PHYS 3061 Introduction to Computer Simulation of Physical

PHYS 3061 Introduction to Computer Simulation of Physical Systems Lab 4. Computing Statistics and Thermodynamic Equilibrium

Some common issues in last lab Why my system blow up ？ There are many possible reasons Unit, Boundary, Force, Verlet method, ……. Before mixing everything, make sure they're right, or you won't be able to find the “Troublemakers”

Some common issues in last lab How to check your force？ Set two atoms 1. 5 sigma apart. Use a pen and paper to calculate the force and compare it with the result of your code How to check your unit？ Use a pen and paper to calculate the energy of a single particle and compare it with the result of your code

How to check your Verlet？

A puzzle in the last lab

Statistical average

Moving Average

Target of this lab Try some statistical tools or system settings, which may be useful in your term project or future simulations 1. Radial Distribution Function (RDF) 2. Autocorrelation 3. Berendsen Thermostat

1. Radial Distribution Function (RDF)

RDF: Specification Sum over all pair with double counting

RDF: Implementation

Tuning your RDF Choice of range of R and ∆r: Do your own testing. ∆r Range of R_MAX must be small, but not too small Try to make sure MOST or ALL of the particle within the range Suggestion: Compute max and min of the radial distribution, divide it by few 10 s of bins

2. Dynamical Properties

3. Heat Bath

3. Berendsen Thermostat

Lab Tasks

Lab Tasks Specification You must submit Source code . xyz file of relevant runs Plots of RDF and/or autocorrelation and/or temperature evolution Due Date: Mar 16 th 23: 59

Term Report 1. Get your topic approved by Professor Zhu Write a short email to Professor Zhu about what you want to do (Both the project and literature topic) Before March 17 th 2. Prepare for Presentation April 19 th 3. Write up the report on the same topic as presentation Note: There is another literature review presentation on April 12 th. Report Due Date: May 15 th If you hand in late, whether your report get graded is uncertain. Depends on when we are required to submit score to department.