During the last four decades there has been a remarkable development in optimization and optimal control. Due to its wide variety of applications, many scientists and researchers have paid attention to fields of optimization and optimal control. A huge number of new theoretical, algorithmic, and computational results have been observed in the last few years. This book gives the latest advances, and due to the rapid development of these fields, there are no other recent publications on the same topics.

Key features:

Provides a collection of selected contributions giving a state-of-the-art account of recent developments in the field

Covers a broad range of topics in optimization and optimal control, including unique applications

Includes chapters written by experts in their respective disciplines

Appeals to a broad audience of researchers, practitioners, and advanced graduate students in applied mathematics and engineering

This contributed volume is based on talks given at the August 2016 summer school "Fluids Under Pressure," held in Prague as part of the "Prague-Sum" series. Written by experts in their respective fields, chapters explore the complex role that pressure plays in physics, mathematical modeling, and fluid flow analysis. Specific topics covered include: Oceanic and atmospheric dynamics Incompressible flows Viscous compressible flows Well-posedness of the Navier-Stokes equations Weak solutions to the Navier-Stokes equations Fluids Under Pressure will be a valuable resource for graduate students and researchers studying fluid flow dynamics.

The book answers long-standing questions on scientific modeling and inference across multiple perspectives and disciplines, including logic, mathematics, physics and medicine. The different chapters cover a variety of issues, such as the role models play in scientific practice; the way science shapes our concept of models; ways of modeling the pursuit of scientific knowledge; the relationship between our concept of models and our concept of science. The book also discusses models and scientific explanations; models in the semantic view of theories; the applicability of mathematical models to the real world and their effectiveness; the links between models and inferences; and models as a means for acquiring new knowledge. It analyzes different examples of models in physics, biology, mathematics and engineering. Written for researchers and graduate students, it provides a cross-disciplinary reference guide to the notion and the use of models and inferences in science.

Chemical Modelling: Applications and Theory comprises critical literature reviews of all aspects of molecular modelling. Molecular modelling in this context refers to modelliing the structure, properties and reactions of atoms, molecules and materials. Each chapter provides a selective review of recent literature, incorporating sufficient historical perspective for the non-specialist to gain an understanding. With chemical modelling covering such a wide range of subjects, this Specialist Periodical Report serves as the first port of call to any chemist, biochemist, materials scientist or molecular physicist needing to acquaint themselves with major developments in the area.

Collecting together contributed lectures and mini-courses, this book details the research presented in a special semester titled "Geometric mechanics - variational and stochastic methods" run in the first half of 2015 at the Centre Interfacultaire Bernoulli (CIB) of the Ecole Polytechnique Federale de Lausanne. The aim of the semester was to develop a common language needed to handle the wide variety of problems and phenomena occurring in stochastic geometric mechanics. It gathered mathematicians and scientists from several different areas of mathematics (from analysis, probability, numerical analysis and statistics, to algebra, geometry, topology, representation theory, and dynamical systems theory) and also areas of mathematical physics, control theory, robotics, and the life sciences, with the aim of developing the new research area in a concentrated joint effort, both from the theoretical and applied points of view. The lectures were given by leading specialists in different areas of mathematics and its applications, building bridges among the various communities involved and working jointly on developing the envisaged new interdisciplinary subject of stochastic geometric mechanics.

Aerobic granular sludge technology will play an important role as an innovative technology alternative to the present activated sludge process in industrial and municipal wastewater treatment in the near future. Intended to fill the gaps in the studies of aerobic granular sludge, this thesis comprehensively investigates the formation, characterization and mathematical modeling of aerobic granular sludge, through integrating the process engineering tools and advanced molecular microbiology. The research results of this thesis contributed significantly to the advance of understanding and optimization of the bacterial granulation processes, the next generation of technology for cost-effective biological wastewater treatment. Dr. Bing-Jie Ni works at Advanced Water Management Centre (AWMC) of The University of Queensland, Australia.

A billiard is a dynamical system in which a point particle alternates between free motion and specular reflections fromthe boundaryof a domain."Exterior Billiards" presents billiards in the complement of domains and their applications in aerodynamics and geometrical optics.

This book distinguishes itself from existing literature by presenting billiard dynamics "outside" bounded domains, including scattering, resistance, invisibility and retro-reflection. It begins with an overview of the mathematical notations used throughout the book and a brief review of the main results. Chapters 2 and 3 are focused on problems of minimal resistance and Newton s problem in media with positive temperature. In chapters 4 and 5, scattering of billiards bynonconvex and rough domains is characterized and some related special problems of optimal mass transportation are studied. Applications in aerodynamics are addressed next and problems of invisibility and retro-reflection within the framework of geometric optics conclude the text.

The book will appeal to mathematicians working in dynamical systems and calculus of variations. Specialists working in the areas of applications discussed will also find it useful."

This book introduces a unique, packet-based co-design control framework for networked control systems. It begins by providing a comprehensive survey of state-of-the-art research on networked control systems, giving readers a general overview of the field. It then verifies the proposed control framework both theoretically and experimentally - the former using multiple control methodologies, and the latter using a unique online test rig for networked control systems. The framework investigates in detail the most common, communication constraints, including network-induced delays, data packet dropout, data packet disorders, and network access constraints, as well as multiple controller design and system analysis tools such as model predictive control, linear matrix inequalities and optimal control. This unique and complete co-design framework greatly benefits researchers, graduate students and engineers in the fields of control theory and engineering.

Since information in the brain is processed by the exchange of spikes among neurons, a study of such group dynamics is extremely important in understanding hippocampus dependent memory. These spike patterns and local field potentials (LFPs) have been analyzed by various statistical methods. These studies have led to important findings of memory information processing. For example, memory-trace replay, a reactivation of behaviorally induced neural patterns during subsequent sleep, has been suggested to play an important role in memory consolidation. It has also been suggested that a ripple/sharp wave event (one of the characteristics of LFPs in the hippocampus) and spiking activity in the cortex have a specific relationship that may facilitate the consolidation of hippocampal dependent memory from the hippocampus to the cortex. The book will provide a state-of-the-art finding of memory information processing through the analysis of multi-neuronal data. The first half of the book is devoted to this analysis aspect. Understanding memory information representation and its consolidation, however, cannot be achieved only by analyzing the data. It is extremely important to construct a computational model to seek an underlying mathematical principle. In other words, an entire picture of hippocampus dependent memory system would be elucidated through close collaboration among experiments, data analysis, and computational modeling. Not only does computational modeling benefit the data analysis of multi-electrode recordings, but it also provides useful insight for future experiments and analyses. The second half of the book will be devoted to the computational modeling of hippocampus-dependent memory.

This unique text/reference presents a fresh look at nonlinear processing through nonlinear eigenvalue analysis, highlighting how one-homogeneous convex functionals can induce nonlinear operators that can be analyzed within an eigenvalue framework. The text opens with an introduction to the mathematical background, together with a summary of classical variational algorithms for vision. This is followed by a focus on the foundations and applications of the new multi-scale representation based on non-linear eigenproblems. The book then concludes with a discussion of new numerical techniques for finding nonlinear eigenfunctions, and promising research directions beyond the convex case. Topics and features: introduces the classical Fourier transform and its associated operator and energy, and asks how these concepts can be generalized in the nonlinear case; reviews the basic mathematical notion, briefly outlining the use of variational and flow-based methods to solve image-processing and computer vision algorithms; describes the properties of the total variation (TV) functional, and how the concept of nonlinear eigenfunctions relate to convex functionals; provides a spectral framework for one-homogeneous functionals, and applies this framework for denoising, texture processing and image fusion; proposes novel ways to solve the nonlinear eigenvalue problem using special flows that converge to eigenfunctions; examines graph-based and nonlocal methods, for which a TV eigenvalue analysis gives rise to strong segmentation, clustering and classification algorithms; presents an approach to generalizing the nonlinear spectral concept beyond the convex case, based on pixel decay analysis; discusses relations to other branches of image processing, such as wavelets and dictionary based methods. This original work offers fascinating new insights into established signal processing techniques, integrating deep mathematical concepts from a range of different fields, which will be of great interest to all researchers involved with image processing and computer vision applications, as well as computations for more general scientific problems.

This volume covers a wide range of topics that fall under the 'philosophy of quantifiers', a philosophy that spans across multiple areas such as logic, metaphysics, epistemology and even the history of philosophy. It discusses the import of quantifier variance in the model theory of mathematics. It advances an argument for the uniqueness of quantifier meaning in terms of Evert Beth's notion of implicit definition and clarifies the oldest explicit formulation of quantifier variance: the one proposed by Rudolf Carnap. The volume further examines what it means that a quantifier can have multiple meanings and addresses how existential vagueness can induce vagueness in our modal notions. Finally, the book explores the role played by quantifiers with respect to various kinds of semantic paradoxes, the logicality issue, ontological commitment, and the behavior of quantifiers in intensional contexts.

Over the past 25 years, Harold and Darren Franck have investigated hundreds of accidents involving vehicles of almost every shape, size, and type imaginable. In Mathematical Methods for Accident Reconstruction: A Forensic Engineering Perspective, these seasoned experts demonstrate the application of mathematics to modeling accident reconstructions involving a range of moving vehicles, including automobiles, small and large trucks, bicycles, motorcycles, all-terrain vehicles, and construction equipment such as hoists and cranes.

The book is anchored on basic principles of physics that may be applied to any of the above-named vehicles or equipment. Topics covered include the foundations of measurement, the various energy methods used in reconstruction, momentum methods, vehicle specifications, failure analysis, geometrical characteristics of highways, and softer scientific issues such as visibility, perception, and reaction.

The authors examine the fundamental characteristics of different vehicles, discuss the retrieval of data from crash data recorders, and review low speed impacts with an analysis of staged collisions. Finally, the book details standards and protocols for accident reconstruction.

Exploring a broad range of accident scenarios and also acknowledging the limits of applicability of the various physical methods employed, the breadth and depth of the book s coverage makes it a critical reference for engineers and scientists who perform vehicular accident reconstructions.

This monograph presents results of the analytical and numerical modeling of convective heat and mass transfer in different rotating flows caused by (i) system rotation, (ii) swirl flows due to swirl generators, and (iii) surface curvature in turns and bends. Volume forces (i.e. centrifugal and Coriolis forces), which influence the flow pattern, emerge in all of these rotating flows. The main part of this work deals with rotating flows caused by system rotation, which includes several rotating-disk configurations and straight pipes rotating about a parallel axis. Swirl flows are studied in some of the configurations mentioned above. Curvilinear flows are investigated in different geometries of two-pass ribbed and smooth channels with 180 Degrees bends. The author demonstrates that the complex phenomena of fluid flow and convective heat transfer in rotating flows can be successfully simulated using not only the universal CFD methodology, but in certain cases by means of the integral methods, self-similar and analytical solutions. The book will be a valuable read for research experts and practitioners in the field of heat and mass transfer.

Because of its ability to treat both regions with irregular boundaries and with different material types, the finite element method is increasingly being applied to surface water and soil transport problems and this is the focus of the present volume. The method is ideally suited to simulation of complex real applications for resolving environmental issues and for conducting environmental impact studies. The present volume focuses on the two main areas of environmental modeling with finite elements and the supporting finite element methodology. Five chapters are devoted to ocean and coastal engineering, one to other surface water problems, several to ground water modeling and contaminant transport, including radioactive waste, and the remainder to mathematical models, particularly for mixed finite elements and nonlinear problems. Environmental problems are of increasing topicality and importance today. Special care has been taken in organizing and editing the material to form the right combination of modeling, methodology, and applications studies to form a cohesive treatment appropriate for a graduate course or seminar on the subject. It is aimed in particular at engineers working in computational environmental fluid mechanics and transport processes.

The content of the book collects some contributions related to the talks presented during the INdAM Workshop "Fractional Differential Equations: Modelling, Discretization, and Numerical Solvers", held in Rome, Italy, on July 12–14, 2021. All contributions are original and not published elsewhere. The main topic of the book is fractional calculus, a topic that addresses the study and application of integrals and derivatives of noninteger order. These operators, unlike the classic operators of integer order, are nonlocal operators and are better suited to describe phenomena with memory (with respect to time and/or space). Although the basic ideas of fractional calculus go back over three centuries, only in recent decades there has been a rapid increase in interest in this field of research due not only to the increasing use of fractional calculus in applications in biology, physics, engineering, probability, etc., but also thanks to the availability of new and more powerful numerical tools that allow for an efficient solution of problems that until a few years ago appeared unsolvable. The analytical solution of fractional differential equations (FDEs) appears even more difficult than in the integer case. Hence, numerical analysis plays a decisive role since practically every type of application of fractional calculus requires adequate numerical tools. The aim of this book is therefore to collect and spread ideas mainly coming from the two communities of numerical analysts operating in this field - the one working on methods for the solution of differential problems and the one working on the numerical linear algebra side - to share knowledge and create synergies. At the same time, the book intends to realize a direct bridge between researchers working on applications and numerical analysts. Indeed, the book collects papers on applications, numerical methods for differential problems of fractional order, and related aspects in numerical linear algebra.The target audience of the book is scholars interested in recent advancements in fractional calculus.

"Combat Modeling" is a systematic learning resource and reference text for the quantitative analysis of combat. After a brief overview, authors Washburn and Kress present individual chapters on shooting without feedback; shooting with feedback; target defense; attrition models; game theory and wargames; search; unmanned aerial vehicles; and terror and insurgency. Three appendices provide a review of basic probability concepts, probability distributions, and Markov models; an introduction to optimization models; and a discussion of Monte-Carlo simulations. Drawing on their many years of experience at the Naval Postgraduate School in Monterey, California, Washburn and Kress have created a reference that will provide the tools and techniques for analysts involved in the underpinnings of combat decisions. This is a book that can be used as a military manual, reference book, and textbook for military courses on this vital subject.

With an emphasis on models and techniques, this textbook introduces many of the fundamental concepts of stochastic modeling that are now a vital component of almost every scientific investigation. In particular, emphasis is placed onlaying the foundationfor solvingproblemsin reliability, insurance, finance, and credit risk.

The material has been carefully selected to cover the basic concepts and techniques on each topic, making this an ideal introductory gateway to more advanced learning. With exercises and solutions to selected problems accompanying each chapter, this textbook is for a wide audience including advanced undergraduate and beginning-level graduate students, researchers, and practitioners in mathematics, statistics, engineering, and economics."

This book presents the textile-, mathematical and mechanical background for the modelling of fiber based structures such as yarns, braided and knitted textiles. The hierarchical scales of these textiles and the structural elements at the different levels are analysed and the methods for their modelling are presented. The author reports about problems, methods and algorithms and possible solutions from his twenty year experience in the modelling and software development of CAD for textiles.

This book focuses on recent research in modern optimization and its implications in control and data analysis. This book is a collection of papers from the conference "Optimization and Its Applications in Control and Data Science" dedicated to Professor Boris T. Polyak, which was held in Moscow, Russia on May 13-15, 2015. This book reflects developments in theory and applications rooted by Professor Polyak's fundamental contributions to constrained and unconstrained optimization, differentiable and nonsmooth functions, control theory and approximation. Each paper focuses on techniques for solving complex optimization problems in different application areas and recent developments in optimization theory and methods. Open problems in optimization, game theory and control theory are included in this collection which will interest engineers and researchers working with efficient algorithms and software for solving optimization problems in market and data analysis. Theoreticians in operations research, applied mathematics, algorithm design, artificial intelligence, machine learning, and software engineering will find this book useful and graduate students will find the state-of-the-art research valuable.

This volume presents original papers ranging from an experimental study on cavitation jets to an up-to-date mathematical analysis of the Navier-Stokes equations for free boundary problems, reflecting topics featured at the International Conference on Mathematical Fluid Dynamics, Present and Future, held 11-14 November 2014 at Waseda University in Tokyo. The contributions address subjects in one- and two-phase fluid flows, including cavitation, liquid crystal flows, plasma flows, and blood flows. Written by internationally respected experts, these papers highlight the connections between mathematical, experimental, and computational fluid dynamics. The book is aimed at a wide readership in mathematics and engineering, including researchers and graduate students interested in mathematical fluid dynamics.

The focus of these conference proceedings is on research, development, and applications in the fields of numerical geometry, scientific computing and numerical simulation, particularly in mesh generation and related problems. In addition, this year's special focus is on Voronoi diagrams and their applications, celebrating the 150th birthday of G.F. Voronoi. In terms of content, the book strikes a balance between engineering algorithms and mathematical foundations. It presents an overview of recent advances in numerical geometry, grid generation and adaptation in terms of mathematical foundations, algorithm and software development and applications. The specific topics covered include: quasi-conformal and quasi-isometric mappings, hyperelastic deformations, multidimensional generalisations of the equidistribution principle, discrete differential geometry, spatial and metric encodings, Voronoi-Delaunay theory for tilings and partitions, duality in mathematical programming and numerical geometry, mesh-based optimisation and optimal control methods. Further aspects examined include iterative solvers for variational problems and algorithm and software development. The applications of the methods discussed are multidisciplinary and include problems from mathematics, physics, biology, chemistry, material science, and engineering.

Modeling Students' Mathematical Modeling Competencies offers welcome clarity and focus to the international research and professional community in mathematics, science, and engineering education, as well as those involved in the sciences of teaching and learning these subjects.

This second edition, now featuring new material, focuses on the valuation principles that are common to most derivative securities. A wide range of financial derivatives commonly traded in the equity and fixed income markets are analysed, emphasising aspects of pricing, hedging and practical usage. This second edition features additional emphasis on the discussion of Ito calculus and Girsanovs Theorem, and the risk-neutral measure and equivalent martingale pricing approach. A new chapter on credit risk models and pricing of credit derivatives has been added. Up-to-date research results are provided by many useful exercises.

This thesis addresses one of the most fundamental challenges for modern science: how can the brain as a network of neurons process information, how can it create and store internal models of our world, and how can it infer conclusions from ambiguous data? The author addresses these questions with the rigorous language of mathematics and theoretical physics, an approach that requires a high degree of abstraction to transfer results of wet lab biology to formal models. The thesis starts with an in-depth description of the state-of-the-art in theoretical neuroscience, which it subsequently uses as a basis to develop several new and original ideas. Throughout the text, the author connects the form and function of neuronal networks. This is done in order to achieve functional performance of biological brains by transferring their form to synthetic electronics substrates, an approach referred to as neuromorphic computing. The obvious aspect that this transfer can never be perfect but necessarily leads to performance differences is substantiated and explored in detail. The author also introduces a novel interpretation of the firing activity of neurons. He proposes a probabilistic interpretation of this activity and shows by means of formal derivations that stochastic neurons can sample from internally stored probability distributions. This is corroborated by the author's recent findings, which confirm that biological features like the high conductance state of networks enable this mechanism. The author goes on to show that neural sampling can be implemented on synthetic neuromorphic circuits, paving the way for future applications in machine learning and cognitive computing, for example as energy-efficient implementations of deep learning networks. The thesis offers an essential resource for newcomers to the field and an inspiration for scientists working in theoretical neuroscience and the future of computing.