This monograph presents a graduate-level treatment of partial differential equations (PDEs) for engineers. The book begins with a review of the geometrical interpretation of systems of ODEs, the appearance of PDEs in engineering is motivated by the general form of balance laws in continuum physics. Four chapters are devoted to a detailed treatment of the single first-order PDE, including shock waves and genuinely non-linear models, with applications to traffic design and gas dynamics. The rest of the book deals with second-order equations. In the treatment of hyperbolic equations, geometric arguments are used whenever possible and the analogy with discrete vibrating systems is emphasized. The diffusion and potential equations afford the opportunity of dealing with questions of uniqueness and continuous dependence on the data, the Fourier integral, generalized functions (distributions), Duhamel's principle, Green's functions and Dirichlet and Neumann problems. The target audience primarily comprises graduate students in engineering, but the book may also be beneficial for lecturers, and research experts both in academia in industry.

This is the first book to introduce the irrational elliptic function series, providing a theoretical treatment for the smooth and discontinuous system and opening a new branch of applied mathematics. The discovery of the smooth and discontinuous (SD) oscillator and the SD attractors discussed in this book represents a further milestone in nonlinear dynamics, following on the discovery of the Ueda attractor in 1961 and Lorenz attractor in 1963. This particular system bears significant similarities to the Duffing oscillator, exhibiting the standard dynamics governed by the hyperbolic structure associated with the stationary state of the double well. However, there is a substantial departure in nonlinear dynamics from standard dynamics at the discontinuous stage. The constructed irrational elliptic function series, which offers a way to directly approach the nature dynamics analytically for both smooth and discontinuous behaviours including the unperturbed periodic motions and the perturbed chaotic attractors without any truncation, is of particular interest. Readers will also gain a deeper understanding of the actual nonlinear phenomena by means of a simple mechanical model: the theory, methodology, and the applications in various interlinked disciplines of sciences and engineering. This book offers a valuable resource for researchers, professionals and postgraduate students in mechanical engineering, non-linear dynamics, and related areas, such as nonlinear modelling in various fields of mathematics, physics and the engineering sciences.

Mathematical methods and theories with interdisciplinary applications are presented in this book. The eighteen contributions presented in this Work have been written by eminent scientists; a few papers are based on talks which took place at the International Conference at the Hellenic Artillery School in May 2015. Each paper evaluates possible solutions to long-standing problems such as the solvability of the direct electromagnetic scattering problem, geometric approaches to cyber security, ellipsoid targeting with overlap, non-equilibrium solutions of dynamic networks, measuring ballistic dispersion, elliptic regularity theory for the numerical solution of variational problems, approximation theory for polynomials on the real line and the unit circle, complementarity and variational inequalities in electronics, new two-slope parameterized achievement scalarizing functions for nonlinear multiobjective optimization, and strong and weak convexity of closed sets in a Hilbert space. Graduate students, scientists, engineers and researchers in pure and applied mathematical sciences, operations research, engineering, and cyber security will find the interdisciplinary scientific perspectives useful to their overall understanding and further research.

This contributed volume comprises research articles and reviews on topics connected to the mathematical modeling of cellular systems. These contributions cover signaling pathways, stochastic effects, cell motility and mechanics, pattern formation processes, as well as multi-scale approaches. All authors attended the workshop on "Modeling Cellular Systems" which took place in Heidelberg in October 2014. The target audience primarily comprises researchers and experts in the field, but the book may also be beneficial for graduate students.

This book is intended as a text for a one-semester course on Mathematical and Computational Neuroscience for upper-level undergraduate and beginning graduate students of mathematics, the natural sciences, engineering, or computer science. An undergraduate introduction to differential equations is more than enough mathematical background. Only a slim, high school-level background in physics is assumed, and none in biology. Topics include models of individual nerve cells and their dynamics, models of networks of neurons coupled by synapses and gap junctions, origins and functions of population rhythms in neuronal networks, and models of synaptic plasticity. An extensive online collection of Matlab programs generating the figures accompanies the book.

This landmark monograph presents the most recent mathematical developments in the analysis of ionospheric distortions of SAR images and offers innovative new strategies for their mitigation. As a prerequisite to addressing these topics, the book also discusses the radar ambiguity theory as it applies to synthetic aperture imaging and the propagation of radio waves through the ionospheric plasma, including the anisotropic and turbulent cases. In addition, it covers a host of related subjects, such as the mathematical modeling of extended radar targets (as opposed to point-wise targets) and the scattering of radio waves off those targets, as well as the theoretical analysis of the start-stop approximation, which is used routinely in SAR signal processing but often without proper justification. The mathematics in this volume is clean and rigorous - no assumptions are hidden or ambiguously stated. The resulting work is truly interdisciplinary, providing both a comprehensive and thorough exposition of the field, as well as an accurate account of a range of relevant physical processes and phenomena. The book is intended for applied mathematicians interested in the area of radar imaging or, more generally, remote sensing, as well as physicists and electrical/electronic engineers who develop/operate spaceborne SAR sensors and perform the data processing. The methods in the book are also useful for researchers and practitioners working on other types of imaging. Moreover, the book is accessible to graduate students in applied mathematics, physics, engineering, and related disciplines. Praise for Transionospheric Synthetic Aperture Imaging: "I perceive that this text will mark a turning point in the field of synthetic aperture radar research and practice. I believe this text will instigate a new era of more rigorous image formation relieving the research, development and practitioner communities of inconsistent physical assumptions and numerical approaches." - Richard Albanese, Senior Scientist, Albanese Defense and Energy Development LLC

Partition functions arise in combinatorics and related problems of statistical physics as they encode in a succinct way the combinatorial structure of complicated systems. The main focus of the book is on efficient ways to compute (approximate) various partition functions, such as permanents, hafnians and their higher-dimensional versions, graph and hypergraph matching polynomials, the independence polynomial of a graph and partition functions enumerating 0-1 and integer points in polyhedra, which allows one to make algorithmic advances in otherwise intractable problems. The book unifies various, often quite recent, results scattered in the literature, concentrating on the three main approaches: scaling, interpolation and correlation decay. The prerequisites include moderate amounts of real and complex analysis and linear algebra, making the book accessible to advanced math and physics undergraduates.

This book introduces readers to the principles of laser interaction with biological cells and tissues with varying degrees of organization. In addition to considering the problems of biomedical cell diagnostics, and modeling the scattering of laser irradiation of blood cells for biological structures (dermis, epidermis, vascular plexus), it presents an analytic theory based on solving the wave equation for the electromagnetic field. It discusses a range of mathematical modeling topics, including optical characterization of biological tissue with large-scale and small-scale inhomogeneities in the layers; heating blood vessels using laser irradiation on the outer surface of the skin; and thermo-chemical denaturation of biological structures based on the example of human skin. In this second edition, a new electrodynamic model of the interaction of laser radiation with blood cells is presented for the structure of cells and the in vitro prediction of optical properties. The approach developed makes it possible to determine changes in cell size as well as modifications in their internal structures, such as transformation and polymorphism nucleus scattering, which is of interest for cytological studies. The new model is subsequently used to calculate the size distribution function of irregular-shape particles with a variety of forms and structures, which allows a cytological analysis of the observed deviations from normal cells.

This book presents the latest research in computational methods for modeling and simulating brain disorders. In particular, it shows how mathematical models can be used to study the relationship between a given disorder and the specific brain structure associated with that disorder. It also describes the emerging field of computational psychiatry, including the study of pathological behavior due to impaired functional connectivity, pathophysiological activity, and/or aberrant decision-making. Further, it discusses the data analysis techniques that will be required to analyze the increasing amount of data being generated about the brain. Lastly, the book offers some tips on the application of computational models in the field of quantitative systems pharmacology. Mainly written for computational scientists eager to discover new application fields for their model, this book also benefits neurologists and psychiatrists wanting to learn about new methods.

Instabilities of fluid flows and the associated transitions between different possible flow states provide a fascinating set of problems that have attracted researchers for over a hundred years. This book addresses state-of-the-art developments in numerical techniques for computational modelling of fluid instabilities and related bifurcation structures, as well as providing comprehensive reviews of recently solved challenging problems in the field.

This book reports on the latest advances in and applications of memristors, memristive devices and systems. It gathers 20 contributed chapters by subject experts, including pioneers in the field such as Leon Chua (UC Berkeley, USA) and R.S. Williams (HP Labs, USA), who are specialized in the various topics addressed in this book, and covers broad areas of memristors and memristive devices such as: memristor emulators, oscillators, chaotic and hyperchaotic memristive systems, control of memristive systems, memristor-based min-max circuits, canonic memristors, memristive-based neuromorphic applications, implementation of memristor-based chaotic oscillators, inverse memristors, linear memristor devices, delayed memristive systems, flux-controlled memristive emulators, etc. Throughout the book, special emphasis is given to papers offering practical solutions and design, modeling, and implementation insights to address current research problems in memristors, memristive devices and systems. As such, it offers a valuable reference book on memristors and memristive devices for graduate students and researchers with a basic knowledge of electrical and control systems engineering.

There have been substantial developments in meshfree methods, particle methods, and generalized finite element methods since the mid 1990s. The growing interest in these methods is in part due to the fact that they offer extremely flexible numerical tools and can be interpreted in a number of ways. For instance, meshfree methods can be viewed as a natural extension of classical finite element and finite difference methods to scattered node configurations with no fixed connectivity. Furthermore, meshfree methods have a number of advantageous features that are especially attractive when dealing with multiscale phenomena: A-priori knowledge about the solution's particular local behavior can easily be introduced into the meshfree approximation space, and coarse scale approximations can be seamlessly refined by adding fine scale information. However, the implementation of meshfree methods and their parallelization also requires special attention, for instance with respect to numerical integration.

This book systematically studies how game theory can be used to improve security in chemical industrial areas, capturing the intelligent interactions between security managers and potential adversaries. The recent unfortunate terrorist attacks on critical infrastructures show that adversaries are intelligent and strategic. Game theoretic models have been extensively used in some domains to model these strategic adversaries. However, there is a lack of such advanced models to be employed by chemical security managers. In this book, game theoretic models for protecting chemical plants as well as clusters are proposed. Different equilibrium concepts are explored, with user-friendly explanation of how to reflect them to realistic cases. Based on efficient analysis of the properties of security issues in chemical plants/clusters, models in this book are capable to support resources allocations, cost-effectiveness analysis, cooperation incentives and alike.

This book presents a selection of advanced case studies that cover a substantial range of issues and real-world challenges and applications in space engineering. Vital mathematical modeling, optimization methodologies and numerical solution aspects of each application case study are presented in detail, with discussions of a range of advanced model development and solution techniques and tools. Space engineering challenges are discussed in the following contexts: *Advanced Space Vehicle Design *Computation of Optimal Low Thrust Transfers *Indirect Optimization of Spacecraft Trajectories *Resource-Constrained Scheduling, *Packing Problems in Space *Design of Complex Interplanetary Trajectories *Satellite Constellation Image Acquisition *Re-entry Test Vehicle Configuration Selection *Collision Risk Assessment on Perturbed Orbits *Optimal Robust Design of Hybrid Rocket Engines *Nonlinear Regression Analysis in Space Engineering *Regression-Based Sensitivity Analysis and Robust Design *Low-Thrust Multi-Revolution Orbit Transfers *Modeling and Optimization of Balance Layout Problems *Pilot-Induced Oscillations Alleviation *Modeling and Optimization of Hybrid Transfers to Near-Earth Objects *Probabilistic Safety Analysis of the Collision Between Space Debris and Satellite *Flatness-based Low-thrust Trajectory Optimization for Spacecraft Proximity Operations The contributing authors are expert researchers and practitioners in either the space engineering and/or in the applied optimization fields. Researchers and practitioners working in various applied aspects of space engineering will find this book practical and informative. Academics, graduate and post-graduate students in aerospace engineering, applied mathematics, operations research, optimization, and optimal control, will find this book useful.

Starting with an introduction to the numerous features of Mathematica (R), this book continues with more complex material. It provides the reader with lots of examples and illustrations of how the benefits of Mathematica (R) can be used. Composed of eleven chapters, it includes the following: A chapter on several sorting algorithms Functions (planar and solid) with many interesting examples Ordinary differential equations Advantages of Mathematica (R) dealing with the Pi number The power of Mathematica (R) working with optimal control problems Introduction to Mathematica (R) with Applications will appeal to researchers, professors and students requiring a computational tool.

This book provides a survey on different kinds of Feistel ciphers, with their definitions and mathematical/computational properties. Feistel ciphers are widely used in cryptography in order to obtain pseudorandom permutations and secret-key block ciphers. In Part 1, we describe Feistel ciphers and their variants. We also give a brief story of these ciphers and basic security results. In Part 2, we describe generic attacks on Feistel ciphers. In Part 3, we give results on DES and specific Feistel ciphers. Part 4 is devoted to improved security results. We also give results on indifferentiability and indistinguishability.

This modern take on partial differential equations does not require knowledge beyond vector calculus and linear algebra. The author focuses on the most important classical partial differential equations, including conservation equations and their characteristics, the wave equation, the heat equation, function spaces, and Fourier series, drawing on tools from analysis only as they arise. Within each section the author creates a narrative that answers the five questions: What is the scientific problem we are trying to understand? How do we model that with PDE? What techniques can we use to analyze the PDE? How do those techniques apply to this equation? What information or insight did we obtain by developing and analyzing the PDE? The text stresses the interplay between modeling and mathematical analysis, providing a thorough source of problems and an inspiration for the development of methods.

This book presents recent research on Advanced Computing in Industrial Mathematics, which is one of the most prominent interdisciplinary areas and combines mathematics, computer science, scientific computations, engineering, physics, chemistry, medicine, etc. Further, the book presents the tools of Industrial Mathematics, which are based on mathematical models, and the corresponding computer codes, which are used to perform virtual experiments to obtain new data or to better understand the existing experimental results. The book gathers the peer-reviewed papers presented during the 10th Annual Meeting of the Bulgarian Section of SIAM (BGSIAM) from December 21 to 22, 2015 in Sofia, Bulgaria.

This book describes a novel methodology for studying algorithmic skills, intended as cognitive activities related to rule-based symbolic transformation, and argues that some human computational abilities may be interpreted and analyzed as genuine examples of extended cognition. It shows that the performance of these abilities relies not only on innate neurocognitive systems or language-related skills, but also on external tools and general agent-environment interactions. Further, it asserts that a low-level analysis, based on a set of core neurocognitive systems linking numbers and language, is not sufficient to explain some specific forms of high-level numerical skills, like those involved in algorithm execution. To this end, it reports on the design of a cognitive architecture for modeling all the relevant features involved in the execution of algorithmic strategies, including external tools, such as paper and pencils. The first part of the book discusses the philosophical premises for endorsing and justifying a position in philosophy of mind that links a modified form of computationalism with some recent theoretical and scientific developments, like those introduced by the so-called dynamical approach to cognition. The second part is dedicated to the description of a Turing-machine-inspired cognitive architecture, expressly designed to formalize all kinds of algorithmic strategies.

This book tackles the challenging question which mathematical formalisms and possibly new physical notions should be developed for quantitatively describing human cognition and behavior, in addition to the ones already developed in the physical and cognitive sciences. Indeed, physics is widely used in modeling social systems, where, in particular, new branches of science such as sociophysics and econophysics have arisen. However, many if not most characteristic features of humans like willingness, emotions, memory, future prediction, and moral norms, to name but a few, are not yet properly reflected in the paradigms of physical thought and theory. The choice of a relevant formalism for modeling mental phenomena requires the comprehension of the general philosophical questions related to the mind-body problem. Plausible answers to these questions are investigated and reviewed, notions and concepts to be used or to be taken into account are developed and some challenging questions are posed as open problems. This text addresses theoretical physicists and neuroscientists modeling any systems and processes where human factors play a crucial role, philosophers interested in applying philosophical concepts to the construction of mathematical models, and the mathematically oriented psychologists and sociologists, whose research is fundamentally related to modeling mental processes.

This contributed volume offers a collection of papers presented at the 2016 Network Games, Control, and Optimization conference (NETGCOOP), held at the University of Avignon in France, November 23-25, 2016. These papers highlight the increasing importance of network control and optimization in many networking application domains, such as mobile and fixed access networks, computer networks, social networks, transportation networks, and, more recently, electricity grids and biological networks. Covering a wide variety of both theoretical and applied topics in the areas listed above, the authors explore several conceptual and algorithmic tools that are needed for efficient and robust control operation, performance optimization, and better understanding the relationships between entities that may be acting cooperatively or selfishly in uncertain and possibly adversarial environments. As such, this volume will be of interest to applied mathematicians, computer scientists, engineers, and researchers in other related fields.

The book is designed for advanced graduate students as well as postdoctoral researchers across several disciplines (e.g., mathematics, physics and engineering), as it provides them with tools and techniques that are essential in performing research on the flow problems of visco-plastic fluids. The following topics are treated: analysis of classical visco-plastic fluid models mathematical modeling of flows of visco-plastic fluids computing flows of visco-plastic fluids rheology of visco-plastic fluids and visco-plastic suspensions application of visco-plastic fluids in engineering sciences complex flows of visco-plastic fluids.

This edited volume provides an overview the state-of-the-art in the field of cognitive neuroscience of memory consolidation. In a number of sections, the editors collect contributions of leading researchers . The topical focus lies on current issues of interest such as memory consolidation including working and long-term memory. In particular, the role of sleep in relation to memory consolidation will be addressed. The target audience primarily comprises research experts in the field of cognitive neuroscience but the book may also be beneficial for graduate students.

The book surveys the state-of-the-art methods that are currently available to model and simulate the presence of rigid particles in a fluid flow. For particles that are very small relative to the characteristic flow scales and move without interaction with other particles, effective equations of motion for particle tracking are formulated and applied (e.g. in gas-solid flows). For larger particles, for particles in liquid-solid flows and for particles that interact with each other or possibly modify the overall flow detailed model are presented. Special attention is given to the description of the approximate force coupling method (FCM) as a more general treatment for small particles, and derivations in the context of low Reynolds numbers for the particle motion as well as application at finite Reynolds numbers are provided. Other topics discussed in the book are the relation to higher resolution immersed boundary methods, possible extensions to non-spherical particles and examples of applications of such methods to dispersed multiphase flows.

This book presents practical applications of the finite element method to general differential equations. The underlying strategy of deriving the finite element solution is introduced using linear ordinary differential equations, thus allowing the basic concepts of the finite element solution to be introduced without being obscured by the additional mathematical detail required when applying this technique to partial differential equations. The author generalizes the presented approach to partial differential equations which include nonlinearities. The book also includes variations of the finite element method such as different classes of meshes and basic functions. Practical application of the theory is emphasised, with development of all concepts leading ultimately to a description of their computational implementation illustrated using Matlab functions. The target audience primarily comprises applied researchers and practitioners in engineering, but the book may also be beneficial for graduate students.