PHYS 325: Solutions to Homework #6

• Solution to problem 1(a)

• Solution to problem 1(b)
  
      python hw6.1b.py 0.1
      python hw6.1b.py 0.5
      python hw6.1b.py 1.0

• Solution to problem 2(a)
  
      (i)   D = 1, L = 10, T = 37.9
      (ii)  D = 4, L = 10, T = 9.6
      (iii) D = 1, L = 5, T = 9.6
  
  These are consistent with the scaling  T ∝ L²/D  presented in class.

• Solution to problem 2(b)
  
      Steady state solution is T[-1] = 0.5.

• Solution to problem 3
  
      PBAR = 5, TMAX = 10, J = 1501, DT = 0.01
      PBAR = 10, TMAX = 5, J = 3001, DT = 0.0025
      PBAR = 20, TMAX = 2.5, J = 7501, DT = 0.001

• Solution to problem 4, part 1
  
      python hw6.4a.py 8
      python hw6.4a.py 10
      python hw6.4a.py 12

• Solution to problem 4, part 2
  
      python hw6.4b.py
  Just demonstrates the time-dependent solution.
  
  There is fairly good agreement between the time-dependent and time-independent results, considering the very different assumptions made.