Stochastic Methods in Advanced Scientific Computing

ISBN-13: 9781498796330 / Angielski / Twarda / 2024 / 450 str.

Kurt Langfeld; Biagio Lucini; Massimo D'Elia

Opis

The purpose of the book is to introduce the reader to advanced concepts in the analysis of stochastic models, starting from a detailed, intuitive presentation of basic concepts. Special emphasis is placed on problem solving and numerical implementations, with detailed solutions to the results and source code in the C programming language provided.

Spis treści

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

O autorze

Kurt Langfeld is Professor of Theoretical Physics and Director of the research Centre for Mathematical Sciences at Plymouth University. His fields of expertise are the numerical methods for simulating Quantum Field Theories and for Particle Physics. In 1999, he completed his "Habilitation" and was awarded the Venia Legendi. In 2005, he became Professor for Theoretical Physics at the University of Tübingen. In 2006, he joined the Particle Physics group at Plymouth University, where, in April 2012, he became full Professor for Theoretical Physics. He has served as a reviewer for the Engineering and Physical Sciences Research Council (EPSRC), the Austrian council FWF and for the Swiss National Supercomputing Center (CSCS). He regularly reviews manuscripts submitted to the high-profile journals in particle physics and has published about 100 papers in these journals. Biagio Lucini is Professor and Head of the Mathematics Department at Swansea University. Before joining Swansea University in 2005, he was a Postdoctoral Fellow at the Rudolf Peierls Centre for Theoretical Physics (Oxford University, UK) from 2000 to 2003 and at the Theoretical Physics Institute of ETH (Zurich, Switzerland) from 2003 to 2005. He has been a Marie Curie Fellow (2001-2003) and a Royal Society University Research Fellow (2005-2013). His fields of activity are Monte Carlo calculations in Statistical Mechanics and Particle Physics. In particular, his interests are in Phase Transitions and Critical Phenomena, including efficient algorithms for simulations near criticality using High Performance Computing architectures. He is referee for various high-profile international journals and funding agencies and author of more than 100 papers, with around 3000 citations. Massimo D’Elia is currently Associate Professor in Theoretical Physics at the Physics Department of the University of Pisa. He has been Postdoctoral Fellow at the University of Cyprus and at ETH, Zurich, and Assistant Professor at the Physics Department of the University of Genoa. He is an expert in Lattice Gauge Theories and their implementation on HPC infrastructures. He has obtained various achievements in the study of QCD at finite temperature and density and in external backgrounds, developing innovative computational approaches to the study of QCD in extreme conditions. He has served as a reviewer for major scientific journals in the field and for national funding programs (NSF). He is author of one textbook (with C.M. Becchi, "Introduction to the Basic Concepts of Modern Physics", Springer, 2007, 2010, 2016) and of around 180 papers, with more than 4000 citations