As the sequel to the proceedings of the International Conference of Continuum Mechanics Focusing on Singularities (CoMFoS15), the proceedings of CoMFoS16 present further advances and new topics in mathematical theory and numerical simulations related to various aspects of continuum mechanics. These include fracture mechanics, shape optimization, modeling of earthquakes, material structure, interface dynamics and complex systems.. The authors are leading researchers with a profound knowledge of mathematical analysis from the fields of applied mathematics, physics, seismology, engineering, and industry. The book helps readers to understand how mathematical theory can be applied to various industrial problems, and conversely, how industrial problems lead to new mathematical challenges.

This multi-contributed volume provides a practical, applications-focused introduction to nonlinear acoustical techniques for nondestructive evaluation. Compared to linear techniques, nonlinear acoustical/ultrasonic techniques are much more sensitive to micro-cracks and other types of small distributed damages. Most materials and structures exhibit nonlinear behavior due to the formation of dislocation and micro-cracks from fatigue or other types of repetitive loadings well before detectable macro-cracks are formed. Nondestructive evaluation (NDE) tools that have been developed based on nonlinear acoustical techniques are capable of providing early warnings about the possibility of structural failure before detectable macro-cracks are formed. This book presents the full range of nonlinear acoustical techniques used today for NDE. The expert chapters cover both theoretical and experimental aspects, but always with an eye towards applications. Unlike other titles currently available, which treat nonlinearity as a physics problem and focus on different analytical derivations, the present volume emphasizes NDE applications over detailed analytical derivations. The introductory chapter presents the fundamentals in a manner accessible to anyone with an undergraduate degree in Engineering or Physics and equips the reader with all of the necessary background to understand the remaining chapters. This self-contained volume will be a valuable reference to graduate students through practising researchers in Engineering, Materials Science, and Physics. Represents the first book on nonlinear acoustical techniques for NDE applications Emphasizes applications of nonlinear acoustical techniques Presents the fundamental physics and mathematics behind nonlinear acoustical phenomenon in a simple, easily understood manner Covers a variety of popular NDE techniques based on nonlinear acoustics in a single volume

This thesis presents a pioneering method for gleaning the maximum information from the deepest images of the far-infrared universe obtained with the Herschel satellite, reaching galaxies fainter by an order of magnitude than in previous studies. Using these high-quality measurements, the author first demonstrates that the vast majority of galaxy star formation did not take place in merger-driven starbursts over 90% of the history of the universe, which suggests that galaxy growth is instead dominated by a steady infall of matter. The author further demonstrates that massive galaxies suffer a gradual decline in their star formation activity, providing an alternative path for galaxies to stop star formation. One of the key unsolved questions in astrophysics is how galaxies acquired their mass in the course of cosmic time. In the standard theory, the merging of galaxies plays a major role in forming new stars. Then, old galaxies abruptly stop forming stars through an unknown process. Investigating this theory requires an unbiased measure of the star formation intensity of galaxies, which has been unavailable due to the dust obscuration of stellar light.

Modeling Uncertainty: An Examination of Stochastic Theory, Methods, and Applications, is a volume undertaken by the friends and colleagues of Sid Yakowitz in his honor. Fifty internionally known scholars have collectively contributed 30 papers on modeling uncertainty to this volume. Each of these papers was carefully reviewed and in the majority of cases the original submission was revised before being accepted for publication in the book. The papers cover a great variety of topics in probability, statistics, economics, stochastic optimization, control theory, regression analysis, simulation, stochastic programming, Markov decision process, application in the HIV context, and others. There are papers with a theoretical emphasis and others that focus on applications. A number of papers survey the work in a particular area and in a few papers the authors present their personal view of a topic. It is a book with a considerable number of expository articles, which are accessible to a nonexpert - a graduate student in mathematics, statistics, engineering, and economics departments, or just anyone with some mathematical background who is interested in a preliminary exposition of a particular topic. Many of the papers present the state of the art of a specific area or represent original contributions which advance the present state of knowledge. In sum, it is a book of considerable interest to a broad range of academic researchers and students of stochastic systems.

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 proposes a reliable and repeatable method for implementing Spoof Surface Plasmon (SSP) modes in the design of various circuit components. It also presents the first equivalent circuit model for plasmonic structures, which serves as an insightful guide to designing SSP-based circuits. Today, electronic circuits and systems are developing rapidly and becoming an indispensable part of our daily life; however the issue of compactness in integrated circuits remains a formidable challenge. Recently, the Spoof Surface Plasmon (SSP) modes have been proposed as a novel platform for highly compact electronic circuits. Despite extensive research efforts in this area, there is still an urgent need for a systematic design method for plasmonic circuits. In this thesis, different SSP-based transmission lines, antenna feeding networks and antennas are designed and experimentally evaluated. With their high field confinement, the SSPs do not suffer from the compactness limitations of traditional circuits and are capable of providing an alternative platform for the future generation of electronic circuits and electromagnetic systems.

This book is a collection of papers presented at the 23rd International Conference on Domain Decomposition Methods in Science and Engineering, held on Jeju Island, Korea on July 6-10, 2015. Domain decomposition methods solve boundary value problems by splitting them into smaller boundary value problems on subdomains and iterating to coordinate the solution between adjacent subdomains. Domain decomposition methods have considerable potential for a parallelization of the finite element methods, and serve a basis for distributed, parallel computations.

An Introduction to Wavelets is the first volume in a new series, WAVELET ANALYSIS AND ITS APPLICATIONS. This is an introductory treatise on wavelet analysis, with an emphasis on spline wavelets and time-frequency analysis. Among the basic topics covered in this book are time-frequency localization, integral wavelet transforms, dyadic wavelets, frames, spline-wavelets, orthonormal wavelet bases, and wavelet packets. In addition, the author presents a unified treatment of nonorthogonal, semiorthogonal, and orthogonal wavelets. This monograph is self-contained, the only prerequisite being a basic knowledge of function theory and real analysis. It is suitable as a textbook for a beginning course on wavelet analysis and is directed toward both mathematicians and engineers who wish to learn about the subject. Specialists may use this volume as a valuable supplementary reading to the vast literature that has already emerged in this field.
Key Features
* This is an introductory treatise on wavelet analysis, with an emphasis on spline-wavelets and time-frequency analysis
* This monograph is self-contained, the only prerequisite being a basic knowledge of function theory and real analysis
* Suitable as a textbook for a beginning course on wavelet analysis

This prizewinning PhD thesis presents a general discussion of the orbital motion close to solar system small bodies (SSSBs), which induce non-central asymmetric gravitational fields in their neighborhoods. It introduces the methods of qualitative theory in nonlinear dynamics to the study of local/global behaviors around SSSBs. Detailed mechanical models are employed throughout this dissertation, and specific numeric techniques are developed to compensate for the difficulties of directly analyzing. Applying this method, several target systems, like asteroid 216 Kleopatra, are explored in great detail, and the results prove to be both revealing and pervasive for a large group of SSSBs.

The book covers fundamentals of the theory of optimal methods for solving ill-posed problems, as well as ways to obtain accurate and accurate-by-order error estimates for these methods. The methods described in the current book are used to solve a number of inverse problems in mathematical physics. Contents Modulus of continuity of the inverse operator and methods for solving ill-posed problems Lavrent'ev methods for constructing approximate solutions of linear operator equations of the first kind Tikhonov regularization method Projection-regularization method Inverse heat exchange problems

This monograph describes advances in the theory of extremal problems in classes of functions defined by a majorizing modulus of continuity w. In particular, an extensive account is given of structural, limiting, and extremal properties of perfect w-splines generalizing standard polynomial perfect splines in the theory of Sobolev classes. In this context special attention is paid to the qualitative description of Chebyshev w-splines and w-polynomials associated with the Kolmogorov problem of n-widths and sharp additive inequalities between the norms of intermediate derivatives in functional classes with a bounding modulus of continuity. Since, as a rule, the techniques of the theory of Sobolev classes are inapplicable in such classes, novel geometrical methods are developed based on entirely new ideas. The book can be used profitably by pure or applied scientists looking for mathematical approaches to the solution of practical problems for which standard methods do not work. The scope of problems treated in the monograph, ranging from the maximization of integral functionals, characterization of the structure of equimeasurable functions, construction of Chebyshev splines through applications of fixed point theorems to the solution of integral equations related to the classical Euler equation, appeals to mathematicians specializing in approximation theory, functional and convex analysis, optimization, topology, and integral equations

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This book presents selected papers from the 3rd International Workshop on Computational Engineering held in Stuttgart from October 6 to 10, 2014, bringing together innovative contributions from related fields with computer science and mathematics as an important technical basis among others. The workshop discussed the state of the art and the further evolution of numerical techniques for simulation in engineering and science. We focus on current trends in numerical simulation in science and engineering, new requirements arising from rapidly increasing parallelism in computer architectures, and novel mathematical approaches. Accordingly, the chapters of the book particularly focus on parallel algorithms and performance optimization, coupled systems, and complex applications and optimization.

This book introduces readers to MesoBioNano (MBN) Explorer - a multi-purpose software package designed to model molecular systems at various levels of size and complexity. In addition, it presents a specially designed multi-task toolkit and interface - the MBN Studio - which enables the set-up of input files, controls the simulations, and supports the subsequent visualization and analysis of the results obtained. The book subsequently provides a systematic description of the capabilities of this universal and powerful software package within the framework of computational molecular science, and guides readers through its applications in numerous areas of research in bio- and chemical physics and material science - ranging from the nano- to the mesoscale. MBN Explorer is particularly suited to computing the system's energy, to optimizing molecular structure, and to exploring the various facets of molecular and random walk dynamics. The package allows the use of a broad variety of interatomic potentials and can, e.g., be configured to select any subset of a molecular system as rigid fragments, whenever a significant reduction in the number of dynamical degrees of freedom is required for computational practicalities. MBN Studio enables users to easily construct initial geometries for the molecular, liquid, crystalline, gaseous and hybrid systems that serve as input for the subsequent simulations of their physical and chemical properties using MBN Explorer. Despite its universality, the computational efficiency of MBN Explorer is comparable to that of other, more specialized software packages, making it a viable multi-purpose alternative for the computational modeling of complex molecular systems. A number of detailed case studies presented in the second part of this book demonstrate MBN Explorer's usefulness and efficiency in the fields of atomic clusters and nanoparticles, biomolecular systems, nanostructured materials, composite materials and hybrid systems, crystals, liquids and gases, as well as in providing modeling support for novel and emerging technologies. Last but not least, with the release of the 3rd edition of MBN Explorer in spring 2017, a free trial version will be available from the MBN Research Center website (mbnresearch.com).

This book presents a new approach to modeling carbon structures such as graphene and carbon nanotubes using finite element methods, and addresses the latest advances in numerical studies for these materials. Based on the available findings, the book develops an effective finite element approach for modeling the structure and the deformation of grapheme-based materials. Further, modeling processing for single-walled and multi-walled carbon nanotubes is demonstrated in detail.

Markov process theory is basically an extension of ordinary calculus to accommodate functions whos time evolutions are not entirely deterministic. It is a subject that is becoming increasingly important for many fields of science. This book develops the single-variable theory of both continuous and jump Markov processes in a way that should appeal especially to physicists and chemists at the senior and graduate level.
Key Features
* A self-contained, prgamatic exposition of the needed elements of random variable theory
* Logically integrated derviations of the Chapman-Kolmogorov equation, the Kramers-Moyal equations, the Fokker-Planck equations, the Langevin equation, the master equations, and the moment equations
* Detailed exposition of Monte Carlo simulation methods, with plots of many numerical examples
* Clear treatments of first passages, first exits, and stable state fluctuations and transitions
* Carefully drawn applications to Brownian motion, molecular diffusion, and chemical kinetics

This monograph presents an application of concepts and methods from algebraic topology to models of concurrent processes in computer science and their analysis. Taking well-known discrete models for concurrent processes in resource management as a point of departure, the book goes on to refine combinatorial and topological models. In the process, it develops tools and invariants for the new discipline directed algebraic topology, which is driven by fundamental research interests as well as by applications, primarily in the static analysis of concurrent programs. The state space of a concurrent program is described as a higher-dimensional space, the topology of which encodes the essential properties of the system. In order to analyse all possible executions in the state space, more than "just" the topological properties have to be considered: Execution paths need to respect a partial order given by the time flow. As a result, tools and concepts from topology have to be extended to take privileged directions into account. The target audience for this book consists of graduate students, researchers and practitioners in the field, mathematicians and computer scientists alike.

This book presents a methodology based on inverse problems for use in solutions for fault diagnosis in control systems, combining tools from mathematics, physics, computational and mathematical modeling, optimization and computational intelligence. This methodology, known as fault diagnosis - inverse problem methodology or FD-IPM, unifies the results of several years of work of the authors in the fields of fault detection and isolation (FDI), inverse problems and optimization. The book clearly and systematically presents the main ideas, concepts and results obtained in recent years. By formulating fault diagnosis as an inverse problem, and by solving it using metaheuristics, the authors offer researchers and students a fresh, interdisciplinary perspective for problem solving in these fields. Graduate courses in engineering, applied mathematics and computing also benefit from this work.

This book outlines a possible future theoretical perspective for systemics, its conceptual morphology and landscape while the Good-Old-Fashioned-Systemics (GOFS) era is still under way. The change from GOFS to future systemics can be represented, as shown in the book title, by the conceptual change from Collective Beings to Quasi-systems. With the current advancements, problems and approaches occurring in contemporary science, systemics are moving beyond the traditional frameworks used in the past. From Collective Beings to Coherent Quasi-Systems outlines a conceptual morphology and landscape for a new theoretical perspective for systemics introducing the concept of Quasi-systems. Advances in domains such as theoretical physics, philosophy of science, cell biology, neuroscience, experimental economics, network science and many others offer new concepts and technical tools to support the creation of a fully transdisciplinary General Theory of Change. This circumstance requires a deep reformulation of systemics, without forgetting the achievements of established conventions. The book is divided into two parts. Part I, examines classic systemic issues from new theoretical perspectives and approaches. A new general unified framework is introduced to help deal with topics such as dynamic structural coherence and Quasi-systems. This new theoretical framework is compared and contrasted with the traditional approaches. Part II focuses on the process of translation into social culture of the theoretical principles, models and approaches introduced in Part I. This translation is urgent in post-industrial societies where emergent processes and problems are still dealt with by using the classical or non-systemic knowledge of the industrial phase.

This volume offers a fundamentally different way of conceptualizing time and reality. Today, we see time predominantly as the linear-sequential order of events, and reality accordingly as consisting of facts that can be ordered along sequential time. But what if this conceptualization has us mistaking the "exhausts" for the "real thing", i.e. if we miss the best, the actual taking place of reality as it occurs in a very differently structured, primordial form of time, the time-space of the present? In this new conceptual framework, both the sequential aspect of time and the factual aspect of reality are emergent phenomena that come into being only after reality has actually taken place. In the new view, facts are just the "traces" that the actual taking place of reality leaves behind on the co-emergent "canvas'' of local spacetime. Local spacetime itself emerges only as facts come into being - and only facts can be adequately localized in it. But, how does reality then actually occur? It is conceived as a "constellatory self-unfolding", characterized by strong self-referentiality, and taking place in the primordial form of time, the not yet sequentially structured "time-space of the present". Time is seen here as an ontophainetic platform, i.e. as the stage on which reality can first occur. This view of time (and, thus, also space) seems to be very much in accordance with what we encounter in quantum physics before the so-called collapse of the wave function. In parallel, classical and relativistic physics largely operate within the factual portrait of reality, and the sequential aspect of time, respectively. Only singularities constitute an important exemption: here the canvas of local spacetime - that emerged together with factization - melts down again. In the novel framework quantum reduction and singularities can be seen and addressed as inverse transitions: In quantum physical state reduction reality "gains" the chrono-ontological format of facticity, and the sequential aspect of time becomes applicable. In singularities, by contrast, the inverse happens: Reality loses its local spacetime formation and reverts back into its primordial, pre-local shape - making in this way the use of causality relations, Boolean logic and the dichotomization of subject and object obsolete. For our understanding of the relation between quantum and relativistic physics this new view opens up fundamentally new perspectives: Both are legitimate views of time and reality, they just address very different chrono-ontological portraits, and thus should not lead us to erroneously subjugating one view under the other. The task of the book is to provide a formal framework in which this radically different view of time and reality can be addressed properly. The mathematical approach is based on the logical and topological features of the Borromean Rings. It draws upon concepts and methods of algebraic and geometric topology - especially the theory of sheaves and links, group theory, logic and information theory, in relation to the standard constructions employed in quantum mechanics and general relativity, shedding new light on the pestilential problems of their compatibility. The intended audience includes physicists, mathematicians and philosophers with an interest in the conceptual and mathematical foundations of modern physics.

This book explores the use of numerical relativity (NR) methods to solve cosmological problems, and describes one of the first uses of NR to study inflationary physics. NR consists in the solution of Einstein's Equation of general relativity, which governs the evolution of matter and energy on cosmological scales, and in systems where there are strong gravitational effects, such as around black holes. To date, NR has mainly been used for simulating binary black hole and neutron star mergers like those detected recently by LIGO. Its use as a tool in fundamental problems of gravity and cosmology is novel, but rapidly gaining interest. In this thesis, the author investigates the initial condition problem in early universe cosmology - whether an inflationary expansion period could have "got going" from initially inhomogeneous conditions - and identifies criteria for predicting the robustness of particular models. State-of-the-art numerical relativity tools are developed in order to address this question, which are now publicly available.

This book represents a collection of papers presented at the 2nd World Congress on Integrated Computational Materials Engineering (ICME), a specialty conference organized by The Minerals, Metals & Materials Society (TMS).

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.