Ecosystems, the human brain, ant colonies, and economic networks are all complex systems displaying collective behaviour, or emergence, beyond the sum of their parts. Complexity science is the systematic investigation of these emergent phenomena, and stretches across disciplines, from physics and mathematics, to biological and social sciences. This introductory textbook provides detailed coverage of this rapidly growing field, accommodating readers from a variety of backgrounds, and with varying levels of mathematical skill. Part I presents the underlying principles of complexity science, to ensure students have a solid understanding of the conceptual framework. The second part introduces the key mathematical tools central to complexity science, gradually developing the mathematical formalism, with more advanced material provided in boxes. A broad range of end of chapter problems and extended projects offer opportunities for homework assignments and student research projects, with solutions available to instructors online. Key terms are highlighted in bold and listed in a glossary for easy reference, while annotated reading lists offer the option for extended reading and research.

The Classical Stefan Problem: Basic Concepts, Modelling and Analysis with Quasi-Analytical Solutions and Methods, New Edition, provides fundamental theory, concepts, modelling and analysis of the physical, mathematical, thermodynamical and metallurgical properties of classical Stefan and Stefan-like problems as applied to heat transfer problems involving phase-changes, such as from liquid to solid. This self-contained work reports and derives the results from tensor analysis, differential geometry, non-equilibrium thermodynamics, physics and functional analysis, and is thoroughly enriched with many appropriate references for an in-depth background reading on theorems. This new edition includes more than 400 pages of new material on quasi-analytical solutions and methods of classical Stefan and Stefan-like problems. The book aims to bridge the gap between the theoretical and solution aspects of the afore-mentioned problems.

This book highlights latest advancement in Mathematics, Physics and Chemistry. With the theme of "Innovative Science towards Sustainability and Industrial Revolution 4.0", ICFAS 2020 brings together leading experts, scientific communities and industrialists working in the field of applied sciences and mathematics from all over the world to share the most recent developments and cutting-edge discoveries addressing sustainability and industrial revolution 4.0 in the field. The conference topics include green materials, molecular modelling, catalysis, nanodevices and nanosystems, smart materials applications, solar cells technology, computational mathematics, data analysis and visualization, and numerical analysis. The contents of this book are useful for researchers, students, and industrial practitioners in the areas of Mathematics, Physics and Chemistry as most of the topics are in line with IR 4.0.

Flocks of birds, schools of fish and swarms of locusts display amazing forms of collective motion, while huge numbers of glow worms can emit light signals with almost unbelievable synchronization. These and many other collective phenomena in animal societies take place according to laws very similar to those governing the collective behavior in the inanimate nature, such as the magnetization of iron and the light radiation of lasers. During recent years, this has led to the study of swarm behavior as a challenging new field of science, in which ideas from the physical world are applied in order to understand the formation and structure of animal swarms. From these studies, it has become clear that such collective behavior of animals emerges in a self-organized way, without any need of overall coordination. In this book, we present different swarm phenomena of the animal world and compare them to their counterparts in physics, in a conceptual and non-technical way, addressed to a general readership.

Application of New Cybernetics in Physics describes the application of new cybernetics to physical problems and the resolution of basic physical paradoxes by considering external observer influence. This aids the reader in solving problems that were solved incorrectly or have not been solved. Three groups of problems of the new cybernetics are considered in the book: (a) Systems that can be calculated based on known physics of subsystems. This includes the external observer influence calculated from basic physical laws (ideal dynamics) and dynamics of a physical system influenced even by low noise (observable dynamics). (b) Emergent systems. This includes external noise from the observer by using the black box model (complex dynamics), external noise from the observer by using the observer's intuition (unpredictable dynamics), defining boundaries of application of scientific methods for system behavior prediction, and the role of the observer's intuition for unpredictable systems. (c) Methods for solution of basic physical paradoxes by using methods of the new cybernetics: the entropy increase paradox, Schroedinger's cat paradox (wave package reduction in quantum mechanics), the black holes information paradox, and the time wormholes grandfather paradox. All of the above paradoxes have the same resolution based on the principles of new cybernetics. Indeed, even a small interaction of an observer with an observed system results in their time arrows' alignment (synchronization) and results in the paradox resolution and appearance of the universal time arrow.

This book focuses on Creep in Ceramics. The book consists of two parts. In part A general knowledge of creep in ceramics is considered, while part B specifies creep in technologically important ceramics, namely creep in oxide ceramics, carnides and nitrides. While covering all relevant information regarding raw materials and characterization of creep in ceramics, the book also summarizes most recent innovations and developments in this field as a result of extensive literature search.

This book explores water geothermometry, a highly relevant topic in the exploration and exploitation of geothermal energy. Presenting theoretical geothermometers and indicators of CO2 fugacity, it describes a rigorous new approach entirely based on thermodynamics. The book will appeal to geothermal geoscientists, especially those working in research institutions and companies around the globe. It is also of interest to students on advanced courses in applied geochemistry, water-rock interaction and other related areas.

'The four laws that do not drive the universe: elements of thermodynamics for the curious and intelligent. The second purpose of Ben-NaimaEURO (TM)s book is to explain thermodynamics and show its relationship to information theory. This explanation makes the present book worth reading in its own right. Ben-NaimaEURO (TM)s discussion of the information basis of the second law is lucid and well worth reading.'CHOICEThis book provides a clear and mystery-free presentation of the central concepts in thermodynamics - probability, entropy, Helmholtz energy and Gibbs energy. It presents the concepts of entropy, free energy and various formulations of the Second Law in a friendly, simple language. It is devoid of all kinds of fancy and pompous statements made by authors of popular science books who write on this subject.The book focuses on the Four Laws of Thermodynamics. As it is said in the dedication page, this book is addressed to readers who might have already been exposed to Atkins' book having a similar title. It challenges both the title, and the contents of Atkins' book, Four Laws That Drive The Universe. One can glean from the title of this new book that the author's views are diametrically opposed to the views of Atkins.The book is addressed to any curious and intelligent reader. It aims to tickle, and hopefully to satisfy your curiosity. It also aims to challenge your gray matter, and to enrich your knowledge by telling you some facts and ideas regarding the Four Laws of Thermodynamics.

This book presents methodologies for analysing large data sets produced by the direct numerical simulation (DNS) of turbulence and combustion. It describes the development of models that can be used to analyse large eddy simulations, and highlights both the most common techniques and newly emerging ones. The chapters, written by internationally respected experts, invite readers to consider DNS of turbulence and combustion from a formal, data-driven standpoint, rather than one led by experience and intuition. This perspective allows readers to recognise the shortcomings of existing models, with the ultimate goal of quantifying and reducing model-based uncertainty. In addition, recent advances in machine learning and statistical inferences offer new insights on the interpretation of DNS data. The book will especially benefit graduate-level students and researchers in mechanical and aerospace engineering, e.g. those with an interest in general fluid mechanics, applied mathematics, and the environmental and atmospheric sciences.

This book is the distilled essence of the author teaching statistical mechanics to juniors, seniors and graduate students for over 50 years in various course settings. It uses a unique approach that leads naturally into the development of all possible ensembles. Much of the later chapters on polymers has previously been available only in the literature. Throughout the book, the assumption is made that the reader is still relatively raw, and mathematical detail is provided that other books leave to the abilities of the reader. While this produces a plethora of equations that mature scientists would regard as unnecessary, it is intended to help those just coming into the field and who want to get the idea without suffering hours of agony wondering, 'where did that come from?'.

This book is the distilled essence of the author teaching statistical mechanics to juniors, seniors and graduate students for over 50 years in various course settings. It uses a unique approach that leads naturally into the development of all possible ensembles. Much of the later chapters on polymers has previously been available only in the literature. Throughout the book, the assumption is made that the reader is still relatively raw, and mathematical detail is provided that other books leave to the abilities of the reader. While this produces a plethora of equations that mature scientists would regard as unnecessary, it is intended to help those just coming into the field and who want to get the idea without suffering hours of agony wondering, 'where did that come from?'.

In this new textbook, a number of unusual applications are discussed in addition to the usual topics covered in a course on Statistical Physics. Examples are: statistical mechanics of powders, Peierls instability, graphene, Bose-Einstein condensates in a trap, Casimir effect and the quantum Hall effect. Superfluidity and super-conductivity (including the physics of high-temperature superconductors) have also been discussed extensively.The emphasis on the treatment of these topics is pedagogic, introducing the basic tenets of statistical mechanics, with extensive and thorough discussion of the postulates, ensembles, and the relevant statistics. Many standard examples illustrate the microcanonical, canonical and grand canonical ensembles, as well as the Bose-Einstein and Fermi-Dirac statistics.A special feature of this text is the detailed presentation of the theory of second-order phase transitions and the renormalization group, emphasizing the role of disorder. Non-equilibrium statistical physics is introduced via the Boltzmann transport equation. Additional topics covered here include metastability, glassy systems, the Langevin equation, Brownian motion, and the Fokker-Planck equation.Graduate students will find the presentation readily accessible, since the topics have been treated with great deal of care and attention to detail.

Temperature and heat, entropy and order or disorder are key classical concepts of physics. These are challenged by searching matter under extreme conditions, such as high (relativistic) energy, strong acceleration or gravitation, or unusual complexity due to long range correlations. In our quest for quark matter all these conditions might occur simultaneously. This book, strongly motivated by the authors' everyday research experiences in the field of high-energy heavy-ion collisions, aims to bundle these challenges to modern physics.

The main topic is at the heart of thermodynamics --the very concept of temperature, its use and extensions. New developments on this issue are both applications and foundations of non-extensive statistics, as well as concepts borrowed from gravity and string theory to describe the surprisingly statistical behavior of elementary matter at the highest accelerator energies of the world.

The reader will benefit from bringing these new developments in one book together, by having the view of classical and modern concepts at the heart of physics across the problems related to high-energy, high acceleration and high complexity.

After reviewing the classical approaches, the author discusses the dual-gravity and non-extensive statistical aspects of heavy-ion collisions, describing these experimental findings with the use of the concept of temperature."

This textbook establishes a theoretical framework for understanding deep learning models of practical relevance. With an approach that borrows from theoretical physics, Roberts and Yaida provide clear and pedagogical explanations of how realistic deep neural networks actually work. To make results from the theoretical forefront accessible, the authors eschew the subject's traditional emphasis on intimidating formality without sacrificing accuracy. Straightforward and approachable, this volume balances detailed first-principle derivations of novel results with insight and intuition for theorists and practitioners alike. This self-contained textbook is ideal for students and researchers interested in artificial intelligence with minimal prerequisites of linear algebra, calculus, and informal probability theory, and it can easily fill a semester-long course on deep learning theory. For the first time, the exciting practical advances in modern artificial intelligence capabilities can be matched with a set of effective principles, providing a timeless blueprint for theoretical research in deep learning.

This textbook introduces thermodynamics with a modern approach, starting from four fundamental physical facts (the atomic nature of matter, the indistinguishability of atoms and molecules of the same species, the uncertainty principle, and the existence of equilibrium states) and analyzing the behavior of complex systems with the tools of information theory, in particular with Shannon's measure of information (or SMI), which can be defined on any probability distribution. SMI is defined and its properties and time evolution are illustrated, and it is shown that the entropy is a particular type of SMI, i.e. the SMI related to the phase-space distribution for a macroscopic system at equilibrium. The connection to SMI allows the reader to understand what entropy is and why isolated systems follow the Second Law of Thermodynamics. The Second Llaw is also formulated for other systems, not thermally isolated and even open with respect to the transfer of particles. All the fundamental aspects of thermodynamics are derived and illustrated with several examples in the first part of the book. The second part addresses important applications of thermodynamics, covering phase transitions, mixtures and solutions (including the Kirkwood-Buff approach and solvation thermodynamics), chemical equilibrium, and the outstanding properties of water.This textbook is unique in two aspects. First, thermodynamics is introduced with a novel approach, based on information theory applied to macroscopic systems at equilibrium. It is shown that entropy is a particular case of Shannon's measure of information (SMI), and the properties and time evolution of the SMI are used to explain the Second Law of Thermodynamics. This represents a real breakthrough, as classical thermodynamics cannot explain entropy, nor clarify why systems should obey the Second Law. Second, this textbook offers the reader the possibility to get in touch with important and advanced applications of thermodynamics, to address the topics discussed in the second part of the book. Although they may go beyond the content of a typical introductory course on thermodynamics, some of them can be important in the curriculum chosen by the student. At the same time, they are of appealing interest to more advanced scholars.

'Ben-Naim convincingly argues that SMI not only gives a simpler and more broadly applicable definition of entropy, but also clears up much of the historical and modern confusion surrounding the second law. This book will interest any individual who wants to understand how SMI gives a clear definition of entroy.'CHOICE ConnectThis book discusses the proper definitions of entropy, the valid interpretation of entropy and some useful applications of the concept of entropy. Unlike many books which apply the concept of entropy to systems for which it is not even defined (such as living systems, black holes and the entire universe), these applications will help the reader to understand the meaning of entropy. It also emphasizes the limitations of the applicability of the concept of entropy and the Second Law of Thermodynamics. As with the previous books by the author, this book aims at a clear and mystery-free presentation of the central concept in thermodynamics - the entropy.In this book, the concepts of entropy and the Second Law are presented in a friendly, simple language. It is devoid of all kinds of fancy and pompous statements made by authors of popular science books who write on this subject.

'Ben-Naim convincingly argues that SMI not only gives a simpler and more broadly applicable definition of entropy, but also clears up much of the historical and modern confusion surrounding the second law. This book will interest any individual who wants to understand how SMI gives a clear definition of entroy.'CHOICE ConnectThis book discusses the proper definitions of entropy, the valid interpretation of entropy and some useful applications of the concept of entropy. Unlike many books which apply the concept of entropy to systems for which it is not even defined (such as living systems, black holes and the entire universe), these applications will help the reader to understand the meaning of entropy. It also emphasizes the limitations of the applicability of the concept of entropy and the Second Law of Thermodynamics. As with the previous books by the author, this book aims at a clear and mystery-free presentation of the central concept in thermodynamics - the entropy.In this book, the concepts of entropy and the Second Law are presented in a friendly, simple language. It is devoid of all kinds of fancy and pompous statements made by authors of popular science books who write on this subject.

This book is a compilation of selected reviews by Professor Michael E Fisher. Fisher's major contributions to physics have been in equilibrium statistical mechanics, and have spanned the entire range of that subject. He has been credited with bringing together, and teaching a common language to chemists and physicists working on diverse problems of phase transitions.About the Book by the AuthorTalking informally in a clear way came naturally once intrigued by a field of science; that helped me accept the invitation to publish a collection of review articles. And working actively in an area has led me to express what is new in basic terms, with lots of figures framed, typically, via two- or three-dimensional images. Also encouraging was that my reviews - with crucial references - were recognized in 1983 by the U.S. National Academy of Sciences through their James Murray Luck Award for 'excellence in scientific reviewing.'However, the first article in this collection is by my postdoctoral mentor, Cyril Domb, whose inaugural lecture at King's College London was entitled: 'Statistical Physics and its Problems.' This provides readers with a context for some of the topics later reviewed in greater depth. Among the aspects then explained, are the various critical exponents: , , , and - the special exponents and for the correlation functions, and the scaling relations. Phase diagrams are examined thoroughly along with tricritical and bicritical points, Kosterlitz-Thouless points, protocriticality, etc. Random walks along with vicious walkers and their reunions are introduced. Biophysics is touched upon. The final article: 'Statistical Physics in the Oeuvre of Chen Ning Yang,' stems from the 2015 Conference on 60 Years of Yang-Mills Gauge Field Theories.In conclusion, it is hoped that a wide range of readers (and some experts also!) will enjoy dipping into the variety of reviews collected here.

This book is a compilation of selected reviews by Professor Michael E Fisher. Fisher's major contributions to physics have been in equilibrium statistical mechanics, and have spanned the entire range of that subject. He has been credited with bringing together, and teaching a common language to chemists and physicists working on diverse problems of phase transitions.About the Book by the AuthorTalking informally in a clear way came naturally once intrigued by a field of science; that helped me accept the invitation to publish a collection of review articles. And working actively in an area has led me to express what is new in basic terms, with lots of figures framed, typically, via two- or three-dimensional images. Also encouraging was that my reviews - with crucial references - were recognized in 1983 by the U.S. National Academy of Sciences through their James Murray Luck Award for 'excellence in scientific reviewing.'However, the first article in this collection is by my postdoctoral mentor, Cyril Domb, whose inaugural lecture at King's College London was entitled: 'Statistical Physics and its Problems.' This provides readers with a context for some of the topics later reviewed in greater depth. Among the aspects then explained, are the various critical exponents: , , , and - the special exponents and for the correlation functions, and the scaling relations. Phase diagrams are examined thoroughly along with tricritical and bicritical points, Kosterlitz-Thouless points, protocriticality, etc. Random walks along with vicious walkers and their reunions are introduced. Biophysics is touched upon. The final article: 'Statistical Physics in the Oeuvre of Chen Ning Yang,' stems from the 2015 Conference on 60 Years of Yang-Mills Gauge Field Theories.In conclusion, it is hoped that a wide range of readers (and some experts also!) will enjoy dipping into the variety of reviews collected here.

Preface. From the preface to the Russian edition. Introduction. I: Properties of exact solutions of nondegenerate and degenerate ordinary differential equations. II: Direct methods for constructing exact solutions of semilinear parabolic equations. III: Singularities of nonsmooth solutions to quasilinear parabolic and hyperbolic equations. IV: Wave asymptotic solutions of degenerate semilinear parabolic and hyperbolic equations. V: Finite asymptotic solutions of degenerate equations. VI: Models for mass transfer processes. VII: The flow around a plate. References. Appendix: Justification of asymptotic solutions; S.A. Vakulenko.

These proceedings of the 18th International Conference on Difference Equations and Applications cover a number of different aspects of difference equations and discrete dynamical systems, as well as the interplay between difference equations and dynamical systems. The conference was organized by the Department of Mathematics at the Universitat Autonoma de Barcelona (UAB) under the auspices of the International Society of Difference Equations (ISDE) and held in Barcelona (Catalonia, Spain) in July 2012. Its purpose was to bring together experts and novices in these fields to discuss the latest developments. The book gathers contributions in the field of combinatorial and topological dynamics, complex dynamics, applications of difference equations to biology, chaotic linear dynamics, economic dynamics and control and asymptotic behavior, and periodicity of difference equations. As such it is of interest to researchers and scientists engaged in the theory and applications of difference equations and discrete dynamical systems.

Fundamentals of the Finite Element Method for Heat and Mass Transfer, Second Edition is a comprehensively updated new edition and is a unique book on the application of the finite element method to heat and mass transfer. Addresses fundamentals, applications and computer implementation Educational computer codes are freely available to download, modify and use Includes a large number of worked examples and exercises Fills the gap between learning and research

Statistical mechanics is concerned with defining the thermodynamic properties of a macroscopic sample in terms of the properties of the microscopic systems of which it is composed. The previous book Introduction to Statistical Mechanics provided a clear, logical, and self-contained treatment of equilibrium statistical mechanics starting from Boltzmann's two statistical assumptions, and presented a wide variety of applications to diverse physical assemblies. An appendix provided an introduction to non-equilibrium statistical mechanics through the Boltzmann equation and its extensions. The coverage in that book was enhanced and extended through the inclusion of many accessible problems. The current book provides solutions to those problems. These texts assume only introductory courses in classical and quantum mechanics, as well as familiarity with multi-variable calculus and the essentials of complex analysis. Some knowledge of thermodynamics is also assumed, although the analysis starts with an appropriate review of that topic. The targeted audience is first-year graduate students and advanced undergraduates, in physics, chemistry, and the related physical sciences. The goal of these texts is to help the reader obtain a clear working knowledge of the very useful and powerful methods of equilibrium statistical mechanics and to enhance the understanding and appreciation of the more advanced texts.

This latest edition enhances the material of the first edition with a derivation of the value of the action for each of the Harrington-Shepard calorons/anticalorons that are relevant for the emergence of the thermal ground state. Also included are discussions of the caloron center versus its periphery, the role of the thermal ground state in U(1) wave propagation, photonic particle-wave duality, and calculational intricacies and book-keeping related to one-loop scattering of massless modes in the deconfining phase of an SU(2) Yang-Mills theory. Moreover, a derivation of the temperature-redshift relation of the CMB in deconfining SU(2) Yang-Mills thermodynamics and its application to explaining an apparent early re-ionization of the Universe are given. Finally, a mechanism of mass generation for cosmic neutrinos is proposed.