This book investigates the common nature of granular and active systems, which is rooted in their intrinsic out-of-equilibrium behavior, with the aim of finding minimal models able to reproduce and predict the complex collective behavior observed in experiments and simulations. Granular and active matter are among the most studied systems in out-of-equilibrium statistical physics. The book guides readers through the derivation of a fluctuating hydrodynamic description of granular and active matter by means of controlled and transparent mathematical assumptions made on a lattice model. It also shows how a macroscopic description can be provided from microscopic requirements, leading to the prediction of collective states such as cooling, swarming, clustering and the transitions among them. The analytical and numerical results shed new light on the physical connection between the local, microscopic properties of few particles and the macroscopic collective motion of the whole system.

Perturbative Algebraic Quantum Field Theory (pAQFT), the subject of this book, is a complete and mathematically rigorous treatment of perturbative quantum field theory (pQFT) that doesn't require the use of divergent quantities and works on a large class of Lorenzian manifolds. We discuss in detail the examples of scalar fields, gauge theories and the effective quantum gravity. pQFT models describe a wide range of physical phenomena and have remarkable agreement with experimental results. Despite this success, the theory suffers from many conceptual problems. pAQFT is a good candidate to solve many, if not all, of these conceptual problems. Chapters 1-3 provide some background in mathematics and physics. Chapter 4 concerns classical theory of the scalar field, which is subsequently quantized in chapters 5 and 6. Chapter 7 covers gauge theory and chapter 8 discusses effective quantum gravity. The book aims to be accessible to researchers and graduate students, who are interested in the mathematical foundations of pQFT.

This book is about dark matter's particle nature and the implications of a new symmetry that appears when a hypothetical dark matter particle is heavy compared to known elementary particles. Dark matter exists and composes about 85% of the matter in the universe, but it cannot be explained in terms of the known elementary particles. Discovering dark matter's particle nature is one of the most pressing open problems in particle physics. This thesis derives the implications of a new symmetry that appears when the hypothetical dark matter particle is heavy compared to the known elementary particles, a situation which is well motivated by the null results of searches at the LHC and elsewhere. The new symmetry predicts a universal interaction between dark matter and ordinary matter, which in turn may be used to determine the event rate and detectable energy in dark matter direct detection experiments. The computation of heavy wino and higgsino dark matter presented in this work has become a benchmark for the field of direct detection. This thesis has also spawned a new field of investigation in dark matter indirect detection, determining heavy WIMP annihilation rates using effective field theory methods. It describes a new formalism for implementing Lorentz invariance constraints in nonrelativistic theories, with a surprising result at 1/M^4 order that contradicts the prevailing ansatz in the past 20 years of heavy quark literature. The author has also derived new perturbative QCD results to provide the definitive analysis of key Standard Model observables such as heavy quark scalar matrix elements of the nucleon. This is an influential thesis, with impacts in dark matter phenomenology, field theory formalism and precision hadronic physics.

This book presents Markov and quantum processes as two sides of a coin called generated stochastic processes. It deals with quantum processes as reversible stochastic processes generated by one-step unitary operators, while Markov processes are irreversible stochastic processes generated by one-step stochastic operators. The characteristic feature of quantum processes are oscillations, interference, lots of stationary states in bounded systems and possible asymptotic stationary scattering states in open systems, while the characteristic feature of Markov processes are relaxations to a single stationary state. Quantum processes apply to systems where all variables, that control reversibility, are taken as relevant variables, while Markov processes emerge when some of those variables cannot be followed and are thus irrelevant for the dynamic description. Their absence renders the dynamic irreversible. A further aim is to demonstrate that almost any subdiscipline of theoretical physics can conceptually be put into the context of generated stochastic processes. Classical mechanics and classical field theory are deterministic processes which emerge when fluctuations in relevant variables are negligible. Quantum mechanics and quantum field theory consider genuine quantum processes. Equilibrium and non-equilibrium statistics apply to the regime where relaxing Markov processes emerge from quantum processes by omission of a large number of uncontrollable variables. Systems with many variables often self-organize in such a way that only a few slow variables can serve as relevant variables. Symmetries and topological classes are essential in identifying such relevant variables. The third aim of this book is to provide conceptually general methods of solutions which can serve as starting points to find relevant variables as to apply best-practice approximation methods. Such methods are available through generating functionals. The potential reader is a graduate student who has heard already a course in quantum theory and equilibrium statistical physics including the mathematics of spectral analysis (eigenvalues, eigenvectors, Fourier and Laplace transformation). The reader should be open for a unifying look on several topics.

The aim of this book is to give a physical treatment of the kinetic theory of gases and magnetoplasmas, covering the standard material in as simple a way as possible, using mean-free-path arguments when possible and identifying problem areas where received theory has either failed or has fallen short of expectations. Examples are provided by strong shock waves, ultrasonic waves (high Knudsen numbers), and transport across strong magnetic fields. Examples of problem areas provided by strong shock waves, ultrasonic waves (high Knudsen numbers), and transport across strong magnetic fields. One of the paradoxes arising in kinetic theory concerns the fluid pressure. Collisions are necessary for a fluid force to result, yet standard kinetic theory does not entail this, being satisfied to bypass Newton's equations by defining pressure as a momentum flux. This omission usually has no adverse consequences, but with increasing Knudsen number, it leads to errors. This text pays particular attention to pressure, explaining the importance of allowing for its collisional nature from the outset in developing kinetic theory.

The monograph compares two approaches that describe the statistical stability phenomenon - one proposed by the probability theory that ignores violations of statistical stability and another proposed by the theory of hyper-random phenomena that takes these violations into account. There are five parts. The first describes the phenomenon of statistical stability. The second outlines the mathematical foundations of probability theory. The third develops methods for detecting violations of statistical stability and presents the results of experimental research on actual processes of different physical nature that demonstrate the violations of statistical stability over broad observation intervals. The fourth part outlines the mathematical foundations of the theory of hyper-random phenomena. The fifth part discusses the problem of how to provide an adequate description of the world. The monograph should be interest to a wide readership: from university students on a first course majoring in physics, engineering, and mathematics to engineers, post-graduate students, and scientists carrying out research on the statistical laws of natural physical phenomena, developing and using statistical methods for high-precision measurement, prediction, and signal processing over broad observation intervals. To read the book, it is sufficient to be familiar with a standard first university course on mathematics.

This book provides an emerging computational intelligence tool in the framework of collective intelligence for modeling and controlling distributed multi-agent systems referred to as Probability Collectives. In the modified Probability Collectives methodology a number of constraint handling techniques are incorporated, which also reduces the computational complexity and improved the convergence and efficiency. Numerous examples and real world problems are used for illustration, which may also allow the reader to gain further insight into the associated concepts.

This book provides a series of concise lectures on the fundamental theories of statistical mechanics, carefully chosen examples and a number of problems with complete solutions.
Modern physics has opened the way for a thorough examination of infra-structure of nature and understanding of the properties of matter from an atomistic point of view. Statistical mechanics is an essential bridge between the laws of nature on a microscopic scale and the macroscopic behaviour of matter. A good training in statistical mechanics thus provides a basis for modern physics and is indispensable to any student in physics, chemistry, biophysics and engineering sciences who wishes to work in these rapidly developing scientific and technological fields.
The collection of examples and problems is comprehensive. The problems are grouped in order of increasing difficulty.

Topological surgery is a mathematical technique used for creating new manifolds out of known ones. In this book the authors observe that it also occurs in natural phenomena of all scales: 1-dimensional surgery happens during DNA recombination and when cosmic magnetic lines reconnect; 2-dimensional surgery happens during tornado formation and cell mitosis; and they conjecture that 3-dimensional surgery happens during the formation of black holes from cosmic strings, offering an explanation for the existence of a black hole's singularity. Inspired by such phenomena, the authors present a new topological model that extends the formal definition to a continuous process caused by local forces. Lastly, they describe an intrinsic connection between topological surgery and a chaotic dynamical system exhibiting a "hole drilling" behavior. The authors' model indicates where to look for the forces causing surgery and what deformations should be observed in the local submanifolds involved. These predictions are significant for the study of phenomena exhibiting surgery and they also open new research directions. This novel study enables readers to gain a better understanding of the topology and dynamics of various natural phenomena, as well as topological surgery itself and serves as a basis for many more insightful observations and new physical implications.

This monograph investigates violations of statistical stability of physical events, variables, and processes and develops a new physical-mathematical theory taking into consideration such violations - the theory of hyper-random phenomena. There are five parts. The first describes the phenomenon of statistical stability and its features, and develops methods for detecting violations of statistical stability, in particular when data is limited. The second part presents several examples of real processes of different physical nature and demonstrates the violation of statistical stability over broad observation intervals. The third part outlines the mathematical foundations of the theory of hyper-random phenomena, while the fourth develops the foundations of the mathematical analysis of divergent and many-valued functions. The fifth part contains theoretical and experimental studies of statistical laws where there is violation of statistical stability. The monograph should be of particular interest to engineers and scientists in general who study the phenomenon of statistical stability and use statistical methods for high-precision measurements, prediction, and signal processing over long observation intervals.

The study of network theory is a highly interdisciplinary field, which has emerged as a major topic of interest in various disciplines ranging from physics and mathematics, to biology and sociology. This book promotes the diverse nature of the study of complex networks by balancing the needs of students from very different backgrounds. It references the most commonly used concepts in network theory, provides examples of their applications in solving practical problems, and clear indications on how to analyse their results. In the first part of the book, students and researchers will discover the quantitative and analytical tools necessary to work with complex networks, including the most basic concepts in network and graph theory, linear and matrix algebra, as well as the physical concepts most frequently used for studying networks. They will also find instruction on some key skills such as how to proof analytic results and how to manipulate empirical network data. The bulk of the text is focused on instructing readers on the most useful tools for modern practitioners of network theory. These include degree distributions, random networks, network fragments, centrality measures, clusters and communities, communicability, and local and global properties of networks. The combination of theory, example and method that are presented in this text, should ready the student to conduct their own analysis of networks with confidence and allow teachers to select appropriate examples and problems to teach this subject in the classroom.

This thesis covers several important topics relevant to our understanding of quark-gluon plasma. It describes measurement of the third-order harmonic flow using two-particle correlations and isolation of flow and non-flow contributions to particle correlations in gold-gold collisions. The work also investigates long-range longitudinal correlations in small systems of deuteron-gold collisions. The former is related to the hydrodynamic transport properties of the quark-gluon plasma created in gold-gold collisions. The latter pertains to the question whether hydrodynamics is applicable to small systems, such as deuteron-gold collisions, and whether the quark-gluon plasma can be formed in those small-system collisions. The work presented in this thesis was conducted with the STAR experiment at the Relativistic Heavy Ion Collider at Brookhaven National Laboratory, where the center-of-mass energy of both collision systems was a factor of 100 larger than the rest mass of the colliding nuclei. The results contained in this thesis are highly relevant to our quest for deeper understanding of quantum chromodynamics. The results obtained challenge the interpretation of previous works from several other experiments on small systems, and provoke a fresh look at the physics of hydrodynamics and particle correlations pertinent to high energy nuclear collisions.

This book elaborates on the asymptotic behaviour, when N is large, of certain N-dimensional integrals which typically occur in random matrices, or in 1+1 dimensional quantum integrable models solvable by the quantum separation of variables. The introduction presents the underpinning motivations for this problem, a historical overview, and a summary of the strategy, which is applicable in greater generality. The core aims at proving an expansion up to o(1) for the logarithm of the partition function of the sinh-model. This is achieved by a combination of potential theory and large deviation theory so as to grasp the leading asymptotics described by an equilibrium measure, the Riemann-Hilbert approach to truncated Wiener-Hopf in order to analyse the equilibrium measure, the Schwinger-Dyson equations and the boostrap method to finally obtain an expansion of correlation functions and the one of the partition function. This book is addressed to researchers working in random matrices, statistical physics or integrable systems, or interested in recent developments of asymptotic analysis in those fields.

This thesis develops a nested sampling algorithm into a black box tool for directly calculating the partition function, and thus the complete phase diagram of a material, from the interatomic potential energy function. It represents a significant step forward in our ability to accurately describe the finite temperature properties of materials. In principle, the macroscopic phases of matter are related to the microscopic interactions of atoms by statistical mechanics and the partition function. In practice, direct calculation of the partition function has proved infeasible for realistic models of atomic interactions, even with modern atomistic simulation methods. The thesis also shows how the output of nested sampling calculations can be processed to calculate the complete PVT (pressure-volume-temperature) equation of state for a material, and applies the nested sampling algorithm to calculate the pressure-temperature phase diagrams of aluminium and a model binary alloy.

This book presents the first experiment revealing several unexplored non-equilibrium properties of quantum many-body states, and addresses the interplay between the Kondo effect and superconductivity by probing shot noise. In addition, it describes in detail nano-fabrication techniques for carbon nanotube quantum dots, and a measurement protocol and principle that probes both equilibrium and non-equilibrium quantum states of electrons. The book offers various reviews of topics in mesoscopic systems: shot noise measurement, carbon nanotube quantum dots, the Kondo effect in quantum dots, and quantum dots with superconducting leads, which are relevant to probing non-equilibrium physics. These reviews offer particularly valuable resources for readers interested in non-equilibrium physics in mesoscopic systems. Further, the cutting-edge experimental results presented will allow reader to catch up on a vital new trend in the field.

This thesis both broadens and deepens our understanding of the Brownian world. It addresses new problems in diffusion theory that have recently attracted considerable attention, both from the side of nanotechnology and from the viewpoint of pure academic research. The author focusses on the difussion of interacting particles in restricted geometries and under externally controlled forces. These geometries serve, for example, to model ion transport through narrow channels in cell membranes or a Brownian particle diffusing in an optical trap, now a paradigm for both theory and experiment. The work is exceptional in obtaining explicit analytically formulated answers to such realistic, experimentally relevant questions. At the same time, with its detailed exposition of the problems and a complete set of references, it presents a clear and broadly accessible introduction to the domain. Many of the problem settings and the corresponding exact asymptotic laws are completely new in diffusion theory.

This thesis describes the stand-alone discovery and measurement of the Higgs boson in its decays to two W bosons using the Run-I ATLAS dataset. This is the most precise measurement of gluon-fusion Higgs boson production and is among the most significant results attained at the LHC. The thesis provides an exceptionally clear exposition on a complicated analysis performed by a large team of researchers. Aspects of the analysis performed by the author are explained in detail; these include new methods for evaluating uncertainties on the jet binning used in the analysis and for estimating the background due to associated production of a W boson and an off-shell photon. The thesis also describes a measurement of the WW cross section, an essential background to Higgs boson production. The primary motivation of the LHC was to prove or disprove the existence of the Higgs boson. In 2012, CERN announced this discovery and the resultant ATLAS publication contained three decay channels: gg, ZZ, and WW.

In this book the dynamics of the non-ideal oscillatory system, in which the excitation is influenced by the response of the oscillator, is presented. Linear and nonlinear oscillators with one or more degrees of freedom interacting with one or more energy sources are treated. This concerns for example oscillating systems excited by a deformed elastic connection, systems excited by an unbalanced rotating mass, systems of parametrically excited oscillator and an energy source, frictionally self-excited oscillator and an energy source, energy harvesting system, portal frame - non-ideal source system, non-ideal rotor system, planar mechanism - non-ideal source interaction. For the systems the regular and irregular motions are tested. The effect of self-synchronization, chaos and methods for suppressing chaos in non-ideal systems are considered. In the book various types of motion control are suggested. The most important property of the non-ideal system connected with the jump-like transition from a resonant state to a non-resonant one is discussed. The so called 'Sommerfeld effect', resonant unstable state and jumping of the system into a new stable state of motion above the resonant region is explained. A mathematical model of the system is solved analytically and numerically. Approximate analytical solving procedures are developed. Besides, simulation of the motion of the non-ideal system is presented. The obtained results are compared with those for the ideal case. A significant difference is evident. The book aims to present the established results and to expand the literature in non-ideal vibrating systems. A further intention of the book is to give predictions of the effects for a system where the interaction between an oscillator and the energy source exist. The book is targeted at engineers and technicians dealing with the problem of source-machine system, but is also written for PhD students and researchers interested in non-linear and non-ideal problems.

This thesis discusses the random Euclidean bipartite matching problem, i.e., the matching problem between two different sets of points randomly generated on the Euclidean domain. The presence of both randomness and Euclidean constraints makes the study of the average properties of the solution highly relevant. The thesis reviews a number of known results about both matching problems and Euclidean matching problems. It then goes on to provide a complete and general solution for the one dimensional problem in the case of convex cost functionals and, moreover, discusses a potential approach to the average optimal matching cost and its finite size corrections in the quadratic case. The correlation functions of the optimal matching map in the thermodynamical limit are also analyzed. Lastly, using a functional approach, the thesis puts forward a general recipe for the computation of the correlation function of the optimal matching in any dimension and in a generic domain.

Microcontinuum Field Theories constitutes an extension of classical field theories - of elastic solids, viscous fluids, electromagnetism, and the like - to microscopic length and time scales. Material bodies are viewed as collections of a large number of deformable particles (sub-continua), suitable for modeling blood, porous media, polymers, liquid crystals, slurries, and composite materials. This volume extends and applies the ideas developed in the first volume, Microcontinuum Field Theories: Foundations and Solids, to liquid crystals, biological fluids, and other microstretch and micomorphic fluids. The theory makes it possible to discuss properties of such materials that are beyond the scope of classical field theories and may provide a basis for the resolution of some outstanding problems, such as turbulence.

Various experimental techniques have been advanced in recent years to measure non-equilibrium energy transformations on themicroscopic scale of single molecules. In general, the systems studied inthe correspondingexperiments are exposed to strong thermal fluctuations and thus the relevant energetic variables such as work and heat become stochastic.

This thesis addresses challenging theoretical problems in this active field of current research: 1) Exact analytical solutions of work and heat distributions for isothermal non-equilibrium processes in suitable models are obtained; 2) Corresponding solutions for cyclic processes involving two different heat reservoirs are found; 3) Optimization of periodic driving protocols for such cyclic processes with respect to maximal output power, efficiency and minimal power fluctuations is studied.

The exact solutions for work and heat distributionsprovide areference for theoretical investigations of more complicated models, giving insight into the structure of the tail of work distributions andserving asvaluable test cases for simulations of the underlying stochastic processes."

Focused on recent advances, this book covers theoretical foundations as well as various applications. It presents modern mathematical modeling approaches to the qualitative and numerical analysis of solutions for complex engineering problems in physics, mechanics, biochemistry, geophysics, biology and climatology. Contributions by an international team of respected authors bridge the gap between abstract mathematical approaches, such as applied methods of modern analysis, algebra, fundamental and computational mechanics, nonautonomous and stochastic dynamical systems on the one hand, and practical applications in nonlinear mechanics, optimization, decision making theory and control theory on the other. As such, the book will be of interest to mathematicians and engineers working at the interface of these fields.

The book offers a snapshot of the theories and applications of soft computing in the area of complex systems modeling and control. It presents the most important findings discussed during the 5th International Conference on Modelling, Identification and Control, held in Cairo, from August 31-September 2, 2013. The book consists of twenty-nine selected contributions, which have been thoroughly reviewed and extended before their inclusion in the volume. The different chapters, written by active researchers in the field, report on both current theories and important applications of soft-computing. Besides providing the readers with soft-computing fundamentals, and soft-computing based inductive methodologies/algorithms, the book also discusses key industrial soft-computing applications, as well as multidisciplinary solutions developed for a variety of purposes, like windup control, waste management, security issues, biomedical applications and many others. It is a perfect reference guide for graduate students, researchers and practitioners in the area of soft computing, systems modeling and control.

This monograph, suitable for use as an advanced text, presents the statistical mechanics of solids from the perspective of the material properties of the solid state.

These proceedings comprise invited and contributed papers presented at PLMMP-2014, addressing modern problems in the fields of liquids, solutions and confined systems, critical phenomena, as well as colloidal and biological systems. The book focuses on state-of-the-art developments in contemporary physics of liquid matter. The papers presented here are organized into four parts: (i) structure of liquids in confined systems, (ii) phase transitions, supercritical liquids and glasses, (iii) colloids, and (iv) medical and biological aspects and cover the most recent developments in the broader field of liquid state including interdisciplinary problems.