This book is the productof my research at the EndowedChair of Corporate Finance and Capital Markets at the European Business School. Many people devoted their inspiration, time, and knowledge in order to support me with my interdisciplinary research. Thank you all for your support. Especially, I thank my academic supervisor Prof. Ulrich Hommel, Ph.D., who provided me with the freedom to pursue my research interests and who always s- ported me generously. In addition, I am very grateful to my co-supervisor Prof. Dr. Susanne Strahringer (TU Dresden), who graciously accepted the task of refer- ing my book. Also, I thank Prof. Dr. Matthias Krause of the Chair for Theoretical Computer Science in Mannheim for the technical and computer scienti?c support. During my research visits I received generous support from Prof. Yaneer Bar- Yam (NECSI and Harvard) and Prof. John D. Sterman (MIT), who introduced me to the ?eld of System Dynamics and Complex Systems, as well as from Prof. Victor Mossotti (U.S. Geological Survey), Prof. Hiroki Sayama (NECSI and Bingh- ton), Prof. Markus de Aguiar (Universidade Estadual de Campinas), Prof. Michel Baranger (MIT), Prof. Jay W. Forrester (MIT), and Prof. Brian D. Josephson (Cambridge). Thank you very much for numerous inspiring discussions.

Humans engage in a seemingly endless variety of different behaviors, of which some are found across species, while others are conceived of as typically human. Most generally, behavior comes about through the interplay of various constraints - informational, mechanical, neural, metabolic, and so on - operating at multiple scales in space and time. Over the years, consensus has grown in the research community that, rather than investigating behavior only from bottom up, it may be also well understood in terms of concepts and laws on the phenomenological level. Such top down approach is rooted in theories of synergetics and self-organization using tools from nonlinear dynamics. The present compendium brings together scientists from all over the world that have contributed to the development of their respective fields departing from this background. It provides an introduction to deterministic as well as stochastic dynamical systems and contains applications to motor control and coordination, visual perception and illusion, as well as auditory perception in the context of speech and music.

This is a masters/graduate level textbook on statistical physics. The basics of the discipline and its application in the current topics of interest like BoseEinstein condensate, statistical astrophysics and phase transitions have been discussed with thoroughness.

This is a systematic introduction and development of a course material tried successful over a number of years. Feedback from the students tells that it has immensely helped them in their later research.

This textbook provides an exposition of equilibrium thermodynamics and its applications to several areas of physics with particular attention to phase transitions and critical phenomena. The applications include several areas of condensed matter physics and include also a chapter on thermochemistry. Phase transitions and critical phenomena are treated according to the modern development of the field, based on the ideas of universality and on the Widom scaling theory. For each topic, a mean-field or Landau theory is presented to describe qualitatively the phase transitions. These theories include the van der Waals theory of the liquid-vapor transition, the Hildebrand-Heitler theory of regular mixtures, the Griffiths-Landau theory for multicritical points in multicomponent systems, the Bragg-Williams theory of order-disorder in alloys, the Weiss theory of ferromagnetism, the Neel theory of antiferromagnetism, the Devonshire theory for ferroelectrics and Landau-de Gennes theory of liquid crystals. This new edition presents expanded sections on phase transitions, liquid crystals and magnetic systems, for all problems detailed solutions are provided. It is intended for students in physics and chemistry and provides a unique combination of thorough theoretical explanation and presentation of applications in both areas. Chapter summaries, highlighted essentials and problems with solutions enable a self sustained approach and deepen the knowledge. It is intended for students in physics and chemistry and provides a unique combination of thorough theoretical explanation and presentation of applications in both areas. Chapter summaries, highlighted essentials and problems with solutions enable a self sustained approach and deepen the knowledge.

Symmetry is at the heart of our understanding of matter. This book tells the fascinating story of the constituents of matter from a common symmetry perspective. The standard model of elementary particles and the periodic table of chemical elements have the common goal to bring order in the bewildering chaos of the constituents of matter. Their success relies on the presence of fundamental symmetries in their core. The purpose of Shattered Symmetry is to share the admiration for the power and the beauty of these symmetries. The reader is taken on a journey from the basic geometric symmetry group of a circle to the sublime dynamic symmetries that govern the motions of the particles. Along the way the theory of symmetry groups is gradually introduced with special emphasis on its use as a classification tool and its graphical representations. This is applied to the unitary symmetry of the eightfold way of quarks, and to the four-dimensional symmetry of the hydrogen atom. The final challenge is to open up the structure of Mendeleev's table which goes beyond the symmetry of the hydrogen atom. Breaking this symmetry to accommodate the multi-electron atoms requires us to leave the common ground of linear algebras and explore the potential of non-linearity.

The European Conference on Complex Systems, held under the patronage of the Complex Systems Society, is an annual event that has become the leading European conference devoted to complexity science. ECCS'12, its ninth edition, took place in Brussels, during the first week of September 2012. It gathered about 650 scholars representing a wide range of topics relating to complex systems research, with emphasis on interdisciplinary approaches. More specifically, the following tracks were covered:

1. Foundations of Complex Systems

2. Complexity, Information and Computation

3. Prediction, Policy and Planning, Environment

4. Biological Complexity

5. Interacting Populations, Collective Behavior

6. Social Systems, Economics and Finance

This book contains a selection of the contributions presented at the conference and its satellite meetings. Its contents reflect the extent, diversity and richness of research areas in the field, both fundamental and applied.

"

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.

Complex Nonlinearity: Chaos, Phase Transitions, Topology Change and Path Integrals is a book about prediction & control of general nonlinear and chaotic dynamics of high-dimensional complex systems of various physical and non-physical nature and their underpinning geometro-topological change.

The book starts with a textbook-like expose on nonlinear dynamics, attractors and chaos, both temporal and spatio-temporal, including modern techniques of chaos-control. Chapter 2 turns to the edge of chaos, in the form of phase transitions (equilibrium and non-equilibrium, oscillatory, fractal and noise-induced), as well as the related field of synergetics. While the natural stage for linear dynamics comprises of flat, Euclidean geometry (with the corresponding calculation tools from linear algebra and analysis), the natural stage for nonlinear dynamics is curved, Riemannian geometry (with the corresponding tools from nonlinear, tensor algebra and analysis). The extreme nonlinearity - chaos - corresponds to the topology change of this curved geometrical stage, usually called configuration manifold. Chapter 3 elaborates on geometry and topology change in relation with complex nonlinearity and chaos. Chapter 4 develops general nonlinear dynamics, continuous and discrete, deterministic and stochastic, in the unique form of path integrals and their action-amplitude formalism. This most natural framework for representing both phase transitions and topology change starts with Feynman's sum over histories, to be quickly generalized into the sum over geometries and topologies. The last Chapter puts all the previously developed techniques together and presents the unified form of complex nonlinearity. Here we have chaos, phase transitions, geometrical dynamics and topology change, all working together in the form of path integrals.

The objective of this book is to provide a serious reader with a serious scientific tool that will enable them to actually perform a competitive research in modern complex nonlinearity. It includes a comprehensive bibliography on the subject and a detailed index. Target readership includes all researchers and students of complex nonlinear systems (in physics, mathematics, engineering, chemistry, biology, psychology, sociology, economics, medicine, etc.), working both in industry/clinics and academia.

From the basics of thermodynamics to solutions for modern dynamical problems —the complete beginner's guide to statistical mechanics.

Unlike most books on statistical mechanics, this one is written for advanced students in chemistry, chemical engineering, biophysics, and related fields. It targets readers with no prior exposure to statistical mechanics and provides a complete introduction to all the important principles, concepts, and equations, while maintaining a level of mathematical sophistication that most advanced chemistry students will find manageable. The emphasis is on finding solutions to common problems in chemistry. Topics covered include:

• The Maxwell-Boltzmann velocity distribution for molecules in a gas, partition functions, and calculation of thermodynamic properties
• Ensembles (including the grand canonical ensemble), independent particles, and thermodynamic properties of atoms and molecules
• Practical introductions to quantum statistical mechanics and classical statistical mechanics
• Applications to electrons in metals and semiconductors; bosons and fermions; imperfect gases; transport properties; dipole moments in electric and magnetic fields; and distribution functions and correlation functions in fluids
• Time-dependent techniques for handling both simple and modern dynamical problems —the Liouville equation, time-correlation functions, and the Langevin equation.

Clearly written, and with a minimum of theory, Statistical Mechanics for Chemists takes you step by step through mathematical manipulations and explains the physical and chemical bases for each procedure. It is a valuable resource for advanced students in chemistry, chemical engineering, biophysics, and related fields.

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 text provides an overview of important theory, principles, and concepts in the field of thermodynamics, making this abstract and complex subject easy to comprehend while building practical skills in the process. It enhances understanding of heat transfer, steam tables, energy concepts, power generation, psychrometry, refrigeration cycles, and more. Practical, easily accessible case studies illustrate various thermodynamics principles. Each chapter concludes with a list of questions or problems, with answers at the back of the book.

In this new textbook, a number of unusual applications are discussed in addition to the usual topics covered in a course on Statistical Physics. Examples are: statistical mechanics of powders, Peierls instability, graphene, Bose-Einstein condensates in a trap, Casimir effect and the quantum Hall effect. Superfluidity and super-conductivity (including the physics of high-temperature superconductors) have also been discussed extensively.The emphasis on the treatment of these topics is pedagogic, introducing the basic tenets of statistical mechanics, with extensive and thorough discussion of the postulates, ensembles, and the relevant statistics. Many standard examples illustrate the microcanonical, canonical and grand canonical ensembles, as well as the Bose-Einstein and Fermi-Dirac statistics.A special feature of this text is the detailed presentation of the theory of second-order phase transitions and the renormalization group, emphasizing the role of disorder. Non-equilibrium statistical physics is introduced via the Boltzmann transport equation. Additional topics covered here include metastability, glassy systems, the Langevin equation, Brownian motion, and the Fokker-Planck equation.Graduate students will find the presentation readily accessible, since the topics have been treated with great deal of care and attention to detail.

This book offers a didactic and a self-contained treatment of the physics of liquid and flowing matter with a statistical mechanics approach. Experimental and theoretical methods that were developed to study fluids are now frequently applied to a number of more complex systems generically referred to as soft matter. As for simple liquids, also for complex fluids it is important to understand how their macroscopic behavior is determined by the interactions between the component units. Moreover, in recent years new and relevant insights have emerged from the study of anomalous phases and metastable states of matter. In addition to the traditional topics concerning fluids in normal conditions, the authors of this book discuss recent developments in the field of disordered systems in condensed and soft matter. In particular they emphasize computer simulation techniques that are used in the study of soft matter and the theories and study of slow glassy dynamics. For these reasons the book includes a specific chapter about metastability, supercooled liquids and glass transition. The book is written for graduate students and active researchers in the field.

This monograph is a comprehensive and cohesive exposition of power-law statistics. Following a bottom-up construction from a foundational bedrock - the power Poisson process - this monograph presents a unified study of an assortment of power-law statistics including: Pareto laws, Zipf laws, Weibull and Frechet laws, power Lorenz curves, Levy laws, power Newcomb-Benford laws, sub-diffusion and super-diffusion, and 1/f and flicker noises. The bedrock power Poisson process, as well as the assortment of power-law statistics, are investigated via diverse perspectives: structural, stochastic, fractal, dynamical, and socioeconomic. This monograph is poised to serve researchers and practitioners - from various fields of science and engineering - that are engaged in analyses of power-law statistics.

This book presents sensemaking strategies to support security planning and design. Threats to security are becoming complex and multifaceted and increasingly challenging traditional notions of security. The security landscape is characterized as 'messes' and 'wicked problems' that proliferate in this age of complexity. Designing security solutions in the face of interconnectedness, volatility and uncertainty, we run the risk of providing the right answer to the wrong problem thereby resulting in unintended consequences. Sensemaking is the activity that enables us to turn the ongoing complexity of the world into a "situation that is comprehended explicitly in words and that serves as a springboard into action" (Weick, Sutcliffe, Obstfeld, 2005). It is about creating an emerging picture of our world through data collection, analysis, action, and reflection. The importance of sensemaking to security is that it enables us to plan, design and act when the world as we knew it seems to have shifted. Leveraging the relevant theoretical grounding and thought leadership in sensemaking, key examples are provided, thereby illustrating how sensemaking strategies can support security planning and design. This is a critical analytical and leadership requirement in this age of volatility, uncertainty, complexity and ambiguity that characterizes the security landscape. This book is useful for academics, graduate students in global security, and government and security planning practitioners.

This book describes fundamental physical principles, together with their mathematical formulations, for modelling the propagation of signals in nerve fibres. Above all, it focuses on the complex electro-mechano-thermal process that produces an ensemble of waves composed of several components, besides the action potential. These components include mechanical waves in the biomembrane and axoplasm, together with the temperature change. Pursuing a step-by-step approach, the content moves from physics and mathematics, to describing the physiological effects, and finally to modelling the coupling effects. The assumptions and hypotheses used for modelling, as well as selected helpful concepts from continuum mechanics, are systematically explained, and the modelling is illustrated using the outcomes of numerical simulation. The book is chiefly intended for researchers and graduate students, providing them with a detailed description of how to model the complex physiological processes in nerve fibres.

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.

This text presents an intuitive and robust mathematical image of fundamental particle physics based on a novel approach to quantum field theory, which is guided by four carefully motivated metaphysical postulates. In particular, the book explores a dissipative approach to quantum field theory, which is illustrated for scalar field theory and quantum electrodynamics, and proposes an attractive explanation of the Planck scale in quantum gravity. Offering a radically new perspective on this topic, the book focuses on the conceptual foundations of quantum field theory and ontological questions. It also suggests a new stochastic simulation technique in quantum field theory which is complementary to existing ones. Encouraging rigor in a field containing many mathematical subtleties and pitfalls this text is a helpful companion for students of physics and philosophers interested in quantum field theory, and it allows readers to gain an intuitive rather than a formal understanding.

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

The aim of this book is to provide the fundamentals of statistical physics and its application to condensed matter. The combination of statistical mechanics and quantum mechanics has provided an understanding of properties of matter leading to spectacular technological innovations and discoveries in condensed matter which have radically changed our daily life.The book gives the steps to follow to understand fundamental theories and to apply these to real materials.

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.

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.

This book presents the state of the art in social simulation as presented at the Social Simulation Conference 2019 in Mainz, Germany. It covers the developments in applications and methods of social simulation, addressing societal issues such as socio-ecological systems and policymaking. Methodological issues discussed include large-scale empirical calibration, model sharing and interdisciplinary research, as well as decision-making models, validation and the use of qualitative data in simulation modeling. Research areas covered include archaeology, cognitive science, economics, organization science and social simulation education. This book gives readers insight into the increasing use of social simulation in both its theoretical development and in practical applications such as policymaking whereby modeling and the behavior of complex systems is key. The book appeals to students, researchers and professionals in the various fields.

This book shows how neural networks are applied to computational mechanics. Part I presents the fundamentals of neural networks and other machine learning method in computational mechanics. Part II highlights the applications of neural networks to a variety of problems of computational mechanics. The final chapter gives perspectives to the applications of the deep learning to computational mechanics.

Based on courses given at the universities of Texas and California, this book treats an active field of research that touches upon the foundations of physics and chemistry. It presents, in as simple a manner as possible, the basic mechanisms that determine the dynamical evolution of both classical and quantum systems in sufficient generality to include quantum phenomena. The book begins with a discussion of Noether's theorem, integrability, KAM theory, and a definition of chaotic behavior; continues with a detailed discussion of area-preserving maps, integrable quantum systems, spectral properties, path integrals, and periodically driven systems; and concludes by showing how to apply the ideas to stochastic systems. The presentation is complete and self-contained; appendices provide much of the needed mathematical background, and there are extensive references to the current literature; while problems at the ends of chapters help students clarify their understanding. This new edition has an updated presentation throughout, and a new chapter on open quantum systems.