**PHY ****412: ****Computational Physics**** (4)**

*Prerequisites*: *PHY 305: **Classical Mechanics, *

* PHY 306: Statistical Mechanics, Numerical Methods*

*Introduction:*Computer simulations and problems in material science, Numerical methods and programming in Fortran 90/95, A brief review of classical mechanics and statistical mechanics, Quantum mechanics as a starting point.

*Monte Carlo simulations:*** **Importance sampling and the metropolis method, basic Monte Carlo algorithm, trial moves, random number generators, estimators. Applications and hands-on sessions–solid-liquid phase-transition in the Lennard-Jones fluid and the magnetic transition in the Ising model. Advanced applications–Monte Carlo in various ensembles, Kinetic Monte Carlo, Monte Carlo methods for rigid molecules and polymers.

*Molecular Dynamics: *The basic idea of MD, numerical integration of equations of motion – Verlet and velocity Verlet algorithms, classical force-fields – bonded and non-bonded interactions, parameterization of force-fields.
Applications and hands-on sessions – determining the diffusion constant and radial distribution functions of a Lennard-Jones fluid using an Anderson thermostat, end-to-end distance and radius of gyration of a solvated polymer using bead-spring model.
Advanced applications – MD in various ensembles – thermostats and baro-stats, constrained MD.

*Some Tricks of the trade: *Neighbour lists, Multiple time step methods, How to handle long-range forces

*Advanced techniques: *Biased Monte Carlo Schemes, Rare Event, Brownian dynamics, Dissipative particle dynamics

*Suggested Books*:

- D. Frenkel and B. Smit,
*Understanding Molecular Simulations*(ed. 2) - A. R. Leach,
*Molecular Modeling* - M. P. Allen and D. J. Tildesley,
*Computer Simulation of Liquids* - J. M. Thijssen,
*Computational Physics* - T. Pang,
*An introduction to computational physics* - V. Rajaraman,
*Computer Programming in Fortran 90 and 95*

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