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This classic textbook, thoroughly revised and updated for its third edition, introduces the basic methods of computational physics. Clear, concise and practical, the new edition includes an additional chapter on machine learning and is supported with sample programs in Python. First, readers are presented with the numerical techniques that every computational scientist should have in their toolbox, including approximation of functions, numerical calculus, differential and partial differential equations, spectral analysis, linear algebra and matrix operations. The author then provides self-contained introductions to the research areas of molecular dynamics, fluid dynamics, Monte Carlo simulations, genetic algorithms and machine learning. Important concepts are illustrated with relevant examples, and each chapter concludes with a selection of exercises. Suitable for upper-division undergraduate to graduate courses on computational physics and scientific computing, this book is also a useful resource for anyone interested in using computation to solve scientific problems.
Introducing the kinetics of phase transformations, in a manner that is relevant to all materials, from polymers and ceramics to metals and electronic materials. It builds up from simple discussions of interfaces to the complex primary phase transformations used to create engineering materials, and introduces students to real-world industry tools, including materials databases and CALPHAD-based codes. All assumptions are clearly stated, and all derivations presented in full, allowing students to focus on core concepts and the implications of results, and it is accompanied by 125 end-of-chapter homework problems, Python code examples, and solutions for instructors. Culminating with a discussion of transformation rates that synthesizes concepts presented throughout the text, including three example capstone projects, this is the ideal introduction for senior undergraduate and graduate students studying phase transformations.
Quantum field theory (QFT) is one of the great achievements of physics, of profound interest to mathematicians, yet standard texts often assume a physicist's background or adopt an abstract mathematical perspective. This thoroughly updated edition bridges that gap. While maintaining a rigorous approach wherever possible, it focuses on explaining what physicists do and why, using precise mathematical language. Written for readers with a background in mathematics but no prior knowledge of physics, and largely self-contained, it presents both essential physical ideas and the necessary mathematical tools in detail. This revised edition has been improved throughout, with many clarifications to the text and the inclusion of solutions to selected exercises to enhance its use for self-study. It will appeal to mathematicians seeking an accessible path into QFT and to physics students wanting greater rigor.
This book comprises a unique collection of insights into Nobel laureate Giorgio Parisi's groundbreaking work across physics, ranging from high-energy physics and spin glasses to turbulence and collective animal behaviour. Originating from a series of seminars at the Sapienza University of Rome, each chapter focuses on one of Parisi's seminal contributions, penned by leading experts who highlight the depth and interdisciplinary impact of his ideas. The volume revisits widely disseminated achievements like the Altarelli-Parisi equations and replica symmetry breaking, and presents lesser-known work, revealing hidden connections between seemingly distant domains. Enhanced by lively discussions and a personal retrospective from Parisi himself, this book is both a tribute to a visionary scientist and an invitation to discover the unifying threads woven throughout modern physics. Showcasing how one thinker's creativity can reshape entire landscapes of knowledge, it is invaluable for experienced researchers and motivated graduate students in the field of theoretical physics.
Women working in physics navigate unique challenges that your male colleagues rarely have to consider. This practical, research-based guide will help you tackle the various issues you are likely to encounter during your education and career in academia or industry. With each chapter focusing on a specific problem, the guidance is presented in a question-and-answer format that allows you to navigate directly to the advice you need. Chapters address a broad range of challenges, from thriving as a student and interviewing for jobs to improving self-confidence and timing maternity leave. Focus is placed on immediate and practical advice with the intention of constructing a positive framework that helps you improve your circumstances in an imperfect environment. Enriched with advice and stories from a group of women physicists with diverse experiences, the book provides you with the necessary tools and support for continuing your journey with confidence.
This book presents an advanced treatment of classical electromagnetism that expands on the central content and methods of the theory. It emphasizes the core ideas of electromagnetism in a way that provides new insights into physics and the applied mathematics in which it is expressed. The book presents the theory in a form that relates electromagnetic fields to their charge and current density sources as directly as possible based on Green's functions and relatively easily interpreted integral equations, Jefimenko's equations. Electromagnetism is more than Maxwell's equations or the integral equations for the electromagnetic fields: the charge and current density sources are governed by their own equations of motion which are compatible with Newton's laws of motion including electromagnetic forces. These forces depend in turn on electromagnetic fields. This mutual and self-consistent interplay between the motion of the sources and the electromagnetic fields is a theme of this book.
This book provides a comprehensive introduction to equilibrium and non-equilibrium Green's function methods in many-body physics. It begins with a derivation of second quantisation for relativistic systems based on the many-body relativistic Dirac equation and its non-relativistic limit. The properties of equilibrium Green's functions are then described, with discussion of the two-time and Matsubara function methods. The coverage of non-equilibrium Green's function methods includes the diagrammatic techniques applicable to electrons and phonons using both the perturbation and variational approaches. Specific applications to steady-state and time-dependent quantum transport are presented in the final chapters. The book's accessible explanations, detailed derivations, and systematic treatment of the underlying theory make it a valuable resource for graduate students and early-career researchers. More than 200 problems have been included to support learning, with selected solutions available at the end of each chapter. Instructors benefit from access to the full solutions manual.
The study of periodic partial differential equations has experienced significant growth in recent decades, driven by emerging applications in fields such as photonic crystals, metamaterials, fluid dynamics, carbon nanostructures, and topological insulators. This book provides a uniquely comprehensive overview for mathematicians, physicists, and material scientists engaged in the analysis and construction of periodic media. It describes all the mathematical objects, tools, problems, and techniques involved. Topics covered are central for areas such as spectral theory of PDEs, homogenization, condensed matter physics and optics. Although it is not a textbook, some basic proofs, background material, and references to an extensive bibliography providing pointers to the wider literature are included to allow graduate students to access the content.
Designed to build confident analytical abilities, this book introduces a scaffolded five-step strategy for solving problems in classical mechanics. With progressive problem sets spanning kinematics, forces, momentum, rotational motion, and more, it focuses on deepening conceptual understanding beyond the basic application of formulae. This highly pedagogical approach highlights the importance of determining which principles apply under given conditions, and each problem is accompanied by the full mathematical solution and a visualisation of the underlying physical concepts at play. Guided exercises allow students to reinforce their understanding and turn passive solution-checking into active learning. Written for undergraduate physics and engineering students keen to develop more efficient and fluent problem-solving skills and improved exam results, it also provides instructors with a novel and effective teaching framework for tutorials and assessments.
Spontaneous symmetry breaking lies at the heart of modern physics, shaping our understanding of matter, forces, and even the universe itself. From condensed matter physics to particle physics and cosmology, spontaneous symmetry breaking unifies phenomena that at first seem worlds apart. This graduate-level text offers a comprehensive yet accessible guide to the conceptual theory and practical consequences of spontaneous symmetry breaking. It introduces topics ranging from Noether's theorem, thermodynamic limits, and gauge freedoms to Nambu–Goldstone modes, topological defects, effective field theory, the Mermin–Wagner–Hohenberg–Coleman theorem, and the Anderson–Higgs mechanism within the Standard Model. Packed with exercises, with solutions available online, in-depth projects, and a myth-busting FAQ section addressing common pitfalls, this book equips readers to master both the fundamentals and modern frontiers of spontaneous symmetry breaking, making it an indispensable resource for students, teachers, and researchers.
Bubbles have unique properties that make them of great importance in disparate fields such as energy production, acoustics, chemical engineering, material processing, biomedicine, food science and a host of others which, on the surface, appear to have little in common. Bringing together information scattered in many hundreds of sources, this book provides a unified treatment of the subject, illustrating the roots of this surprising versatility with a wealth of examples. The emphasis is on physics, explained with words and images before introducing a limited mathematical apparatus. Building on the foundation of the compressible and incompressible Rayleigh-Plesset equation, the treatment continues with the volume oscillations of gas bubbles and associated scattering and emission of sound, the diffusion of dissolved gases and of heat, boiling, nucleation and the behavior of bubbles in elastic and visco-elastic media. The book concludes with chapters on biomedical applications, sonochemistry, acoustic and flow cavitation and bubbly liquids.
This graduate-level volume is a coherent and self-contained introduction to Quantum Field Theory, uniquely focused on geometric and non-perturbative aspects. The first part covers quantum fields and Euclidean path integral, Yang-Mills field theories, and Wilsonian renormalization. Wilson's notion of the effective field theory and its heavy implication for the QFT framework itself are given particular attention. Next, geometrical and topological aspects are thoroughly treated, accompanied by a healthy dose of underlying mathematics. Anomalies, or quantum failures of classical symmetries, follow as crucial litmus tests for self-consistency, which are delineated in unprecedented detail, spanning decades of development. In the final part, the book asks how relativistic gravity, known to resist standard quantization schemes, may reconcile with the quantum world. This question is approached by invoking d=2 Weyl anomaly, Hawking effects, black hole partition functions, and the renormalization of fundamental strings, with a view toward quantum gravity and superstring theory.
Phase transitions take place when a substance changes from one physical state to another, and they are of fundamental importance in science and engineering with applications ranging from superconductivity to climate science. This Student's Guide coherently examines the underlying dynamics of phase transitions, beginning with a detailed description of phase diagrams and their graphical interpretation, before introducing the van der Waals equations of state. It progresses to more advanced topics such as mean-field theory in magnetic systems, phase transitions in binary mixtures, and other more exotic types of phase transitions in liquid crystals, superconductors, and superfluids. A separate chapter covers the unique and subtle phase transition dynamics of water. The book includes numerous worked examples and problems, with full solutions available online. It will be a valuable resource for students and lifelong learners in the physical sciences and engineering.
The culmination of years of teaching experience, this book provides a modern introduction to the mathematical theory of interacting particle systems. Assuming a background in probability and measure theory, it has been designed to support a one-semester course at a Master or Ph.D. level. It also provides a useful reference for researchers, containing several results that have not appeared in print in this form before. An emphasis is placed on graphical representations, which are used to give a construction that is intuitively easier to grasp than the traditional generator approach. Also included is an extensive look at duality theory, along with discussions of mean-field methods, phase transitions and critical behaviour. The text is illustrated with the results of numerical simulations and features exercises in every chapter. The theory is demonstrated on a range of models, reflecting the modern state of the subject and highlighting the scope of possible applications.
This comprehensive and up-to-date manual accompanies the third edition of Bernard Schutz's A First Course in General Relativity. It offers step-by-step guidance through more than 200 selected exercises, providing detailed solutions and explanatory comments which are cross-referenced to the relevant equations and sections in Schutz's text. The material is further extended by the inclusion of 168 supplementary problems that highlight conceptual challenges and direct readers to the most useful supporting literature. A comprehensive index and bolded keywords allow for quick navigation, while an appendix of useful results makes the book a lasting reference for advanced undergraduate and graduate students, instructors, and self-directed learners seeking a deeper understanding of the subject. A Mathematica notebook and tables of exercises and supplementary problems are freely available as online resources, with instructors benefiting from access to solutions to selected exercises and problems.
Recent observations of the afterglow of the Big Bang, commonly referred to as the Cosmic Microwave Background radiation, have greatly advanced our understanding of the early Universe and have helped reinforce the observational foundations of modern cosmology. This volume provides a comprehensive pedagogical overview of all aspects of the Cosmic Microwave Background radiation. Topics covered include theory, current observations, instrumentation, statistical analyses and the astrophysics of Galactic and other microwave foregrounds. These latter topics are important as much of the contemporary work in cosmology focuses on perfecting experimental techniques and on mitigating and assessing sources of error. Bringing together the latest research and scientific developments from the primary literature into one book, this is a go-to resource for graduate students and researchers working in cosmology and astrophysics.
Philosophical problems fundamentally infuse the theory and practice of astronomy. Bringing together fifteen historians, eleven philosophers, and four pioneering scientists, this volume provides a rigorous yet largely accessible examination of the conceptual and methodological challenges that lie at the intersection of philosophy and astronomy – broadly construed to include astrophysics, cosmology, space science, and astrobiology. Drawing largely on interdisciplinary advances from the past two centuries, the book's chapters tackle metaphysical inquiries into the fundamental nature of reality, the limits of reasoning, the problematic nature of observation and inference, the role of technology, and the epistemology of concepts such as space, time, life, and intelligence. Discussions are anchored to fascinating theories and examples from the 'canals' of Mars to exoplanets, black holes, dark matter, and the multiverse. Written primarily for practicing scientists, this volume will also serve historians and philosophers of science, as well as the curious general reader.
Driven by advances in data science and machine learning, photonics has evolved rapidly in recent years and has transformed into a highly interdisciplinary field, connecting fundamental research with cutting-edge applications. Inspired by recent Nobel Prizes in Physics in 2021 and 2024, Conti highlights the interplay between photonics and spin glasses, a key concept for understanding the link between photon propagation and complex systems. Beginning with a study of black-body radiation, the book then revisits laser theory using techniques from non-equilibrium statistical mechanics. Through a step-by-step exploration of important photonic experiments, it bridges foundational concepts and advances in optical computing, with a focus on developing efficient hardware for classical and quantum artificial intelligence. This reveals the profound ties between complexity, photonics, and the future of AI technologies. The book will be a valuable resource for advanced undergraduate and graduate students and more practised researchers.