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MathGroup Archive 2004

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RE : Parametric plot

  • To: mathgroup at smc.vnet.net
  • Subject: [mg49213] RE : [mg49195] Parametric plot
  • From: "Florian Jaccard" <florian.jaccard at eiaj.ch>
  • Date: Thu, 8 Jul 2004 02:50:46 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Hello !

If you meant So/Km and Vmax/Km :

If you want t on the horizontal axe , you can for example proceed like this
(but there are a lot of other ways...) :

equa = (so/km)*x - Log[1 - x] == (vmax/km)*t; 

<< "Graphics`Graphics`"

<< "Graphics`ImplicitPlot`"

DisplayTogether[(ImplicitPlot[equa /. {so -> #1, vmax -> 15, km -> 10}, {t,
0, 15}, {x, 0, 1}, 
      PlotStyle -> Hue[#1/200]] & ) /@ {1, 20, 100}, 
   (Graphics[{Hue[#1[[2]]/200], Text["so=", {#1[[1]], 1.5}], Text[#1[[2]],
{#1[[1]] + 0.8, 1.5}]}] & ) /@ 
    {{2, 1}, {6, 20}, {10, 100}}, ImageSize -> 600, AxesLabel -> {"t", "x"},

   TextStyle -> {FontSize -> 12}, PlotRange -> {{-0.2, 15}, {-1, 2}}]; 


If you want x on the horizontal axe :

f[x_] := ((so/km)*x - Log[1 - x])*(km/vmax)

<< "Graphics`Legend`"; << "Graphics`Colors`"

Plot[Evaluate[(f[x] /. {so -> #1, vmax -> 15, km -> 10} & ) /@ {1, 20,
100}], {x, 0, 1}, 
   PlotStyle -> {Red, Blue, Green}, PlotLegend -> {"so=1", "so=20",
"so=100"}, LegendPosition -> {1.1, 0}, 
   ImageSize -> 500, AxesLabel -> {"x", "t"}];


N.B. Avoid using capital letters as first letter of variables!


F.Jaccard

-----Message d'origine-----
De : Danilo Bianchi [mailto:kaiowaa at bol.com.br] 
Envoyé : mercredi, 7. juillet 2004 07:42
À : mathgroup at smc.vnet.net
Objet : [mg49195] Parametric plot

A str batch reactor model following Michaelis-Menten kinetics gives
the function:
(S0\Km)x - Log[1 - x] = (Vmax\Km) t
where x is the proportion of substrate converted, S0 is, say, 1, 20
and 100 g/L, Km is 10 and Vmax is 15.
How to plot the curves (in the same graphic) for x varying from zero
to 1 against t (from zero to 15, with the given values?




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