Question

(8). The one dimensional neutron diffusion equation with a (plane) source at x-0 is d'f(x) n (2) +002 f (x)-00(x) dx where f(x) is the flux of neutrons (f(x)→0 as x→±o), Q δ (x) is the (plane) source at x-0 (5(x) is the Dirac delta function), and o is a constant. This problem involves finding the solution to this equation using Fourier Transforms. You may use the formulas derived in class for the Fourier Transform of derivatives, but otherwise compute all the integrals (i.e. do not use tables). Note: If you were in class Monday when I did this example, try computing the result for a plane source at x-x', ie. replace δ(x) with δ(x-x'), and using your solution (which is a Green's Function) to compute f(x) for a continuous source function g(x) (with lg(x)l-»0 as lx l->oo, so that the Fourier Transform of g(x) exists) (a). Apply Fourier Transforms to this equation (ie. let g(k)-(IN2π) j f(x) exp(-ikx)dx, and write the corresponding equation which is satisfied by g(k)) (b). Solve the equation in part (a) for g(k) in the transformed space. (c).Transform your solution back into x-space using f(x)-(1/N21t) J g(k) exp(ikx)dk to obtain the solution f(x) for-oo

Answer 1

I'm sorry if there are any calculations in the final answer reported.Cheers and All the best :)

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