This book systematically introduces the nonlinear adiabatic evolution theory of quantum many-body systems. The nonlinearity stems from a mean-field treatment of the interactions between particles, and the adiabatic dynamics of the system can be accurately described by the nonlinear Schroedinger equation. The key points in this book include the adiabatic condition and adiabatic invariant for nonlinear system; the adiabatic nonlinear Berry phase; and the exotic virtual magnetic field, which gives the geometric meaning of the nonlinear Berry phase. From the quantum-classical correspondence, the linear and nonlinear comparison, and the single particle and interacting many-body difference perspectives, it shows a distinct picture of adiabatic evolution theory. It also demonstrates the applications of the nonlinear adiabatic evolution theory for various physical systems. Using simple models it illustrates the basic points of the theory, which are further employed for the solution of complex problems of quantum theory for many-particle systems. The results obtained are supplemented by numerical calculations, presented as tables and figures.

This book contains selected papers of NSC08, the 2nd Conference on Nonlinear Science and Complexity, held 28-31 July, 2008, Porto, Portugal. It focuses on fundamental theories and principles, analytical and symbolic approaches, computational techniques in nonlinear physics and mathematics. Topics treated include - Chaotic Dynamics and Transport in Classic and Quantum Systems - Complexity and Nonlinearity in Molecular Dynamics and Nano-Science - Complexity and Fractals in Nonlinear Biological Physics and Social Systems - Lie Group Analysis and Applications in Nonlinear Science - Nonlinear Hydrodynamics and Turbulence - Bifurcation and Stability in Nonlinear Dynamic Systems - Nonlinear Oscillations and Control with Applications - Celestial Physics and Deep Space Exploration - Nonlinear Mechanics and Nonlinear Structural Dynamics - Non-smooth Systems and Hybrid Systems - Fractional dynamical systems

"Fundamental Aspects of Plasma Chemical Physics: Transport "develops basic and advanced concepts of plasma transport to the modern treatment of the Chapman-Enskog method for the solution of the Boltzmann transport equation.

The book invites the reader to consider actual problems of the transport of thermal plasmas with particular attention to the derivation of diffusion- and viscosity-type transport cross sections, stressing the role of resonant charge-exchange processes in affecting the diffusion-type collision calculation of viscosity-type collision integrals.

A wide range of topics is then discussed including (1) the effect of non-equilibrium vibrational distributions on the transport of vibrational energy, (2) the role of electronically excited states in the transport properties of thermal plasmas, (3) the dependence of transport properties on the multitude of Saha equations for multi-temperature plasmas, and (4) the effect of the magnetic field on transport properties.

Throughout the book, worked examples are provided to clarify concepts and mathematical approaches.

This book is the second of a series of three published by the Bari group on fundamental aspects of plasma chemical physics. The first book, "Fundamental Aspects of Plasma Chemical Physics: Thermodynamics," is dedicated to plasma thermodynamics; and the third, "Fundamental Aspects of Plasma Chemical Physics: Kinetics," deals with plasma kinetics.

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 was inspired by the general observation that the great theories of modern physics are based on simple and transparent underlying mathematical structures - a fact not usually emphasized in standard physics textbooks - which makes it easy for mathematicians to understand their basic features. It is a textbook on quantum theory intended for advanced undergraduate or graduate students: mathematics students interested in modern physics, and physics students who are interested in the mathematical background of physics and are dissatisfied with the level of rigor in standard physics courses. More generally, it offers a valuable resource for all mathematicians interested in modern physics, and all physicists looking for a higher degree of mathematical precision with regard to the basic concepts in their field.

Product design is characterized by a steady increase in complexity. The main focus of this book is a structural approach on complexity management. This means, system structures are considered in order to address the challenge of complexity in all aspects of product design. Structures arise from the complex dependencies of system elements. Thus, the identification of system structures provides access to the understanding of system behavior in practical applications.

The book presents a methodology that enables the analysis, control and optimization of complex structures, and the applicability of domain-spanning problems. The methodology allows significant improvements on handling system complexity by creating improved system understanding on the one hand and optimizing product design that is robust for system adaptations on the other hand. Developers can thereby enhance project coordination and improve communication between team members and as a result shorten development time. The practical application of the methodology is described by means of two detailed examples.

These lecture notes are dedicated to the most recent theoretical applications of Black Hole solutions in high-energy physics. The main motivation of this volume is to present the latest black hole backgrounds that are relevant for gauge/gravity correspondence. Leading scientists in the field explain effective techniques for finding singular and cosmological solutions embedded in gauged supergravity, shedding light on underlying properties and symmetries. Starting from a basic level, the mathematical structures underlying black holes and cosmologies are revealed, helping the reader grasp the connection between theoretical approaches and physical observations with insights into possible future developments from both a theoretical and experimental point of view. The topics covered in this volume are based on lectures delivered during the "Theoretical Frontiers in Black Holes and Cosmology" school, held in Natal in June 2015.

Superstring theory is a promising theory which can potentially unify all the forces and the matters in particle physics. A new multi-dimensional object which is called "D-brane" was found. It drastically changed our perspective of a unified world. We may live on membrane-like hypersurfaces in higher dimensions ("braneworld scenario"), or we can create blackholes at particle accelarators, or the dynamics of quarks is shown to be equivalent to the higher dimensional gravity theory. All these scenarios are explained in this book with plain words but with little use of equations and with many figures. The book starts with a summary of long-standing problems in elementary particle physics and explains the D-branes and many applications of them. It ends with future roads for a unified ultimate theory of our world.

In July 2009, many experts in the mathematical modeling of biological sciences gathered in Les Houches for a 4-week summer school on the mechanics and physics of biological systems. The goal of the school was to present to students and researchers an integrated view of new trends and challenges in physical and mathematical aspects of biomechanics. While the scope for such a topic is very wide, they focused on problems where solid and fluid mechanics play a central role. The school covered both the general mathematical theory of mechanical biology in the context of continuum mechanics but also the specific modeling of particular systems in the biology of the cell, plants, microbes, and in physiology.
These lecture notes are organized (as was the school) around five different main topics all connected by the common theme of continuum modeling for biological systems: Bio-fluidics, Bio-gels, Bio-mechanics, Bio-membranes, and Morphogenesis. These notes are not meant as a journal review of the topic but rather as a gentle tutorial introduction to the readers who want to understand the basic problematic in modeling biological systems from a mechanics perspective.

Computational intelligence encompasses a wide variety of techniques that allow computation to learn, to adapt, and to seek. That is, they may be designed to learn information without explicit programming regarding the nature of the content to be retained, they may be imbued with the functionality to adapt to maintain their course within a complex and unpredictably changing environment, and they may help us seek out truths about our own dynamics and lives through their inclusion in complex system modeling. These capabilities place our ability to compute in a category apart from our ability to erect suspension bridges, although both are products of technological advancement and reflect an increased understanding of our world. In this book, we show how to unify aspects of learning and adaptation within the computational intelligence framework. While a number of algorithms exist that fall under the umbrella of computational intelligence, with new ones added every year, all of them focus on the capabilities of learning, adapting, and helping us seek. So, the term unified computational intelligence relates not to the individual algorithms but to the underlying goals driving them. This book focuses on the computational intelligence areas of neural networks and dynamic programming, showing how to unify aspects of these areas to create new, more powerful, computational intelligence architectures to apply to new problem domains.

This doctoral thesis focuses on the search for new phenomena in top-antitop quark (tt) final states with additional b-quark jets at the LHC. It uses the full Run 1 dataset collected by the ATLAS experiment in proton-proton collisions at s=8 TeV. The final state of interest consists of an isolated lepton, a neutrino and at least six jets with at least four b-tagged jets, a challenging experimental signature owing to the large background from tt+heavy-flavor production. This final state is characteristic of ttH production, with the Higgs boson decaying into bb, a process that allows direct probing of the top-Higgs Yukawa coupling. This signature is also present in many extensions of the Standard Model that have been proposed as solutions to the hierarchy problem, such as supersymmetry or composite Higgs models, which predict the pair production of bosonic or fermionic top quark partners, or the anomalous production of four-top-quark events. All these physics processes have been searched for using an ambitious search strategy that has been developed on the basis of a combination of state-of-art theoretical predictions and a sophisticated statistical analysis to constrain in-situ the large background uncertainties. As a result, the most restrictive bounds to date on the above physics processes have been obtained.

DNA replication is arguably the most crucial process at work in living cells. It is the mechanism by which organisms pass their genetic information from one generation to the next and life on Earth would be unthinkable without it. Despite the discovery of DNA structure in the 1950s, the mechanism of its replication remains rather elusive. This work makes important contributions to this line of research. In particular, it addresses two key questions in the area of DNA replication: which evolutionary forces drive the positioning of replication origins in the chromosome and how is the spatial organization of replication factories achieved inside the nucleus of a cell?. A cross-disciplinary approach uniting physics and biology is at the heart of this research. Along with experimental support, statistical physics theory produces optimal origin positions and provides a model for replication fork assembly in yeast. Advances made here can potentially further our understanding of disease mechanisms such as the abnormal replication in cancer.

This book highlights the latest findings on nonlinear dynamical systems including two types of attractors: self-excited and hidden attractors. Further, it presents both theoretical and practical approaches to investigating nonlinear dynamical systems with self-excited and hidden attractors. The book includes 20 chapters contributed by respected experts, which focus on various applications such as biological systems, memristor-based systems, fractional-order systems, finance systems, business cycles, oscillators, coupled systems, hyperchaotic systems, flexible robot manipulators, electronic circuits, and control models. Special attention is given to modeling, design, circuit realization, and practical applications to address recent research problems in nonlinear dynamical systems. The book provides a valuable reference guide to nonlinear dynamical systems for engineers, researchers, and graduate students, especially those whose work involves mechanics, electrical engineering, and control systems.

This hard bound spinoff from a special issue of the Journal of Elasticity (volume 100: 1-2) features an English translation of an important 1955 paper by Walter Noll, Die Herteitung der Grundgleichungen der Thermomechanik der Kontinua aus der statistischen Mechanik. In this paper, Noll addresses and analyses the seminal paper of Irving and Kirkwood, published five years earlier, on The Statistical Mechanical Theory of Transport Processes. IV, The Equations of Hydrodynamics. Noll gives new interpretations and provides a firm setting for ideas advanced by Irving & Kirkwood that clearly and directly relate to the basic principles of continuum mechanics. However, the original German paper of Noll seems not to have gained the attention that it deserved as the field of statistical mechanics grew both fundamentally and in applications. By providing an English translation of Noll s paper, Lehoucq & Von Lilienfeld-Toal have provided a great service to the scientific community. The Noll translation is presented here to expose fundamental ideas of statistical mechanics that are of major importance in the modeling of small-scale behavior and its link to macroscopic observations. In recent years there has been a rapidly increasing reliance upon and interest in multi scale methods in computation. This has accentuated the need to establish meaningful connections between atomistic and continuum descriptions of contact interactions such as stress and heat flux. In recognition of Noll s contribution, the translation is accompanied by four relevant and invited papers, including one, entitled Thoughts on the Concept of Stress, by Noll himself.

The project reported here was a search for new super symmetric particles in proton-proton collisions at the LHC. It has produced some of the world's best exclusion limits on such new particles. Furthermore, dedicated simulation studies and data analyses have also yielded essential input to the upgrade activities of the CMS collaboration, both for the Phase-1 pixel detector upgrade and for the R&D studies in pursuit of a Phase-2 end cap calorimeter upgrade.

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.

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.

Several of the very foundations of the cosmological standard model the baryon asymmetry of the universe, dark matter, and the origin of the hot big bang itself still call for an explanation from the perspective of fundamental physics. This workadvocates one intriguing possibility for a consistent cosmology that fills in the theoretical gaps while being fully in accordance with the observational data. At very high energies, the universe might have been in a false vacuum state that preserved B-L, the difference between the baryon number B and the lepton number L as a local symmetry. In this state, the universe experienced a stage of hybrid inflation that only ended when the false vacuum became unstable and decayed, in the course of a waterfall transition, into a phase with spontaneously broken B-L symmetry. This B-L Phase Transition was accompanied by tachyonic preheating that transferred almost the entire energy of the false vacuum into a gas of B-L Higgs bosons, which in turn decayed into heavy Majorana neutrinos. Eventually, these neutrinos decayed into massless radiation, thereby producing the entropy of the hot big bang, generating the baryon asymmetry of the universe via the leptogenesis mechanism and setting the stage for the production of dark matter. Next to a variety of conceptual novelties and phenomenological predictions, the main achievement of the thesis is hence the fascinating notion that the leading role in the first act of our universe might have actually been played by neutrinos.
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The purpose of the science of complexity is to provide, if not a unified approach, at least useful tools to tackling complex problems in various scientific domains. Generally, complexity is considered a fundamental challenge to the reductionist approach in science as a whole and to its ideas of certainty and randomness.

The overall behaviour of a complex system is different from and more than the sum of its parts. The behaviour of non-linear complex systems depends on the interaction (often with retroactive effects) among its constituent parts and not so much (or not only) on the characteristics of these parts themselves; the sum of the behaviour of single parts does not necessarily provide us with an explanation of the aggregate behaviour of a system.

All this is true for economic systems. These are based on the activities of single economic agents. Each individual can obtain only partial knowledge that is focussed around its "world" (local information) and react to external shocks in different ways (local rationality).

The aim of this book is to provide an overview to recent developments in theory and empirical research that view economic systems as complex phenomena whose aggregate dynamics can often not be inferred from its microscopic (microeconomic) building blocks. The collection of papers represented in this volume is dedicated to the memory of Massimo Salzano, who has been a fervent and eloquent advocate of the complexity approach.

The contributions have been presented at a conference held to celebrate Massimo's 60th birthday (Ecople -Economics: From Tradition of Complexity, Capri, 2-4 June, 2006), one year before he unexpectedly passed away in 2007.

This work addresses dynamical aspects of quantum criticality in two space dimensions. It probes two energy scales: the amplitude (Higgs) mode, which describes fluctuations of the order parameter amplitude in the broken symmetry phase and the dual vortex superfluid stiffness. The results demonstrate that the amplitude mode can be probed arbitrarily close to criticality in the universal line shape of the scalar susceptibility and the optical conductivity. The hallmark of quantum criticality is the emergence of softening energy scales near the phase transition. In addition, the author employs the charge-vortex duality to show that the capacitance of the Mott insulator near the superfluid to insulator phase transition serves as a probe for the dual vortex superfluid stiffness. The numerical methods employed are described in detail, in particular a worm algorithm for O(N) relativistic models and methods for numerical analytic continuation of quantum Monte Carlo data. The predictions obtained are particularly relevant to recent experiments in cold atomic systems and disordered superconductors.

This thesis provides an introduction to the physics of the Standard Model and beyond, and to the methods used to analyse Large Hadron Collider (LHC) data. The 'hierarchy problem', astrophysical data and experiments on neutrinos indicate that new physics can be expected at the now accessible TeV scale. This work investigates extensions of the Standard Model with gravitons and gravitinos (in the context of supergravity). The production of these particles in association with jets is studied as one of the most promising avenues for researching new physics at the LHC. Advanced simulation techniques and tools, such as algorithms allowing the computation of Feynman graphs and helicity amplitudes are first developed and then employed.

This text focuses on the algebraic formulation of quantum field theory, from the introductory aspects to the applications to concrete problems of physical interest. The book is divided in thematic chapters covering both introductory and more advanced topics. These include the algebraic, perturbative approach to interacting quantum field theories, algebraic quantum field theory on curved spacetimes (from its structural aspects to the applications in cosmology and to the role of quantum spacetimes), algebraic conformal field theory, the Kitaev's quantum double model from the point of view of local quantum physics and constructive aspects in relation to integrable models and deformation techniques. The book is addressed to master and graduate students both in mathematics and in physics, who are interested in learning the structural aspects and the applications of algebraic quantum field theory.

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.

Gaining a theoretical understanding of the properties of ultra-relativistic dense matter has been one of the most important and challenging goals in quantum chromodynamics (QCD). In this thesis, the author analyzes dense quark matter in QCD with gauge group SU(2) using low-energy effective theoretical techniques and elucidates a novel connection between statistical properties of the Dirac operator spectrum at high baryon chemical potential and a special class of random matrix theories. This work can be viewed as an extension of a similar correspondence between QCD and matrix models which was previously known only for infinitesimal chemical potentials. In future numerical simulations of dense matter the analytical results reported here are expected to serve as a useful tool to extract physical observables such as the BCS gap from numerical data on the Dirac spectrum.

This book describes significant tractable models used in solid mechanics - classical models used in modern mechanics as well as new ones. The models are selected to illustrate the main ideas which allow scientists to describe complicated effects in a simple manner and to clarify basic notations of solid mechanics. A model is considered to be tractable if it is based on clear physical assumptions which allow the selection of significant effects and relatively simple mathematical formulations. The first part of the book briefly reviews classical tractable models for a simple description of complex effects developed from the 18th to the 20th century and widely used in modern mechanics. The second part describes systematically the new tractable models used today for the treatment of increasingly complex mechanical objects - from systems with two degrees of freedom to three-dimensional continuous objects.