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Viser: Stochastic Methods in Advanced Scientific Computing
Stochastic Methods in Advanced Scientific Computing
Kurt Langfeld, Biagio Lucini og Massimo D'Elia
(2023)
Sprog: Engelsk
CRC Press LLC
1.071,00 kr.
Denne bog er endnu ikke udgivet. Den forventes Jun 2023.
Detaljer om varen
- Hardback: 450 sider
- Udgiver: CRC Press LLC (Juni 2023)
- Forfattere: Kurt Langfeld, Biagio Lucini og Massimo D'Elia
- ISBN: 9781498796330
Stochastic phenomena play a central role in various scientific disciplines and underpin applications in popular industrial sectors. The purpose of the book is to introduce the reader to advanced concepts in the analysis of stochastic models starting from a detailed, intuitive and yet rigorous presentation of basic concepts. A special emphasis will be placed on problem solving and numerical implementations, with detailed solutions to all of the results and source code in the C programming language provided. The book will also cover recent specialised techniques for popular problems, providing a valuable reference for advanced readers with an active interest in the field.
Introduction. Random numbers and probability distribution. Central limit theorem. Beyond the Normal distribution. Exercises. Random walks. Random walk as a Markov process. Random walks in 1 and 2 dimensions. Levy flight. Random walks with potentials. Exercises. Monte Carlo methods. Objectives and concepts. Monte-Carlo integration. Statistical models. Introduction to Statistical Mechanics. The 2D Ising model. The 3-state Potts model in 3D: Finite size scaling. Gauge theories as statistical systems. Advanced MC simulation techniques. Langevin simulations. Hybrid Monte-Carlo simulations. Non-local Monte-Carlo update. Multicanonical simulations. Micro-canonical simulations. Density-of-States techniques. Exercises and computer experiments. From Statistical Systems to Quantum Field Theory. The O(2) model. SU(2) Yang-Mills theory. SU(N) gauge theories. Current challenges in Monte-Carlo Simulations. Sign- and overlap problems. Theories with sign problems. Topological modes and ergodicity problems. Appendix: High-Performance Computing
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