Readership: Undergraduates, graduate students, and research scientists in computational physics, engineering, physical science, applied physics, and fractals.

This book offers a complete introduction and overview to the basics and fundamentals of computational methods that have been developed in physics at the undergraduate and upper-division levels. It details how to make a physical problem computable and tractable with a computer, through the use of numerous examples and solved problems ranging from classical mechanics, thermodynamics, and molecular dynamics, to quantum mechanics, random processes, and more. The book directly teaches the reader how to implement these techniques within a physical problem.

There is an increasing need for undergraduate students in physics to have a core set of computational tools. Most problems in physics benefit from numerical methods, and many of them resist analytical solution altogether. This textbook presents numerical techniques for solving familiar physical problems where a complete solution is inaccessible using traditional mathematical methods. The numerical techniques for solving the problems are clearly laid out, with a focus on the logic and applicability of the method. The same problems are revisited multiple times using different numerical techniques, so readers can easily compare the methods. The book features over 250 end-of-chapter exercises. A website hosted by the author features a complete set of programs used to generate the examples and figures, which can be used as a starting point for further investigation. A link to this can be found at www.cambridge.org/9781107034303.

This book presents an introduction to Evolutionary Game Theory (EGT) which is an emerging field in the area of complex systems attracting the attention of researchers from disparate scientific communities. EGT allows one to represent and study several complex phenomena, such as the emergence of cooperation in social systems, the role of conformity in shaping the equilibrium of a population, and the dynamics in biological and ecological systems.Since EGT models belong to the area of complex systems, statistical physics constitutes a fundamental ingredient for investigating their behavior. At the same time, the complexity of some EGT models, such as those realized by means of agent-based methods, often require the implementation of numerical simulations. Therefore, beyond providing an introduction to EGT, this book gives a brief overview of the main statistical physics tools (such as phase transitions and the Ising model) and computational strategies for simulating evolutionary games (such as Monte Carlo algorithms on lattices). This book will appeal to students and researchers in this burgeoning field of complex systems.

Volume 71 of Reviews in Mineralogy and Geochemistry represents an extensive review of the material presented by the invited speakers at a short course on Theoretical and Computational Methods in Mineral Physics held prior (December 10-12, 2009) to the Annual fall meeting of the American Geophysical Union in San Francisco, California. The meeting was held at the Doubletree Hotel & Executive Meeting Center in Berkeley, California. Contents: Density functional theory of electronic structure: a short course for mineralogists and geophysicists The Minnesota density functionals and their applications to problems in mineralogy and geochemistry Density-functional perturbation theory for quasi-harmonic calculations Thermodynamic properties and phase relations in mantle minerals investigated by first principles quasiharmonic theory First principles quasiharmonic thermoelasticity of mantle minerals An overview of quantum Monte Carlo methods Quantum Monte Carlo studies of transition metal oxides Accurate and efficient calculations on strongly correlated minerals with the LDA+U method: review and perspectives Spin-state crossover of iron in lower-mantle minerals: results of DFT+U investigations Simulating diffusion Modeling dislocations and plasticity of deep earth materials Theoretical methods for calculating the lattice thermal conductivity of minerals Evolutionary crystal structure prediction as a method for the discovery of minerals and materials Multi-Mbar phase transitions in minerals Computer simulations on phase transitions in ice Iron at Earth’s core conditions from first principles calculations First-principles molecular dynamics simulations of silicate melts: structural and dynamical properties Lattice dynamics from force-fields as a technique for mineral physics An efficient cluster expansion method for binary solid solutions: application to the halite-silvite, NaCl-KCl, system Large scale simulations Thermodynamics of the Earth’s mantle

On the occasion of the 150th anniversary of Sophus Lie, an International Work shop "Modern Group Analysis: advanced analytical and computational methods in mathematical physics" has been organized in Acireale (Catania, Sicily, October 27 31, 1992). The Workshop was aimed to enlighten the present state ofthis rapidly expanding branch of applied mathematics. Main topics of the Conference were: • classical Lie groups applied for constructing invariant solutions and conservation laws; • conditional (partial) symmetries; • Backlund transformations; • approximate symmetries; • group analysis of finite-difference equations; • problems of group classification; • software packages in group analysis. The success of the Workshop was due to the participation of many experts in Group Analysis from different countries. This book consists of selected papers presented at the Workshop. We would like to thank the Scientific Committee for the generous support of recommending invited lectures and selecting the papers for this volume, as well as the members of the Organizing Committee for their help. The Workshop was made possible by the financial support of several sponsors that are listed below. It is also a pleasure to thank our colleague Enrico Gregorio for his invaluable help of this volume.

This book investigates in detail the emerging deep learning (DL) technique in computational physics, assessing its promising potential to substitute conventional numerical solvers for calculating the fields in real-time. After good training, the proposed architecture can resolve both the forward computing and the inverse retrieve problems. Pursuing a holistic perspective, the book includes the following areas. The first chapter discusses the basic DL frameworks. Then, the steady heat conduction problem is solved by the classical U-net in Chapter 2, involving both the passive and active cases. Afterwards, the sophisticated heat flux on a curved surface is reconstructed by the presented Conv-LSTM, exhibiting high accuracy and efficiency. Additionally, a physics-informed DL structure along with a nonlinear mapping module are employed to obtain the space/temperature/time-related thermal conductivity via the transient temperature in Chapter 4. Finally, in Chapter 5, a series of the latest advanced frameworks and the corresponding physics applications are introduced. As deep learning techniques are experiencing vigorous development in computational physics, more people desire related reading materials. This book is intended for graduate students, professional practitioners, and researchers who are interested in DL for computational physics.

The physics of plasmas is an extremely rich and complex subject as the variety of topics addressed in this book demonstrates. This richness and complexity demands new and powerful techniques for investigating plasma physics. An outgrowth from his graduate course teaching, now with corrections, Tajima's text provides not only a lucid introduction to computational plasma physics, but also offers the reader many examples of the way numerical modeling, properly handled, can provide valuable physical understanding of the nonlinear aspects so often encountered in both laboratory and astrophysical plasmas. Included here are computational methods for modern nonlinear physics as applied to hydrodynamic turbulence, solitons, fast reconnection of magnetic fields, anomalous transports, dynamics of the sun, and more. The text contains examples of problems now solved using computational techniques including those concerning finite-size particles, spectral techniques, implicit differencing, gyrokinetic approaches, and particle simulation.

Computational Physics is a vigorous subject due to its interdisciplinary nature. In this spirit, the volume brings together lecture notes from leading computational physicists in quite disparate areas of research interest. The resulting collection of essays should be a valuable resource in an area where there are few standard textbooks at the present time.The volume is made up of lecture notes and introductory articles representative of the Summer School on Computational Physics which was held at the Australian National University in 1996. Several of the authors are world-renowned for their contributions to this new — and rapidly evolving — area, and this volume will be a useful supplement to textbooks at the graduate, advanced undergraduate, and professional levels.

Computational Approaches in Physics reviews computational schemes which are used in the simulations of physical systems. These range from very accurate ab initio techniques up to coarse-grained and mesoscopic schemes. The choice of the method is based on the desired accuracy and computational efficiency. A bottom-up approach is used to present the various simulation methods used in Physics, starting from the lower level and the most accurate methods, up to particle-based ones. The book outlines the basic theory underlying each technique and its complexity, addresses the computational implications and issues in the implementation, as well as present representative examples. A link to the most common computational codes, commercial or open source is listed in each chapter. The strengths and deficiencies of the variety of techniques discussed in this book are presented in detail and visualization tools commonly used to make the simulation data more comprehensive are also discussed. In the end, specific techniques are used as bridges across different disciplines. To this end, examples of different systems tackled with the same methods are presented. The appendices include elements of physical theory which are prerequisites in understanding the simulation methods.