This book gives a rigorous treatment of entanglement measures in the general context of quantum field theory. It covers a broad range of models and the use of fields allows us to properly take the localization of systems into account. The required mathematical techniques are introduced in a self-contained way.

Written by two specialists with over twenty-five years of experience in the field, this valuable text presents a wide range of topics within the growing field of nonequilibrium molecular dynamics (NEMD). It introduces theories which are fundamental to the field - namely, nonequilibrium statistical mechanics and nonequilibrium thermodynamics - and provides state-of-the-art algorithms and advice for designing reliable NEMD code, as well as examining applications for both atomic and molecular fluids. It discusses homogenous and inhomogenous flows and pays considerable attention to highly confined fluids, such as nanofluidics. In addition to statistical mechanics and thermodynamics, the book covers the themes of temperature and thermodynamic fluxes and their computation, the theory and algorithms for homogenous shear and elongational flows, response theory and its applications, heat and mass transport algorithms, applications in molecular rheology, highly confined fluids (nanofluidics), the phenomenon of slip and how to compute it from basic microscopic principles, and generalized hydrodynamics.

This book touches upon various aspects of a very interesting, and growing in popularity category of models of dynamical systems. These are the so-called fractional-order systems. Such models are not only relevant for many fields of science and technology, but may also find numerous applications in other disciplines applying the mathematical modelling tools. Thus, the book is intended for a very wide audience of professionals who want to expand their knowledge of systems modelling and its applications. The book includes the selections of papers presented at the International Conference on Fractional Calculus and its Applications organized by the Warsaw University of Technology and was held online on 6-8 September 2021. The International Conference on Fractional Calculus and its Applications (ICFDA) has an almost twenty years history. It started in Bordeaux (France) in 2004, followed by Porto (Portugal) 2006, Istanbul (Turkey) 2008, Badajoz (Spain) 2010, Nanjing (China) 2012, Catania (Italy) 2014, Novi Sad (Serbia) 2016, Amman (Jordan) 2018. Next ICFDA was planned in 2020 in Warsaw (Poland), but COVID-19 pandemic shifted it to 6-8 September 2021. Hence, the organizers were forced to change the form of the conference to the online one. In the volume twenty eight high-quality research papers presented during the ICFDA 2021 eleven Regular Sessions with an additional online Discussion Session are presented. The presented papers are scientifically inspiring, leading to new fruitful ideas. They cover a very broad range of many disciplines. Nowadays, and especially in such a subject as fractional calculus, it is very difficult to assign papers to specific scientific areas. So, many of the papers included have an interdisciplinary character.

This book offers a unified perspective on the study of complex systems for scholars of various disciplines, including mathematics, physics, computer science, biology, economics and social science. The contributions, written by leading scientists, cover a broad set of topics, including new approaches to data science, the connection between scaling limits and conformal field theories, and new ideas on the Legendre duality approach in statistical mechanics of disordered systems. The volume moreover explores results on extreme values of correlated random variables and their connection with the Riemann zeta functions, the relation between diffusion phenomena and complex systems, and the Brownian web, which appears as the universal scaling limit of several probabilistic models. Written for researchers from a broad range of scientific fields, this text examines a selection of recent developments in complex systems from a rigorous perspective.

Thermodynamics Problem Solving in Physical Chemistry: Study Guide and Map is an innovative and unique workbook that guides physical chemistry students through the decision-making process to assess a problem situation, create appropriate solutions, and gain confidence through practice solving physical chemistry problems. The workbook includes six major sections with 20 - 30 solved problems in each section that span from easy, single objective questions to difficult, multistep analysis problems. Each section of the workbook contains key points that highlight major features of the topic to remind students of what they need to apply to solve problems in the topic area. Key Features: Provides instructor access to a visual map depicting how all equations used in thermodynamics are connected and how they are derived from the three major energy laws. Acts as a guide in deriving the correct solution to a problem. Illustrates the questions students should ask themselves about the critical features of the concepts to solve problems in physical chemistry Can be used as a stand-alone product for review of Thermodynamics questions for major tests.

Thermodynamics is fundamental to university and college curricula in chemistry, physics, engineering and many life sciences around the world. It is also notoriously difficult for students to understand, learn and apply. What makes this book different, and special, is the clarity of the text. The writing style is fluid, natural and lucid, and everything is explained in a logical and transparent manner. Thermodynamics is a deep, and important, branch of science, and this book does not make it "easy". But it does make it intelligible. This book introduces a new, 'Fourth Law' of Thermodynamics' based on the notion of Gibbs free energy, which underpins almost every application of thermodynamics and which the authors claim is worthy of recognition as a 'law'. The last four chapters bring thermodynamics into the twenty-first century, dealing with bioenergetics (how living systems capture and use free energy), macromolecule assembly (how proteins fold), and macromolecular aggregation (how, for example, virus capsids assemble). This is of great current relevance to students of biochemistry, biochemical engineering and pharmacy, and is covered in very few other texts on thermodynamics. The book also contains many novel and effective examples, such as the explanation of why friction is irreversible, the proof of the depression of the freezing point, and the explanation of the biochemical standard state.

This book focuses on the development and set-up of fibre Bragg grating (FBG) and no-core fibre (NCF) sensors. It discusses the properties of the sensors and modelling of the resulting devices, which include electronic, optoelectronic, photovoltaic, and spintronic devices. In addition to providing detailed explanations of the properties of FBG and NCF sensors, it features a wealth of instructive illustrations and tables, helping to visualize the respective devices' functions.

Combustion is a fascinating phenomenon coupling complex chemistry to transport mechanisms and nonlinear fluid dynamics. This book provides an up-to-date and comprehensive presentation of the nonlinear dynamics of combustion waves and other non-equilibrium energetic systems. The major advances in this field have resulted from analytical studies of simplified models performed in close relation with carefully controlled laboratory experiments. The key to understanding the complex phenomena is a systematic reduction of the complexity of the basic equations. Focusing on this fundamental approach, the book is split into three parts. Part I provides physical insights for physics-oriented readers, Part II presents detailed technical analysis using perturbation methods for theoreticians, and Part III recalls the necessary background knowledge in physics, chemistry and fluid dynamics. This structure makes the content accessible to newcomers to the physics of unstable fronts in flows, whilst also offering advanced material for scientists who wish to improve their knowledge.

Multilayer networks, in particular multilayer social networks, where users belong to and interact on different networks at the same time, are an active research area in social network analysis, computer science, and physics. These networks have traditionally been studied within these separate research communities, leading to the development of several independent models and methods to deal with the same set of problems. This book unifies and consolidates existing practical and theoretical knowledge on multilayer networks including data collection and analysis, modeling, and mining of multilayer social network systems, the evolution of interconnected social networks, and dynamic processes such as information spreading. A single real dataset is used to illustrate the concepts presented throughout the book, demonstrating both the practical utility and the potential shortcomings of the various methods. Researchers from all areas of network analysis will learn new aspects and future directions of this emerging field.

This book presents an innovative control system design process motivated by renewable energy electric grid integration problems. The concepts developed result from the convergence of research and development goals which have important concepts in common: exergy flow, limit cycles, and balance between competing power flows. A unique set of criteria is proposed to design controllers for a class of nonlinear systems. A combination of thermodynamics with Hamiltonian systems provides the theoretical foundation which is then realized in a series of connected case studies. It allows the process of control design to be viewed as a power flow control problem, balancing the power flowing into a system against that being dissipated within it and dependent on the power being stored in it - an interplay between kinetic and potential energies. Human factors and the sustainability of self-organizing systems are dealt with as advanced topics.

Thermodynamically constrained averaging theory provides a consistent method for upscaling conservation and thermodynamic equations for application in the study of porous medium systems. The method provides dynamic equations for phases, interfaces, and common curves that are closely based on insights from the entropy inequality. All larger scale variables in the equations are explicitly defined in terms of their microscale precursors, facilitating the determination of important parameters and macroscale state equations based on microscale experimental and computational analysis. The method requires that all assumptions that lead to a particular equation form be explicitly indicated, a restriction which is useful in ascertaining the range of applicability of a model as well as potential sources of error and opportunities to improve the analysis.

The book provides a systematic view on flammability and a collection of solved engineering problems in the fields of dilution and purge, mine gas safety, clean burning safety and gas suppression modeling. For the first time, fundamental principles of energy conservation are used to develop theoretical flammability diagrams and are then explored to understand various safety-related mixing problems. This provides the basis for a fully-analytical solution to any flammability problem. Instead of the traditional view that flammability is a fundamental material property, here flammability is discovered to be a result of the explosibility of air and the ignitability of fuel, or a process property. By exploring the more fundamental concepts of explosibility and ignitability, the safety targets of dilution and purge can be better defined and utilized for guiding safe operations in process safety. This book provides various engineering approaches to mixture flammability, benefiting not only the safety students, but also field operators, as a useful resource for the safe handling of flammable gases and liquids. It will be useful to anyone who worries about the ignition potential of a flammable mixture.

Rich with examples and applications, this textbook provides a coherent and self-contained introduction to ergodic theory, suitable for a variety of one- or two-semester courses. The authors' clear and fluent exposition helps the reader to grasp quickly the most important ideas of the theory, and their use of concrete examples illustrates these ideas and puts the results into perspective. The book requires few prerequisites, with background material supplied in the appendix. The first four chapters cover elementary material suitable for undergraduate students - invariance, recurrence and ergodicity - as well as some of the main examples. The authors then gradually build up to more sophisticated topics, including correlations, equivalent systems, entropy, the variational principle and thermodynamical formalism. The 400 exercises increase in difficulty through the text and test the reader's understanding of the whole theory. Hints and solutions are provided at the end of the book.

This work presents a series of experiments with ultracold one-dimensional Bose gases, which establish said gases as an ideal model system for exploring a wide range of non-equilibrium phenomena. With the help of newly developed tools, like full distributions functions and phase correlation functions, the book reveals the emergence of thermal-like transient states, the light-cone-like emergence of thermal correlations and the observation of generalized thermodynamic ensembles. This points to a natural emergence of classical statistical properties from the microscopic unitary quantum evolution, and lays the groundwork for a universal framework of non-equilibrium physics. The thesis investigates a central question that is highly contested in quantum physics: how and to which extent does an isolated quantum many-body system relax? This question arises in many diverse areas of physics, and many of the open problems appear at vastly different energy, time and length scales, ranging from high-energy physics and cosmology to condensed matter and quantum information. A key challenge in attempting to answer this question is the scarcity of quantum many-body systems that are both well isolated from the environment and accessible for experimental study.

This book systematically interprets and documents new, unifying principles and basic laws describing the most relevant aspects of hierarchy. To do so, it discusses recent experiments and models that are simple and realistic enough to reproduce the observations, and develops concepts for a better understanding of the complexity of systems consisting of many organisms. The book covers systems ranging from flocks of birds to groups of people. Although it focuses on hierarchical collective behavior in general, two aspects pop up in the majority of cases: collective motion and dynamically changing, partially directed networks (and the natural relation between the two). In addition, it offers a brief description of the most relevant definitions and concepts involved in the context of hierarchies, presenting both a review of the current literature and a number of new experimental and computational results in more detail. It is a valuable resource for students and scholars pursuing research on the structure of interactions within the collectives of animals and humans.

This book addresses the application of methods used in statistical physics to complex systems-from simple phenomenological analogies to more complex aspects, such as correlations, fluctuation-dissipation theorem, the concept of free energy, renormalization group approach and scaling. Statistical physics contains a well-developed formalism that describes phase transitions. It is useful to apply this formalism for damage phenomena as well. Fractals, the Ising model, percolation, damage mechanics, fluctuations, free energy formalism, renormalization group, and scaling, are some of the topics covered in Statistical Physics of Phase Transitions.

This book explores the working principles of all kinds of turbomachines. The same theoretical framework is used to analyse the different machine types. Fundamentals are first presented and theoretical concepts are then elaborated for particular machine types, starting with the simplest ones.For each machine type, the author strikes a balance between building basic understanding and exploring knowledge of practical aspects. Readers are invited through challenging exercises to consider how the theory applies to particular cases and how it can be generalised. The book is primarily meant as a course book. It teaches fundamentals and explores applications. It will appeal to senior undergraduate and graduate students in mechanical engineering and to professional engineers seeking to understand the operation of turbomachines. Readers will gain a fundamental understanding of turbomachines. They will also be able to make a reasoned choice of turbomachine for a particular application and to understand its operation. Basic design of the simplest turbomachines as a centrifugal fan, an axial steam turbine or a centrifugal pump, is also possible using the topics covered in the book.

This book covers the major problems of turbulence and turbulent processes, including physical phenomena, their modeling and their simulation. After a general introduction in Chapter 1 illustrating many aspects dealing with turbulent flows, averaged equations and kinetic energy budgets are provided in Chapter 2. The concept of turbulent viscosity as a closure of the Reynolds stress is also introduced. Wall-bounded flows are presented in Chapter 3 and aspects specific to boundary layers and channel or pipe flows are also pointed out. Free shear flows, namely free jets and wakes, are considered in Chapter 4. Chapter 5 deals with vortex dynamics. Homogeneous turbulence, isotropy and dynamics of isotropic turbulence are presented in Chapters 6 and 7. Turbulence is then described both in the physical space and in the wave number space. Time dependent numerical simulations are presented in Chapter 8, where an introduction to large eddy simulation is offered. The last three chapters of the book summarize remarkable digital techniques current and experimental. Many results are presented in a practical way, based on both experiments and numerical simulations. The book is written for a advanced engineering students as well as postgraduate engineers and researchers. For students, it contains the essential results as well as details and demonstrations whose oral transmission is often tedious. At a more advanced level, the text provides numerous references which allow readers to find quickly further study regarding their work and to acquire a deeper knowledge on topics of interest.

This book presents a solution for direct and inverse heat conduction problems, discussing the theoretical basis for the heat transfer process and presenting selected theoretical and numerical problems in the form of exercises with solutions. The book covers one-, two- and three dimensional problems which are solved by using exact and approximate analytical methods and numerical methods. An accompanying CD-Rom includes computational solutions of the examples and extensive FORTRAN code.

This book is an introduction to maximum-entropy models of random graphs with given topological properties and their applications. Its original contribution is the reformulation of many seemingly different problems in the study of both real networks and graph theory within the unified framework of maximum entropy. Particular emphasis is put on the detection of structural patterns in real networks, on the reconstruction of the properties of networks from partial information, and on the enumeration and sampling of graphs with given properties. After a first introductory chapter explaining the motivation, focus, aim and message of the book, chapter 2 introduces the formal construction of maximum-entropy ensembles of graphs with local topological constraints. Chapter 3 focuses on the problem of pattern detection in real networks and provides a powerful way to disentangle nontrivial higher-order structural features from those that can be traced back to simpler local constraints. Chapter 4 focuses on the problem of network reconstruction and introduces various advanced techniques to reliably infer the topology of a network from partial local information. Chapter 5 is devoted to the reformulation of certain "hard" combinatorial operations, such as the enumeration and unbiased sampling of graphs with given constraints, within a "softened" maximum-entropy framework. A final chapter offers various overarching remarks and take-home messages.By requiring no prior knowledge of network theory, the book targets a broad audience ranging from PhD students approaching these topics for the first time to senior researchers interested in the application of advanced network techniques to their field.

This book extends the development of the thermodynamic theory of specific intermolecular interactions to element-organic and specific organometallic compounds. The fundamentals of an unconventional approach to the theory of H-bonding and specific interactions are formulated, based on a concept of pentacoordinate carbon atoms. Prof. Baev has introduced the theory already in his successful books "Specific Intermolecular Interactions of Organic Compounds" and "Specific Intermolecular Interactions of Nitrogenated and Bioorganic Compounds". In this book he also demonstrates it for element organic and specific organometallic compounds, a class of substances which is of great importance in synthetic chemistry and catalysis. Furthermore, organic compound classes, that have not been treated in the previous books, are included. New types of hydrogen bonds and specific interactions are substantiated and their energies are determined on the basis of the developed methodology. In this way, the influence of the molecular structure on the energy and on intermolecular interactions can be discussed for these particular compound classes.

This book is a short, but complete, introduction to the Loewner equation and the SLEs, which are a family of random fractal curves, as well as the relevant background in probability and complex analysis. The connection to statistical physics is also developed in the text in an example case. The book is based on a course (with the same title) lectured by the author. First three chapters are devoted to the background material, but at the same time, give the reader a good understanding on the overview on the subject and on some aspects of conformal invariance. The chapter on the Loewner equation develops in detail the connection of growing hulls and the differential equation satisfied by families of conformal maps. The Schramm-Loewner evolutions are defined and their basic properties are studied in the following chapter, and the regularity properties of random curves as well as scaling limits of discrete random curves are investigated in the final chapter. The book is aimed at graduate students or researchers who want to learn the subject fairly quickly.

Making Flory-Huggins Practical: Thermodynamics of Polymer-Containing Mixtures, by B. A. Wolf
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Aqueous Solutions of Polyelectrolytes: Vapor-Liquid Equilibrium and Some Related Properties, by G. Maurer, S. Lammertz, and L. Ninni Sch fer
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Gas-Polymer Interactions: Key Thermodynamic Data and Thermophysical Properties, by J.-P. E. Grolier, and S. A.E. Boyer
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Interfacial Tension in Binary Polymer Blends and the Effects of Copolymers as Emulsifying Agents, by S. H. Anastasiadis
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Theory of Random Copolymer Fractionation in Columns, by Sabine Enders
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Computer Simulations and Coarse-Grained Molecular Models Predicting the Equation of State of Polymer Solutions, by K. Binder, B. Mognetti, W. Paul, P. Virnau, and L. Yelash
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Modeling of Polymer Phase Equilibria Using Equations of State, by G. Sadowski

The study of nonlinear localized excitations is a long-standing challenge for research in basic and applied science, as well as engineering, due to their importance in understanding and predicting phenomena arising in nonlinear and complex systems, but also due to their potential for the development and design of novel applications. This volume is a compilation of chapters representing the current state-of-the-art on the field of localized excitations and their role in the dynamics of complex physical systems.

This work addresses the gap in the current collective action literature exposed by the new Information and Communication Technologies (ICTs) landscape by bringing together qualitative and quantitative studies from computational and social sciences. The book offers a rigorous and systematic investigation of both methodological and theoretical underpinnings and, thus, collectively promotes a symbiotic and synergistic advancement of the multiple interconnected disciplines in studying online collective actions. More specifically, the book is intended to illuminate several fundamental and powerful yet theoretically undeveloped and largely unexplored aspects of collective action in the participatory media (e.g., social media). Through in-depth exploration of relevant concepts, theories, methodologies, applications, and case studies, the reader will gain an advanced understanding of collective action with the advent of the new generation of ICTs enabled by social media and the Internet. The developed theories will be valuable and comprehensive references for those interested in examining the role of ICTs not only in collective action but also in decision and policy making, understanding the dynamics of interaction, collaboration, cooperation, communication, as well as information flow and propagation, and social network research for years to come. Further, the book also serves as an extensive repository of data sets and tools that can be used by researchers leading to a deeper and more fundamental understanding of the dynamics of the crowd in online collective actions.