This exercise is to be handed in (questions 1 and 2) and emailed or placed on a webpage (question 1) to Dr Adler by 18:00 on the evening of the day of the 5th pair of lectures. Late exercises will be penalised at 2(/10) points per day. Descriptions may be placed on a website or printed or handwritten in English or Hebrew, if handwritten must be clearly written. No points will be deducted for mistakes in English and I probably wouldn't notice any in Hebrew. Note that for question 1 you can use any computer and language; for question 2 you must use the fortran programs but can use any computer, although I recommend phelafel, phclasses or aluf.

1. ** Exact Enumeration ** Write a program that enumerates
*NW(x,N),* the total number of random walks of* N*
steps that reach the point
* x,*
for all *x* for *N=4,5,6,7* and *8.*
(Hint: use the results *NW(0,4)=NW(+/-1,3)* and
*NW(+/-2,4)=NW(+/-1,3)+NW(+/-3,3)* that were discussed in class.)
You can use any language or computer for this.
Describe your results in words on paper (printed or handwritten
as you prefer)
and email (or place on a webpage) your
program to Dr Adler at phr76ja@tx.technion.ac.il
Both the program by email and the description on paper
are needed for a correct answer.

This is the last time I am asking you to email homework - from
here on its all printed on either real paper or the web.

2. ** Simulation ** Use the programs
rwalk1.f and cplot.f to draw graphs of
*P _{N}(x)*, the probability that after

3.** Optional question for 5 point bonus.**
We will reach parallel programming later in the semester, but if you already
know how to do it, you may take this optional 5 point bonus question any time
before we start learning parallel coding together.
The targil is to simulate the random walk process for 100 walkers with a walk
of 1000 steps each and present results for the mean square displacement of
the
whole system. 5 points will be given for a truly parallel code where the
walkers are divided between processors using MPI commands. You can get help at:
here.

If you have access to another parallel machine great; if not you will need an account on TAMNUN and need to learn to use TAMNUN, see Dr Adler to arrange this.

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