Engineering Math

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;