This book is the seventh volume of review chapters on advanced problems of phase transitions and critical phenomena, the former six volumes appeared in 2004, 2007, 2012, 2015, 2018, and 2020. The aim of the book is to provide reviews in those aspects of criticality and related subjects that are currently attracting much attention due to essential new contributions.The book consists of five chapters. They discuss criticality of complex systems, where the new, emergent properties appear via collective behaviour of simple elements as well as historical aspects of studies in the field of critical phenomena. Since all complex systems involve cooperative behaviour between many interconnected components, the field of phase transitions and critical phenomena provides a very natural conceptual and methodological framework for their study.As the first six volumes, this book is based on the review lectures that were given in Lviv (Ukraine) at the 'Ising lectures' - a traditional annual workshop on complex systems, phase transitions and critical phenomena which aims to bring together experts in these fields with university students and those who are interested in the subject.

The book focuses on the study of the temporal behavior of complex many-particle systems. The phenomenon of time and its role in the temporal evolution of complex systems is a remaining mystery. The book presents the necessity of the interdisciplinary point of view regarding on the phenomenon of time.The aim of the present study is to summarize and formulate in a concise but clear form the trends and approaches to the concept of time from a broad interdisciplinary perspective exposing tersely the complementary approaches and theories of time in the context of thermodynamics, statistical physics, cosmology, theory of information, biology and biophysics, including the problem of time and aging. Various approaches to the problem show that time is an extraordinarily interdisciplinary and multifaceted underlying notion which plays an extremely important role in various natural complex processes.

This book contains an extensive illustration of use of finite difference method in solving the boundary value problem numerically. A wide class of differential equations has been numerically solved in this book. Starting with differential equations of elementary functions like hyperbolic, sine and cosine, we have solved those of special functions like Hermite, Laguerre and Legendre. Those of Airy function, of stationary localised wavepacket, of the quantum mechanical problem of a particle in a 1D box, and the polar equation of motion under gravitational interaction have also been solved. Mathematica 6.0 has been used to solve the system of linear equations that we encountered and to plot the numerical data. Comparison with known analytic solutions showed nearly perfect agreement in every case. On reading this book, readers will become adept in using the method.

This short textbook covers roughly 13 weeks of lectures on advanced statistical mechanics at the graduate level. It starts with an elementary introduction to the theory of ensembles from classical mechanics, and then goes on to quantum statistical mechanics with density matrix. These topics are covered concisely and briefly. The advanced topics cover the mean-field theory for phase transitions, the Ising models and their exact solutions, and critical phenomena and their scaling theory. The mean-field theories are discussed thoroughly with several different perspectives - focusing on a single degree, or using Feynman-Jensen-Bogoliubov inequality, cavity method, or Landau theory. The renormalization group theory is mentioned only briefly. As examples of computational and numerical approach, there is a chapter on Monte Carlo method including the cluster algorithms. The second half of the book studies nonequilibrium statistical mechanics, which includes the Brownian motion, the Langevin and Fokker-Planck equations, Boltzmann equation, linear response theory, and the Jarzynski equality. The book ends with a brief discussion of irreversibility. The topics are supplemented by problem sets (with partial answers) and supplementary readings up to the current research, such as heat transport with a Fokker-Planck approach.

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.

Simulating for a crisis is far more than creating a simulation of a crisis situation. In order for a simulation to be useful during a crisis, it should be created within the space of a few days to allow decision makers to use it as quickly as possible. Furthermore, during a crisis the aim is not to optimize just one factor, but to balance various, interdependent aspects of life. In the COVID-19 crisis, decisions had to be made concerning e.g. whether to close schools and restaurants, and the (economic) consequences of a 3 or 4-week lock-down had to be considered. As such, rather than one simulation focusing on a very limited aspect, a framework allowing the simulation of several different scenarios focusing on different aspects of the crisis was required. Moreover, the results of the simulations needed to be easily understandable and explainable: if a simulation indicates that closing schools has no effect, this can only be used if the decision makers can explain why this is the case. This book describes how a simulation framework was created for the COVID-19 crisis, and demonstrates how it was used to simulate a wide range of scenarios that were relevant for decision makers at the time. It also discusses the usefulness of the approach, and explains the decisions that had to be made along the way as well as the trade-offs. Lastly, the book examines the lessons learned and the directions for the further development of social simulation frameworks to make them better suited to crisis situations, and to foster a more resilient society.

This book approaches economic problems from a systems thinking and feedback perspective. By introducing system dynamics methods (including qualitative and quantitative techniques) and computer simulation models, the respective contributions apply feedback analysis and dynamic simulation modeling to important local, national, and global economics issues and concerns. Topics covered include: an introduction to macro modeling using a system dynamics framework; a system dynamics translation of the Phillips machine; a re-examination of classical economic theories from a feedback perspective; analyses of important social, ecological, and resource issues; the development of a biophysical economics module for global modelling; contributions to monetary and financial economics; analyses of macroeconomic growth, income distribution and alternative theories of well-being; and a re-examination of scenario macro modeling. The contributions also examine the philosophical differences between the economics and system dynamics communities in an effort to bridge existing gaps and compare methods. Many models and other supporting information are provided as online supplementary files. Consequently, the book appeals to students and scholars in economics, as well as to practitioners and policy analysts interested in using systems thinking and system dynamics modeling to understand and improve economic systems around the world. "Clearly, there is much space for more collaboration between the advocates of post-Keynesian economics and system dynamics! More generally, I would like to recommend this book to all scholars and practitioners interested in exploring the interface and synergies between economics, system dynamics, and feedback thinking." Comments in the Foreword by Marc Lavoie, Emeritus Professor, University of Ottawa and University of Sorbonne Paris Nord

This book aims to gather the insight of leading experts on corruption and anti-corruption studies working at the scientific frontier of this phenomenon using the multidisciplinary tools of data and network science, in order to present current theoretical, empirical, and operational efforts being performed in order to curb this problem. The research results strengthen the importance of evidence-based approaches in the fight against corruption in all its forms, and foster the discussion about the best ways to convert the obtained knowledge into public policy. The contributed chapters provide comprehensive and multidisciplinary approaches to handle the non-trivial structural and dynamical aspects that characterize the modern social, economic, political and technological systems where corruption takes place. This book will serve a broad multi-disciplinary audience from natural to social scientists, applied mathematicians, including law and policymakers.

This book intends to introduce some recent results on passivity of complex dynamical networks with single weight and multiple weights. The book collects novel research ideas and some definitions in complex dynamical networks, such as passivity, output strict passivity, input strict passivity, finite-time passivity, and multiple weights. Furthermore, the research results previously published in many flagship journals are methodically edited and presented in a unified form. The book is likely to be of interest to university researchers and graduate students in Engineering and Mathematics who wish to study the passivity of complex dynamical networks.

This thesis focuses on experimental studies on collective motion using swimming bacteria as model active-matter systems. It offers comprehensive reviews of state-of-the-art theories and experiments on collective motion from the viewpoint of nonequilibrium statistical physics. The author presents his experimental studies on two major classes of collective motion that had been well studied theoretically. Firstly, swimming filamentous bacteria in a thin fluid layer are shown to exhibit true, long-range orientational order and anomalously strong giant density fluctuations, which are considered universal and landmark signatures of collective motion by many numerical and theoretical works but have never been observed in real systems. Secondly, chaotic bacterial turbulence in a three-dimensional dense suspension without any long-range order as described in the first half is demonstrated to be capable of achieving antiferromagnetic vortex order by imposing a small number of constraints with appropriate periodicity. The experimental results presented significantly advance our fundamental understanding of order and fluctuations in collective motion of motile elements and their future applications.

This book provides analytical and numerical methods for the estimation of dimension characteristics (Hausdorff, Fractal, Caratheodory dimensions) for attractors and invariant sets of dynamical systems and cocycles generated by smooth differential equations or maps in finite-dimensional Euclidean spaces or on manifolds. It also discusses stability investigations using estimates based on Lyapunov functions and adapted metrics. Moreover, it introduces various types of Lyapunov dimensions of dynamical systems with respect to an invariant set, based on local, global and uniform Lyapunov exponents, and derives analytical formulas for the Lyapunov dimension of the attractors of the Henon and Lorenz systems. Lastly, the book presents estimates of the topological entropy for general dynamical systems in metric spaces and estimates of the topological dimension for orbit closures of almost periodic solutions to differential equations.

This book is intended as reference material for students and professors interested in air pollution modeling at the graduate level as well as researchers and professionals involved in developing and utilizing air pollution models. Current developments in air pollution modeling are explored as a series of contributions from researchers at the forefront of their field. This newest contribution on air pollution modeling and its application is focused on local, urban, regional and intercontinental modeling; emission modeling and processing; data assimilation and air quality forecasting; model assessment and evaluation; aerosol transformation. Additionally, this work also examines the relationship between air quality and human health and the effects of climate change on air quality. This work is a collection of selected papers presented at the 37th International Technical Meeting on Air Pollution Modeling and its Application, held in Hamburg, Germany, September 23-27, 2019.

This book explores the role of exaptation in diverse areas of life, with examples ranging from biology to economics, social sciences and architecture. The concept of exaptation, introduced in evolutionary biology by Gould and Vrba in 1982, describes the possibility that already existing traits can be exploited for new purposes throughout the evolutionary process. Edited by three active scholars in the fields of biology, physics and economics, the book presents an interdisciplinary collection of expert viewpoints illustrating the importance of exaptation for interpreting current reality in various fields of investigation. Using the lenses of exaptation, the contributing authors show how to view the overall macroscopic landscape as comprising many disciplines, all working in unity within a single complex system. This book is the first to discuss exaptation in both hard and soft disciplines and highlights the role of this concept in understanding the birth of innovation by identifying key elements and ideas. It also offers a comprehensive guide to the emerging interdisciplinary field of exaptation, provides didactic explanations of the basic concepts, and avoids excessive jargon and heavy formalism. Its target audience includes graduate students in physics, biology, mathematics, economics, psychology and architecture; it will also appeal to established researchers in the humanities who wish to explore or enter this new science-driven interdisciplinary field.

Science often deals with hard-to-see phenomena, and they only stand out and become real when viewed through the lens of complex statistical tools. This book is not a textbook about statistics applied to science - there are already many excellent books to choose from - rather, it tries to give an overview of the basic principles that physical scientists use to analyze their data and bring out the order of Nature from the fog of background noise.

Integrable models have a fascinating history with many important discoveries that dates back to the famous Kepler problem of planetary motion. Nowadays it is well recognised that integrable systems play a ubiquitous role in many research areas ranging from quantum field theory, string theory, solvable models of statistical mechanics, black hole physics, quantum chaos and the AdS/CFT correspondence, to pure mathematics, such as representation theory, harmonic analysis, random matrix theory and complex geometry. Starting with the Liouville theorem and finite-dimensional integrable models, this book covers the basic concepts of integrability including elements of the modern geometric approach based on Poisson reduction, classical and quantum factorised scattering and various incarnations of the Bethe Ansatz. Applications of integrability methods are illustrated in vast detail on the concrete examples of the Calogero-Moser-Sutherland and Ruijsenaars-Schneider models, the Heisenberg spin chain and the one-dimensional Bose gas interacting via a delta-function potential. This book has intermediate and advanced topics with details to make them clearly comprehensible.

This book gathers contributions on a variety of flowing collective systems. While primarily focusing on pedestrian dynamics, they also reflect the latest developments in areas such as vehicular traffic and granular flows and address related emerging topics such as self-propelled particles, data transport, swarm behavior, intercellular transport, and collective dynamics of biological systems. Combining fundamental research and practical applications in the various fields discussed, the book offers a valuable asset for researchers and practitioners alike.

The aim of this book is to present Classical Thermodynamics in a unified way, from the most fundamental principles to non-uniform systems, thereby requiring the introduction of coarse graining methods, leading for instance to phase field methods. Solutions thermodynamics and temperature-concentration phase diagrams are covered, plus also a brief introduction to statistical thermodynamics and topological disorder. The Landau theory is included along with a general treatment of multicomponent instabilities in various types of thermodynamic applications, including phase separation and order-disorder transitions. Nucleation theory and spinodal decomposition are presented as extreme cases of a single approach involving the all-important role of fluctuations.In this way, it is hoped that this coverage will reconcile in a unified manner techniques generally presented separately in physics and materials texts.

In a comprehensive treatment of Statistical Mechanics from thermodynamics through the renormalization group, this book serves as the core text for a full-year graduate course in statistical mechanics at either the Masters or Ph.D. level. Each chapter contains numerous exercises, and several chapters treat special topics which can be used as the basis for student projects. The concept of scaling is introduced early and used extensively throughout the text. At the heart of the book is an extensive treatment of mean field theory, from the simplest decoupling approach, through the density matrix formalism, to self-consistent classical and quantum field theory as well as exact solutions on the Cayley tree. Proceeding beyond mean field theory, the book discusses exact mappings involving Potts models, percolation, self-avoiding walks and quenched randomness, connecting various athermal and thermal models. Computational methods such as series expansions and Monte Carlo simulations are discussed, along with exact solutions to the 1D quantum and 2D classical Ising models. The renormalization group formalism is developed, starting from real-space RG and proceeding through a detailed treatment of Wilson's epsilon expansion. Finally the subject of Kosterlitz-Thouless systems is introduced from a historical perspective and then treated by methods due to Anderson, Kosterlitz, Thouless and Young. Altogether, this comprehensive, up-to-date, and engaging text offers an ideal package for advanced undergraduate or graduate courses or for use in self study.

This book discusses non-equilibrium quantum many-body dynamics, recently explored in an analog quantum simulator of strongly correlated ultracold atoms. The first part presents a field-theoretical analysis of the experimental observability of the Higgs amplitude mode that emerges as a relativistic collective excitation near a quantum phase transition of superfluid Bose gases in an optical lattice potential. The author presents the dynamical susceptibilities to external driving of the microscopic parameters, taking into account a leading-order perturbative correction from quantum and thermal fluctuations and shows clear signatures of the Higgs mode in these observables. This is the first result that strongly supports the stability of the Higgs mode in three-dimensional optical lattices even in the presence of a spatially inhomogeneous confinement potential and paves the way for desktop observations of the Higgs mode. In the second part, the author applies the semi-classical truncated-Wigner approximation (TWA) to far-from-equilibrium quantum dynamics. Specifically, he considers the recent experiments on quantum-quench dynamics in a Bose-Hubbard quantum simulator. A direct comparison shows remarkable agreement between the numerical results from TWA and the experimental data. This result clearly indicates the potential of such a semi-classical approach in reliably simulating many-body systems using classical computers. The book also includes several chapters providing comprehensive reviews of the recent studies on cold-atomic quantum simulation and various theoretical methods, including the Schwinger-boson approach in strongly correlated systems and the phase-space semi-classical method for far-from-equilibrium quantum dynamics. These chapters are highly recommended to students and young researchers who are interested in semi-classical approaches in non-equilibrium quantum dynamics.

This volume shares and makes accessible new research lines and recent results in several branches of theoretical and mathematical physics, among them Quantum Optics, Coherent States, Integrable Systems, SUSY Quantum Mechanics, and Mathematical Methods in Physics. In addition to a selection of the contributions presented at the "6th International Workshop on New Challenges in Quantum Mechanics: Integrability and Supersymmetry", held in Valladolid, Spain, 27-30 June 2017, several high quality contributions from other authors are also included. The conference gathered 60 participants from many countries working in different fields of Theoretical Physics, and was dedicated to Prof. Veronique Hussin-an internationally recognized expert in many branches of Mathematical Physics who has been making remarkable contributions to this field since the 1980s. The reader will find interesting reviews on the main topics from internationally recognized experts in each field, as well as other original contributions, all of which deal with recent applications or discoveries in the aforementioned areas.

This book studies the fundamental aspects of many-body physics in quantum systems open to an external world. Recent remarkable developments in the observation and manipulation of quantum matter at the single-quantum level point to a new research area of open many-body systems, where interactions with an external observer and the environment play a major role. The first part of the book elucidates the influence of measurement backaction from an external observer, revealing new types of quantum critical phenomena and out-of-equilibrium dynamics beyond the conventional paradigm of closed systems. In turn, the second part develops a powerful theoretical approach to study the in- and out-of-equilibrium physics of an open quantum system strongly correlated with an external environment, where the entanglement between the system and the environment plays an essential role. The results obtained here offer essential theoretical results for understanding the many-body physics of quantum systems open to an external world, and can be applied to experimental systems in atomic, molecular and optical physics, quantum information science and condensed matter physics.

Since 1950, the Highway Capacity Manual has been a standard used in the planning, design, analysis, and operation of virtually any highway traffic facility in the United States. It has also been widely used around the globe and has inspired the development of similar manuals in other countries. This book is Volume II of a series on the conceptual and research origins of the methodologies found in the Highway Capacity Manual. It focuses on the most complex points in a traffic system: signalized and unsignalized intersections, and the concepts and methodologies developed over the years to model their operations. It also includes an overview of the fundamental concepts of capacity and level of service, particularly as applied to intersections. The historical roots of the manual and its contents are important to understanding current methodologies, and improving them in the future. As such, this book is a valuable resource for current and future users of the Highway Capacity Manual, as well as researchers and developers involved in advancing the state-of-the-art in the field.

This book explores recent developments in theoretical research and data analysis of real-world complex systems, organized in three parts, namely Entropy, information, and complexity functions Multistability, oscillations, and rhythmic synchronization Diffusions, rotation, and convection in fluids The collection of works devoted to the memory of Professor Valentin Afraimovich provides a deep insight into the recent developments in complexity science by introducing new concepts, methods, and applications in nonlinear dynamical systems covering physical problems and mathematical modelling relevant to economics, genetics, engineering vibrations, as well as classic problems in physics, fluid and climate dynamics, and urban dynamics. The book facilitates a better understanding of the mechanisms and phenomena in nonlinear dynamics and develops the corresponding mathematical theory to apply nonlinear design to practical engineering. It can be read by mathematicians, physicists, complex systems scientists, IT specialists, civil engineers, data scientists, and urban planners.

This book contains contributions presented at the 12th International Conference on Complex Networks (CompleNet), 24-26 May 2021. CompleNet is an international conference on complex networks that brings together researchers and practitioners from diverse disciplines-from sociology, biology, physics, and computer science-who share a passion to better understand the interdependencies within and across systems. CompleNet is a venue to discuss ideas and findings about all types networks, from biological, to technological, to informational and social. It is this interdisciplinary nature of complex networks that CompleNet aims to explore and celebrate.

This volume gathers selected contributions from the participants of the Banff International Research Station (BIRS) workshop Coupled Mathematical Models for Physical and Biological Nanoscale Systems and their Applications, who explore various aspects of the analysis, modeling and applications of nanoscale systems, with a particular focus on low dimensional nanostructures and coupled mathematical models for their description. Due to the vastness, novelty and complexity of the interfaces between mathematical modeling and nanoscience and nanotechnology, many important areas in these disciplines remain largely unexplored. In their efforts to move forward, multidisciplinary research communities have come to a clear understanding that, along with experimental techniques, mathematical modeling and analysis have become crucial to the study, development and application of systems at the nanoscale. The conference, held at BIRS in autumn 2016, brought together experts from three different communities working in fields where coupled mathematical models for nanoscale and biosystems are especially relevant: mathematicians, physicists (both theorists and experimentalists), and computational scientists, including those dealing with biological nanostructures. Its objectives: summarize the state-of-the-art; identify and prioritize critical problems of major importance that require solutions; analyze existing methodologies; and explore promising approaches to addressing the challenges identified. The contributions offer up-to-date introductions to a range of topics in nano and biosystems, identify important challenges, assess current methodologies and explore promising approaches. As such, this book will benefit researchers in applied mathematics, as well as physicists and biologists interested in coupled mathematical models and their analysis for physical and biological nanoscale systems that concern applications in biotechnology and medicine, quantum information processing and optoelectronics.