This book focuses on mixed crystals formed by molecular substances. The emphasis lies on the elucidation of the structural and thermodynamic properties of two-component systems. Thanks to the fact that the research efforts have been directed to a number of families of chemically coherent substances, rather than to a collection of isolated systems, the knowledge of mixed crystals has substantially increased. This is reflected by the discovery of several empirical relationships between thermodynamic properties, crystallographic properties, and also between thermodynamic mixing properties and exothermodynamic parameters, such as the structural mismatch between the components of the binary systems. This book is a benchmark for material scientists and a unique starting point for anyone interested in mixed crystals.

This book tells the story of the power generation gas turbine from the perspective of one of the leading companies in the field over a period of nearly 100 years, written by an engineer. Especially in times of imminent global economic crises it appears to be worthwhile to reflect on real economic values based on engineering ingenuity and enduring management of technological leadership. Though the book is primarily designed as a technical history of the BBC/ABB/Alstom power generation gas turbines, its scope is sufficiently broad to cover general development trends, including parallel competitor activities. A special benefit is the historical breakdown to the gas turbine component level, so that the book actually outlines the development of axial compressors from early beginnings, the progress in combustion technology towards extraordinary low emission values and that of axial turbines with special emphasis on early turbine cooling innovations. The sheer length of certain engineering developments over several decades allows interesting historic observations and deductions on inherent business mechanisms, the effects of technology preparations and organisational consequences. A look into the mirror of the past provides revelations on the impact of far-reaching business decisions. 2017 Winner of the Historian Engineer Award of the ASME (American Society of Mechanical Engineers

Exactly solvable models are very important in physics. They are important not just from a theoretical point of view but also from the experimentalist's perspective because in such cases theoretical results and experimental results can be compared without ambiguity. This 1999 book is about an important class of exactly solvable models in physics. The subject area is the Bethe-ansatz approach for a number of one-dimensional models, and the setting up of equations within this approach to determine the thermodynamics of these systems. It is a topic that crosses the boundaries between condensed matter physics, mathematics and field theory. The derivation and application of thermodynamic Bethe-ansatz equations for one-dimensional models are explained in detail. This technique is indispensable for physicists studying the low-temperature properties of one-dimensional substances. This book, written by one of the top physicists in this field, and the originator of much of the work in the subject, will be of great interest to theoretical condensed matter physicists.

This thesis establishes a multifaceted extension of the deterministic control framework that has been a workhorse of nonequilibrium statistical mechanics, to stochastic, discrete, and autonomous control mechanisms. This facilitates the application of ideas from stochastic thermodynamics to the understanding of molecular machines in nanotechnology and in living things. It also gives a scale on which to evaluate the nonequilibrium energetic efficiency of molecular machines, guidelines for designing effective synthetic machines, and a perspective on the engineering principles that govern efficient microscopic energy transduction far from equilibrium. The thesis also documents the author's design, analysis, and interpretation of the first experimental demonstration of the utility of this generally applicable method for designing energetically-efficient control in biomolecules. Protocols designed using this framework systematically reduced dissipation, when compared to naive protocols, in DNA hairpins across a wide range of experimental unfolding speeds and between sequences with wildly different physical characteristics.

This book represents the experience of successful researchers from four continents on a broad range of intelligent systems, and it hints how to avoid anticipated conflicts and problems during multidisciplinary innovative research from Industry 4.0 and/or Internet of Things through modern machine learning, and software agent applications to open data science big data/advance analytics/visual analytics/text mining/web mining/knowledge discovery/deep data mining issues. The considered intelligent part is essential in most smart/control systems, cyber security, bioinformatics, virtual reality, robotics, mathematical modelling projects, and its significance rapidly increases in other technologies. Theoretical foundations of fuzzy sets, mathematical and non-classical logic also are rapidly developing.

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.

Multi-phase flows are part of our natural environment such as tornadoes, typhoons, air and water pollution and volcanic activities as well as part of industrial technology such as power plants, combustion engines, propulsion systems, or chemical and biological industry. The industrial use of multi-phase systems requires analytical and numerical strategies for predicting their behavior. .In its fourth extended edition the successful monograph package Multiphase Flow Daynmics contains theory, methods and practical experience for describing complex transient multi-phase processes in arbitrary geometrical configurations, providing a systematic presentation of the theory and practice of numerical multi-phase fluid dynamics.

In the present third volume methods for describing of the thermal interactions in multiphase dynamics are provided. In addition a large number of valuable experiments is collected and predicted using the methods introduced in this monograph. In this way the accuracy of the methods is revealed to the reader.

This fourth edition includes various updates, extensions, improvements and corrections.

"The literature in the field of multiphase flows is numerous. Therefore, it is very important to have a comprehensive and systematic overview including useful numerical methods. The volumes have the character of a handbook and accomplish this function excellently. The models are described in detail and a great number of comprehensive examples and some cases useful for testing numerical solutions are included. These two volumes are very useful for scientists and practicing engineers in the fields of technical thermodynamics, chemical engineering, fluid mechanics, and for mathematicians with interest in technical problems. Besides, they can give a good overview of the dynamically developing, complex field of knowledge to students. This monograph is highly recommended,

BERND PLATZER, ZAAM

In the present third volume methods for describing of the thermal interactions in multiphase dynamics are provided. In addition a large number of valuable experiments is collected and predicted using the methods introduced in this monograph. In this way the accuracy of the methods is revealed to the reader.

This fourth edition includes various updates, extensions, improvements and corrections.

"The literature in the field of multiphase flows is numerous. Therefore, it is very important to have a comprehensive and systematic overview including useful numerical methods. The volumes have the character of a handbook and accomplish this function excellently. The models are described in detail and a great number of comprehensive examples and some cases useful for testing numerical solutions are included. These two volumes are very useful for scientists and practicing engineers in the fields of technical thermodynamics, chemical engineering, fluid mechanics, and for mathematicians with interest in technical problems. Besides, they can give a good overview of the dynamically developing, complex field of knowledge to students. This monograph is highly recommended,

BERND PLATZER, ZAAM

In this book basic and some more advanced thermodynamics and phase as well as stability diagrams relevant for diffusion studies are introduced. Following, Fick s laws of diffusion, atomic mechanisms, interdiffusion, intrinsic diffusion, tracer diffusion and the Kirkendall effect are discussed. Short circuit diffusion is explained in detail with an emphasis on grain boundary diffusion.Recent advances in the area of interdiffusion will be introduced. Interdiffusion in multi-component systems is also explained. Many practical examples will be given, such that researches working in this area can learn the practical evaluation of various diffusion parameters from experimental results. Large number of illustrations and experimental results are used to explain the subject. This book will be appealing for students, academicians, engineers and researchers in academic institutions, industry research and development laboratories."

This book gathers the lecture notes of courses given at the 2010 summer school in theoretical physics in Les Houches, France, Session XCIV. Written in a pedagogical style, this volume illustrates how the field of quantum gases has flourished at the interface between atomic physics and quantum optics, condensed matter physics, nuclear and high-energy physics, non-linear physics and quantum information. The physics of correlated atoms in optical lattices is covered from both theoretical and experimental perspectives, including the Bose and Fermi Hubbard models, and the description of the Mott transition. Few-body physics with cold atoms has made spectacular progress and exact solutions for 3-body and 4-body problems have been obtained. The remarkable collisional stability of weakly bound molecules is at the core of the studies of molecular BEC regimes in Fermi gases. Entanglement in quantum many-body systems is introduced and is a key issue for quantum information processing. Rapidly rotating quantum gases and optically induced gauge fields establish a remarkable connection with the fractional quantum Hall effect for electrons in semiconductors. Dipolar quantum gases with long range and anisotropic interaction lead to new quantum degenerate regimes in atoms with large magnetic moments, or electrically aligned polar molecules. Experiments with ultracold fermions show how quantum gases serve as ''quantum simulators'' of complex condensed matter systems through measurements of the equation of state. Similarly, the recent observation of Anderson localization of matter waves in a disordered optical potential makes a fruitful link with the behaviour of electrons in disordered systems.

This book formulates a unified approach to the description of many-particle systems combining the methods of statistical physics and quantum field theory. The benefits of such an approach are in the description of phase transitions during the formation of new spatially inhomogeneous phases, as well in describing quasi-equilibrium systems with spatially inhomogeneous particle distributions (for example, self-gravitating systems) and metastable states. The validity of the methods used in the statistical description of many-particle systems and models (theory of phase transitions included) is discussed and compared. The idea of using the quantum field theory approach and related topics (path integration, saddle-point and stationary-phase methods, Hubbard-Stratonovich transformation, mean-field theory, and functional integrals) is described in detail to facilitate further understanding and explore more applications. To some extent, the book could be treated as a brief encyclopedia of methods applicable to the statistical description of spatially inhomogeneous equilibrium and metastable particle distributions. Additionally, the general approach is not only formulated, but also applied to solve various practically important problems (gravitating gas, Coulomb-like systems, dusty plasmas, thermodynamics of cellular structures, non-uniform dynamics of gravitating systems, etc.).

The use of thermodynamics in biological research can be equated to an energy book-keeping system. While the structure and function of a molecule is important, it is equally important to know what drives the energy force. This volume presents sophisticated methods for estimating the thermodynamic parameters of specific protein-protein, protein-DNA and small molecule interactions.

* Elucidates the relationships between structure and energetics and their applications to molecular design, aiding researchers in the design of medically important molecules * Provides a "must-have" methods volume that keeps MIE buyers and online subscribers up-to-date with the latest research * Offers step-by-step lab instructions, including necessary equipment, from a global research community

This Volume 5 of the successful book package "Multiphase Flow Dynamics" is devoted to nuclear thermal hydraulics which is a substantial part of nuclear reactor safety. It provides knowledge and mathematical tools for adequate description of the process of transferring the fission heat released in materials due to nuclear reactions into its environment. It step by step introduces into the heat release inside the fuel, temperature fields in the fuels, the "simple" boiling flow in a pipe described using ideas of different complexity like equilibrium, non equilibrium, homogeneity, non homogeneity. Then the "simple" three-fluid boiling flow in a pipe is described by gradually involving the mechanisms like entrainment and deposition, dynamic fragmentation, collisions, coalescence, turbulence. All heat transfer mechanisms are introduced gradually discussing their uncertainty. Different techniques are introduced like boundary layer treatments or integral methods. Comparisons with experimental data at each step demonstrate the success of the different ideas and models. After an introduction of the design of the reactor pressure vessels for pressurized and boiling water reactors the accuracy of the modern methods is demonstrated using large number of experimental data sets for steady and transient flows in heated bundles. Starting with single pipe boiling going through boiling in the rod bundles the analysis of complete vessel including the reactor is finally demonstrated. Then a powerful method for nonlinear stability analysis of flow boiling and condensation is introduced. Models are presented and their accuracies are investigated for describing critical multiphase flow at different level of complexity. Therefore the book presents a complete coverage of the modern Nuclear Thermal Hydrodynamics. This present third edition includes various updates, extensions, improvements and corrections.

Experts of fluid dynamics agree that turbulence is nonlinear and nonlocal. Because of a direct correspondence, nonlocality also implies fractionality. Fractional dynamics is the physics related to fractal (geometrical) systems and is described by fractional calculus. Up-to-present, numerous criticisms of linear and local theories of turbulence have been published. Nonlinearity has established itself quite well, but so far only a very small number of general nonlocal concepts and no concrete nonlocal turbulent flow solutions were available. This book presents the first analytical and numerical solutions of elementary turbulent flow problems, mainly based on a nonlocal closure. Considerations involve anomalous diffusion (Levy flights), fractal geometry (fractal- , bi-fractal and multi-fractal model) and fractional dynamics. Examples include a new 'law of the wall' and a generalization of Kraichnan's energy-enstrophy spectrum that is in harmony with non-extensive and non-equilibrium thermodynamics (Tsallis thermodynamics) and experiments. Furthermore, the presented theories of turbulence reveal critical and cooperative phenomena in analogy with phase transitions in other physical systems, e.g., binary fluids, para-ferromagnetic materials, etc.; the two phases of turbulence identifying the laminar streaks and coherent vorticity-rich structures. This book is intended, apart from fluids specialists, for researchers in physics, as well as applied and numerical mathematics, who would like to acquire knowledge about alternative approaches involved in the analytical and numerical treatment of turbulence.

Scheck's textbook starts with a concise introduction to classical thermodynamics, including geometrical aspects. Then a short introduction to probabilities and statistics lays the basis for the statistical interpretation of thermodynamics. Phase transitions, discrete models and the stability of matter are explained in great detail.Thermodynamics has a special role in theoretical physics. Due to the general approach of thermodynamics the field has as a bridging function between several areas like the theory of condensed matter, elementary particle physics, astrophysics and cosmology. The classical thermodynamics describes predominantly averaged properties of matter, reaching from few particle systems and state of matter to stellar objects. Statistical Thermodynamics covers the same fields, but explores them in greater depth and unifies classical statistical mechanics with quantum theory of multiple particle systems. The content is presented as two tracks: the fast track for master students, providing the essentials, and the intensive track for all wanting to get in depth knowledge of the field. Clearly labelled material and sections guide students through the preferred level of treatment. Numerous problems and worked examples will provide successful access to Statistical Physics and Thermodynamics.

This book is an introduction to the theory, practice, and implementation of the Lattice Boltzmann (LB) method, a powerful computational fluid dynamics method that is steadily gaining attention due to its simplicity, scalability, extensibility, and simple handling of complex geometries. The book contains chapters on the method's background, fundamental theory, advanced extensions, and implementation. To aid beginners, the most essential paragraphs in each chapter are highlighted, and the introductory chapters on various LB topics are front-loaded with special "in a nutshell" sections that condense the chapter's most important practical results. Together, these sections can be used to quickly get up and running with the method. Exercises are integrated throughout the text, and frequently asked questions about the method are dealt with in a special section at the beginning. In the book itself and through its web page, readers can find example codes showing how the LB method can be implemented efficiently on a variety of hardware platforms, including multi-core processors, clusters, and graphics processing units. Students and scientists learning and using the LB method will appreciate the wealth of clearly presented and structured information in this volume.

Thermal and statistical physics has established the principles and procedures needed to understand and explain the properties of systems consisting of macroscopically large numbers of particles. By developing microscopic statistical physics and macroscopic classical thermodynamic descriptions in tandem, Statistical and Thermal Physics: An Introduction provides insight into basic concepts and relationships at an advanced undergraduate level. This second edition is updated throughout, providing a highly detailed, profoundly thorough, and comprehensive introduction to the subject and features exercises within the text as well as end-of-chapter problems. Part I of this book consists of nine chapters, the first three of which deal with the basics of equilibrium thermodynamics, including the fundamental relation. The following three chapters introduce microstates and lead to the Boltzmann definition of the entropy using the microcanonical ensemble approach. In developing the subject, the ideal gas and the ideal spin system are introduced as models for discussion. The laws of thermodynamics are compactly stated. The final three chapters in Part I introduce the thermodynamic potentials and the Maxwell relations. Applications of thermodynamics to gases, condensed matter, and phase transitions and critical phenomena are dealt with in detail. Initial chapters in Part II present the elements of probability theory and establish the thermodynamic equivalence of the three statistical ensembles that are used in determining probabilities. The canonical and the grand canonical distributions are obtained and discussed. Chapters 12-15 are concerned with quantum distributions. By making use of the grand canonical distribution, the Fermi-Dirac and Bose-Einstein quantum distribution functions are derived and then used to explain the properties of ideal Fermi and Bose gases. The Planck distribution is introduced and applied to photons in radiation and to phonons on solids. The last five chapters cover a variety of topics: the ideal gas revisited, nonideal systems, the density matrix, reactions, and irreversible thermodynamics. A flowchart is provided to assist instructors on planning a course. Key Features: Fully updated throughout, with new content on exciting topics, including black hole thermodynamics, Heisenberg antiferromagnetic chains, entropy and information theory, renewable and nonrenewable energy sources, and the mean field theory of antiferromagnetic systems Additional problem exercises with solutions provide further learning opportunities Suitable for advanced undergraduate students in physics or applied physics. Michael J.R. Hoch spent many years as a visiting scientist at the National High Magnetic Field Laboratory at Florida State University, USA. Prior to this, he was a professor of physics and the director of the Condensed Matter Physics Research Unit at the University of the Witwatersrand, Johannesburg, where he is currently professor emeritus in the School of Physics.

This book bridges the current gap between the theory of symmetry-based dynamics and its application to model and analyze complex systems. As an alternative approach, the authors use the symmetry of the system directly to formulate the appropriate models, and also to analyze the dynamics. Complex systems with symmetry arise in a wide variety of fields, including communication networks, molecular dynamics, manufacturing businesses, ecosystems, underwater vehicle dynamics, celestial and spacecraft dynamics and continuum mechanics. A general approach for their analysis has been to derive a detailed model of their individual parts, connect the parts and note that the system contains some sort of symmetry, then attempt to exploit this symmetry in order to simplify numerical computations. This approach can result in highly complicated models that are difficult to analyze even numerically. The alternative approach, while nonstandard, is not entirely new among the mathematics community. However, there is much less familiarity with the techniques of symmetry-breaking bifurcation, as they apply to the engineering, design and fabrication, of complex systems, in particular, nonlinear sensor devices with special emphasis on the conceptualization and development of new technologies of magnetic sensors such as fluxgate magnetometers and SQUID (Superconducting Quantum Interference Devices), E-- (electric-field) sensors, and communication and navigation systems that require multiple frequencies of operation, such as radar and antenna devices as well as gyroscopic systems.

This book concentrates on the properties of the stationary states in chaotic systems of particles or fluids, leaving aside the theory of the way they can be reached. The stationary states of particles or of fluids (understood as probability distributions on microscopic configurations or on the fields describing continua) have received important new ideas and data from numerical simulations and reviews are needed. The starting point is to find out which time invariant distributions come into play in physics. A special feature of this book is the historical approach. To identify the problems the author analyzes the papers of the founding fathers Boltzmann, Clausius and Maxwell including translations of the relevant (parts of) historical documents. He also establishes a close link between treatment of irreversible phenomena in statistical mechanics and the theory of chaotic systems at and beyond the onset of turbulence as developed by Sinai, Ruelle, Bowen (SRB) and others: the author gives arguments intending to support strongly the viewpoint that stationary states in or out of equilibrium can be described in a unified way. In this book it is the "chaotic hypothesis," which can be seen as an extension of the classical ergodic hypothesis to non equilibrium phenomena, that plays the central role. It is shown that SRB - often considered as a kind of mathematical playground with no impact on physical reality - has indeed a sound physical interpretation; an observation which to many might be new and a very welcome insight. Following this, many consequences of the chaotic hypothesis are analyzed in chapter 3 - 4 and in chapter 5 a few applications are proposed. Chapter 6 is historical: carefully analyzing the old literature on the subject, especially ergodic theory and its relevance for statistical mechanics; an approach which gives the book a very personal touch. The book contains an extensive coverage of current research (partly from the authors and his coauthors publications) presented in enough detail so that advanced students may get the flavor of a direction of research in a field which is still very much alive and progressing. Proofs of theorems are usually limited to heuristic sketches privileging the presentation of the ideas and providing references that the reader can follow, so that in this way an overload of this text with technical details could be avoided.

Statistical Mechanics: Fundamentals and Model Solutions, Second Edition Fully updated throughout and with new chapters on the Mayer expansion for classical gases and on cluster expansion for lattice models, this new edition of Statistical Mechanics: Fundamentals and Model Solutions provides a comprehensive introduction to equilibrium statistical mechanics for advanced undergraduate and graduate students of mathematics and physics. The author presents a fresh approach to the subject, setting out the basic assumptions clearly and emphasizing the importance of the thermodynamic limit and the role of convexity. With problems and solutions, the book clearly explains the role of models for physical systems, and discusses and solves various models. An understanding of these models is of increasing importance as they have proved to have applications in many areas of mathematics and physics. Features Updated throughout with new content from the field An established and well-loved textbook Contains new problems and solutions for further learning opportunity Author Professor Teunis C. Dorlas is at the Dublin Institute for Advanced Studies, Ireland.

This book provides an ideal introduction to the use of Feynman path integrals in the fields of quantum mechanics and statistical physics. It is written for graduate students and researchers in physics, mathematical physics, applied mathematics as well as chemistry. The material is presented in an accessible manner for readers with little knowledge of quantum mechanics and no prior exposure to path integrals. It begins with elementary concepts and a review of quantum mechanics that gradually builds the framework for the Feynman path integrals and how they are applied to problems in quantum mechanics and statistical physics. Problem sets throughout the book allow readers to test their understanding and reinforce the explanations of the theory in real situations. Features: Comprehensive and rigorous yet, presents an easy-to-understand approach. Applicable to a wide range of disciplines. Accessible to those with little, or basic, mathematical understanding.

The original work by M.D. Sturge has been updated and expanded to include new chapters covering non-equilibrium and biological systems. This second edition re-organizes the material in a more natural manner into four parts that continues to assume no previous knowledge of thermodynamics. The four divisions of the material introduce the subject inductively and rigorously, beginning with key concepts of equilibrium thermodynamics such as heat, temperature and entropy. The second division focuses on the fundamentals of modern thermodynamics: free energy, chemical potential and the partition function. The second half of the book is then designed with the flexibility to meet the needs of both the instructor and the students, with a third section focused on the different types of gases: ideal, Fermi-Dirac, Bose-Einstein, Black Body Radiation and the Photon gases. In the fourth and final division of the book, modern thermostatistical applications are addressed: semiconductors, phase transitions, transport processes, and finally the new chapters on non-equilibrium and biological systems. Key Features: Provides the most readable, thorough introduction to statistical physics and thermodynamics, with magnetic, atomic, and electrical systems addressed alongside development of fundamental topics at a non-rigorous mathematical level. Includes brand-new chapters on biological and chemical systems and non-equilibrium thermodynamics, as well as extensive new examples from soft condensed matter and correction of typos from the prior edition. Incorporates new numerical and simulation exercises throughout the book. Adds more worked examples, problems, and exercises.

This book will help readers understand thermodynamic properties caused by magnetic fields. Providing a concise review of time independent magnetic fields, it goes on to discuss the thermodynamic properties of magnetizing materials of different shapes, and finally, the equilibrium properties of superconductors of different shapes and also of different sizes. Chapters are accompanied by problems illustrating the applications of the principles to optimize and enhance understanding. This book will be of interest to advanced undergraduates, graduate students, and researchers specializing in thermodynamics, solid state physics, magnetism, and superconductivity. Features: The first book to provide comprehensive coverage of thermodynamics in magnetic fields, only previously available, in part, in journal articles Chapters include problems and worked solutions demonstrating real questions in contemporary superconductivity, such as properties of vortex matter

First published in 1922, this book represents the first attempt to popularise the more accessible aspects of Albert Einstein's general theory of relativity. Eschewing the mathematical components that put the theory beyond many people's grasp, the author employs metaphorical examples and thought experiments to convey the fundamental ideas and assertions of one of physics' most famous principles - which remains the accepted description of gravitation more than a century after its first publication. This book will of interest to students of physics as an introductory basis to aid further study.

The third edition of Engineering Flow and Heat Exchange is the most practical textbook available on the design of heat transfer and equipment. This book is an excellent introduction to real-world applications for advanced undergraduates and an indispensable reference for professionals. The book includes comprehensive chapters on the different types and classifications of fluids, how to analyze fluids, and where a particular fluid fits into a broader picture. This book includes various a wide variety of problems and solutions - some whimsical and others directly from industrial applications. Numerous practical examples of heat transfer Different from other introductory books on fluids Clearly written, simple to understand, written for students to absorb material quickly Discusses non-Newtonian as well as Newtonian fluids Covers the entire field concisely Solutions manual with worked examples and solutions provided