A zipper with N links. Each link has 2 states: closed (energy = 0) and open (energy = E). We require that the zipper can only unzip from the left end, and that the link number s can only open if all links to the left (1,2,..., s-1) are already open.
(a) What is the partition function for the zipper?
(b) What is the average number of open links in the limit (i) >> τ and (ii) << τ
A zipper with N links. Each link has 2 states: closed (energy = 0) and open...
5. Consider a polymer consisting of N links (like links of a chain) of length L. The links are massless. One end of the polymer is fixed at height z = 0. The other end is attached to a mass m. Each link can pivot about its attachment with the previous link or the fixed end so that a link may carry the polymer "up" or "down" a distance L. For example, the figure shows a polymer containing four links,...
3. Consider the generalized one-dimensional Ising model with link-dependent interactions J. In other words, we have N spins s, in a chain and energy N-1 SiSi+1 We recover a standard Ising model (with B 0 and open boundary condi tions) if we set JiJN-1-J a) Show that the canonical partition function is Hint: You can do this by induction and carefully comparing the states of the N-spin chain to those of the (N - 1)-spin chain.] b) Show that the...
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8. Nucleon resonances with spin 3/2 include the Δ(1232) (with charge states ++, +, 0, and , plus similar higher energy resonances, Δ(1600), Δ(1700) and Δ(1920). In each case, the number in parentheses indicates the (approximate) resonance mass (or rest energy) in MeV. When pions of energy Er scatter from nucleons (protons and neutrons) in a target at rest in the lab frame, these resonances can be produced, e.g., π + N → Δ(1232). Each resonance appears as a peak...
Problem #1 A) A closed box has 5 molecules and is then partitioned instantaneously into 4 equally sized compartments. What is the probability of there being 4 particles in the top left compartment? B) Now imagine the same experiment as part A, but with 3 million molecules. What is the range of molecules that are in each partition 95% of the time?Hint: ±2 standard deviations is 95% of the normal distribution. Problem #2 The game of UC poker is similar...
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3:09 × Drill Set 1-new-PHYS 242.docx 2. (i A uniformly charged ring has radius a-0.15m and total charge Q- 24 nC (see figure below) 0 What is the circumference of the ring, and thus the charge per unit length (charge density) of the ring Cm) charge density (ii) To find the potential (voltage) at point (P) distant (along the ring's axis) from the ring center, we can first find the E-field as we did in chapter 21, by considering the...
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**Only [Harder] Question** Problem 2. Consider a firm that has a cost function of c(y) = 5y 2 + 50, 000. In other words, this is a firm with a fixed cost of $50,000 (which might be something like the cost of rent on the firm’s building, which they have to pay whether they produce any output or not) and a variable cost of $5Y 2 , (which we’ll think of as the cost of the labor and machinery necessary...
Major Homework #2 Implement a C program major_hw2.c to solve the 15-puzzle problem using the A* search algorithm. Please include pictures that the code runs and shows the different states as it reaches goal state please. 1. Objectives • To gain more experience on using pointers and linked lists in C programs. • To learn how to solve problems using state space search and A* search algorithm. 2. Background A* search and 15-puzzle problem have been introduced in the class....