Advanced Simulations in Many-particle Physics - NTMF024
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Advanced Monte Carlo and molecular dynamics methods, their application to critical, nonequilibrium and
quantum systems: cluster algorithms for lattice models, transport coefficients, kinetic MC, quantum Monte Carlo,
simulations from the first principles. Suitable for the 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)
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Ústní zkouška Last update: Houfek Karel, doc. RNDr., Ph.D. (11.06.2019)
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I. Nezbeda, J. Kolafa, M. Kotrla, Úvod do počítačových simulací: Metody Monte Carlo a molekulární dynamiky, Karolinum 2003. D. Landau a 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, 1999. D. Frenkel, B. Smit, Understanding molecular simulation, Academic Press, San Diego, USA 2002. M. Kotrla: Numerical simulations in the theory of crystal growth, Comp. Phys. Comm. 97, 82-100 (1996). Last update: Houfek Karel, doc. RNDr., Ph.D. (14.05.2022)
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Zkouška je ústní, požadavky odpovídají sylabu, v detailech pak tomu, co bylo během semestru odpřednášeno. Last update: Houfek Karel, doc. RNDr., Ph.D. (11.06.2019)
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Phase transitions and critical phenomena
Methods of inserting particles, Gibbs ensemble, phase equilibrium, critical temperature by scaling with a system size, critical slowing down, cluster algorithms for spin models. Simulation of realistic systems Long-range forces, Ewald summation, simulation of molecular systems, methods conserving bond length and angles, phase equilibrium. Special algorithms and techniques Random number generation, multispin coding for Ising model and cellular automata, multiscale simulations. Non-equilibrium systems close to equilibrium Calculation of kinetic coefficients, time correlation functions, Einstein relation, non-equilibrium MD, self-diffusion in lattice gas, equilibrium and con-equilibrium calculation of viscosity and dielectric constant. Kinetic Monte Carlo Choice of kinetics and rates, time in kinetic MC, "n-fold way" algorithm, model of adsorption and desorption. Simulation of growth processes Simulation of simple growth models (Eden, Edwars-Wilkinson model etc.), kinetic roughening, Laplacian growth, diffusion limited aggregation (DLA), solid-on-solid models, realistic simulations of crystal growth. Optimalization problems Traveling salesman problem, simulated annealing, calculation of diffusion in lattice gas, calculation of energy barriers by molecular statics, finding the minimal energy path in a system on N particles, method "elastic nudged band". Quantum simulations Variational quantum MC, canonical quantum MC, isomorphism of quantum and classical systems, sign problem, first principle calculations, method of density functional. Last update: Kotrla Miroslav, RNDr., CSc. (19.05.2011)
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