empty figure for a given code

I am getting an empty figure for the code below, not sure if the range for Theta is correctly written, i tried with Theta= [0, 120] and Theta= [0:10: 120] but still getting empty figure.

I need to get 5 decreasing curves, with a in y axis and Theta in x axis.

clc
global K A ;

K = 482; %g/ L
A = 1.01; % (X0/Y S0)+1 
Theta= 0: 120;
a0= 1;


a1 = ((a0*K-a0+K+Theta)- sqrt((Theta.^2)-2*a0*Theta-2*a0*K*Theta-2*K*Theta+(a0^2)+(a0^2)*(K^2)-2*a0*(K^2)+(K^2)-2*(a0^2)*K+2*a0*K))/(2*(K-A+ Theta));

a2 = ((a1*K-a1+K+Theta)- sqrt((Theta.^2)-2*a1*Theta-2*a1*K*Theta-2*K*Theta+(a1^2)+(a1^2)*(K^2)-2*a1*(K^2)+(K^2)-2*(a1^2)*K+2*a1*K))/(2*(K-A+ Theta));

a3 = ((a2*K-a2+K+Theta)- sqrt((Theta.^2)-2*a2*Theta-2*a2*K*Theta-2*K*Theta+(a2^2)+(a2^2)*(K^2)-2*a2*(K^2)+(K^2)-2*(a2^2)*K+2*a2*K))/(2*(K-A+ Theta));

a4 = ((a3*K-a3+K+Theta)- sqrt((Theta.^2)-2*a3*Theta-2*a3*K*Theta-2*K*Theta+(a3^2)+(a3^2)*(K^2)-2*a3*(K^2)+(K^2)-2*(a3^2)*K+2*a3*K))/(2*(K-A+ Theta));

a5 = ((a4*K-a4+K+Theta)- sqrt((Theta.^2)-2*a4*Theta-2*a4*K*Theta-2*K*Theta+(a4^2)+(a4^2)*(K^2)-2*a4*(K^2)+(K^2)-2*(a4^2)*K+2*a4*K))/(2*(K-A+ Theta));


figure
plot(Theta,a0,Theta,a1,Theta,a2,Theta,a3,Theta,a4,Theta,a5);
xlabel('dimensionless residence time')
ylabel('Substrate Fraction')
axis ([0 120 0 1]);
legend('N1','N2','N3','N4','N5')
fh=figure (1);
title ('Substrate conversion with residence time')                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       
disp([a0(1,end),a1(1,end),a2(1,end),a3(1,end),a4(1,end),a5(1,end)])

Answer 1

[darova]

You forgot the dot (element-wise operator)

You can simplify your code using for loop

a0 = 1;
for i = 1:5
    a0 = ((a0*K-a0+K+Theta)- % ...
    line(Theta,a0)
end

Answer 2

[DGM]

I'm not sure what your formulae should be for your tasks, but keep in mind the geometry of your variables. While a0 is a scalar as defined, if you're expecting to have any curves to plot, these expressions should be producing vectors. Since we're operating on vectors, we need to pay attention to what we mean when we use multiplication, exponentiation and division operators. If we just want to operate on the elements of the vectors, then use elementwise operators, otherwise you're doing array multiplication and the size will change. In this case, a1, a2, etc were all scalars, so there wasn't anything noticeable to plot.

clc; clf
global K A ;
K = 482; %g/ L
A = 1.01; % (X0/Y S0)+1 
Theta= 0: 120;

% a0 etc were scalar, but should be vectors.  use elementwise ops where appropriate
a0 = ones(size(Theta));
a1 = ((a0*K-a0+K+Theta) - sqrt((Theta.^2) - 2*a0.*Theta - 2*a0*K.*Theta - 2*K*Theta ...
	+ (a0.^2)*(1+K^2) - 2*a0*(K^2) + (K^2) - 2*(a0.^2)*K + 2*a0*K))./(2*(K-A+Theta));
a2 = ((a1*K-a1+K+Theta) - sqrt((Theta.^2) - 2*a1.*Theta - 2*a1*K.*Theta - 2*K*Theta ...
	+ (a1.^2)*(1+K^2) - 2*a1*(K^2) + (K^2) - 2*(a1.^2)*K + 2*a1*K))./(2*(K-A+Theta));
a3 = ((a2*K-a2+K+Theta) - sqrt((Theta.^2) - 2*a2.*Theta - 2*a2*K.*Theta - 2*K*Theta ...
	+ (a2.^2)*(1+K^2) - 2*a2*(K^2) + (K^2) - 2*(a2.^2)*K + 2*a2*K))./(2*(K-A+Theta));
a4 = ((a3*K-a3+K+Theta) - sqrt((Theta.^2) - 2*a3.*Theta - 2*a3*K.*Theta - 2*K*Theta ...
	+ (a3.^2)*(1+K^2) - 2*a3*(K^2) + (K^2) - 2*(a3.^2)*K + 2*a3*K))./(2*(K-A+Theta));
a5 = ((a4*K-a4+K+Theta) - sqrt((Theta.^2) - 2*a4.*Theta - 2*a4*K.*Theta - 2*K*Theta ...
	+ (a4.^2)*(1+K^2) - 2*a4*(K^2) + (K^2) - 2*(a4.^2)*K + 2*a4*K))./(2*(K-A+Theta));

figure
% plot() is going to only plot the real component.  is that what you want?
% you can use real() or imag() to get the components, or abs() to get the magnitude
plot(Theta,real(a0),Theta,real(a1),Theta,real(a2),Theta,real(a3),Theta,real(a4),Theta,real(a5));
%plot(Theta,imag(a0),Theta,imag(a1),Theta,imag(a2),Theta,imag(a3),Theta,imag(a4),Theta,imag(a5));

% you may need to adjust your limits if you use imag() instead
axis ([0 120 0 1]);

xlabel('dimensionless residence time')
ylabel('Substrate Fraction')
legend('N1','N2','N3','N4','N5','location','southwest')
title ('Substrate conversion with residence time') 

disp([a0(1,end),a1(1,end),a2(1,end),a3(1,end),a4(1,end),a5(1,end)])

This produces curves, but a1, etc are complex-valued vectors. You'll have to determine if that's expected and how you want to handle it. What component is of importance? By default, plot() only draws the real component.