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Last update: T_UTF (20.04.2015)
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Last update: doc. RNDr. Karel Houfek, Ph.D. (11.06.2019)
Ústní zkouška |
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Last update: T_UTF (20.04.2015)
M. Plischke, B. Bergensen, Equilibrium statistical Physics, World Scientific, Singapore, 1994 (2. vydání)
K. Huang, Statistical Mechanics, John Wiley & Sons, Singapore, 1987 (2. vydání)
A. L. Barabasi, H. E. Stanley, Fractal Concepts is Surface Growth, Cambridge University Press, Cambridge, 1995
N. G. Van Kampen, Stochastic Processes in Physics and Chemistry, North-Holland, Amsterdam, 1981
M. Newman, Networks: An Introduction, Oxford University Press, 2010.
H. Nishimori, Statistical Physics of Spin Glasses and Information Processing, Oxford University Press, 2001. |
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Last update: doc. RNDr. Karel Houfek, Ph.D. (11.06.2019)
Zkouška je ústní, požadavky odpovídají sylabu, v detailech pak tomu, co bylo během semestru odpřednášeno. |
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Last update: T_UTF (20.04.2015)
Phenomenology of critical phenomena, order parameter, critical temperature, singular behaviour near critical temperature, critical exponents, universality. Scaling hypothesis and scaling relations, universality classes.
Ising model and equivalent models, Bragg-Williams mean field approximations, mean field critical exponents, exact solution in 1D. High temperature expansions, analysis of series. Markov process, stochastic differential equations, Fokker-Planck equation, Langevin equation, kinetic Ising model, phase ordering, Glauber and Kawasaki dynamics.
Dynamic scaling: examples of time evolution of interfaces in experiments and discrete models, roughness, growth and dynamical exponents. Dynamical universality classes in growth: random deposition, Edwards-Wilkinson equation, Kardar-Parisi-Zhang equation. Cellular automata and self-organized criticality, game of life, sand piles, BTW model, asymmetric exclusion model and other traffic problems.
Network theory: Erdös-Rényiho model, small worlds, scale-free networks, robustness of networks, examples: internet, social networks, power grids, multi-agent systems.
Combinatorial Optimization: P-NP-NP complete problems, simulated annealing. Applications: spin glasses, traveling salesman problem, K-SAT. |