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Modeling Algal Growth in MATLAB Using Photosynthetic Factory Dynamics

This MATLAB code simulates algal growth using the photosynthetic factory model, focusing on the Porphyridium sp. strain. It assumes constant light intensity and initializes all cells to an inactive state. Two runs are conducted: the first with Me=0 and the second with Me=0.05908 h^−1. The model calculates changes in cell concentrations over time, plotting results for active and inactive cells. Future improvements include incorporating light intensity as a function of cell concentration and adjusting system dimensions in calculations.

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Modeling Algal Growth in MATLAB Using Photosynthetic Factory Dynamics

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  1. Matlab Model

  2. Assumptions • Use the photosynthetic factory model. • Assume light intensity is constant, not a function of anything. • All cells are initially in the inactive state. • For the 1st runs, assume Me=0 • For the 2nd run, set Me=0.05908h-1 • All the constants are from Merchuk et. al. 1996, 2000,2004) • The algae strain they used was Porphyridum sp.

  3. Matlab Code function algae2() tspan=[0 10000]; xzero=[1 0 8000 0]; [t,x]=ode45(@dalgaedt,tspan, xzero); x(:,4)=1-x(:,1)-x(:,2); figure (1) plot(t, x(:,3)) hold figure (2) plot(t,x(:,1), t,x(:,2), t, x(:,4)) end function dxdt=dalgaedt(t,x) alpha=0.001935; beta=5.7848e-7; gamma=0.1460; delta=0.0004796; k=3.6467e-4; Io=250; Me= 0; dxdt=zeros(size(x)); dxdt(1)=(-alpha*Io*x(1))+(gamma*x(2))+(delta*(1-x(1)-x(2))); dxdt(2)=(alpha*Io*x(1))-(gamma*x(2))-(beta*Io*x(2)); dxdt(3)=(k*gamma*x(2)*x(3))-(Me*x(3)); end

  4. For Me=0, xo=106 cell/ ml ,x1=1, t=10000s,

  5. For Me=1.6411e-5, xo=106 cell/ ml ,x1=1, t=10000s,

  6. What’s Next • Add the light intensity as a function of cell concentration. • Include the dimensions of the system in the calculations.

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