The properties of the harmonic oscillator with random frequency or/and random damping formed the content of the first edition. The second edition includes hundreds of publications on this subject since 2005. The noisy oscillator continues to be the subject of intensive studies in physics, chemistry, biology, and social sciences.The new and the latest type of a stochastic oscillator has also been considered, namely, an oscillator with random mass. Such model describes, among other phenomena, Brownian motion with adhesion, where the molecules of the surrounding medium not only randomly collide, but also stick to the Brownian particle for some (random) time, thereby changing its mass. This edition contains two new chapters, eight new sections and an expanded bibliography. A wide group of researchers, students and teachers will benefit from this book.

Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chif1ese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics," "CFD," "completely integrable systems," "chaos, synergetics and large-scale order," which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics."

A small army of physicists, chemists, mathematicians, and engineers has joined forces to attack a classic problem, the "reversibility paradox", with modern tools. This book describes their work from the perspective of computer simulation, emphasizing the authors' approach to the problem of understanding the compatibility, and even inevitability, of the irreversible second law of thermodynamics with an underlying time-reversible mechanics. Computer simulation has made it possible to probe reversibility from a variety of directions and "chaos theory" or "nonlinear dynamics" has supplied a useful vocabulary and a set of concepts, which allow a fuller explanation of irreversibility than that available to Boltzmann or to Green, Kubo and Onsager. Clear illustration of concepts is emphasized throughout, and reinforced with a glossary of technical terms from the specialized fields which have been combined here to focus on a common theme.The book begins with a discussion, contrasting the idealized reversibility of basic physics against the pragmatic irreversibility of real life. Computer models, and simulation, are next discussed and illustrated. Simulations provide the means to assimilate concepts through worked-out examples. State-of-the-art analyses, from the point of view of dynamical systems, are applied to many-body examples from nonequilibrium molecular dynamics and to chaotic irreversible flows from finite-difference, finite-element, and particle-based continuum simulations. Two necessary concepts from dynamical-systems theory - fractals and Lyapunov instability - are fundamental to the approach.Undergraduate-level physics, calculus, and ordinary differential equations are sufficient background for a full appreciation of this book, which is intended for advanced undergraduates, graduates, and research workers. The generous assortment of examples worked out in the text will stimulate readers to explore the rich and fruitful field of study which links fundamental reversible laws of physics to the irreversibility surrounding us all.This expanded edition stresses and illustrates computer algorithms with many new worked-out examples, and includes considerable new material on shockwaves, Lyapunov instability and fluctuations.

This book presents a clear and readable description of one of the most mysterious concepts of physics: Entropy. It contains a self-learning kit that guides the reader in understanding the concepts of entropy. In the first part, the reader is asked to play the familiar twenty-Question game. Once the reader feels comfortable with playing this game and acquires proficiency in playing the game effectively (intelligently), he or she will be able to capture the elusive and used-to-be mysterious concept of entropy.There will be no more speculative or arbitrary interpretations, nor "older" or "modern" views of entropy. This book will guide readers in choosing their own interpretation of entropy.

The spectacular success of the scientific enterprise over the last four hundred years has led to the promise of an all encompassing vision of the natural world. In this elegant picture, everything we observe is based upon just a few fundamental processes and entities. The almost infinite variety and complexity of the world is thus the product of emergence. But the concept of emergence is fraught with controversy and confusion. This book ponders the question of how emergence should be understood within the scientific picture, and whether a complete vision of the world can be attained that includes consciousness.

The structure of the theory ofthermodynamics has changed enormously since its inception in the middle of the nineteenth century. Shortly after Thomson and Clausius enunciated their versions of the Second Law, Clausius, Maxwell, and Boltzmann began actively pursuing the molecular basis of thermo dynamics, work that culminated in the Boltzmann equation and the theory of transport processes in dilute gases. Much later, Onsager undertook the elucidation of the symmetry oftransport coefficients and, thereby, established himself as the father of the theory of nonequilibrium thermodynamics. Com bining the statistical ideas of Gibbs and Langevin with the phenomenological transport equations, Onsager and others went on to develop a consistent statistical theory of irreversible processes. The power of that theory is in its ability to relate measurable quantities, such as transport coefficients and thermodynamic derivatives, to the results of experimental measurements. As powerful as that theory is, it is linear and limited in validity to a neighborhood of equilibrium. In recent years it has been possible to extend the statistical theory of nonequilibrium processes to include nonlinear effects. The modern theory, as expounded in this book, is applicable to a wide variety of systems both close to and far from equilibrium. The theory is based on the notion of elementary molecular processes, which manifest themselves as random changes in the extensive variables characterizing a system. The theory has a hierarchical character and, thus, can be applied at various levels of molecular detail."

This book is a collection of papers contributed by some of the greatest names in the areas of chaos and nonlinear dynamics. Each paper examines a research topic at the frontier of the area of dynamical systems. As well as reviewing recent results, each paper also discusses the future perspectives of each topic. The result is an invaluable snapshot of the state of the ?eld by some of the most important researchers in the area. The ?rst contribution in this book (the section entitled "How did you get into Chaos?") is actually not a paper, but a collection of personal accounts by a number of participants of the conference held in Aberdeen in September 2007 to honour Celso Grebogi's 60th birthday. At the instigation of James Yorke, many of the most well-known scientists in the area agreed to share their tales on how they got involved in chaos during a celebratory dinner in Celso's honour during the conference. This was recorded in video, we felt that these accounts were a valuable historic document for the ?eld. So we decided to transcribe it and include it here as the ?rst section of the book.

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 wide-ranging and accessible book serves as a fascinating guide to the strategies and concepts that help us understand the boundaries between physics, on the one hand, and sociology, economics, and biology on the other. From cooperation and criticality to flock dynamics and fractals, the author addresses many of the topics belonging to the broad theme of complexity. He chooses excellent examples (requiring no prior mathematical knowledge) to illuminate these ideas and their implications. The lively style and clear description of the relevant models will appeal both to novices and those with an existing knowledge of the field.

This is a book about thermodynamics, not history, but it adopts a semi-historical approach in order to highlight different approaches to entropy. The book does not follow a rigid temporal order of events, nor it is meant to be comprehensive. It includes solved examples for a solid understanding. The division into chapters under the names of key players in the development of the field is not intended to separate these individual contributions entirely, but to highlight their different approaches to entropy. This structure helps to provide a different view-point from other text-books on entropy.

Nonadiabatic transition is a highly multidisciplinary concept and phenomenon, constituting a fundamental mechanism of state and phase changes in various dynamical processes of physics, chemistry and biology, such as molecular dynamics, energy relaxation, chemical reaction, and electron and proton transfer. Control of molecular processes by laser fields is also an example of time-dependent nonadiabatic transition.In this new edition, the original chapters are updated to facilitate enhanced understanding of the concept and applications. Three new chapters - comprehension of nonadiabatic chemical dynamics, control of chemical dynamics, and manifestation of molecular functions - are also added.

This book presents quantum kinetic theory in a comprehensive way. The focus is on density operator methods and on non-equilibrium Green functions. The theory allows to rigorously treat nonequilibrium dynamics in quantum many-body systems. Of particular interest are ultrafast processes in plasmas, condensed matter and trapped atoms that are stimulated by rapidly developing experiments with short pulse lasers and free electron lasers. To describe these experiments theoretically, the most powerful approach is given by non-Markovian quantum kinetic equations that are discussed in detail, including computational aspects.

The science of 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 aim of this book is to provide a clear, logical, and self-contained treatment of equilibrium statistical mechanics starting from Boltzmann's two statistical assumptions, and to present a wide variety of applications to diverse physical assemblies. The coverage is enhanced and extended through an extensive set of accessible problems. An appendix provides an introduction to non-equilibrium statistical mechanics through the Boltzmann equation and its extensions. The book assumes 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 assumed, although the book 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 this text 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.

Thermostable Proteins: Structural Stability and Design provides a comprehensive, updated account of the physical basis of enhanced stability of thermophilic proteins and the design of tailor-made thermostable proteins, paving the way for their possible industrial applications. This book is devoted to understanding the survival mechanisms of "thermophilic life forms" at the molecular level with an emphasis on design strategies.

The review chapters presented in Thermostable Proteins span a wide range of protein thermostability research. Basic structural, thermodynamic, and kinetic principles are explained and molecular strategies for the adaptation to high temperatures are delineated. In addition, this book covers:

• Computing and simulation methods in current and future thermostability research, especially in nonempirical situations
• How rigidity theory is used to improve the thermal adaptation of mesophiles
• Subtilisin-like serine proteases and their significant engineering applications
• The state of knowledge concerning structure function relations and the origins of their structural stability
• Computational and experimental approaches for the design of proteins with increased thermal stability based on sequences or three-dimensional structures

Understanding the molecular basis of how thermostable and hyperthermostable proteins gain and maintain their stability and biological function at high temperatures remains an important scientific challenge. A more detailed knowledge of protein stability not only deepens our understanding of protein structure but also helps in obtaining insights into processes that drive protein activities folding, unfolding, and misfolding essential to biological function.

The science of 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 aim of this book is to provide a clear, logical, and self-contained treatment of equilibrium statistical mechanics starting from Boltzmann's two statistical assumptions, and to present a wide variety of applications to diverse physical assemblies. The coverage is enhanced and extended through an extensive set of accessible problems. An appendix provides an introduction to non-equilibrium statistical mechanics through the Boltzmann equation and its extensions. The book assumes 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 assumed, although the book 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 this text 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 book looks at global atmospheric processes from a physical standpoint using available current and past observational data taken from measurements of relevant atmospheric parameters. It describes various aspects of the current atmospheric state and its future evolution, focusing primarily on the energetic balance of the Earth and atmosphere, and taking into consideration the multi-faceted global equilibrium between these two systems, carbon, and water. The analysis presented in this book restricts itself to those objects and processes that allow us to obtain reliable conclusions and numerical estimations, in contrast to current climate models with much larger numbers of parameters for describing the same problems. As a result, in spite of the roughness of numerical parameters, the book unveils a reliable and transparent physical picture of energetic phenomena in the global atmosphere. In particular, it shows that approximately only one-fourth of atmospheric water returns from the atmosphere to the Earth in the form of free molecules. It was shown that the contemporary warming of our planet has an anthropogenic character, and that the average global temperature increases due to an increase of the concentration of atmospheric CO2 molecules, via an increase in atmospheric moisture, as well as an increase in the amount of aerosols in the atmosphere. Accumulation of atmospheric carbon dioxide plays a subsidiary role in this process and gives approximately one-third in a change of the global temperature, while an increase in the amount of atmospheric water by as little as only 0.3% per year explains the observed warming of the Earth. The book shows how the greenhouse instability of the atmosphere evidently has its origins in the Eocene epoch, presenting an analysis of the influence of various types of global energetic processes on the climate that differs from the official stance on these problems.

The wide application of technologies in new mechanical, electronic and biomedical systems calls for materials and structures with non-conventional properties (e.g materials with 'memory'). Of equal importance is the understanding of the physical behaviour of these materials and consequently developing mathematical modelling techniques for prediction.

This self contained text discusses the mathematical modelling used with these types of electromagnetic materials. It provides a carefully structured, coherent, and comprehensive treatment of electromagnetism of continuous media. The authors provide a systematic review of known subjects along with original results about thermodynamics of electromagnetic materials, well-posedness of initial boundary-value problems, variational settings, and wave propagation. Models of non-linear materials, non-local materials (superconductors), and hysteretic (magnetic) materials are also developed in detail.

This is one of the very few books focusing on relativistic statistical mechanics, and is written by a leading expert in this special field. It started from the notion of relativistic kinetic theory, half a century ago, exploding into relativistic statistical mechanics. This will interest specialists of various fields, especially the (classical and quantum) plasma physics. However, quantum physics - to which a major part is devoted - will be of more interest since, not only it applies to quantum plasma physics, but also to nuclear matter and to strong magnetic field, cosmology, etc. Although the domain of gauge theory is not covered in this book, the topic is not completely forgotten, in particular in the domain of plasma physics. This book is particularly readable for graduate students and a fortiori to young researchers for whom it offers methods and also appropriate schemes to deal with the current problems encountered in astrophysics, in strong magnetic, in nuclear or even in high energy physics.

The book aims to explain the basic ideas of thermal physics intuitively and in the simplest possible way. It is aimed at making the reader feel comfortable with the ideas of entropy and free energy. Thermal physics is prone to misunderstanding, confusion and is often being overlooked. However, a good foundation is necessary to prepare the reader for advanced level studies.

This book explores the challenges our society faces in making the transition to renewable resource use in a way that is truly sustainable - environmentally, economically and socially. After exploring the physical limits the laws of thermodynamics impose on resource exploitation, the book outlines options for managing resources within these limits. It then moves on to look at the resources themselves (from fossil fuels, through minerals to renewable resources such as timber) and the salient question of how the relentless increase in consumption is putting untenable strain on resource use. Case studies investigate what is being done across a range of sectors - and what is and isn't working. The second half of the book turns to solutions, from the promise of industrial ecology to a new economy based on renewable resources such as biobased materials from agricultural crops and forests. Suitable for under- and postgraduate courses on environmental limits and resource use, and continuing professional development - particularly resource management, materials, industrial ecology, energy, resource economics and engineering.

This book explores the challenges our society faces in making the transition to renewable resource use in a way that is truly sustainable - environmentally, economically and socially. After exploring the physical limits the laws of thermodynamics impose on resource exploitation, the book outlines options for managing resources within these limits. It then moves on to look at the resources themselves (from fossil fuels, through minerals to renewable resources such as timber) and the salient question of how the relentless increase in consumption is putting untenable strain on resource use. Case studies investigate what is being done across a range of sectors - and what is and isn't working. The second half of the book turns to solutions, from the promise of industrial ecology to a new economy based on renewable resources such as biobased materials from agricultural crops and forests. Suitable for under- and postgraduate courses on environmental limits and resource use, and continuing professional development - particularly resource management, materials, industrial ecology, energy, resource economics and engineering.

This book covers in great detail the Rouse-segment-based molecular theories in polymer viscoelasticity -- the Rouse theory and the extended reptation theory (based on the framework of the Doi-Edwards theory) -- that have been shown to explain experimental results in a consistently quantitative way. The explanation for the 3.4 power law of viscosity, quantitative line-shape analyses of viscoelastic responses and agreements between different sorts of viscoelastic responses, the consistency between the viscoelasticity and diffusion results, the clarification of the onset of entangelement, the discovery of the number of entanglement strands per cubed entanglement distance being a universal constant and the basic mechanism of the glass transition-related thermorheological complexity are discussed or shown in great detail. The mystery behind the success of the Rouse-segment-based molecular theories over the entropic region of a viscoelastic response is revealed by the Monte Carlo simulations on the Fraenkel chains. Specifically, the simulation studies give a natural explanation for the coexistence of the energy-driven and entropy-driven modes in a viscoelastic response and provide a theoretical basis resolving the paradox that the experimentally determined sizes of Rouse and Kuhn segments are nearly the same. This book starts from a very fundamental level; each chapter is built upon the contents of the previous chapters. Thus, the readers may use the book as a textbook and eventually reach an advanced research level. This book is also a useful source of reference for physicists, chemists and material scientists.

Pendulum is the simplest nonlinear system, which, however, provides the means for the description of different phenomena in Nature that occur in physics, chemistry, biology, medicine, communications, economics and sociology. The chaotic behavior of pendulum is usually associated with the random force acting on a pendulum (Brownian motion). Another type of chaotic motion (deterministic chaos) occurs in nonlinear systems with only few degrees of freedom. This book presents a comprehensive description of these phenomena going on in underdamped and overdamped pendula subject to additive and multiplicative periodic and random forces. No preliminary knowledge, such as complex mathematical or numerical methods, is required from a reader other than undergraduate courses in mathematical physics. A wide group of researchers, along with students and teachers will, thus, benefit from this definitive book on nonlinear dynamics.

This book provides a comprehensive introduction to the theory of phase transitions and critical phenomena. The content covers a period of more than 100 years of theoretical research of condensed matter phases and phase transitions providing a clear interrelationship with experimental problems. It starts from certain basic University knowledge of thermodynamics, statistical physics and quantum mechanics. The text is illustrated with classic examples of phase transitions. Various types of phase transition and (multi)critical points are introduced and explained. The classic aspects of the theory are naturally related with the modern developments. This interrelationship and the field-theoretical renormalization group method are presented in details. The main applications of the renormalization group methods are presented. Special attention is paid to the description of quantum phase transitions. This edition contains a more detailed presentation of the renormalization group method and its applications to particular systems.

This book provides a comprehensive introduction to the theory of phase transitions and critical phenomena. The content covers a period of more than 100 years of theoretical research of condensed matter phases and phase transitions providing a clear interrelationship with experimental problems. It starts from certain basic University knowledge of thermodynamics, statistical physics and quantum mechanics. The text is illustrated with classic examples of phase transitions. Various types of phase transition and (multi)critical points are introduced and explained. The classic aspects of the theory are naturally related with the modern developments. This interrelationship and the field-theoretical renormalization group method are presented in details. The main applications of the renormalization group methods are presented. Special attention is paid to the description of quantum phase transitions. This edition contains a more detailed presentation of the renormalization group method and its applications to particular systems.