Simulations in Many-particle Physics - NTMF021
Title: Simulace ve fyzice mnoha částic
Guaranteed by: Institute of Theoretical Physics (32-UTF)
Faculty: Faculty of Mathematics and Physics
Actual: from 2020
Semester: winter
E-Credits: 6
Hours per week, examination: winter s.:3/1, C+Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: taught
Language: Czech, English
Teaching methods: full-time
Additional information: http://utf.mff.cuni.cz/vyuka/NTMF021
Guarantor: doc. RNDr. Karel Houfek, Ph.D.
doc. RNDr. Milan Předota, Ph.D.
Teacher(s): doc. RNDr. Karel Houfek, Ph.D.
doc. RNDr. Milan Předota, Ph.D.
Classification: Physics > Theoretical and Math. Physics
Is co-requisite for: NTMF024
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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.
Last update: Houfek Karel, doc. RNDr., Ph.D. (13.05.2022)
Course completion requirements -

Credit is given for solving assigned tasks. The exam is oral.

Last update: Houfek Karel, doc. RNDr., Ph.D. (12.05.2023)
Literature -

D. Landau, K. Binder, A Guide to Monte Carlo Simulations in Statistical Physics, Cambridge University Press 2002

M.E.J. Newman, G.T. Barkema, Monte Carlo Methods in Statistical Physics, Oxford University Press 2002

D. Frenkel, B. Smit, Understanding molecular simulation, Academic Press, San Diego, USA 2002

Last update: Houfek Karel, doc. RNDr., Ph.D. (12.05.2023)
Requirements to the exam -

The oral examination follows the syllabus of the course as covered by the lectures. The exam consists of two parts: a question about Monte Carlo simulations and a question about molecular dynamics simulations. The grade is determined on the basis of the evaluation of both parts, possibly taking into account the results of credit homeworks.

Last update: Houfek Karel, doc. RNDr., Ph.D. (12.05.2023)
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.

Last update: Houfek Karel, doc. RNDr., Ph.D. (12.05.2023)