify[
> Integrate[ \[Alpha]^2/
> Sqrt[\[Omega]]*(\[Omega] Cos[t \[Omega]0] Sin[
> t \[Omega]] - \[Omega]0 Cos[t \[Omega]] Sin[
> t \[Omega]0])/(\[Omega]^2 - \[Omega]0^2), {\[Omega],
> 0, \[Infinity]},
> Assumptions -> {\[Alpha]> 0, \[Omega]0> 0, t> 0}], {\[Alpha]>
> 0, \[Omega]0> 0, \[Omega]> 0, t> 0}];
>
>
> \[CapitalDelta][\[Alpha]_, \[Omega]0_, t_] :=
> Re[Simplify[J1[\[Alpha], \[Omega]0, t]]];
>
> In[7]:= \[CapitalDelta][0.1, 0.5, 0.1, 5.]
>
> Out[7]= 0.199423
>
> J2[\[Alpha]_, \[Omega]0_] =
> FullSimplify[
> Integrate[ \[Alpha]^2/
> Sqrt[\[Omega]]*-\[Omega]0/(\[Omega]^2 - \[Omega]0^2), {\[Omega],
> 0, \[Infinity]},
> Assumptions -> {\[Alpha]> 0, \[Omega]0> 0, \[Lambda]>
> 0}], {\[Alpha]> 0, \[Omega]0> 0}];
> J3[\[Alpha]_, \[Omega]0_, t_] =
> FullSimplify[
> Integrate[ \[Alpha]^2/
> Sqrt[\[Omega]]*(\[Omega]0 Cos[t \[Omega]] Cos[
> t \[Omega]0])/(\[Omega]^2 - \[Omega]0^2), {\[Omega],
> 0, \[Infinity]},
> Assumptions -> {\[Alpha]> 0, \[Omega]0> 0, t> 0}], {\[Alpha]>
> 0, \[Omega]0> 0, t> 0}];
>
>
> During evaluation of In[8]:= Integrate::idiv: Integral of 1/((\
> \[Lambda]^2+\[Omega]^2) (\[Omega]^2-\[Omega]0^2)) does not converge \
> on {0,\[Infinity]}.>>
>
> J4[\[Alpha]_, \[Omega]0_, t_] =
> FullSimplify[
> Integrate[ \[Alpha]^2/
> Sqrt[\[Omega]]*(\[Omega] Sin[t \[Omega]] Sin[
> t \[Omega]0])/(\[Omega]^2 - \[Omega]0^2), {\[Omega],
> 0, \[Infinity]},
> Assumptions -> {\[Alpha]> 0, \[Omega]0> 0, t> 0}], {\[Alpha]>
> 0, \[Omega]0> 0, t> 0}];
>
>
> \[CapitalPi][\[Alpha]_, \[Omega]0_, t_] :=
> Re[Simplify[
> J2[\[Alpha], \[Omega]0] + J3[\[Alpha], \[Omega]0, t] +
> J4[\[Alpha], \[Omega]0, t]]];
>
> In[12]:= \[CapitalPi][0.1, 0.5, 0.1, 5.]
>
> Out[12]= 0.42693
>
> J5[\[Alpha]_, \[Omega]0_, \[Lambda]_, t_] =
> FullSimplify[
> Integrate[ \[Alpha]^2/
> Sqrt[\[Omega]]*(\[Omega]0 Cos[t \[Omega]0] Sin[
> t \[Omega]] - \[Omega] Cos[t \[Omega]] Sin[
> t \[Omega]0])/(\[Omega]^2 - \[Omega]0^2), {\[Omega],
> 0, \[Infinity]},
> Assumptions -> {\[Alpha]> 0, \[Omega]0> 0, \[Lambda]> 0,
> t> 0}], {\[Alpha]> 0, \[Omega]0> 0, \[Lambda]> 0, t> 0}];
>
> \[Gamma][\[Alpha]_, \[Omega]0_, t_] :=
> Re[Simplify[J5[\[Alpha], \[Omega]0, t]]];
>
> In[15]:= \[Gamma][0.1, 0.5, 0.1, 5.]
>
> Out[15]= 0.168173
>
> \[CapitalGamma][\[Alpha]_, \[Omega]0_, t_] =
> FullSimplify[
> Integrate[2*\[Gamma][\[Alpha], \[Omega]0, s], {s, 0, t},
> Assumptions -> {\[Alpha]> 0, \[Omega]0> 0}], {\[Alpha]>
> 0, \[Omega]0> 0}];
>
> Subscript[\[CapitalDelta], \[CapitalGamma]][\[Alpha]_, \[Omega]0_,
> t_] = FullSimplify[
> Integrate[J1[\[Alpha], \[Omega]0, s], {s, 0, t},
> Assumptions -> {\[Alpha]> 0, \[Omega]0> 0}], {\[Alpha]>
> 0, \[Omega]0> 0}];
>
> In[18]:= Subscript[\[CapitalDelta], \[CapitalGamma]][0.1, 0.5, 0.1, \
> 5.]
>
> Out[18]= 1.04639
>
>
> \[CapitalDelta]co[\[Alpha]_, \[Omega]0_, t_] =
> Re[FullSimplify[
> Integrate[
> J1[\[Alpha], \[Omega]0, s]*Cos[2 \[Omega]0 (t - s)], {s, 0, t},
> Assumptions -> {\[Alpha]> 0, \[Omega]0> 0, t> 0}], {\[Alpha]>
> 0, \[Omega]0> 0, t> 0}]];
>
> \[CapitalDelta]si[\[Alpha]_, \[Omega]0_, t_] =
> Re[FullSimplify[
> Integrate[
> J1[\[Alpha], \[Omega]0, s]*Sin[2 \[Omega]0 (t - s)], {s, 0, t},
> Assumptions -> {\[Alpha]> 0, \[Omega]0> 0, \[Lambda]> 0,
> t> 0}], {\[Alpha]> 0, \[Omega]0> 0, t> 0}]];
>
> \[CapitalPi]co[\[Alpha]_, \[Omega]0_, t_] =
> Re[FullSimplify[
> Integrate[(J2[\[Alpha], \[Omega]0, s] +
> J3[\[Alpha], \[Omega]0, s] + J4[\[Alpha], \[Omega]0, s])*
> Cos[2 \[Omega]0 (t - s)], {s, 0, t},
> Assumptions -> {\[Alpha]> 0, \[Omega]0> 0, t> 0}], {\[Alpha]>
> 0, \[Omega]0> 0, \[Lambda]> 0, t> 0}]];
>
> \[CapitalPi]si[\[Alpha]_, \[Omega]0_, t_] =
> Re[FullSimplify[
> Integrate[(J2[\[Alpha], \[Omega]0, s] +
> J3[\[Alpha], \[Omega]0, s] + J4[\[Alpha], \[Omega]0, s])*
> Sin[2 \[Omega]0 (t - s)], {s, 0, t},
> Assumptions -> {\[Alpha]> 0, \[Omega]0> 0, t> 0}], {\[Alpha]>
> 0, \[Omega]0> 0, t> 0}]];
>
> Out[22]= $Aborted
>
> \[CapitalDelta]co[0.1, 0.5, 0.1, 5.]
>
> -0.198356 - 1.08996*10^-17 \[ImaginaryI]
>
> \[CapitalDelta]si[0.1, 0.5, 0.1, 5.]
>
> 0.404226+ 0. \[ImaginaryI]
>
> \[CapitalPi]co[0.1, 0.5, 0.1, 5.]
>
> 0.148022- 5.29091*10^-17 \[ImaginaryI]
>
> \[CapitalPi]si[0.1, 0.5, 0.1, 5.]
>
> 0.54091- 5.42101*10^-17 \[ImaginaryI]
>
> Clear[A0]
>
> A0[r_] = {{Cosh[2 r], 0}, {0, Cosh[2 r]}};
> B0 = {{b, 0}, {0, b}};
>
> Clear[At]
>
> At[\[Alpha]_, \[Omega]0_, t_, r_] :=
> Re[A0[r] + {{Subscript[\[CapitalDelta], \[CapitalGamma]][\[Alpha], \
> \[Omega]0,
> t] + (\[CapitalDelta]co[\[Alpha], \[Omega]0,
> t] - \[CapitalDelta]si[\[Alpha], \[Omega]0,
> t]), -(\[CapitalDelta]si[\[Alpha], \[Omega]0,
> t] - \[CapitalPi]co[\[Alpha], \[Omega]0,
> t])}, {-(\[CapitalDelta]si[\[Alpha], \[Omega]0,
> t] - \[CapitalPi]co[\[Alpha], \[Omega]0, t]),
> Subscript[\[CapitalDelta], \[CapitalGamma]][\[Alpha], \[Omega]0,
> t] - (\[CapitalDelta]co[\[Alpha], \[Omega]0,
> t] - \[CapitalDelta]si[\[Alpha], \[Omega]0, t])}}];
>
> MatrixForm[ArrayFlatten[At[0.1, 0.5, 0.1, 5., 1.]]]
>
> \!\(\*
> TagBox[
> RowBox[{"(", "\[NoBreak]", GridBox[{
> {"4.206008542870848`",
> RowBox[{"-", "0.25620413800854397`"}]},
> {
> RowBox[{"-", "0.25620413800854397`"}], "5.411172395695137`"}
> },
> GridBoxAlignment->{
> "Columns" -> {{Left}}, "ColumnsIndexed" -> {},
> "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
> GridBoxSpacings->{"Columns" -> {
> Offset[0.27999999999999997`], {
> Offset[0.7]},
> Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
> Offset[0.2], {
> Offset[0.4]},
> Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
> Function[BoxForm`e$,
> MatrixForm[BoxForm`e$]]]\)
>
> Ct[\[Omega]0_, t_, r_] =
> ArrayFlatten[{{Sinh[2 r]/2 Cos [2 \[Omega]0 t],
> Sinh[2 r]/2 Sin [2 \[Omega]0 t]}, {Sinh[2 r]/2 Cos [
> 2 \[Omega]0 t], -Sinh[2 r]/2 Cos [2 \[Omega]0 t]}}];
>
> MatrixForm[ArrayFlatten[Ct[0.1, 5., 1.]]]
>
> \[Sigma]t[\[Alpha]_, \[Omega]0_, t_, r_] =
> ArrayFlatten[{At[\[Alpha], \[Omega]0, t, r],
> Ct[\[Omega]0, t, r]}, {Transpose[Ct[\[Omega]0, t, r]],
> At[\[Alpha], \[Omega]0, t, r]}];
> MatrixForm[ArrayFlatten[\[Sigma]t[0.1, 0.5, 5., 1.]]]
>
> Subscript[I, 1] =
> Simplify[Det[
> At[\[Alpha], \[Omega]0, t, r]], {\[Alpha]> 0, \[Omega]0> 0,
> t> 0, r> 0}]
>
> Subscript[I, 3] =
> Simplify[Det[Ct[\[Omega]0, t, r]], {\[Omega]0> 0, t> 0, r> 0}]
>
>
>
> Subscript[I, 4] =
> Simplify[Det[\[Sigma]t[\[Alpha], \[Omega]0, t, r]], {\[Alpha]>
> 0, \[Omega]0> 0, t> 0, r> 0}];
>
> Subscript[C, +] =
> Simplify[Sqrt[(
> Subscript[I, 1]^2 + Subscript[I, 3]^2 - Subscript[I, 4] +
> Sqrt[(Subscript[I, 1]^2 + Subscript[I, 3]^2 - Subscript[I,
> 4])^2 - (2 Subscript[I, 1]*Subscript[I, 3])^2 ])/(
> 2 Subscript[I, 1])]];
> Subscript[C, -] =
> Simplify[Sqrt[(
> Subscript[I, 1]^2 + Subscript[I, 3]^2 - Subscript[I, 4] -
> Sqrt[(Subscript[I, 1]^2 + Subscript[I, 3]^2 - Subscript[I,
> 4])^2 - (2 Subscript[I, 1]*Subscript[I, 3])^2 ])/(
> 2 Subscript[I, 1])]];
>
> Subscript[a, n] = Simplify[Sqrt[Subscript[I, 1]]];
>
> Subscript[\[Kappa], -] =
> Simplify[
> Sqrt[(Subscript[a, n] - Subscript[C, +])*(Subscript[a, n] -
> Subscript[C, -])]];
>
> Subscript[x, m] =
> Simplify[(Subscript[\[Kappa], -]^2 + 1/4)/(
> 2 Subscript[\[Kappa], -])];
>
> Subscript[E, F][\[Alpha]_, \[Omega]0_, \[Lambda]_, t_, r_] :=
> Re[(Subscript[x, m] + 1/2) ln [
> Subscript[x, m] + 1/2] - (Subscript[x, m] - 1/2) ln [
> Subscript[x, m] - 1/2]];
>
> Subscript[E, F][0.1, 0.5, 5., 1.]
>
> Plot[Subscript[E, F][0.1, 0.5, t, 1.],
> {t, 0, 5}]
>
>
--
Daniel Huber
Metrohm Ltd.
Oberdorfstr. 68
CH-9100 Herisau
Tel. +41 71 353 8585, Fax +41 71 353 8907
E-Mail:<mailto:dh at metrohm.com>
Internet:<http://www.metrohm.com>