PHY 411-506
Homework Assignment 2
Spring 2014
Fermi-Pasta-Ulam-Tsingou Problem and Korteweg - de Vries Solitons
Please format your submission as a single PDF le according to the instructions in the syllabus and submit it on UBlearns before
11:59 pm on Sun
#include tcmathb
#include ﬁCStdlibb
#include ifstreamb
#include <iostreamo
#include astringp
using namespace std:
[I simulation parameters
int N = 54: f/ number of particles
double rho = 1.6; ff density [number per unit volume)
double T = 1.6: ff temperat
Topic 2
Monte Carlo Methods
Lecture 5
Cluster Algorithms to Reduce Critical Slowing Down
Monte Carlo simulations close to a phase transition are aected by critical slowing down. In the 2-D Ising
system, the correlation length becomes very large, and the c
Topic 5
Quantum Monte Carlo
Lecture 1
Variational Quantum Monte Carlo for the Harmonic Oscillator
In this topic, we will study simple quantum mechanical systems of particles which have bound states. The
simplest such system is the quantum harmonic oscilla
Topic 5
Quantum Monte Carlo
Lecture 5
The Path Integral Monte Carlo Method
The Path Integral formulation of quantum mechanics was suggested by Dirac Rev. Mod. Phys. 17, 195-199
(1945), and extensively developed by Feynman, Rev. Mod. Phys. 20, 367-387 (194
Topic 5
Quantum Monte Carlo
Lecture 4
The Diusion Monte Carlo (DMC) Method
In this approach, the ground state of the system is found by modeling a diusion process.
Diusion and random walks
Consider a random walk on a lattice with spacing a in one dimensio
Topic 3
Polymers and Neurons
Lecture 6
Articial Neural Networks in High Energy Physics
The review article by C. Peterson and T. Rognvaldsson, An introduction to articial neural networks,
Proc. 1991 CERN Summer School of Computing, CERN Yellow Report 92-02
Topic 6
Quantum Field Theory
Lecture 3
Hadron Collisions and Parton Distribution Functions
The Cross Section for Z Boson Production at the LHC
S. Chatrchyan et al., CMS Collaboration, Measurement of the Drell-Yan cross section in pp collisions at
s = 7 Te
Topic 6
Quantum Field Theory
Lecture 4
Lattice Gauge Theories and Lattice QCD
Unlike the QED ne structure constant , the QCD coupling parameter s(Q) depends strongly on the
energy (inverse distance) scale at which the strong interaction takes place. Pertu
Topic 6
Quantum Field Theory
Lecture 5
Lattice Quantumchromodynamics
Perturbation theory in the QCD coupling s(Q) can be used only at high energies Q
1 GeV. Predictions
for low energy properties, such as the spectrum of mesons and baryons, the decays of u
Topic 6
Quantum Field Theory
Lecture 2
High Energy Cross Sections by Monte Carlo Quadrature
Thomson Scattering in Electrodynamics
Jackson, Classical Electrodynamics, Section 14.8 Thomson Scattering of Radiation
Jackson Figures 14.17 and 14.18: Dierential
Topic 6
Quantum Field Theory
Lecture 1
Monte Carlo Quadrature in Quantum Field Theory
Applications of relativistic quantum eld theories like the Standard Model of elementary particles generally
use perturbative Feynman diagram methods to compute cross sec
Topic 5
Quantum Monte Carlo
Lecture 3
VMC for Helium: Slater-Jastrow Functions and Cusp Conditions
The choice of variational wave function is the most important step in doing a variational Monte Carlo
calculation.
With a well-chosen trial wave function, w
Topic 3
Polymers and Neurons
Lecture 4
The Hodgkin-Huxley Neuron Model
Neuron Structure and Function
Neurons are nerve cells with a cell body or soma which contains the nucleus and protein manufacturing
apparatus, an axon which propagates action potential
Topic 1
Molecular Dynamics
Lecture 1
What is Molecular Dynamics?
A molecule in Molecular Dynamics is a general term for a particle with mass, position and velocity, which
is subject to forces and moves according to Newtons equations of motion.
Molecular D
PHY 411-506
Homework Assignment 7
Spring 2014
Electronic Structure
Please format your submission as a single PDF le according to the instructions in the syllabus and submit it on UBlearns before
11:59 pm on Sunday, April 6.
1. (17 points) A variational ca
Topic 3
Polymers and Neurons
Lecture 2
Monte Carlo Methods for Protein Folding
Bovine Cytochrome C studied using THz spectroscopy by Markelz Group and modeled by Dr. Zheng
Biophys. J. 100, 1058-1065 (2011) on the left, is a bipolymer with 105 amino acids.
Topic 2
Monte Carlo Methods
Lecture 4
Critical Phenomena, Divergences, and Critical Slowing Down
The Metropolis Monte Carlo method works very well in simulating the properties of the 2-D Ising model.
However, close to the Curie temperature Tc, the simulat
Topic 1
Molecular Dynamics
Lecture 4
Molecular Dynamics Simulation of Argon
The fundamental work on this problem was done by A. Rahman, Phys. Rev. 136, A405 (1964). It was
extended in many important ways by L. Verlet, Phys. Rev. 159, 98 (1967), who introd