% Potentially useful functions for HW Set #6 % you can copy the contents of this file to your main function %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% function CMrate = Cell_Multiplication(Ncells,Nutrients,P,params) % computes the Cell Multiplication rate (cells/s) in the CSTR % inputs: % Ncells number of cells in the CSTR % Nutrients concentration of Nutrients in the CSTR (moles/liter) % P concentration of Product in CSTR, [=] moles/liter % params values of [k1,k2,k3,c1,c2,d] as listed in problem statement. k1 = params(1); c1=params(4); d=params(6); CMrate = k1.*Ncells.*Nutrients./((1+c1.*Nutrients).*(1+d.*P)); return; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% function NCrate = Nutrient_Consumption(Ncells,Nutrients,P,params) % computes the nutrient consumption rate in the CSTR (moles/s) % inputs: % Ncells number of cells in the CSTR % Nutrients concentration of Nutrients in the CSTR (moles/liter) % P concentration of Product in CSTR, [=] moles/liter % params values of [k1,k2,k3,c1,c2,d] as listed in problem statement. k2 = params(2); c2 = params(5); NCrate = k2*Ncells*(Nutrients - 1e-6) + c2*Cell_Multiplication(Ncells,Nutrients,P,params); return; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% function Prate = P_production(Ncells,Nutrients,P,params) % computes the product production rate in the CSTR (moles/s) % inputs: % Ncells number of cells in the CSTR % Nutrients concentration of Nutrients in the CSTR (moles/liter) % P concentration of Product in CSTR, [=] moles/liter % params values of [k1,k2,k3,c1,c2,d] as listed in problem statement. k3 = params(3); d=params(6); c1=params(4); Prate = k3.*Ncells.*exp(-d.*P).*((Nutrients-0.01).^2)./(1+c1.*Nutrients); return; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% function params = param_set % sets params as in the problem statement % [k1 k2 k3 c1 c2 d] params = [5e-3 1e-9 1e-8 0.1 1e-7 0.01]; return; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%