The application of statistical methods to physics is essential. This unique book on statistical physics offers an advanced approach with numerous applications to the modern problems students are confronted with. Therefore the text contains more concepts and methods in statistics than the student would need for statistical mechanics alone. Methods from mathematical statistics and stochastics for the analysis of data are discussed as well.

The book is divided into two parts, focusing first on the modeling of statistical systems and then on the analysis of these systems. Problems with hints for solution help the students to deepen their knowledge. The third edition has been updated and enlarged with new sections deepening the knowledge about data analysis. Moreover, a customized set of problems with solutions is accessible on the Web at extras.springer.com."

This book demonstrates how mathematical methods and techniques can be used in synergy and create a new way of looking at complex systems. It becomes clear nowadays that the standard (graph-based) network approach, in which observable events and transportation hubs are represented by nodes and relations between them are represented by edges, fails to describe the important properties of complex systems, capture the dependence between their scales, and anticipate their future developments. Therefore, authors in this book discuss the new generalized theories capable to describe a complex nexus of dependences in multi-level complex systems and to effectively engineer their important functions. The collection of works devoted to the memory of Professor Valentin Afraimovich introduces new concepts, methods, and applications in nonlinear dynamical systems covering physical problems and mathematical modelling relevant to molecular biology, genetics, neurosciences, artificial intelligence as well as classic problems in physics, machine learning, brain and urban dynamics. The book can be read by mathematicians, physicists, complex systems scientists, IT specialists, civil engineers, data scientists, urban planners, and even musicians (with some mathematical background).

This book deals with an important class of many-body systems: those where the interaction potential decays slowly for large inter-particle distances; in particular, systems where the decay is slower than the inverse inter-particle distance raised to the dimension of the embedding space. Gravitational and Coulomb interactions are the most prominent examples, however it has become clear that long-range interactions are more common than previously thought. A satisfactory understanding of properties, generally considered as oddities only a couple of decades ago, has now been reached: ensemble inequivalence, negative specific heat, negative susceptibility, ergodicity breaking, out-of-equilibrium quasi-stationary-states, anomalous diffusion. The book, intended for Master and PhD students, tries to gradually acquaint the reader with the subject. The first two parts describe the theoretical and computational instruments needed to address the study of both equilibrium and dynamical properties of systems subject to long-range forces. The third part of the book is devoted to applications of such techniques to the most relevant examples of long-range systems.

This graduate-level text gives a self-contained exposition of fundamental topics in modern equilibrium and nonequilibrium statistical thermodynamics. The text follows a balanced approach between the macroscopic (thermodynamic) and microscopic (statistical) points of view. The first half of the book deals with equilibrium thermodynamics and statistical mechanics. In addition to standard subjects, the reader will find a detailed account of broken symmetries, critical phenomena and the renormalization group, as well as an introduction to numerical methods. The second half of the book is devoted to nonequilibrium phenomena, first following a macroscopic approach, with hydrodynamics as an important example. Kinetic theory receives a thorough treatment through analysis of the Boltzmann-Lorentz model and the Boltzmann equation. The book concludes with general nonequilibrium methods such as linear response, projection method and the Langevin and Fokker-Planck equations, including numerical simulations. This advanced textbook will be of interest to graduate students and researchers in physics.

This is a textbook which gradually introduces the student to the statistical mechanical study of the different phases of matter and to the phase transitions between them. Throughout, only simple models of both ordinary and soft matter are used but these are studied in full detail. The subject is developed in a pedagogical manner, starting from the basics, going from the simple ideal systems to the interacting systems, and ending with the more modern topics. The textbook provides the student with a complete overview, intentionally at an introductory level, of the theory of phase transitions. All equations and deductions are included.

describes more than thirty Physics practicals at high school and undergraduate level. There's background information on each one, a description of the equipment needed, and how the experiment is performed. Uniquely, for those without access to a real laboratory, the book gives you access to highly detailed 3d simulations of all the experiments.

This book is useful to engineers, researchers, entrepreneurs, and students in different branches of production, engineering, and systems sciences. The polytopic roadmaps are the guidelines inspired by the development stages of cognitive-intelligent systems, and expected to become powerful instruments releasing an abundance of new capabilities and structures for complex engineering systems implementation. The 4D approach developed in previous monographs and correlated with industry 4.0and Fourth Industrial Revolution is continued here toward higher dimensions approaches correlated with polytopic operations, equipment, technologies, industries, and societies. Methodology emphasizes the role of doubling, iteration, dimensionality, and cyclicality around the center, of periodic tables and of conservative and exploratory strategies. Partitions, permutations, classifications, and complexification, as polytopic chemistry, are the elementary operations analyzed. Multi-scale transfer, cyclic operations, conveyors, and assembly lines are the practical examples of operations and equipment. Polytopic flow sheets, online analytical processing, polytopic engineering designs, and reality-inspired engineering are presented. Innovative concepts such as Industry 5.0, polytopic industry, Society 5.0, polytopic society, cyber physical social systems, industrial Internet, and digital twins have been discussed. The general polytopic roadmaps, (GPTR), are proposed as universal guidelines and as common methodologies to synthesize the systemic thinking and capabilities for growing complexity projects implementation.

Many students at undergraduate level struggle with the basic concepts of thermodynamics and statistical physics such as entropy, phase space, y-space, micro-canonical, canonical and grand canonical ensembles, statistical weight (thermodynamic probability), accessible states, density of states, partition function. In this book the author has made every effort to explain these basic concepts and notions in the simplest possible way, keeping in mind the limitations and difficulties of an average student. The book begins with the kinetic theory of gases and transport phenomena and gives the students a thorough grounding in the fundamental aspects of the topics such as Maxwell's law of distribution of molecular speeds, mean free path, viscosity, thermal conduction and diffusion. Next, the topics on equation of state and critical constant are discussed. The chapters from 4 - 9 are devoted to the development of thermodynamic concepts and the application of the laws of thermodynamics to the thermodynamic processes. A sufficient number of solved examples enable the students to test their conceptual understanding and analytical skills. A comprehensive discussion of on the failure of classical theory of radiation and the emergence of quantum concepts viz. the particle nature of radiation is presented in the chapters on radiations. Part II of the book presents a lucid and systematic exposition of the fundamental principles of the most fascinating, exciting, stimulating and challenging subject - statistical physics. The understanding of statistical physics requires knowledge of quantum mechanics at introductory level and a little bit of mathematics of undergraduate level. Though this book provides a self-contained study material, the knowledge of more advanced mathematical tools will make the learning process of statistical physics easier.

Gets right to the point with step-by-step guidance on solving physics problems. Covers all topics in standard general physics courses in the same sequence. Keeps learning about physics fun and engaging through the story of dinosaurs being tested on their knowledge for a final challenge (deflecting an asteroid headed to Earth!). Enables the reader to quickly flip through and locate steps needed for a particular problem. Includes tons of easy to follow diagrams and worked solutions.

This book advances systems thinking by introducing a new philosophy of systemic knowing. It argues that there are inescapable limits to rational understanding. Humankind has always depended on extended ways of knowing to complement the rational-analytic approach. The book establishes that the application of such methods is fundamental to systemic practice. The author advocates embracing two modes of consciousness: intentionality, which Western philosophy has long recognized, and non-intentional awareness, which Eastern philosophy additionally highlights. The simultaneity of these two modes of consciousness, and the variety of knowings they spawn are harnessed for a more holistic, systemic knowing. Four practices from fields related to systems thinking are examined: two contemporary action research methodologies from the US and the UK; the Sumedhian (Indian) approach to inquiry about processes within groups; and a technique of group psychotherapy originating in Eastern Europe. Each of these systematically harnesses knowing using both modes of consciousness. Therefore, the author insists, such approaches must be included in systemic practice, in purposeful and methodical juxtaposition to rational-analytic ways. The book provides examples and guidelines for deployment. "All researchers and practitioners of systems thinking and action research must read this book...Raghav has craftfully blended Eastern and Western wisdom. He uses his immersion into Eastern ways of knowing practically, to elaborate the systems philosophy in rich detail. He has incorporated, from cooperative inquiry as action research, the idea of four ways of knowing: practical, propositional, presentational and experiential, to bolster the foundations of systems thinking" SHANKAR SANKARAN, Professor, University of Technology Sydney, Australia; President International Society of Systems Sciences (ISSS) 2019-2020 "This is a book with the potential to stimulate the emergence of a new paradigm. Raghav shows that systems thinking can transcend rational analysis and incorporate other ways of knowing, such as arts-based methods... also, rather than be overly preoccupied with striving for change, there is value in simply abiding, which comes with a deep appreciation of the ecological relationships we are part of. It's not that rational analysis is wrong - it's that it is only part of a genuinely transformative practice". GERALD MIDGLEY, Co-Director, Centre for Systems Studies, University of Hull; former President, ISSS (2013-14) "Raghav Rajagopalan's writing on generating deep appreciation for the social and ecological interdependencies ties in closely with my own work. The philosophical ideas he develops contain the tracings and essential tones of Gregory Bateson's idea of "Mind" as a process of living complexities reaching well beyond the notion of the body. This book demonstrates outstanding erudition and deep compassion at the same time. It should delight the adventurous reader unafraid of big questions". NORA BATESON, President of the International Bateson Institute

The simulation of turbulent reacting flows, connected with environmental protection and the design of chemical and mechanical processes, is increasingly important. Statistical Mechanics of Turbulent Flows presents a modern overview of basic ways to calculate such flows. It discusses the fundamental problems related to the use of basic equations and their modifications. Special emphasis is placed on the discussion of very promising statistical methods which provide solutions to these problems by models for the underlying stochastic physics of turbulent reacting flows. Their foundations and important new developments up through current challenges are systematically explained. Students and researchers in atmospheric sciences and oceanography, mechanical and chemical engineering and applied mathematics and physics may use Statistical Mechanics of Turbulent Flows as a guide to solve many problems related, e.g. to the assessment of complex atmospheric chemistry, chemical reactor processes, turbulent combustion, and multi-phase flows.

This book provides a comprehensive overview of modern computer-based techniques for analyzing the structure, properties and dynamics of biomolecules and biomolecular processes. It is organized in four main parts; the first one deals with methodology of molecular simulations; the second one with applications of molecular simulations; the third one introduces bioinformatics methods and the use of experimental information in molecular simulations; the last part reports on selected applications of molecular quantum mechanics. This second edition has been thoroughly revised and updated to include the latest progresses made in the respective field of research.

Mathematical Physics for Nuclear Experiments presents an accessible introduction to the mathematical derivations of key equations used in describing and analysing results of typical nuclear physics experiments. Instead of merely showing results and citing texts, crucial equations in nuclear physics such as the Bohr's classical formula, Bethe's quantum mechanical formula for energy loss, Poisson, Gaussian and Maxwellian distributions for radioactive decay, and the Fermi function for beta spectrum analysis, among many more, are presented with the mathematical bases of their derivation and with their physical utility. This approach provides readers with a greater connection between the theoretical and experimental sides of nuclear physics. The book also presents connections between well-established results and ongoing research. It also contains figures and tables showing results from the author's experiments and those of his students to demonstrate experimental outcomes. This is a valuable guide for advanced undergraduates and early graduates studying nuclear instruments and methods, medical and health physics courses as well as experimental particle physics courses. Key features Contains over 500 equations connecting theory with experiments. Presents over 80 examples showing physical intuition and illustrating concepts. Includes 80 exercises, with solutions, showing applications in nuclear and medical physics.

Mathematical Physics for Nuclear Experiments presents an accessible introduction to the mathematical derivations of key equations used in describing and analysing results of typical nuclear physics experiments. Instead of merely showing results and citing texts, crucial equations in nuclear physics such as the Bohr's classical formula, Bethe's quantum mechanical formula for energy loss, Poisson, Gaussian and Maxwellian distributions for radioactive decay, and the Fermi function for beta spectrum analysis, among many more, are presented with the mathematical bases of their derivation and with their physical utility. This approach provides readers with a greater connection between the theoretical and experimental sides of nuclear physics. The book also presents connections between well-established results and ongoing research. It also contains figures and tables showing results from the author's experiments and those of his students to demonstrate experimental outcomes. This is a valuable guide for advanced undergraduates and early graduates studying nuclear instruments and methods, medical and health physics courses as well as experimental particle physics courses. Key features Contains over 500 equations connecting theory with experiments. Presents over 80 examples showing physical intuition and illustrating concepts. Includes 80 exercises, with solutions, showing applications in nuclear and medical physics.

Professionals recognize entropy-enthalpy compensation as an important factor in molecular recognition, lead design, water networks, and protein engineering. It can be experimentally studied by proper combinations of diverse spectroscopic approaches with isothermal titration calorimetry and is clearly related to molecular dynamics. So, how should we treat entropy-enthalpy compensation? Is it a stubborn hindrance that solely complicates the predictability of phenomena otherwise laid on the line by Mother Nature? How should we then deal with it? This book dwells on these posers. It combines two chapters written by globally recognized specialists. Chapter 1 deals with general issues and suggests a definite approach to how we may answer the posers. Chapter 2 shows how the approach outlined might be successfully applied in a rational design of enzymes. This might provide other interesting strategic perspectives in the general theoretical physical chemistry field.

This book contains selected papers of NSC08, the 2nd Conference on Nonlinear Science and Complexity, held 28-31 July, 2008, Porto, Portugal. It focuses on fundamental theories and principles, analytical and symbolic approaches, computational techniques in nonlinear physics and mathematics. Topics treated include - Chaotic Dynamics and Transport in Classic and Quantum Systems - Complexity and Nonlinearity in Molecular Dynamics and Nano-Science - Complexity and Fractals in Nonlinear Biological Physics and Social Systems - Lie Group Analysis and Applications in Nonlinear Science - Nonlinear Hydrodynamics and Turbulence - Bifurcation and Stability in Nonlinear Dynamic Systems - Nonlinear Oscillations and Control with Applications - Celestial Physics and Deep Space Exploration - Nonlinear Mechanics and Nonlinear Structural Dynamics - Non-smooth Systems and Hybrid Systems - Fractional dynamical systems

This book deals with the basic principles and techniques of nonequilibrium statistical mechanics. The importance of this subject is growing rapidly in view of the advances being made, both experimentally and theoretically, in statistical physics, chemical physics, biological physics, complex systems and several other areas. The presentation of topics is quite self-contained, and the choice of topics enables the student to form a coherent picture of the subject. The approach is unique in that classical mechanical formulation takes center stage. The book is of particular interest to advanced undergraduate and graduate students in engineering departments.

"Fundamental Aspects of Plasma Chemical Physics: Transport "develops basic and advanced concepts of plasma transport to the modern treatment of the Chapman-Enskog method for the solution of the Boltzmann transport equation.

The book invites the reader to consider actual problems of the transport of thermal plasmas with particular attention to the derivation of diffusion- and viscosity-type transport cross sections, stressing the role of resonant charge-exchange processes in affecting the diffusion-type collision calculation of viscosity-type collision integrals.

A wide range of topics is then discussed including (1) the effect of non-equilibrium vibrational distributions on the transport of vibrational energy, (2) the role of electronically excited states in the transport properties of thermal plasmas, (3) the dependence of transport properties on the multitude of Saha equations for multi-temperature plasmas, and (4) the effect of the magnetic field on transport properties.

Throughout the book, worked examples are provided to clarify concepts and mathematical approaches.

This book is the second of a series of three published by the Bari group on fundamental aspects of plasma chemical physics. The first book, "Fundamental Aspects of Plasma Chemical Physics: Thermodynamics," is dedicated to plasma thermodynamics; and the third, "Fundamental Aspects of Plasma Chemical Physics: Kinetics," deals with plasma kinetics.

The dynamics of realistic Hamiltonian systems has unusual microscopic features that are direct consequences of its fractional space-time structure and its phase space topology. The book deals with the fractality of the chaotic dynamics and kinetics, and also includes material on non-ergodic and non-well-mixing Hamiltonian dynamics. The book does not follow the traditional scheme of most of today's literature on chaos. The intention of the author has been to put together some of the most complex and yet open problems on the general theory of chaotic systems. The importance of the discussed issues and an understanding of their origin should inspire students and researchers to touch upon some of the deepest aspects of nonlinear dynamics. The book considers the basic principles of the Hamiltonian theory of chaos and some applications including for example, the cooling of particles and signals, control and erasing of chaos, polynomial complexity, Maxwell's Demon, and others. It presents a new and realistic image of the origin of dynamical chaos and randomness. An understanding of the origin of the randomness in dynamical systems, which cannot be of the same origin as chaos, provides new insights in the diverse fields of physics, biology, chemistry and engineering.

* Explores concepts common in textbooks on semiconductors, in addition to topics not included in similar books currently available on the market, such as the topology of Hilbert space in crystals * Contains the latest research and developments in the field * Written in an accessible yet rigorous manner

Building on the material learned by students in their first few years of study, Topics in Statistical Mechanics (Second Edition) presents an advanced level course on statistical and thermal physics. It begins with a review of the formal structure of statistical mechanics and thermodynamics considered from a unified viewpoint. There is a brief revision of non-interacting systems, including quantum gases and a discussion of negative temperatures. Following this, emphasis is on interacting systems. First, weakly interacting systems are considered, where the interest is in seeing how small interactions cause small deviations from the non-interacting case. Second, systems are examined where interactions lead to drastic changes, namely phase transitions. A number of specific examples is given, and these are unified within the Landau theory of phase transitions. The final chapter of the book looks at non-equilibrium systems, in particular the way they evolve towards equilibrium. This is framed within the context of linear response theory. Here fluctuations play a vital role, as is formalised in the fluctuation-dissipation theorem.The second edition has been revised particularly to help students use this book for self-study. In addition, the section on non-ideal gases has been expanded, with a treatment of the hard-sphere gas, and an accessible discussion of interacting quantum gases. In many cases there are details of Mathematica calculations, including Mathematica Notebooks, and expression of some results in terms of Special Functions.

Adding one and one makes two, usually. But sometimes things add up to more than the sum of their parts. This observation, now frequently expressed in the maxim "more is different", is one of the characteristic features of complex systems and, in particular, complex networks. Along with their ubiquity in real world systems, the ability of networks to exhibit emergent dynamics, once they reach a certain size, has rendered them highly attractive targets for research. The resulting network hype has made the word "network" one of the most in uential buzzwords seen in almost every corner of science, from physics and biology to economy and social sciences. The theme of "more is different" appears in a different way in the present v- ume, from the viewpoint of what we call "adaptive networks." Adaptive networks uniquely combine dynamics on a network with dynamical adaptive changes of the underlying network topology, and thus they link classes of mechanisms that were previously studied in isolation. Here adding one and one certainly does not make two, but gives rise to a number of new phenomena, including highly robust se- organization of topology and dynamics and other remarkably rich dynamical beh- iors.

Presents a clear path to developing quantitative multi-phase and multi-component phase field models for solidification and other phase transformation kinetics based on practical grand potential functional Derives explicitly and discusses the quantitative nature of the model formulations through matched interface asymptotic analysis Explores a framework for quantitative treatment of rapid solidification to control solute trapping and solute drag dynamics