Flory Erponent in Random Walks Write a Python Code to simulate random walks on a 2D square lattice starting from the origin. (a) (b) Simulate unrestricted random walks up to n=100 steps, averaging over nu, 2 2 - 104 walks for each n > 3. Plot (ri) as function of n (r2 = 3:2 + :92), and extract the Flory exponent in 1/ (r2) E A t\" (t large), by an eyeball t. Simulate a 2D self-avoiding random walk (SAW). Make sure that each walk of given step-length n (polymer with given molecule number, n) has the same probability, i.e., each step direction should always be selected with probability 1 / 3 (except for the rst step) and paths with intersections should be discarded from the average. Plot (r31) vs. 71. Go to at least 71:50 and use a sufciently large nw. To extract the Flory exponent, rst show analytically that (Tl _ V1 (7%) 1+2 'n. (1) for large n. Replot your 2D SAW data using this relation and determine the value of 1/ by an eyeball t. Re-evaluate 1/ from part (a) with this technique. Investigate uctuations of the 2D random walk by extracting the variance, A(r2), as function of n. Evaluate the exponent a: in 0(t) E A(r2(t)) 0c t\": by TI. the same technique as in part (b). Sketch the result as a \"1-0\" band around (r2) from part (a). Extract the Flory exponent for a SAW on a 3D square lattice using the pro- cedure outlined in part (b). Make sure to use a sufciently large number of walks, am, to obtain reasonable statistics for up to 71250