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Lecturer(s)
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Předota Milan, doc. RNDr. Ph.D.
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Course content
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Content of lectures: 1. Principles of molecular dynamics - Verlet and Gear MD integrators, choice of integrator and integration step. 2. Introduction to the Gromacs program 3. Radial distribution function, expressing the mean value of a quantity (e.g. energy) using the integral of a pair function (e.g. potential) and RDF, long-range energy correction. 4. Temperature in MD, thermostats (velocities rescaling, Berendsen frictional, Andersen). 5. Molecular potentials (intermolecular and intramolecular), combination rules. 6. Integration by MC method - simple and preferential sampling, central limit theorem and error of MC method, comparison with standard numerical integration. 7. Stochastic processes, transition matrix, Markov chains, detailed equilibrium, microscopic reversibility condition, the existence of limiting distribution. 8. Implementation of Monte Carlo step with canonical distribution (generation and acceptance of test configuration). Metropolis and Barker method. 9. Application of MC to geometric problems: random walks, percolation. 10. Thermodynamic MC. 11. Pressure measurements in MD/MC, MD simulations at constant pressure; NPT file in MC. 12. Technical details of MC - algorithm for calculating energy change, generation of test displacement, fraction of acceptance, range of potential vs. system size, boundary conditions. 13. Non-Boltzmann configuration space sampling, methods for efficient configuration space sampling (principles of metadynamics, mean force potential, parallel tempering). Content of exercises: Solution of simulation problems on the computer in accordance with the lecture content using Gromacs software.
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Learning activities and teaching methods
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Monologic (reading, lecture, briefing), Demonstration, Activating (simulations, games, drama)
- Class attendance
- 39 hours per semester
- Preparation for classes
- 30 hours per semester
- Preparation for exam
- 24 hours per semester
- Preparation for credit
- 30 hours per semester
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Learning outcomes
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This course introduces students to the fundamentals of Monte Carlo (MC) and molecular dynamics (MD) methods with an emphasis on modeling in many particle physics. Using the available Gromacs software, students will learn to model simple systems and understand the principles of computer modeling by using computer pseudo-experiments. They will also learn to work in a computer centre (Metacentrum).
Student will understand simulations as a computer (pseudo)experiment, and will be able to prepare, run, and analyze molecular simulations using methods of Monte Carlo and molecular dynamics.
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Prerequisites
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Basics of physics (mechanics), basics of working in Linux (can be quickly gained - basic introduction is part of the course).
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Assessment methods and criteria
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Student performance assessment, Combined exam
Criteria for obtaining the course credit (zápočet): Solving at least 70% of tasks solved during exercises with the help of the teacher. Independent solution of individual tasks to at least 50%. Criterium for passing the exam: At least 50% knowledge of the topic contained in the two drawn questions.
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Recommended literature
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Chung, T. J.: Computational Fluid Dynamics, USA, Cambridge University Press, 2002.
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I. Nezbeda, J. Kolafa, M. Kotrla: Úvod do počítačových simulací: Metody Monte Carlo a molekulární dynamiky, Karolinum 2003.
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Priest, E. R.: Solar Magnetohydrodynamics, London, D. Reidel Publishing Company, 1982.
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Uživatelský manuál a návody (tutorials) k programu GROMACS: http://www.gromacs.org.
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