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# The plot is done using the following mathematica

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Unformatted text preview: tes. The plot is done using the following Mathematica program: ΓΘ In[37]:= Θ1 f Θ_, Α_, Γ_ : Θ 2 ; Α myplot Α_, Γ_ : Plot f Θ, Α, Γ , 1 Θ , Θ, 0, 1 , PlotStyle Thick, Frame True, FrameLabel Style "Θ", 16 , Style "LHS or RHS", 14 , Epilog Style Text "Α " ToString Α , 0.7, 0.9 , 1, 0 , 16 , Style Text "Γ " ToString Γ , 0.7, 0.80 , 1, 0 , 16 The following plots show how the steady states varies with Α and Γ: (22) MultipleSteadyStatesSurfaceReactions.nb In[39]:= myplot 0.2, 0.005 1.0 Α 0.2 Γ 0.005 Out[39]= LHS or RHS 0.8 0.6 0.4 0.2 0.0 0.0 0.2 0.4 0.6 0.8 1.0 Θ In[40]:= myplot 0.12, 0.005 1.2 Out[40]= LHS or RHS 1.0 Α 0.12 Γ 0.005 0.8 0.6 0.4 0.2 0.0 0.0 0.2 0.4 0.6 0.8 1.0 Θ In[43]:= myplot 0.265, 0.005 1.0 Α 0.265 Γ 0.005 0.8 Out[43]= LHS or RHS 4 0.6 0.4 0.2 0.0 0.0 0.2 0.4 0.6 0.8 1.0 Θ We can also use ContourPLot to show the multiplicity of solutions as a fixed value of Γ. Thus we look for the contour G(Θ; Α,Γ=0.005)=0. Here is the...
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