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11 Nov 2019

a) Two instantaneous sources each of strength M are symmetrically placed about the origin (x=0) at locations respectively and released at time t=0. Obtain the solution to the 1d diffusion equation describing the concentration c(x,t) at a time > 0 for . Plot the concentration field, c(x,t)/M, as a function of x for -4<x<4 for different values of Dt ranging from 0 to 2 in steps ( Dt= 0 ; Dt=.05; 0.1; 0.25; 0.5; 1.0; 1.5; 2.0.).

What does the plot looks like for Dt > 5.

b) Find the peak concentration at x=0 and the time to at which it develops. Plot c(0,t) vs t for D = 10-11 cm2/s ; M = 25 g/cm2 and

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(c) Compute and plot the solution with r0 = 102, f0 = 198, and α = 0.01. Determine the period tp either by trial and error or with an event handler.

(d) The point (r0, f0) = (1/α, 2/α) is a stable equilibrium point. If the populations have these initial values, they do not change. If the initial populations are close to these values, they do not change very much. Let u(t) = r(t)−1/α and v(t) = f(t) − 2/α. The functions u(t) and v(t) satisfy another nonlinear system of differential equations, but if the uv terms are ignored, the system becomes linear. What is this linear system? What is the period of its periodic solutions?

Hi, I need the full Matlab code and answers for all parts of the problem. Thanks!

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