Syllabus
* Introduction
Laboratory and computer experiment, Monte Carlo (MC) and Molecular Dynamics (MD) methods. Description of many-body system, inter-molecular forces.
* Elementary MC
Mathematical formulation of the problem, naive and importance sampling, Metropolis algorithm, random number generation.
* MC simulation of lattice systems
Percolation threshold , random walk, Hoshen-Kopelman algorithm for cluster distribution, Ising model - Metropolisův algorithm.
* MC simulation of simple liquid
Radial distribution function, structure factor. Applications: hard-sphere liquid and Lennard-Jones liquid.
* Elementary MD
Equations of motion, Verlet a Gear integrators, measurements in MD, temperature in MD, boundary conditions for continuous system, kinetic coefficients.
* Implementation of MD and examples
Choice of integrator, range of interaction vs. system size. Applications: particles in homogeneous and radial gravitational field, homogenous Lennard-Jones liquid.
* Simulations in various thermodynamic ensembles
MC: simulation in NPT ensemble, grand canonical ensemble, non-Boltzmann sampling of configuration space,
MD: simulation at constant temperature by rescaling of velocities, frictional thermostat, simulation for constant pressure.
Annotation
The aim of the lecture is to explain two basic methods of computer simulations: the Monte Carlo method and the molecular dynamics method, which are used in the study of many-particle systems and in solving other problems.
Students will try both methods by solving assigned tasks. Suitable for 1st and 2nd year of master's studies and for doctoral students in the fields of theoretical physics and mathematical modeling.