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Re: Plot a function with constants

  • To: mathgroup at smc.vnet.net
  • Subject: [mg36013] Re: [mg35998] Plot a function with constants
  • From: BobHanlon at aol.com
  • Date: Mon, 12 Aug 2002 03:34:30 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

In a message dated 8/11/02 6:39:20 AM, remi.dumasNOSPAM at club-internet.fr 
writes:

>I would like to plot this function :
>                     1
>n(e)=______________
>         Exp[b(e-mu)]+1
>
>and get a graphic like that, with the letters
>
>n(e)
> ^
>  |
>  |
>1|   ____________
>  |                           \
>  |                             \
>  |                              |
>  |_______________ \_____________________\ e
>                              mu                                      
>   /
>
>how can i do it, i specified
>SetAttributes{b,constant} etc ... but it don't work
>
>please help me, i use mathematica 4

Needs["Graphics`Legend`"];
Needs["Graphics`Arrow`"];

1/(Exp[b(e-mu)]+1);

Rewrite the expression as

1/(Exp[b*mu(e/mu-1)]+1);

% == %% // Simplify

True

In order to Plot the normalized function you must provide one or more 
specific values for the product b*mu

With[{btm =4, edmMax = 3},
    Plot[1/(Exp[btm(edm-1)]+1), {edm,0,edmMax},
      AxesLabel->
        {ToString[TraditionalForm[e/mu]], "n(e}"},
      PlotStyle -> Hue[2/3],
      Epilog -> {
          Arrow[{.9*edmMax,0}, {1.07*edmMax,0}, HeadCenter->.25],
          Arrow[{0,.9}, {0,1.1}, HeadCenter->.25]},
      PlotRange -> {{0,1.07*edmMax},{0,1.1}}]];


For multiple values

With[{btmMin = -1,btmMax =4,edmMax = 3,n = 6},
    Plot[Evaluate[
        Table[1/(Exp[btm(edm-1)]+1),
 
          {btm,btmMin, btmMax, (btmMax-btmMin)/(n-1)}]],
 
      {edm,0,edmMax},
      AxesLabel->
        {ToString[TraditionalForm[e/mu]], "n(e}"},
      PlotStyle ->
 
        Table[Hue[(btm-btmMin)/(btmMax-btmMin+3)],
 
          {btm,btmMin,btmMax, (btmMax-btmMin)/(n-1)}],
      PlotLegend->
        
        Table[btm, {btm,btmMin,btmMax, (btmMax-btmMin)/(n-1)}],
      LegendPosition->{.85,-.35},
      LegendLabel->"b*mu =",
      Epilog -> {
          Arrow[{.9*edmMax,0}, {1.07*edmMax,0}, HeadCenter->.25],
          Arrow[{0,.9}, {0,1.1}, HeadCenter->.25]},
      PlotRange -> {{0,1.07*edmMax},{0,1.1}},
      ImageSize -> 400]];


Just for laughs
:

With[{btmMin = -4,btmMax =4,edmMax = 2,n = 600},
    Plot[Evaluate[
        Table[1/(Exp[btm(edm-1)]+1),
 
          {btm,btmMin, btmMax, (btmMax-btmMin)/(n-1)}]],
 
      {edm,0,edmMax},
      AxesLabel->
        {ToString[TraditionalForm[e/mu]], "n(e}"},
      PlotStyle ->
 
        Table[Hue[(btm-btmMin)/(btmMax-btmMin+3)],
 
          {btm,btmMin,btmMax, (btmMax-btmMin)/(n-1)}],
      Epilog -> {
          Arrow[{.9*edmMax,0}, {1.07*edmMax,0}, HeadCenter->.25],
          Arrow[{0,.9}, {0,1.1}, HeadCenter->.25]},
      PlotRange -> {{0,1.07*edmMax},{0,1.1}},
      ImageSize -> 400]];


Bob Hanlon
Chantilly, VA  USA


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