This book presents and discusses the state of the art and future perspectives in mathematical modeling and homogenization techniques with the focus on addressing key physiological issues in the context of multiphase healthy and malignant biological materials. The highly interdisciplinary content brings together contributions from scientists with complementary areas of expertise, such as pure and applied mathematicians, engineers, and biophysicists. The book also features the lecture notes from a half-day introductory course on asymptotic homogenization. These notes are suitable for undergraduate mathematics or physics students, while the other chapters are aimed at graduate students and researchers.

This book is part of a two volume set which presents the analysis of nonlinear phenomena as a long-standing challenge for research in basic and applied science as well as engineering. It discusses nonlinear differential and differential equations, bifurcation theory for periodic orbits and global connections. The integrability and reversibility of planar vector fields and theoretical analysis of classic physical models are sketched. This first volume concentrates on the mathematical theory and computational techniques that are essential for the study of nonlinear science, a second volume deals with real-world nonlinear phenomena in condensed matter, biology and optics.

Intersecting two large research areas - numerical analysis and applied probability/queuing theory - this book is a self-contained introduction to the numerical solution of structured Markov chains, which have a wide applicability in queuing theory and stochastic modeling and include M/G/1 and GI/M/1-type Markov chain, quasi-birth-death processes, non-skip free queues and tree-like stochastic processes. Written for applied probabilists and numerical analysts, but accessible to engineers and scientists working on telecommunications and evaluation of computer systems performances, it provides a systematic treatment of the theory and algorithms for important families of structured Markov chains and a thorough overview of the current literature. The book, consisting of nine Chapters, is presented in three parts. Part 1 covers a basic description of the fundamental concepts related to Markov chains, a systematic treatment of the structure matrix tools, including finite Toeplitz matrices, displacement operators, FFT, and the infinite block Toeplitz matrices, their relationship with matrix power series and the fundamental problems of solving matrix equations and computing canonical factorizations. Part 2 deals with the description and analysis of structure Markov chains and includes M/G/1, quasi-birth-death processes, non-skip-free queues and tree-like processes. Part 3 covers solution algorithms where new convergence and applicability results are proved. Each chapter ends with bibliographic notes for further reading, and the book ends with an appendix collecting the main general concepts and results used in the book, a list of the main annotations and algorithms used in the book, and an extensive index.

In this book, recent developments in our understanding of fundamental vortex ring and jet dynamics will be discussed, with a view to shed light upon their near-field behaviour which underpins much of their far-field characteristics. The chapters provide up-to-date research findings by their respective experts and seek to link near-field flow physics of vortex ring and jet flows with end-applications in mind. Over the past decade, our knowledge on vortex ring and jet flows has grown by leaps and bounds, thanks to increasing use of high-fidelity, high-accuracy experimental techniques and numerical simulations. As such, we now have a much better appreciation and understanding on the initiation and near-field developments of vortex ring and jet flows under many varied initial and boundary conditions. Chapter 1 outlines the vortex ring pinch-off phenomenon and how it relates to the initial stages of jet formations and subsequent jet behaviour, while Chapter 2 takes a closer look at the behaviour resulting from vortex ring impingement upon solid boundaries and how the use of a porous surface alters the impingement process. Chapters 3 and 4 focus upon the formation of synthetic jets from vortex ring structures experimentally and numerically, the challenges in understanding the relationships between their generation parameters and how they can be utilized in flow separation control problems. Chapter 5 looks at the use of imposing selected nozzle trailing-edge modifications to effect changes upon the near-field dynamics associated with circular, noncircular and coaxial jets, with a view to control their mixing behaviour. And last but not least, Chapter 6 details the use of unique impinging jet configurations and how they may lend themselves towards greater understanding and operating efficacies in heat transfer problems. This book will be useful to postgraduate students and researchers alike who wish to get up to speed regarding the latest developments in vortex ring and jet flow behaviour and how their interesting flow dynamics may be put into good use in their intended applications.

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

Much research into financial contagion and systematic risks has been motivated by the finding that cross-market correlations (resp. coexceedances) between asset returns increase significantly during crisis periods. Is this increase due to an exogenous shock common to all markets (interdependence) or due to certain types of transmission of shocks between markets (contagion)? Darolles and Gourieroux explain that an attempt to convey contagion and causality in a static framework can be flawed due to identification problems; they provide a more precise definition of the notion of shock to strengthen the solution within a dynamic framework. This book covers the standard practice for defining shocks in SVAR models, impulse response functions, identitification issues, static and dynamic models, leading to the challenges of measurement of systematic risk and contagion, with interpretations of hedge fund survival and market liquidity risks

This book highlights the latest advances in engineering mathematics with a main focus on the mathematical models, structures, concepts, problems and computational methods and algorithms most relevant for applications in modern technologies and engineering. In particular, it features mathematical methods and models of applied analysis, probability theory, differential equations, tensor analysis and computational modelling used in applications to important problems concerning electromagnetics, antenna technologies, fluid dynamics, material and continuum physics and financial engineering. The individual chapters cover both theory and applications, and include a wealth of figures, schemes, algorithms, tables and results of data analysis and simulation. Presenting new methods and results, reviews of cutting-edge research, and open problems for future research, they equip readers to develop new mathematical methods and concepts of their own, and to further compare and analyse the methods and results discussed.The book consists of contributed chapters covering research developed as a result of a focused international seminar series on mathematics and applied mathematics and a series of three focused international research workshops on engineering mathematics organised by the Research Environment in Mathematics and Applied Mathematics at Malardalen University from autumn 2014 to autumn 2015: the International Workshop on Engineering Mathematics for Electromagnetics and Health Technology; the International Workshop on Engineering Mathematics, Algebra, Analysis and Electromagnetics; and the 1st Swedish-Estonian International Workshop on Engineering Mathematics, Algebra, Analysis and Applications.It serves as a source of inspiration for a broad spectrum of researchers and research students in applied mathematics, as well as in the areas of applications of mathematics considered in the book.

This book focuses on bifurcation theory for autonomous and nonautonomous differential equations with discontinuities of different types - those with jumps present either in the right-hand side, or in trajectories or in the arguments of solutions of equations. The results obtained can be applied to various fields, such as neural networks, brain dynamics, mechanical systems, weather phenomena and population dynamics. Developing bifurcation theory for various types of differential equations, the book is pioneering in the field. It presents the latest results and provides a practical guide to applying the theory to differential equations with various types of discontinuity. Moreover, it offers new ways to analyze nonautonomous bifurcation scenarios in these equations. As such, it shows undergraduate and graduate students how bifurcation theory can be developed not only for discrete and continuous systems, but also for those that combine these systems in very different ways. At the same time, it offers specialists several powerful instruments developed for the theory of discontinuous dynamical systems with variable moments of impact, differential equations with piecewise constant arguments of generalized type and Filippov systems.

This book focuses on the theory of the Zakharov system in the context of plasma physics. It has been over 40 years since the system was first derived by V. E. Zakharov - and in the course of those decades, many innovative achievements with major impacts on other research fields have been made. The book represents a first attempt to highlight the mathematical theories that are most important to researchers, including the existence and unique problems, blow-up, low regularity, large time behavior and the singular limit. Rather than attempting to examine every aspect of the Zakharov system in detail, it provides an effective road map to help readers access the frontier of studies on this system.

This book covers original research and the latest advances in symbolic, algebraic and geometric computation; computational methods for differential and difference equations, symbolic-numerical computation; mathematics software design and implementation; and scientific and engineering applications based on features, invited talks, special sessions and contributed papers presented at the 9th (in Fukuoka, Japan in 2009) and 10th (in Beijing China in 2012) Asian Symposium on Computer Mathematics (ASCM). Thirty selected and refereed articles in the book present the conference participants' ideas and views on researching mathematics using computers.

This book focuses on the equation of state (EoS) of compact stars, particularly the intriguing possibility of the "quark star model." The EoS of compact stars is the subject of ongoing debates among astrophysicists and particle physicists, due to the non-perturbative property of strong interaction at low energy scales. The book investigates the tidal deformability and maximum mass of rotating quark stars and triaxially rotating quark stars, and compares them with those of neutron stars to reveal significant differences. Lastly, by combining the latest observations of GW170817, the book suggests potential ways to distinguish between the neutron star and quark star models.

This book offers a timely overview of fractional calculus applications, with a special emphasis on fractional derivatives with Mittag-Leffler kernel. The different contributions, written by applied mathematicians, physicists and engineers, offers a snapshot of recent research in the field, highlighting the current methodological frameworks together with applications in different fields of science and engineering, such as chemistry, mechanics, epidemiology and more. It is intended as a timely guide and source of inspiration for graduate students and researchers in the above-mentioned areas.

To ensure the security and economy of future power system operation in the context of a high degree of renewable energy penetration, this thesis proposes a new distributed algorithm called generalized master-slave-splitting (G-MSS) theory and a new transmission-distribution coordinated energy management (TDCEM) method that is based on the G-MSS theory. The thesis studies the mathematical properties of the G-MSS theory in detail. Based on the G-MSS theory, a distributed TDCEM method - which involves distributed security analysis, distributed voltage stability analysis, distributed economic dispatch and distributed optimal power flow for an integrated transmission-distribution system - is then developed for the first time. The thesis demonstrates that the proposed TDCEM method significantly contributes to more reliable and optimal operation in power systems. The book will benefit researchers, scientists and engineers in the field of power system operation and optimization.

This book covers different, current research directions in the context of variational methods for non-linear geometric data. Each chapter is authored by leading experts in the respective discipline and provides an introduction, an overview and a description of the current state of the art. Non-linear geometric data arises in various applications in science and engineering. Examples of nonlinear data spaces are diverse and include, for instance, nonlinear spaces of matrices, spaces of curves, shapes as well as manifolds of probability measures. Applications can be found in biology, medicine, product engineering, geography and computer vision for instance. Variational methods on the other hand have evolved to being amongst the most powerful tools for applied mathematics. They involve techniques from various branches of mathematics such as statistics, modeling, optimization, numerical mathematics and analysis. The vast majority of research on variational methods, however, is focused on data in linear spaces. Variational methods for non-linear data is currently an emerging research topic. As a result, and since such methods involve various branches of mathematics, there is a plethora of different, recent approaches dealing with different aspects of variational methods for nonlinear geometric data. Research results are rather scattered and appear in journals of different mathematical communities. The main purpose of the book is to account for that by providing, for the first time, a comprehensive collection of different research directions and existing approaches in this context. It is organized in a way that leading researchers from the different fields provide an introductory overview of recent research directions in their respective discipline. As such, the book is a unique reference work for both newcomers in the field of variational methods for non-linear geometric data, as well as for established experts that aim at to exploit new research directions or collaborations. Chapter 9 of this book is available open access under a CC BY 4.0 license at link.springer.com.

With applications in quantum field theory, general relativity and elementary particle physics, this four-volume work studies the invariance of differential operators under Lie algebras, quantum groups and superalgebras. This third volume covers supersymmetry, including detailed coverage of conformal supersymmetry in four and some higher dimensions, furthermore quantum superalgebras are also considered. Contents Lie superalgebras Conformal supersymmetry in 4D Examples of conformal supersymmetry for D > 4 Quantum superalgebras

This book discusses recent research on the stability of various neural networks with constrained signals. It investigates stability problems for delayed dynamical systems where the main purpose of the research is to reduce the conservativeness of the stability criteria. The book mainly focuses on the qualitative stability analysis of continuous-time as well as discrete-time neural networks with delays by presenting the theoretical development and real-life applications in these research areas. The discussed stability concept is in the sense of Lyapunov, and, naturally, the proof method is based on the Lyapunov stability theory. The present book will serve as a guide to enable the reader in pursuing the study of further topics in greater depth and is a valuable reference for young researcher and scientists.

This book uses art photography as a point of departure for learning about physics, while also using physics as a point of departure for asking fundamental questions about the nature of photography as an art. Although not a how-to manual, the topics center around hands-on applications, most-often illustrated by photographic processes that are inexpensive and easily accessible to students (including a versatile new process developed by the author, and herein first described in print). A central theme is the connection between the physical interaction of light and matter on the one hand, and the artistry of the photographic processes and their results on the other. Geometry and the Nature of Light focuses on the physics of light and the optics of lenses, but also includes extended discussions of topics less commonly covered in a beginning text, including symmetry in art and physics, different physical processes of the scattering of light, photograms (photographic shadow prints) and the nature of shadows, elements of 2-dimensional design, pinhole photography and the view camera. Although written at a beginning undergraduate level, the topics are chosen for their role in a more general discussion of the relation between science and art that is of interest to readers of all backgrounds and levels of expertise.

This volume contains the proceedings of the workshop Crossing the Walls in Enumerative Geometry, held in May 2018 at Snowbird, Utah. It features a collection of both expository and research articles about mirror symmetry, quantized singularity theory (FJRW theory), and the gauged linear sigma model. Most of the expository works are based on introductory lecture series given at the workshop and provide an approachable introduction for graduate students to some fundamental topics in mirror symmetry and singularity theory, including quasimaps, localization, the gauged linear sigma model (GLSM), virtual classes, cosection localization, $p$-fields, and Saito's primitive forms. These articles help readers bridge the gap from the standard graduate curriculum in algebraic geometry to exciting cutting-edge research in the field. The volume also contains several research articles by leading researchers, showcasing new developments in the field.

This book gathers the outcomes of the second ECCOMAS CM3 Conference series on transport, which addressed the main challenges and opportunities that computation and big data represent for transport and mobility in the automotive, logistics, aeronautics and marine-maritime fields. Through a series of plenary lectures and mini-forums with lectures followed by question-and-answer sessions, the conference explored potential solutions and innovations to improve transport and mobility in surface and air applications. The book seeks to answer the question of how computational research in transport can provide innovative solutions to Green Transportation challenges identified in the ambitious Horizon 2020 program. In particular, the respective papers present the state of the art in transport modeling, simulation and optimization in the fields of maritime, aeronautics, automotive and logistics research. In addition, the content includes two white papers on transport challenges and prospects. Given its scope, the book will be of interest to students, researchers, engineers and practitioners whose work involves the implementation of Intelligent Transport Systems (ITS) software for the optimal use of roads, including safety and security, traffic and travel data, surface and air traffic management, and freight logistics.

Many open questions in Theoretical Physics pertain to strongly interacting quantum systems such as the quark-gluon plasma (QGP) produced in heavy-ion collisions or the strange-metal phase observed in many high-temperature superconductors. These systems are notoriously difficult to study using traditional methods such as perturbation theory, but the gauge/gravity duality offers a successful alternative approach, which maps strongly interacting quantum gauge theories to computationally tractable, classical gravity theories. This book begins with a pedagogical introduction to how the duality can be used to extract transport properties of quantum systems from their gravity dual. It then presents new results on hydrodynamic transport in strongly interacting quantum fluids, providing strong evidence that the Haack-Yarom identity between second-order transport coefficients holds for all fluids with a classical gravity dual and may be a universal feature of all strongly coupled quantum fluids such as the QGP. Newly derived Kubo formulae, expressing transport coefficients in terms of quantum correlators, hold independently of the duality. Lastly, the book discusses new results on magnetic impurities in strongly correlated metals, including the first dual gravity description of an inter-impurity coupling, crucial for the quantum criticality underlying the strange-metal phase.

In this monograph, the authors present their recently developed theory of electromagnetic interactions. This neoclassical approach extends the classical electromagnetic theory down to atomic scales and allows the explanation of various non-classical phenomena in the same framework. While the classical Maxwell-Lorentz electromagnetism theory succeeds in describing the physical reality at macroscopic scales, it struggles at atomic scales. Here, quantum mechanics traditionally takes over to describe non-classical phenomena such as the hydrogen spectrum and de Broglie waves. By means of modifying the classical theory, the approach presented here is able to consistently explain quantum-mechanical effects, and while similar to quantum mechanics in some respects, this neoclassical theory also differs markedly from it. In particular, the newly developed framework omits probabilistic interpretations of the wave function and features a new fundamental spatial scale which, at the size of the free electron, is much larger than the classical electron radius and is relevant to plasmonics and emission physics. This book will appeal to researchers interested in advanced aspects of electromagnetic theory. Treating the classical approach in detail, including non-relativistic aspects and the Lagrangian framework, and comparing the neoclassical theory with quantum mechanics and the de Broglie-Bohm theory, this work is completely self-contained.

This book focuses on universal nonlinear dynamics model of mesoscale eddies. The results of this book are not only the direct-type applications of pure mathematical limit cycle theory and fractal theory in practice but also the classic combination of nonlinear dynamic systems in mathematics and the physical oceanography. The universal model and experimental verification not only verify the relevant results that are obtained by Euler's form but also, more importantly, are consistent with observational numerical statistics. Due to the universality of the model, the consequences of the system are richer and more complete. The comprehensive and systematic mathematical modeling of mesoscale eddies is one of the major features of the book, which is particularly suited for readers who are interested to learn fractal analysis and prediction in physical oceanography. The book benefits researchers, engineers, and graduate students in the fields of mesoscale eddies, fractal, chaos, and other applications, etc.

This book describes the latest advances in intelligent techniques such as fuzzy logic, neural networks, and optimization algorithms, and their relevance in building intelligent information systems in combination with applied mathematics. The authors also outline the applications of these systems in areas like intelligent control and robotics, pattern recognition, medical diagnosis, time series prediction, and optimization of complex problems. By sharing fresh ideas and identifying new targets/problems it offers young researchers and students new directions for their future research. The book is intended for readers from mathematics and computer science, in particular professors and students working on theory and applications of intelligent systems for real-world applications.

This book features a selection of revised and extended research articles written by prominent researchers who participated in the 26th World Congress on Engineering and Computer Science (WCECS 2018), held in San Francisco, USA, on October 23-25, 2018. Topics covered include engineering mathematics, electrical engineering, communications systems, computer science, chemical engineering, systems engineering, manufacturing engineering and industrial applications. With contributions carefully chosen to represent the most cutting-edge research presented at the conference and highlighting the state of the art in engineering technologies and the physical sciences and their applications, the book is a valuable reference resource for graduate students and researchers working in these fields.

This volume collects contributions written by different experts in honor of Prof. Jaime Munoz Masque. It covers a wide variety of research topics, from differential geometry to algebra, but particularly focuses on the geometric formulation of variational calculus; geometric mechanics and field theories; symmetries and conservation laws of differential equations, and pseudo-Riemannian geometry of homogeneous spaces. It also discusses algebraic applications to cryptography and number theory. It offers state-of-the-art contributions in the context of current research trends. The final result is a challenging panoramic view of connecting problems that initially appear distant.