The aim of this Book is to give an overview, based on the results of nearly three decades of intensive research, of transient chaos. One belief that motivates us to write this book is that, transient chaos may not have been appreciated even within the nonlinear-science community, let alone other scientific disciplines.

This book presents the physical science experiments in a space microgravity environment conducted on board the SJ-10 recoverable satellite, which was launched on April 6th, 2016 and recovered on April 18th, 2016. The experiments described were selected from ~100 proposals from various institutions in China and around the world, and have never previously been conducted in the respective fields. They involve fluid physics and materials science, and primarily investigate the kinetic properties of matter in a space microgravity environment. The book provides a comprehensive review of these experiments, as well as the mission's execution, data collection, and scientific outcomes.

With a foreword by Freeman Dyson, the handbook brings together leading mathematicians and physicists to offer a comprehensive overview of random matrix theory, including a guide to new developments and the diverse range of applications of this approach.
In part one, all modern and classical techniques of solving random matrix models are explored, including orthogonal polynomials, exact replicas or supersymmetry. Further, all main extensions of the classical Gaussian ensembles of Wigner and Dyson are introduced including sparse, heavy tailed, non-Hermitian or multi-matrix models. In the second and larger part, all major applications are covered, in disciplines ranging from physics and mathematics to biology and engineering. This includes standard fields such as number theory, quantum chaos or quantum chromodynamics, as well as recent developments such as partitions, growth models, knot theory, wireless communication or bio-polymer folding.
The handbook is suitable both for introducing novices to this area of research and as a main source of reference for active researchers in mathematics, physics and engineering.

After a short introduction to the fundamentals, this book provides a detailed account of major advances in applying fractional calculus to dynamical systems. Fractional order dynamical systems currently continue to gain further importance in many areas of science and engineering. As with many other approaches to mathematical modeling, the first issue to be addressed is the need to couple a definition of the fractional differentiation or integration operator with the types of dynamical systems that are analyzed. As such, for the fundamentals the focus is on basic aspects of fractional calculus, in particular stability analysis, which is required to tackle synchronization in coupled fractional order systems, to understand the essence of estimators for related integer order systems, and to keep track of the interplay between synchronization and parameter observation. This serves as the common basis for the more advanced topics and applications presented in the subsequent chapters, which include an introduction to the 'Immersion and Invariance' (I&I) methodology, the masterslave synchronization scheme for partially known nonlinear fractional order systems, Fractional Algebraic Observability (FAO) and Fractional Generalized quasi-Synchronization (FGqS) to name but a few. This book is intended not only for applied mathematicians and theoretical physicists, but also for anyone in applied science dealing with complex nonlinear systems.

Learn classical thermodynamics alongside statistical mechanics with this fresh approach to the subjects. Molecular and macroscopic principles are explained in an integrated, side-by-side manner to give students a deep, intuitive understanding of thermodynamics and equip them to tackle future research topics that focus on the nanoscale. Entropy is introduced from the get-go, providing a clear explanation of how the classical laws connect to the molecular principles, and closing the gap between the atomic world and thermodynamics. Notation is streamlined throughout, with a focus on general concepts and simple models, for building basic physical intuition and gaining confidence in problem analysis and model development. Well over 400 guided end-of-chapter problems are included, addressing conceptual, fundamental, and applied skill sets. Numerous worked examples are also provided together with handy shaded boxes to emphasize key concepts, making this the complete teaching package for students in chemical engineering and the chemical sciences.

Thisbook traces the history of the concept of work from its earliest stages and shows that its further formalization leads to equilibrium principle and to the principle of virtual works, and so pointing the way ahead for future research and applications.

The idea that something remains constant in a machine operation is very old and has been expressed by many mathematicians and philosophers such as, for instance, Aristotle. Thus, a concept of energy developed. Another importantidea in machine operation is Archimedes'lever principle.

In modern times the concept of work is analyzed in the context of applied mechanics mainly in Lazare Carnot mechanics and the mechanics of the new generation of polytechnical engineers like Navier, Coriolis and Poncelet. In this context the word "work" is finally adopted. These engineers are also responsible for the incorporation of the concept of work into the discipline of economics when they endeavoured to combine the studyof the work of machines and men together."

The Ising model provides a detailed mathematical description of ferromagnetism and is widely used in statistical physics and condensed matter physics. In this Student's Guide, the author demystifies the mathematical framework of the Ising model and provides students with a clear understanding of both its physical significance, and how to apply it successfully in their calculations. Key topics related to the Ising model are covered, including exact solutions of both finite and infinite systems, series expansions about high and low temperatures, mean-field approximation methods, and renormalization-group calculations. The book also incorporates plots, figures, and tables to highlight the significance of the results. Designed as a supplementary resource for undergraduate and graduate students, each chapter includes a selection of exercises intended to reinforce and extend important concepts, and solutions are also available for all exercises.

Predicting thermodynamic quantities for chemically realistic systems on the basis of atomistic calculations is still, even today, a nontrivial task. Nonetheless, accurate treatment of inter-particle interactions, in terms of quantum chemical first principles methods, is a prerequisite for many applications, because of the complexity of both reactants and solvents in modern molecular sciences. Currently, a straightforward calculation of thermodynamic properties from these methods is only possible for high-temperature and low- density systems. Although the enthalpy of a system can often be predicted to a good level of precision with this ideal gas approach, calculating the entropy contribution to the free energy is problematic, especially as the density of the system increases. This thesis contains a compact and coherent introduction of basic theoretical features. The foundations are then laid for the development of approaches suitable for calculation of condensed phase entropies on the basis of well-established quantum chemical methods. The main emphasis of this work is on realistic systems in solution, which is the most important environment for chemical synthesis. The presented results demonstrate how isolated molecular concepts typically employed in modern quantum chemistry can be extended for the accurate determination of thermodynamic properties by means of scale- transferring approaches.

An introductory textbook exploring the subject of Lagrangian and Hamiltonian dynamics, with a relaxed and self-contained setting. Lagrangian and Hamiltonian dynamics is the continuation of Newton's classical physics into new formalisms, each highlighting novel aspects of mechanics that gradually build in complexity to form the basis for almost all of theoretical physics. Lagrangian and Hamiltonian dynamics also acts as a gateway to more abstract concepts routed in differential geometry and field theories and can be used to introduce these subject areas to newcomers. Journeying in a self-contained manner from the very basics, through the fundamentals and onwards to the cutting edge of the subject, along the way the reader is supported by all the necessary background mathematics, fully worked examples, thoughtful and vibrant illustrations as well as an informal narrative and numerous fresh, modern and inter-disciplinary applications. The book contains some unusual topics for a classical mechanics textbook. Most notable examples include the 'classical wavefunction', Koopman-von Neumann theory, classical density functional theories, the 'vakonomic' variational principle for non-holonomic constraints, the Gibbs-Appell equations, classical path integrals, Nambu brackets and the full framing of mechanics in the language of differential geometry.

This book presents a careful selection of the most important developments of the \phi^4 model, offering a judicious summary of this model with a view to future prospects and the challenges ahead. Over the past four decades, the \phi^4 model has been the basis for a broad array of developments in the physics and mathematics of nonlinear waves. From kinks to breathers, from continuum media to discrete lattices, from collisions of solitary waves to spectral properties, and from deterministic to stochastic models of \phi^4 (and \phi^6, \phi^8, \phi^12 variants more recently), this dynamical model has served as an excellent test bed for formulating and testing the ideas of nonlinear science and solitary waves.

Instantons, or pseudoparticles, are solutions to the equations of motion in classical field theories on a Euclidean spacetime. Instantons are found everywhere in quantum theories as they have many applications in quantum tunnelling. Diverse physical phenomena may be described through quantum tunnelling, for example: the Josephson effect, the decay of meta-stable nuclear states, band formation in tight binding models of crystalline solids, the structure of the gauge theory vacuum, confinement in 2+1 dimensions, and the decay of superheated or supercooled phases. Drawing inspiration from Sidney Coleman's Erice lectures, this volume provides an accessible, detailed introduction to instanton methods, with many applications, making it a valuable resource for graduate students in many areas of physics, from condensed matter, particle and nuclear physics, to string theory. This title, first published in 2017, has been reissued as an Open Access publication on Cambridge Core.

Instantons, or pseudoparticles, are solutions to the equations of motion in classical field theories on a Euclidean spacetime. Instantons are found everywhere in quantum theories as they have many applications in quantum tunnelling. Diverse physical phenomena may be described through quantum tunnelling, for example: the Josephson effect, the decay of meta-stable nuclear states, band formation in tight binding models of crystalline solids, the structure of the gauge theory vacuum, confinement in 2+1 dimensions, and the decay of superheated or supercooled phases. Drawing inspiration from Sidney Coleman's Erice lectures, this volume provides an accessible, detailed introduction to instanton methods, with many applications, making it a valuable resource for graduate students in many areas of physics, from condensed matter, particle and nuclear physics, to string theory. This title, first published in 2017, has been reissued as an Open Access publication on Cambridge Core.

Refrigeration, Air Conditioning and Heat Pumps, Fifth Edition, provides a comprehensive introduction to the principles and practice of refrigeration. Clear and comprehensive, it is suitable for both trainee and professional HVAC engineers, with a straightforward approach that also helps inexperienced readers gain a comprehensive introduction to the fundamentals of the technology. With its concise style and broad scope, the book covers most of the equipment and applications professionals will encounter. The simplicity of the descriptions helps users understand, specify, commission, use, and maintain these systems. It is a must-have text for anyone who needs thorough, foundational information on refrigeration and air conditioning, but without textbook pedagogy. It includes detailed technicalities or product-specific information. New material to this edition includes the latest developments in refrigerants and lubricants, together with updated information on compressors, heat exchangers, liquid chillers, electronic expansion valves, controls, and cold storage. In addition, efficiency, environmental impact, split systems, retail refrigeration (supermarket systems and cold rooms), industrial systems, fans, air infiltration, and noise are also included.

This book focuses on theoretical thermotics, the theory of transformation thermotics and its extended theories for the active control of macroscopic thermal phenomena of artificial systems, which is in sharp contrast to classical thermodynamics comprising the four thermodynamic laws for the passive description of macroscopic thermal phenomena of natural systems. The book covers the basic concepts and mathematical methods, which are necessary to understand thermal problems extensively investigated in physics, but also in other disciplines of engineering and materials. The analyses rely on models solved by analytical techniques accompanied with computer simulations and laboratory experiments. This book serves both as a reference work for senior researchers and a study text for zero beginners.

A modern and broad exposition emphasizing heat transfer by convection. This edition contains valuable new information primarily pertaining to flow and heat transfer in porous media and computational fluid dynamics as well as recent advances in turbulence modeling. Problems of a mixed theoretical and practical nature provide an opportunity to test mastery of the material.

Atmospheric Thermodynamics provides a comprehensive treatment of a subject that can often be intimidating. The text analyses real-life problems and applications of the subject, alongside of guiding the reader through the fundamental basics and covering the first and second laws and the ideal gas law, followed by an emphasis on moist processes in Earth's atmosphere. Water in all its phases is a critical component of weather and the Earth's climate system. With user-friendly chapters that include energy conservation and water and its transformations, the authors write with a willingness to expose assumptions and approximations usually absent in other textbooks. History is woven into the text to provide a context for the time evolution of thermodynamics and its place in atmospheric science and demonstrating how physical reasoning leads to correct explanations of everyday phenomena. Many of the experiments described were done using inexpensive instruments to take advantage of the earth's atmosphere as a freely accessible thermodynamics library. This second edition provides updated treatments of atmospheric measurements and substantially expanded sections that include atmospheric applications of the first and second laws and energy exchange between humans and their atmospheric environment. With 400+ thought provoking problems and 350 references with annotated notes and further reading suggestions, this second edition provides a basic understanding of the fundamentals of this subject while still being a comprehensive reference guide for those working in the field of atmospheric and environmental sciences.

Radio telescopes as well as communication antennas operate under the influence of gravity, temperature and wind. Among those, temperature influences may degrade the performance of a radio telescope through transient changes of the focus, pointing, path length and sensitivity, often in an unpredictable way. Thermal Design and Thermal Behaviour of Radio Telescopes and their Enclosures reviews the design and construction principles of radio telescopes in view of thermal aspects and heat transfer with the variable thermal environment; it explains supporting thermal model calculations and the application and efficiency of thermal protection and temperature control; it presents many measurements illustrating the thermal behaviour of telescopes in the environment of their observatory sites.

The book benefits scientists and radio/communication engineers, telescope designers and construction firms as well as telescope operators, observatory staff, but also the observing astronomer who is directly confronted with the thermal behaviour of a telescope.

Networks are convenient mathematical models to represent the structure of complex systems, from cells to societies. In the last decade, multilayer network science - the branch of the field dealing with units interacting in multiple distinct ways, simultaneously - was demonstrated to be an effective modeling and analytical framework for a wide spectrum of empirical systems, from biopolymers networks (such as interactome and metabolomes) to neuronal networks (such as connectomes), from social networks to urban and transportation networks. In this Element, a decade after one of the most seminal papers on this topic, the authors review the most salient features of multilayer network science, covering both theoretical aspects and direct applications to real-world coupled/interdependent systems, from the point of view of multilayer structure, dynamics and function. The authors discuss potential frontiers for this topic and the corresponding challenges in the field for the next future.

For a one-semester upper-level undergraduate course in Thermal Physics or Thermodynamics.

This book provides a solid introduction to the classical and statistical theories of thermodynamics.

This book provides a comprehensive and self-contained overview of recent progress in nonequilibrium statistical mechanics, in particular, the discovery of fluctuation relations and other time-reversal symmetry relations. The significance of these advances is that nonequilibrium statistical physics is no longer restricted to the linear regimes close to equilibrium, but extends to fully nonlinear regimes. These important new results have inspired the development of a unifying framework for describing both the microscopic dynamics of collections of particles, and the macroscopic hydrodynamics and thermodynamics of matter itself. The book discusses the significance of this theoretical framework in relation to a broad range of nonequilibrium processes, from the nanoscale to the macroscale, and is essential reading for researchers and graduate students in statistical physics, theoretical chemistry and biological physics.

Our original objective in writing this book was to demonstrate how the concept of the equation of motion of a Brownian particle - the Langevin equation or Newtonian-like evolution equation of the random phase space variables describing the motion - first formulated by Langevin in 1908 - so making him inter alia the founder of the subject of stochastic differential equations, may be extended to solve the nonlinear problems arising from the Brownian motion in a potential. Such problems appear under various guises in many diverse applications in physics, chemistry, biology, electrical engineering, etc. However, they have been invariably treated (following the original approach of Einstein and Smoluchowski) via the Fokker-Planck equation for the evolution of the probability density function in phase space. Thus the more simple direct dynamical approach of Langevin which we use and extend here, has been virtually ignored as far as the Brownian motion in a potential is concerned. In addition two other considerations have driven us to write this new edition of The Langevin Equation. First, more than five years have elapsed since the publication of the third edition and following many suggestions and comments of our colleagues and other interested readers, it became increasingly evident to us that the book should be revised in order to give a better presentation of the contents. In particular, several chapters appearing in the third edition have been rewritten so as to provide a more direct appeal to the particular community involved and at the same time to emphasize via a synergetic approach how seemingly unrelated physical problems all involving random noise may be described using virtually identical mathematical methods. Secondly, in that period many new and exciting developments have occurred in the application of the Langevin equation to Brownian motion. Consequently, in order to accommodate all these, a very large amount of new material has been added so as to present a comprehensive overview of the subject.

Providing a systematic introduction to the techniques which are fundamental to quantum field theory, this book pays special attention to the use of these techniques in a wide variety of areas, including ordinary quantum mechanics, quantum mechanics in the second-quantized formulation, relativistic quantum field theory, Euclidean field theory, quantum statistics at finite temperature, and the classical statistics of nonideal gas and spin systems. The extended chapter on variational methods and functional Legendre transformations contains completely original material.

Presenting in a coherent and accessible fashion current results in nanomagnetism, this book constitutes a comprehensive, rigorous and readable account, from first principles of the classical and quantum theories underlying the dynamics of magnetic nanoparticles subject to thermal fluctuations.Starting with the Larmor-like equation for a giant spin, both the stochastic (Langevin) equation of motion of the magnetization and the associated evolution (Fokker-Planck) equation for the distribution function of the magnetization orientations of ferromagnetic nanoparticles (classical spins) in a heat bath are developed along with their solution (using angular momentum theory) for arbitrary magnetocrystalline-Zeeman energy. Thus, observables such as the magnetization reversal time, relaxation functions, dynamic susceptibilities, etc. are calculated and compared with the predictions of classical escape rate theory including in the most general case spin-torque-transfer. Regarding quantum effects, which are based on the reduced spin density matrix evolution equation in Hilbert space as is described at length, they are comprehensively treated via the Wigner-Stratonovich formulation of the quantum mechanics of spins via their orientational quasi-probability distributions on a classically meaningful representation space. Here, as suggested by the relevant Weyl symbols, the latter is the configuration space of the polar angles. Hence, one is led, by mapping the reduced density matrix equation onto that space, to a master equation for the quasi-probability evolution akin to the Fokker-Planck equation which may be solved in a similar way. Thus, one may study in a classical-like manner the evolution of observables with spin number ranging from an elementary spin to molecular clusters to the classical limit, viz. a nanoparticle. The entire discussion hinges on the one-to-one correspondence between polarization operators in Hilbert space and the spherical harmonics allied to concepts of spin coherent states long familiar in quantum optics.Catering for the reader with only a passing knowledge of statistical and quantum mechanics, the book serves as an introductory text on a complicated subject where the literature is remarkably sparse.

In this resource, acknowledged leaders in the field examine current state-of-the-art and recent developments in technology, of flow boiling systems which are affected by convective flows. This important volume consists of expanded and revised peer-reviewed papers presented at the Engineering Foundations's Convective Flow Boiling: An International Conference held in 1995.