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.

This thesis presents the first comprehensive analysis of quantum cascade laser nonlinear dynamics and includes the first observation of a temporal chaotic behavior in quantum cascade lasers. It also provides the first analysis of optical instabilities in the mid-infrared range. Mid-infrared quantum cascade lasers are unipolar semiconductor lasers, which have become widely used in applications such as gas spectroscopy, free-space communications or optical countermeasures. Applying external perturbations such as optical feedback or optical injection leads to a strong modification of the quantum cascade laser properties. Optical feedback impacts the static properties of mid-infrared Fabry-Perot and distributed feedback quantum cascade lasers, inducing power increase; threshold reduction; modification of the optical spectrum, which can become either single- or multimode; and enhanced beam quality in broad-area transverse multimode lasers. It also leads to a different dynamical behavior, and a quantum cascade laser subject to optical feedback can oscillate periodically or even become chaotic. A quantum cascade laser under external control could therefore be a source with enhanced properties for the usual mid-infrared applications, but could also address new applications such as tunable photonic oscillators, extreme events generators, chaotic Light Detection and Ranging (LIDAR), chaos-based secured communications or unpredictable countermeasures.

This book presents a collection of invited research and review contributions on recent advances in (mainly) theoretical condensed matter physics, theoretical chemistry, and theoretical physics. The volume celebrates the 90th birthday of N.H. March (Emeritus Professor, Oxford University, UK), a prominent figure in all of these fields. Given the broad range of interests in the research activity of Professor March, who collaborated with a number of eminent scientists in physics and chemistry, the volume embraces quite diverse topics in physics and chemistry, at various dimensions and energy scales. One thread connecting all these topics is correlation in aggregated states of matter, ranging from nuclear physics to molecules, clusters, disordered condensed phases such as the liquid state, and solid state physics, and the various phase transitions, both structural and electronic, occurring therein. A final chapter leaps to an even larger scale of matter aggregation, namely the universe and gravitation. A further no less important common thread is methodological, with the application of theoretical physics and chemistry, particularly density functional theory and statistical field theory, to both nuclear and condensed matter.

An increasing complexity of models used to predict real-world systems leads to the need for algorithms to replace complex models with far simpler ones, while preserving the accuracy of the predictions. This two-volume handbook covers methods as well as applications. This first volume focuses on real-time control theory, data assimilation, real-time visualization, high-dimensional state spaces and interaction of different reduction techniques.

The thesis presents a tool to create rubble pile asteroid simulants for use in numerical impact experiments, and provides evidence that the asteroid disruption threshold and the resultant fragment size distribution are sensitive to the distribution of internal voids. This thesis represents an important step towards a deeper understanding of fragmentation processes in the asteroid belt, and provides a tool to infer the interior structure of rubble pile asteroids. Most small asteroids are 'rubble piles' - re-accumulated fragments of debris from earlier disruptive collisions. The study of fragmentation processes for rubble pile asteroids plays an essential part in understanding their collisional evolution. An important unanswered question is "what is the distribution of void space inside rubble pile asteroids?" As a result from this thesis, numerical impact experiments can now be used to link surface features to the internal structure and therefore help to answer this question. Applying this model to asteroid Steins, which was imaged from close range by the Rosetta spacecraft, a large hill-like structure is shown to be most likely primordial, while a catena of pits can be interpreted as evidence for the existence of fracturing of pre-existing internal voids.

Heat equation asymptotics of a generalized Ahlfors Laplacian on a manifold with boundary.- Recurrent versus diffusive quantum behavior for time-dependent Hamiltonians.- Perturbations of spectral measures for Feller operators.- A global approach to the location of quantum resonances.- On estimates for the eigen-values in some elliptic problems.- Quantum scattering with long-range magnetic fields.- Spectral invariance and submultiplicativity for Frechet algebras with applications to pseudo-differential operators and ?* -quantization.- Decroissance exponentielle des fonctions propres pour l'operateur de Kac: le cas de la dimension > 1.- Second order perturbations of divergence type operators with a spectral gap.- On the Weyl quantized relativistic Hamiltonian.- Spectral asymptotics for the family of commuting operators.- Pseudo differential operators with negative definite functions as symbol: Applications in probability theory and mathematical physics.- One-dimensional Schroedinger operators with high potential barriers.- General boundary value problems in regions with corners.- Some results for nonlinear equations in cylindrical domains.- Global representation of Langrangian distributions.- Stable asymptotics of the solution to the Dirichlet problem for elliptic equations of second order in domains with angular points or edges.- Maslov operator calculus and non-commutative analysis.- Relative time delay and trace formula for long range perturbations of Laplace operators.- Functional calculus and Fredholm criteria for boundary value problems on noncompact manifolds.- The variable discrete asymptotics of solutions of singular boundary value problems.- Schroedinger operators with arbitrary non-negative potentials.- Abel summability of the series of eigen- and associated functions of the integral and differential operators.- The relativistic oscillator.- On the ratio of odd and even spectral counting functions.- A trace class property of singularly perturbed generalized Schroedinger semi-groups.- Radiation conditions and scattering theory for N-particle Hamiltonians (main ideas of the approach).

This book provides an up-to-date description of the methods needed to face the existence of solutions to some nonlinear boundary value problems. All important and interesting aspects of the theory of periodic solutions of ordinary differential equations related to the physical and mathematical question of resonance are treated. The author has chosen as a model example the periodic problem for a second order scalar differential equation. In a paedagogical style the author takes the reader step by step from the basics to the most advanced existence results in the field.

This thesis describes the application of a Monte Carlo radiative transfer code to accretion disc winds in two types of systems spanning 9 orders of magnitude in mass and size. In both cases, the results provide important new insights. On small scales, the presence of disc winds in accreting white dwarf binary systems has long been inferred from the presence of ultraviolet absorption lines. Here, the thesis shows that the same winds can also produce optical emission lines and a recombination continuum. On large scales, the thesis constructs a simple model of disc winds in quasars that is capable of explaining both the observed absorption and emission signatures - a crucial advance that supports a disc-wind based unification scenario for quasars. Lastly, the thesis also includes a theoretical investigation into the equivalent width distribution of the emission lines in quasars, which reveals a major challenge to all unification scenarios.

This book is about computational methods based on operator splitting. It consists of twenty-three chapters written by recognized splitting method contributors and practitioners, and covers a vast spectrum of topics and application areas, including computational mechanics, computational physics, image processing, wireless communication, nonlinear optics, and finance. Therefore, the book presents very versatile aspects of splitting methods and their applications, motivating the cross-fertilization of ideas.

Never before was anticipation more relevant to the life and activity of humankind than it is today. "It is no overstatement to suggest that humanity's future will be shaped by its capacity to anticipate...." (Research Agenda for the 21st Century, National Science Foundation). The sciences and the humanities can no longer risk explaining away the complexity and interactivity that lie at the foundation of life and living. The perspective of the world that anticipation opens justifies the descriptor "the post-Cartesian Revolution." If anticipation is a valid research domain, what practical relevance can we await? Indeed, anticipation is more than just the latest catch-word in marketing the apps developed by the digital technology industry. Due to spectacular advances in the study of the living, anticipation can claim a legitimate place in current investigations and applications in the sciences and the humanities. Biology, genetics, medicine, as well as politics and cognitive, behavioral, and social sciences, provide rich evidence of anticipatory processes at work. Readers seeking a foundation for an ticipation will find in these pages recent outcomes pertinent to plant life, political anticipation, cognitive science, architecture, computation. The authors contributing to this volume frame experimental data in language that can be shared among experts from all fields of endeavor. The major characteristic is the inference from the richness of data to principles and practical consequences.

This book is the second volume of the proceedings of the joint conference X. International Symposium "Quantum Theory and Symmetries" (QTS-X) and XII. International Workshop "Lie Theory and Its Applications in Physics" (LT-XII), 19-25 June 2017, Varna, Bulgaria. The QTS series started around the core concept that symmetries underlie all descriptions of quantum systems. It has since evolved into a symposium on the frontiers of theoretical and mathematical physics. The LT series covers the whole field of Lie Theory in its widest sense together with its applications in many facets of physics. As an interface between mathematics and physics the workshop serves as a meeting place for mathematicians and theoretical and mathematical physicists. In the division of the material between the two volumes, the Editor has tried to select for the first and second volumes papers that are more oriented toward mathematics and physics, respectively. However, this division is relative since many papers could have been placed in either volume. The topics covered in this volume represent the most modern trends in the fields of the joint conferences: symmetries in string theories, conformal field theory, holography, gravity theories and cosmology, gauge theories, foundations of quantum theory, nonrelativistic and classical theories.

This thesis describes pioneering research on the extension of plasmonics schemes to the regime of high-intensity lasers. By presenting a rich and balanced mix of experimentation, theory and simulation, it provides a comprehensive overview of the emerging field of high field plasmonics, including open issues and perspectives for future research. Combining specially designed targets and innovative materials with ultrashort, high-contrast laser pulses, the author experimentally demonstrates the effects of plasmon excitation on electron and ion emission. Lastly, the work investigates possible further developments with the help of numerical simulations, revealing the potential of plasmonics effects in the relativistic regime for advances in laser-driven sources of radiation, and for the manipulation of extreme light at the sub-micron scale.

This book provides a comprehensive introduction to numerical modeling of size effects in metal plasticity. The main classes of strain gradient plasticity formulations are described and efficiently implemented in the context of the finite element method. A robust numerical framework is presented and employed to investigate the role of strain gradients on structural integrity assessment. The results obtained reveal the need of incorporating the influence on geometrically necessary dislocations in the modeling of various damage mechanisms. Large gradients of plastic strain increase dislocation density, promoting strain hardening and elevating crack tip stresses. This stress elevation is quantified under both infinitesimal and finite deformation theories, rationalizing the experimental observation of cleavage fracture in the presence of significant plastic flow. Gradient-enhanced modeling of crack growth resistance, hydrogen diffusion and environmentally assisted cracking highlighted the relevance of an appropriate characterization of the mechanical response at the small scales involved in crack tip deformation. Particularly promising predictions are attained in the field of hydrogen embrittlement. The research has been conducted at the Universities of Cambridge, Oviedo, Luxembourg, and the Technical University of Denmark, in a collaborative effort to understand, model and optimize the mechanical response of engineering materials.

The present volume contains the Proceedings of the International Conference on Spectral Theory and Mathematical Physics held in Santiago de Chile in November 2014. Main topics are: Ergodic Quantum Hamiltonians, Magnetic Schroedinger Operators, Quantum Field Theory, Quantum Integrable Systems, Scattering Theory, Semiclassical and Microlocal Analysis, Spectral Shift Function and Quantum Resonances. The book presents survey articles as well as original research papers on these topics. It will be of interest to researchers and graduate students in Mathematics and Mathematical Physics.

This workbook is designed to supplement optics textbooks and covers all the traditional topics of geometrical optics. Terms, equations, definitions, and concepts are discussed briefly and explained through a series of problems that are worked out in a step-by-step manner which simplifies the problem-solving process. Additional practice problems are provided at the end of each chapter. * - An indispensable tool when studying for the state and National Boards * - An ideal supplement to optics textbooks * - Covers the traditional topics of geometrical optics.

This monograph investigates the existence of higher order sliding mode in discrete-time systems and propounds a new concept of discrete-time higher order sliding mode. The authors propose a definition of discrete-time higher order sliding mode and a control law is designed by means of a concept for an uncertain linear-time invariant system, as well as the behavior of the closed-loop system is analyzed. Moreover, the book includes a thorough treatment of the probabilistic and non-deterministic case, i.e. stochastic discrete-time higher order sliding mode. The target audience primarily comprises research experts in control theory but the book may also be beneficial for graduate students alike.

The book presents eight well-known and often used algorithms besides nine newly developed algorithms by the first author and his students in a practical implementation framework. Matlab codes and some benchmark structural optimization problems are provided. The aim is to provide an efficient context for experienced researchers or readers not familiar with theory, applications and computational developments of the considered metaheuristics. The information will also be of interest to readers interested in application of metaheuristics for hard optimization, comparing conceptually different metaheuristics and designing new metaheuristics.

This book sets out to give a rigorous mathematical description of the greenhouse effect through the theory of infrared atmospheric emission. In contrast to traditional climatological analysis, this approach eschews empirical relations in favour of a strict thermodynamical derivation, based on data from NASA and from the HITRAN spectroscopy database. The results highlight new aspects of the role of clouds in the greenhouse effect.

In this monograph, the authors develop a comprehensive approach for the mathematical analysis of a wide array of problems involving moving interfaces. It includes an in-depth study of abstract quasilinear parabolic evolution equations, elliptic and parabolic boundary value problems, transmission problems, one- and two-phase Stokes problems, and the equations of incompressible viscous one- and two-phase fluid flows. The theory of maximal regularity, an essential element, is also fully developed. The authors present a modern approach based on powerful tools in classical analysis, functional analysis, and vector-valued harmonic analysis. The theory is applied to problems in two-phase fluid dynamics and phase transitions, one-phase generalized Newtonian fluids, nematic liquid crystal flows, Maxwell-Stefan diffusion, and a variety of geometric evolution equations. The book also includes a discussion of the underlying physical and thermodynamic principles governing the equations of fluid flows and phase transitions, and an exposition of the geometry of moving hypersurfaces.

Soft computing is used where a complex problem is not adequately specified for the use of conventional math and computer techniques. Soft computing has numerous real-world applications in domestic, commercial and industrial situations. This book elaborates on the most recent applications in various fields of engineering.

This work uses techniques of optimization and operations research to develop the first comprehensive survey of the entire field of the optimization of resource, production, and distribution systems. Sten Thore proposes an "economic logistics" that is similar to the well-known concept of military logistics, but which is expanded to include such features as the optimal location of plants, inventories and retail outlets, and the management of hierarchical multi-echelon production, inventory, and distribution systems. The study of individual features of this supply process is familiar from operations research, but Thore joins these elements together into larger analytic structures encompassing the production and distribution system in an entire industry. Following an introductory chapter and a review of the saddle-point theory, coauthored with W. W. Cooper, Thore explores the three dimensions of the supply process synthesis: the spatial dimension (as in simple transportation systems), the vertical dimension (extending from resources to finished consumer goods, as in activity analysis), and the time dimension (as in inventory accumulation and investment). The combination of these then leads to models of such diverse subjects as regional warehouse systems, activity analysis and activity networks, multi-stage warehouse systems of intermediate goods, distribution networks, and spatial equilibrium. Each chapter contains its own exercises which are solved numerically and discussed in great detail, and illustrate such optimization techniques as linear and nonlinear programming, goal programming and goal focusing, chance-constrained programming, and infinite games. This work is designed for use ingraduate courses in economics and mathematics modeling, and will also be a useful addition to college and university library collections.

This book provides the mathematical foundations for Feynman's operator calculus and for the Feynman path integral formulation of quantum mechanics as a natural extension of analysis and functional analysis to the infinite-dimensional setting. In one application, the results are used to prove the last two remaining conjectures of Freeman Dyson for quantum electrodynamics. In another application, the results are used to unify methods and weaken domain requirements for non-autonomous evolution equations. Other applications include a general theory of Lebesgue measure on Banach spaces with a Schauder basis and a new approach to the structure theory of operators on uniformly convex Banach spaces. This book is intended for advanced graduate students and researchers.

This book focuses on the latest applications of nonlinear approaches in engineering and addresses a range of scientific problems. Examples focus on issues in automotive technology, including automotive dynamics, control for electric and hybrid vehicles, and autodriver algorithm for autonomous vehicles. Also included are discussions on renewable energy plants, data modeling, driver-aid methods, and low-frequency vibration. Chapters are based on invited contributions from world-class experts who advance the future of engineering by discussing the development of more optimal, accurate, efficient, cost, and energy effective systems. This book is appropriate for researchers, students, and practising engineers who are interested in the applications of nonlinear approaches to solving engineering and science problems. Presents a broad range of practical topics and approaches; Explains approaches to better, safer, and cheaper systems; Emphasises automotive applications, physical meaning, and methodologies.

This volume comprises the latest developments in both fundamental science and patient-specific applications, discussing topics such as: cellular mechanics; injury biomechanics; biomechanics of heart and vascular system; medical image analysis; and both patient-specific fluid dynamics and solid mechanics simulations. With contributions from researchers world-wide, the Computational Biomechanics for Medicine series of titles provides an opportunity for specialists in computational biomechanics to present their latest methodologies and advancements.