Engineering Math - Quick Reference                                 Home : www.sharetechnote.com

 

 

 

Hill Function

 

It is very usefull function to approximate various degree of Hard Limitor (Similar to Step function) just by changing Ka, A, n in the following equation. This is very widely used in BioChemistry.

 

Example 1 >  When n > = 0

 

 

    n = 2;

    A = 0.5;

    Ka = 1.0;

    L = 0:0.1:10;

     

    Theta = A ./((Ka ./ L).^n .+ 1);

    plot(L,Theta); xlim([L(1),L(length(L))]); ylim([0,1.25 .* max(Theta)]);xlabel('L');ylabel('Theta');

 

Example 2 >   When n > = 0

 

 

    A = 0.5;

    Ka = 1.0;

    L = 0:0.1:10;

     

    for n=0:1.0:10

        Theta = A ./((Ka ./ L).^n .+ 1);

        plot(L,Theta); xlim([L(1),L(length(L))]); ylim([0,1.25 .* max(Theta)]);xlabel('L');ylabel('Theta');

        hold on;

    end;

 

Example 3 >   When n < = 0

 

 

    n = -2;

    A = 0.5;

    Ka = 1.0;

    L = 0:0.1:10;

     

    Theta = A ./((Ka ./ L).^n .+ 1);

    plot(L,Theta); xlim([L(1),L(length(L))]); ylim([0,1.25 .* max(Theta)]);xlabel('L');ylabel('Theta');

 

Example 4 >   When n < = 0

 

 

    A = 0.5;

    Ka = 1.0;

    L = 0:0.1:10;

     

    for n=0:-1.0:-10

        Theta = A ./((Ka ./ L).^n .+ 1);

        plot(L,Theta); xlim([L(1),L(length(L))]); ylim([0,1.25 .* max(Theta)]);xlabel('L');ylabel('Theta');

        hold on;

    end;