Problem 7.28 in An introduction to computer simulation methods by Gould Consider

Question

Problem 7.28 in An introduction to computer simulation methods by Gould

Consider a self avoiding walk on a square lattice. There is an arbitrary origin and the first step taken is up. The walk generated by the three other possible initial directions only differ by a rotation of the whole lattice and do not have to be considered explecitly. The second step can be in three rather than four possible directions because of the constraint cannot return to the origin ( this means no back tracking ). To ensrue that the result is not biased, we generate a random number to choose one of three direction. Successive steps are generated in the same way. Unfortunatly the walk will not go on forever. If the a step leads to a self intersection, the walk is terminated. ( meaning path cannot intersept itself)

(a) Write a program that impletements this algorithm and records the fraction f(N) of successful attempts at consturcting polymer chains with N total monomers. Represent the lattice as a array so that you can record the site that already ahve been visited. What is the qualitative dependence of f(N) on N? What is the maximum value of n that you can reasonaly consider ?

(b) Determine the mean square end to end distance for values of N that you can reasonably consider iwth this sampling method

IF YOU ARE ABLE TO WRITE THE PROGRAM THAT GENERATES THE WALK AND ACCOUNTS THE NUMBER OF STEPS BEFORE AN INTERSECTION OCCURS I WILL GIVE YOU LIFESAVER FULL CREDIT.

Explanation / Answer

Dear.. // random walk in two dimensions public class RandomWalk implements AnimationModel, Runnable, Drawable { private int nwalkers; private int xpositions[ ]; private int ypositions[ ]; private Control myControl = new SAnimationControl(this); private Thread animationThread; private World2D world = new World2D(); private Random random; public RandomWalk() { world.addDrawable(this); random = new Random(); } public void startCalculation() { nwalkers = (int) myControl.getValue("nwalkers"); xpositions = new int[nwalkers]; ypositions = new int[nwalkers]; random.setSeed(7); animationThread = new Thread(this); animationThread.start(); } public void run() { while (animationThread != null) { step(); try { Thread.sleep(100); } catch(InterruptedException e){} } } public void stopCalculation() { animationThread = null; } public void step() { move(); world.render(); } public void continueCalculation() { animationThread = new Thread(this); animationThread.start(); } public void clear(){} public void reset() { myControl.setValue("nwalkers", 200); } void move() { for (int i = 0; i

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