The Handbook of Mathematical Fluid Dynamics is a compendium of essays that provides a survey of the major topics in the subject. Each article traces developments, surveys the results of the past decade, discusses the current state of knowledge and presents major future directions and open problems. Extensive bibliographic material is provided. The book is intended to be useful both to experts in the field and to mathematicians and other scientists who wish to learn about or begin research in mathematical fluid dynamics. The Handbook illuminates an exciting subject that involves rigorous mathematical theory applied to an important physical problem, namely the motion of fluids.

Lissajous figures are produced by combining two oscillations at right angles to each other. The figures, drawn by mechanical devices called harmonographs, have scientific uses, but are also enjoyed for their own beauty. The author has been working with harmonographs since his undergraduate days, building several of them, lecturing on them and has written articles about them. This book is intended for people who enjoy physics or art or both.

Chemistry, physics and biology are by their nature genuinely difficult. Mathematics, however, is man-made, and therefore not as complicated. Two ideas form the basis for this book: 1) to use ordinary mathematics to describe the simplicity in the structure of mathematics and 2) to develop new branches of mathematics to describe natural sciences.

Mathematics can be described as the addition, subtraction or multiplication of planes. Using the exponential scale the authors show that the addition of planes gives the polyhedra, or any solid. The substraction of planes gives saddles. The multiplication of planes gives the general saddle equations and the multispirals. The equation of symmetry is derived, which contains the exponential scale with its functions for solids, the complex exponentials with the nodal surfaces, and the GD (Gauss Distribution) mathematics with finite periodicity.

Piece by piece, the authors have found mathematical functions for the geometrical descriptions of chemical structures and the structure building operations. Using the mathematics for dilatation; twins, trillings, fourlings and sixlings are made, and using GD mathematics these are made periodic. This description of a structure is the nature of mathematics itself. Crystal structures and 3D mathematics are synonyms. Mathematics are used to describe rod packings, Olympic rings and defects in solids. Giant molecules such as cubosomes, the DNA double helix, and certain building blocks in protein structures are also described mathematically.

This book offers a complete guide to designing Linear Fresnel Reflector Systems for concentrating solar radiation. It includes theoretical analyses, computational tools and mathematical formulae to facilitate the development, design, construction and application of these systems. In addition, the book presents a concise yet thorough treatment of the theory behind these systems, and provides useful and efficient calculation procedures that can be used to model and develop their practical applications. Along with the theoretical analyses provided in the book, the physical background is explained using mathematical formulae, illustrations, graphs and tables. Methods are presented for solving the non-linear mathematical systems that describe a significant variety of cases. In addition, MATLAB codes are supplied (both in the text and online). Consequently, readers interested in applying the methodology presented here will have all the source codes at hand, allowing them to easily expand on them by introducing appropriate modifications for their respective design configuration. Given its scope, the book will be of interest to engineers and researchers, who can use their scientific background to help them develop more energy-efficient Linear Fresnel Reflector systems. It will also appeal to students studying these systems for the first time, as it supplies a comprehensive overview of their theoretical analysis and applications.

This book provides an interdisciplinary approach to complexity, combining ideas from areas like complex networks, cellular automata, multi-agent systems, self-organization and game theory. The first part of the book provides an extensive introduction to these areas, while the second explores a range of research scenarios. Lastly, the book presents CellNet, a software framework that offers a hands-on approach to the scenarios described throughout the book. In light of the introductory chapters, the research chapters, and the CellNet simulating framework, this book can be used to teach undergraduate and master's students in disciplines like artificial intelligence, computer science, applied mathematics, economics and engineering. Moreover, the book will be particularly interesting for Ph.D. and postdoctoral researchers seeking a general perspective on how to design and create their own models.

The book contains a detailed account of numerical solutions of differential equations of a number of elementary problems of physics using Euler and second order Runge-Kutta methods using Mathematica 6.0. The problems are motion under constant force (free fall), motion under Hooke's law force (simple harmonic motion), motion under combination of Hooke's law force and a velocity dependent damping force (damped harmonic motion) and radioactive decay law. Also included are uses of Mathematica in dealing with complex numbers, in solving system of linear equations, in carrying out differentiation and integration, and in dealing with matrices.

Beyond Pseudo-Rotations in Pseudo-Euclidean Spaces presents for the first time a unified study of the Lorentz transformation group SO(m, n) of signature (m, n), m, n ? N, which is fully analogous to the Lorentz group SO(1, 3) of Einstein's special theory of relativity. It is based on a novel parametric realization of pseudo-rotations by a vector-like parameter with two orientation parameters. The book is of interest to specialized researchers in the areas of algebra, geometry and mathematical physics, containing new results that suggest further exploration in these areas.

Recent developments in model-predictive control promise remarkable opportunities for designing multi-input, multi-output control systems and improving the control of single-input, single-output systems. This volume provides a definitive survey of the latest model-predictive control methods available to engineers and scientists today. The initial set of chapters present various methods for managing uncertainty in systems, including stochastic model-predictive control. With the advent of affordable and fast computation, control engineers now need to think about using "computationally intensive controls," so the second part of this book addresses the solution of optimization problems in "real" time for model-predictive control. The theory and applications of control theory often influence each other, so the last section of Handbook of Model Predictive Control rounds out the book with representative applications to automobiles, healthcare, robotics, and finance. The chapters in this volume will be useful to working engineers, scientists, and mathematicians, as well as students and faculty interested in the progression of control theory. Future developments in MPC will no doubt build from concepts demonstrated in this book and anyone with an interest in MPC will find fruitful information and suggestions for additional reading.

Analysis and Control of Polynomial Dynamic Models with Biological Applications synthesizes three mathematical background areas (graphs, matrices and optimization) to solve problems in the biological sciences (in particular, dynamic analysis and controller design of QP and polynomial systems arising from predator-prey and biochemical models). The book puts a significant emphasis on applications, focusing on quasi-polynomial (QP, or generalized Lotka-Volterra) and kinetic systems (also called biochemical reaction networks or simply CRNs) since they are universal descriptors for smooth nonlinear systems and can represent all important dynamical phenomena that are present in biological (and also in general) dynamical systems.

This accessible monograph introduces physicists to the general relation between classical and quantum mechanics based on the mathematical idea of deformation quantization and describes an original approach to the theory of quantum integrable systems developed by the author.The first goal of the book is to develop of a common, coordinate free formulation of classical and quantum Hamiltonian mechanics, framed in common mathematical language.In particular, a coordinate free model of quantum Hamiltonian systems in Riemannian spaces is formulated, based on the mathematical idea of deformation quantization, as a complete physical theory with an appropriate mathematical accuracy.The second goal is to develop of a theory which allows for a deeper understanding of classical and quantum integrability. For this reason the modern separability theory on both classical and quantum level is presented. In particular, the book presents a modern geometric separability theory, based on bi-Poissonian and bi-presymplectic representations of finite dimensional Liouville integrable systems and their admissible separable quantizations.The book contains also a generalized theory of classical Stackel transforms and the discussion of the concept of quantum trajectories.In order to make the text consistent and self-contained, the book starts with a compact overview of mathematical tools necessary for understanding the remaining part of the book. However, because the book is dedicated mainly to physicists, despite its mathematical nature, it refrains from highlighting definitions, theorems or lemmas.Nevertheless, all statements presented are either proved or the reader is referred to the literature where the proof is available.

Branches of mathematics and advanced mathematical algorithms can help solve daily problems throughout various fields of applied sciences. Domains like economics, mechanical engineering, and multi-person decision making benefit from the inclusion of mathematics to maximize utility and cooperation across disciplines. There is a need for studies seeking to understand the theories and practice of using differential mathematics to increase efficiency and order in the modern world. Emerging Applications of Differential Equations and Game Theory is a collection of innovative research that examines the recent advancements on interdisciplinary areas of applied mathematics. While highlighting topics such as artificial neuron networks, stochastic optimization, and dynamical systems, this publication is ideally designed for engineers, cryptologists, economists, computer scientists, business managers, mathematicians, mechanics, academicians, researchers, and students.

This book is a rare jewel, describing fundamental research in a highly dynamic field of subatomic physics. It presents an overview of cross section measurements of deeply virtual Compton scattering. Understanding the structure of the proton is one of the most important challenges that physics faces today. A typical tool for experimentally accessing the internal structure of the proton is lepton-nucleon scattering. In particular, deeply virtual Compton scattering at large photon virtuality and small four-momentum transfer to the proton provides a tool for deriving a three-dimensional tomographic image of the proton. Using clear language, this book presents the highly complex procedure used to derive the momentum-dissected transverse size of the proton from a pioneering measurement taken at CERN. It describes in detail the foundations of the measurement and the data analysis, and includes exhaustive studies of potential systematic uncertainties, which could bias the result.

Mathematical Physics with Partial Differential Equations, Second Edition, is designed for upper division undergraduate and beginning graduate students taking mathematical physics taught out by math departments. The new edition is based on the success of the first, with a continuing focus on clear presentation, detailed examples, mathematical rigor and a careful selection of topics. It presents the familiar classical topics and methods of mathematical physics with more extensive coverage of the three most important partial differential equations in the field of mathematical physics-the heat equation, the wave equation and Laplace's equation. The book presents the most common techniques of solving these equations, and their derivations are developed in detail for a deeper understanding of mathematical applications. Unlike many physics-leaning mathematical physics books on the market, this work is heavily rooted in math, making the book more appealing for students wanting to progress in mathematical physics, with particularly deep coverage of Green's functions, the Fourier transform, and the Laplace transform. A salient characteristic is the focus on fewer topics but at a far more rigorous level of detail than comparable undergraduate-facing textbooks. The depth of some of these topics, such as the Dirac-delta distribution, is not matched elsewhere. New features in this edition include: novel and illustrative examples from physics including the 1-dimensional quantum mechanical oscillator, the hydrogen atom and the rigid rotor model; chapter-length discussion of relevant functions, including the Hermite polynomials, Legendre polynomials, Laguerre polynomials and Bessel functions; and all-new focus on complex examples only solvable by multiple methods.

This book presents the theory and practical applications of the Master equation approach, which provides a powerful general framework for model building in a variety of disciplines. The aim of the book is to not only highlight different mathematical solution methods, but also reveal their potential by means of practical examples. Part I of the book, which can be used as a toolbox, introduces selected statistical fundamentals and solution methods for the Master equation. In Part II and Part III, the Master equation approach is applied to important applications in the natural and social sciences. The case studies presented mainly hail from the social sciences, including urban and regional dynamics, population dynamics, dynamic decision theory, opinion formation and traffic dynamics; however, some applications from physics and chemistry are treated as well, underlining the interdisciplinary modelling potential of the Master equation approach. Drawing upon the author's extensive teaching and research experience and consulting work, the book offers a valuable guide for researchers, graduate students and professionals alike.

The best laboratory math text on the market for almost 20 years, this title covers both the general principles of mathematics and specific equations, formulas, and calculations used for laboratory testing. It provides simple, easily understood explanations of calculations commonly used in clinical and biological laboratories. Contains more than 1000 practice problems.

This book presents the latest findings on train operation theories and methods in the context of emergencies. It examines and assesses a range of aspects-including the definition of a railway emergency, transport organization modes in emergencies, calculating railway transport capacity in emergencies, line planning in emergencies, train re-pathing in emergencies and train re-scheduling in emergencies-that are urgently needed in the railway transportation field, which faces the serious challenge of dealing with emergencies worldwide. The book highlights the latest research results in an integrated and systematic way, and the methodology presented is oriented on real-world problems, allowing it to be used not only directly in railway operational management, but also as the point of departure for further applications or theoretical research. As such, the book will be of considerable interest to graduate students and researchers in the field of traffic and transportation engineering.>

Handbook of Statistics: Disease Modelling and Public Health, Part B, Volume 37 addresses new challenges in existing and emerging diseases. As a two part volume, this title covers an extensive range of techniques in the field, with this book including chapters on Reaction diffusion equations and their application on bacterial communication, Spike and slab methods in disease modeling, Mathematical modeling of mass screening and parameter estimation, Individual-based and agent-based models for infectious disease transmission and evolution: an overview, and a section on Visual Clustering of Static and Dynamic High Dimensional Data. This volume covers the lack of availability of complete data relating to disease symptoms and disease epidemiology, one of the biggest challenges facing vaccine developers, public health planners, epidemiologists and health sector researchers.

This book is designed to supplement standard texts and teaching material in the areas of differential equations in engineering such as in Electrical ,Mechanical and Biomedical engineering. Emphasis is placed on the Boundary Value Problems that are often met in these fields.This keeps the the spectrum of the book rather focussed .The book has basically emerged from the need in the authors lectures on "Advanced Numerical Methods in Biomedical Engineering" at Yeditepe University and it is aimed to assist the students in solving general and application specific problems in Science and Engineering at upper-undergraduate and graduate level.Majority of the problems given in this book are self-contained and have varying levels of difficulty to encourage the student. Problems that deal with MATLAB simulations are particularly intended to guide the student to understand the nature and demystify theoretical aspects of these problems. Relevant references are included at the end of each chapter. Here one will also find large number of software that supplements this book in the form of MATLAB script (.m files). The name of the files used for the solution of a problem are indicated at the end of each corresponding problem statement.There are also some exercises left to students as homework assignments in the book. An outstanding feature of the book is the large number and variety of the solved problems that are included in it. Some of these problems can be found relatively simple, while others are more challenging and used for research projects. All solutions to the problems and script files included in the book have been tested using recent MATLAB software.The features and the content of this book will be most useful to the students studying in Engineering fields, at different levels of their education (upper undergraduate-graduate).

This textbook provides an introduction to the growing interdisciplinary field of computational science. It combines a foundational development of numerical methods with a variety of illustrative applications spread across numerous areas of science and engineering. The intended audience is the undergraduate who has completed introductory coursework in mathematics and computer science. Students gain computational acuity by authoring their own numerical routines and by practicing with numerical methods as they solve computational models. This education encourages students to learn the importance of answering: How expensive is a calculation, how trustworthy is a calculation, and how might we model a problem to apply a desired numerical method? The text is written in two parts. Part I provides a succinct, one-term inauguration into the primary routines on which a further study of computational science rests. The material is organized so that the transition to computational science from coursework in calculus, differential equations, and linear algebra is natural. Beyond the mathematical and computational content of Part I, students gain proficiency with elemental programming constructs and visualization, which are presented in MATLAB syntax. The focus of Part II is modeling, wherein students build computational models, compute solutions, and report their findings. The models purposely intersect numerous areas of science and engineering to demonstrate the pervasive role played by computational science.

This book provides a comprehensive treatment of the physics of hysteresis in magnetism and of the mathematical tools used to describe it. Hysteresis in Magnetism discusses from a unified viewpoint the relationsof hysteresis to Maxwells equations, equilibrium and non-equilibrium thermodynamics, non-linear system dynamics, micromagnetics, and domain theory. These aspects are then applied to the interpretation of magnetization reversal mechanisms: coherent rotation and switching in magnetic particles, stochastic domain wall motion and the Barkhausen effect, coercivity mechanisms and magnetic viscosity, rate-dependent hysteresis and eddy-current losses. The book emphasizes the connection between basic physical ideas and phenomenological models of interest to applications, and, in particular, to the conceptual path going from Maxwells equations and thermodynamics to micromagnetics and to Preisach hysteresis modeling.
Key Features
* The reader will get insight into the importance and role of hysteresis in magnetism; In particular, he will learn:
* which are the fingerprints of hysteresis in magnetism
* which are the situations in which hysteresis may appear
* how to describe mathematically these situations
* how to apply these descriptions to magnetic materials
* how to interpret and predict magnetic hysteresis phenomena observed experimentally

The research and review papers presented in this volume provide an overview of the main issues, findings, and open questions in cutting-edge research on the fields of modeling, optimization and dynamics and their applications to biology, economics, energy, finance, industry, physics and psychology. Given the scientific relevance of the innovative applications and emerging issues they address, the contributions to this volume, written by some of the world's leading experts in mathematics, economics and other applied sciences, will be seminal to future research developments and will spark future works and collaborations. The majority of the papers presented in this volume were written by participants of the 4th International Conference on Dynamics, Games and Science: Decision Models in a Complex Economy (DGS IV), held at the National Distance Education University (UNED) in Madrid, Spain in June 2016 and of the 8th Berkeley Bioeconomy Conference: The Future of Biofuels, held at the UC Berkeley Alumni House in April 2015.

Ulam Stability of Operators presents a modern, unified, and systematic approach to the field. Focusing on the stability of functional equations across single variable, difference equations, differential equations, and integral equations, the book collects, compares, unifies, complements, generalizes, and updates key results. Whenever suitable, open problems are stated in corresponding areas. The book is of interest to researchers in operator theory, difference and functional equations and inequalities, differential and integral equations.

It has been known for some time that many of the familiar integrable systems of equations are symmetry reductions of self-duality equations on a metric or on a Yang-Mills connection (for example, the Korteweg-de Vries and nonlinear Schroedinger equations are reductions of the self-dual Yang-Mills equation). This book explores in detail the connections between self-duality and integrability, and also the application of twistor techniques to integrable systems. It has two central themes: first, that the symmetries of self-duality equations provide a natural classification scheme for integrable systems; and second that twistor theory provides a uniform geometric framework for the study of Backlund tranformations, the inverse scattering method, and other such general constructions of integrability theory, and that it elucidates the connections between them.

This book offers a detailed description of the histogram probabilistic multi-hypothesis tracker (H-PMHT), providing an accessible and intuitive introduction to the mathematical mechanics of H-PMHT as well as a definitive reference source for the existing literature on the method. Beginning with basic concepts, the authors then move on to address extensions of the method to a broad class of tracking problems. The latter chapters present applications using recorded data from experimental radar, sonar and video sensor systems. The book is supplemented with software that both furthers readers' understanding and acts as a toolkit for those who wish to apply the methods to their own problems.

This book is a survey of the research work done by the author over the last 15 years, in collaboration with various eminent mathematicians and climate scientists on the subject of tropical convection and convectively coupled waves. In the areas of climate modelling and climate change science, tropical dynamics and tropical rainfall are among the biggest uncertainties of future projections. This not only puts at risk billions of human beings who populate the tropical continents but it is also of central importance for climate predictions on the global scale. This book aims to introduce the non-expert readers in mathematics and theoretical physics to this fascinating topic in order to attract interest into this difficult and exciting research area. The general thyme revolves around the use of new deterministic and stochastic multi-cloud models for tropical convection and convectively coupled waves. It draws modelling ideas from various areas of mathematics and physics and used in conjunction with state-of-the-art satellite and in-situ observations and detailed numerical simulations. After a review of preliminary material on tropical dynamics and moist thermodynamics, including recent discoveries based on satellite observations as well as Markov chains, the book immerses the reader into the area of models for convection and tropical waves. It begins with basic concepts of linear stability analysis and ends with the use of these models to improve the state-of-the-art global climate models. The book also contains a fair amount of exercises that makes it suitable as a textbook complement on the subject.