This edition of the invaluable text Modern Differential Geometry for Physicists contains an additional chapter that introduces some of the basic ideas of general topology needed in differential geometry. A number of small corrections and additions have also been made.These lecture notes are the content of an introductory course on modern, coordinate-free differential geometry which is taken by first-year theoretical physics PhD students, or by students attending the one-year MSc course "Quantum Fields and Fundamental Forces" at Imperial College. The book is concerned entirely with mathematics proper, although the emphasis and detailed topics have been chosen bearing in mind the way in which differential geometry is applied these days to modern theoretical physics. This includes not only the traditional area of general relativity but also the theory of Yang-Mills fields, nonlinear sigma models and other types of nonlinear field systems that feature in modern quantum field theory.The volume is divided into four parts: (i) introduction to general topology; (ii) introductory coordinate-free differential geometry; (iii) geometrical aspects of the theory of Lie groups and Lie group actions on manifolds; (iv) introduction to the theory of fibre bundles. In the introduction to differential geometry the author lays considerable stress on the basic ideas of "tangent space structure", which he develops from several different points of view - some geometrical, others more algebraic. This is done with awareness of the difficulty which physics graduate students often experience when being exposed for the first time to the rather abstract ideas of differential geometry.

This book, on the general topic of hydroaerodynamics, investigates a number of exciting applications in this field, addressing specifically issues that allow seemingly paradoxical issues to be dealt with. The first part is devoted to the study of channel flows, in particular the lateral flow of a viscous and viscous-plastic liquid in a ring channel formed by coaxial cylinders. Specifically, the problem of dissipation of mechanical energy in channel flows of highly viscous liquids is addressed and solved. Furthermore, the mechanism leading to hydrodynamic erosion in intra-field pipelines (known as "channelized effect") is identified. Subsequently, a theory for channel flows with mass transfer through porous walls is developed. In the second part, viscous liquid free flows (jets) are investigated. In particular, a dispersion law for turbulent flow is derived and the existence of dynamic invariance in wake flows of variable density is demonstrated. The third part presents new insights from both theoretical and experimental research into concentrated vortex structure formation and development. The conditions for the existence of Taylor-Goertler vortices are determined and the mechanism for their formation is described. Last but not least, the theory of vortex rings, a particularly interesting problem in hydroaerodynamics, is introduced in the last section of this book. Care has been taken, when selecting original theoretical problems of interest, to make the link with related topics in the published literature. At the same time, all experimental research described in this book is given a meaningful physical interpretation and corroborated by suitable theoretical models and computations.

This volume provides academic discussion on the theory and practice of mathematical analysis of nonlinear and inverse problems in electromagnetics and their applications. From mathematical problem statement to numerical results, the featured articles provide a concise overview of comprehensive approaches to the solution of problems. Articles highlight the most recent research concerning reliable theoretical approaches and numerical techniques and cover a wide range of applications, including acoustics, electromagnetics, optics, medical imaging, and geophysics. The nonlinear and ill-posed nature of inverse problems and the challenges they present when developing new numerical methods are explained, and numerical verification of proposed new methods on simulated and experimental data is provided. Based on the special session of the same name at the 2017 Progress in Electromagnetics Research Symposium, this book offers a platform for interaction between theoretical and practical researchers and between senior and incoming members in the field.

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.

The papers in this volume represent a broad, applied swath of advanced contributions to the 2015 ICSA/Graybill Applied Statistics Symposium of the International Chinese Statistical Association, held at Colorado State University in Fort Collins. The contributions cover topics that range from statistical applications in business and finance to applications in clinical trials and biomarker analysis. Each papers was peer-reviewed by at least two referees and also by an editor. The conference was attended by over 400 participants from academia, industry, and government agencies around the world, including from North America, Asia, and Europe.

Computational complexity is a serious bottleneck for the design process in virtually any engineering area. While migration from prototyping and experimental-based design validation to verification using computer simulation models is inevitable and has a number of advantages, high computational costs of accurate, high-fidelity simulations can be a major issue that slows down the development of computer-aided design methodologies, particularly those exploiting automated design improvement procedures, e.g., numerical optimization. The continuous increase of available computational resources does not always translate into shortening of the design cycle because of the growing demand for higher accuracy and necessity to simulate larger and more complex systems. Accurate simulation of a single design of a given system may be as long as several hours, days or even weeks, which often makes design automation using conventional methods impractical or even prohibitive. Additional problems include numerical noise often present in the simulation data, possible presence of multiple locally optimum designs, as well as multiple conflicting objectives. In this edited book, various techniques that can alleviate solving computationally expensive engineering design problems are presented. One of the most promising approaches is the use of fast replacement models, so-called surrogates, that reliably represent the expensive, simulation-based model of the system/device of interest but they are much cheaper and analytically tractable. Here, a group of international experts summarize recent developments in the area and demonstrate applications in various disciplines of engineering and science. The main purpose of the work is to provide the basic concepts and formulations of the surrogate-based modeling and optimization paradigm, as well as discuss relevant modeling techniques, optimization algorithms and design procedures. Therefore, this book should be useful to researchers and engineers from any discipline where computationally heavy simulations are used on daily basis in the design process.

This book provides a self-study program on how mathematics, computer science and science can be usefully and seamlessly intertwined. Learning to use ideas from mathematics and computation is essential for understanding approaches to cognitive and biological science. As such the book covers calculus on one variable and two variables and works through a number of interesting first-order ODE models. It clearly uses MatLab in computational exercises where the models cannot be solved by hand, and also helps readers to understand that approximations cause errors - a fact that must always be kept in mind.

Broadly organized around the applications of Fourier analysis, "Methods of Applied Mathematics with a MATLAB Overview" covers both classical applications in partial differential equations and boundary value problems, as well as the concepts and methods associated to the Laplace, Fourier, and discrete transforms. Transform inversion problems are also examined, along with the necessary background in complex variables. A final chapter treats wavelets, short-time Fourier analysis, and geometrically-based transforms. The computer program MATLAB is emphasized throughout, and an introduction to MATLAB is provided in an appendix. Rich in examples, illustrations, and exercises of varying difficulty, this text can be used for a one- or two-semester course and is ideal for students in pure and applied mathematics, physics, and engineering.

Focused on recent advances, this book covers theoretical foundations as well as various applications. It presents modern mathematical modeling approaches to the qualitative and numerical analysis of solutions for complex engineering problems in physics, mechanics, biochemistry, geophysics, biology and climatology. Contributions by an international team of respected authors bridge the gap between abstract mathematical approaches, such as applied methods of modern analysis, algebra, fundamental and computational mechanics, nonautonomous and stochastic dynamical systems on the one hand, and practical applications in nonlinear mechanics, optimization, decision making theory and control theory on the other. As such, the book will be of interest to mathematicians and engineers working at the interface of these fields.

This monograph provides a concise presentation of a mathematical approach to metastability, a wide-spread phenomenon in the dynamics of non-linear systems - physical, chemical, biological or economic - subject to the action of temporal random forces typically referred to as noise, based on potential theory of reversible Markov processes. The authors shed new light on the metastability phenomenon as a sequence of visits of the path of the process to different metastable sets, and focuses on the precise analysis of the respective hitting probabilities and hitting times of these sets. The theory is illustrated with many examples, ranging from finite-state Markov chains, finite-dimensional diffusions and stochastic partial differential equations, via mean-field dynamics with and without disorder, to stochastic spin-flip and particle-hop dynamics and probabilistic cellular automata, unveiling the common universal features of these systems with respect to their metastable behaviour. The monograph will serve both as comprehensive introduction and as reference for graduate students and researchers interested in metastability.

This work is dedicated to Wassiliy Leontief's concepts of Input-Output Analysis and to the algebraic properties of Piero Sraffa's seminal models described consequently by matrix algebra and the Perron-Frobenius Theorem. Detailed examples and visualizing graphs are presented for applications of various mathematical methods.

This edited volume offers a clear in-depth overview of research covering a variety of issues in social search and recommendation systems. Within the broader context of social network analysis it focuses on important and up-coming topics such as real-time event data collection, frequent-sharing pattern mining, improvement of computer-mediated communication, social tagging information, search system personalization, new detection mechanisms for the identification of online user groups, and many more. The twelve contributed chapters are extended versions of conference papers as well as completely new invited chapters in the field of social search and recommendation systems. This first-of-its kind survey of current methods will be of interest to researchers from both academia and industry working in the field of social networks.

This monograph addresses the state of the art of reduced order methods for modeling and computational reduction of complex parametrized systems, governed by ordinary and/or partial differential equations, with a special emphasis on real time computing techniques and applications in computational mechanics, bioengineering and computer graphics.

Several topics are covered, including: design, optimization, and control theory in real-time with applications in engineering; data assimilation, geometry registration, and parameter estimation with special attention to real-time computing in biomedical engineering and computational physics; real-time visualization of physics-based simulations in computer science; the treatment of high-dimensional problems in state space, physical space, or parameter space; the interactions between different model reduction and dimensionality reduction approaches; the development of general error estimation frameworks which take into account both model and discretization effects.

This book is primarily addressed to computational scientists interested in computational reduction techniques for large scale differential problems.

This book deals with fractals in understanding problems encountered in earth science, and their solutions. It starts with an analysis of two classes of methods (homogeneous fractals random models, and homogeneous source distributions or "one point" distributions) widely diffused in the geophysical community, especially for studying potential fields and their related source distributions. Subsequently, the use of fractals in potential fields is described by scaling spectral methods for estimation of curie depth. The book also presents an update of the use of the fractal concepts in geological understanding of faults and their significance in geological modelling of hydrocarbon reservoirs. Geophysical well log data provide a unique description of the subsurface lithology; here, the Detrended Fluctuation Analysis technique is presented in case studies located off the west-coast of India. Another important topic is the fractal model of continuum percolation which quantitatively reproduce the flow path geometry by applying the Poiseuille's equation. The pattern of fracture heterogeneity in reservoir scale of natural geological formations can be viewed as spatially distributed self-similar tree structures; here, the authors present simple analytical models based on the medium structural characteristics to explain the flow in natural fractures. The Fractal Differential Adjacent Segregation (F-DAS) is an unconventional approach for fractal dimension estimation using a box count method. The present analysis provides a better understanding of variability of the system (adsorbents - adsorbate interactions). Towards the end of book, the authors discuss multi-fractal scaling properties of seismograms in order to quantify the complexity associated with high-frequency seismic signals. Finally, the book presents a review on fractal methods applied to fire point processes and satellite time-continuous signals that are sensitive to fire occurrences.

During the past three decades, the development of nonlinear analysis, dynamical systems and their applications to science and engineering has stimulated renewed enthusiasm for the theory of Ordinary Differential Equations (ODE).This useful book, which is based on the lecture notes of a well-received graduate course, emphasizes both theory and applications, taking numerous examples from physics and biology to illustrate the application of ODE theory and techniques.Written in a straightforward and easily accessible style, this volume presents dynamical systems in the spirit of nonlinear analysis to readers at a graduate level and serves both as a textbook and as a valuable resource for researchers.This new edition contains corrections and suggestions from the various readers and users. A new chapter on Monotone Dynamical Systems is added to take into account the new developments in ordinary differential equations and dynamical systems.

Newton's classical physics and its underlying ontology are loaded with several metaphysical hypotheses that cannot be justified by rational reasoning nor by experimental evidence. Furthermore, it is well known that some of these hypotheses are not contained in the great theories of Modern Physics, such as the theory of Special Relativity and Quantum Mechanics. This book shows that, on the basis of Newton's classical physics and by rational reconstruction, the theory of Special Relativity as well as Quantum Mechanics can be obtained by partly eliminating or attenuating the metaphysical hypotheses. Moreover, it is shown that these reconstructions do not require additional hypotheses or new experimental results. In the second edition the rational reconstructions are completed with respect to General Relativity and Cosmology. In addition, the statistics of quantum objects is elaborated in more detail with respect to the rational reconstruction of quantum mechanics. The new material completes the approach of the book as much as it is possible at the present state of knowledge. Presumably, the most important contribution that is added to the second edition refers to the problem of interpretation of the three great theories of Modern Physics. It is shown in detail that in the light of rational reconstructions even realistic interpretations of the three theories of Modern Physics are possible and can easily be achieved.

This thesis presents fundamental work that explains two mysteries concerning the trajectory of interplanetary spacecraft. For the first problem, the so-called Pioneer anomaly, a wholly new and innovative method was developed for computing all contributions to the acceleration due to onboard thermal sources. Through a careful analysis of all parts of the spacecraft Pioneer 10 and 11, the application of this methodology has yielded the observed anomalous acceleration. This marks a major achievement, given that this problem remained unsolved for more than a decade. For the second anomaly, the flyby anomaly, a tiny glitch in the velocity of spacecraft that perform gravity assisting maneuvers on Earth, no definitive answer is put forward; however a quite promising strategy for examining the problem is provided and a new mission is proposed. The proposal largely consists in using the Galileo Navigational Satellite System to track approaching spacecraft, and in considering a small test body that approaches Earth from a highly elliptic trajectory.

Der Grundkurs Theoretische Physik deckt in 7 Banden alle fur das Diplom und fur Bachelor/Master-Studiengange massgeblichen Gebiete ab. Jeder Band vermittelt das im jeweiligen Semester notwendige theoretisch-physikalische Rustzeug. UEbungsaufgaben mit ausfuhrlichen Loesungen dienen der Vertiefung des Stoffs. Der 4. Band behandelt die Gebiete Thermodynamik und Relativitatstheorie. Fur die Neuauflage wurde er grundlegend uberarbeitet und um 24 Aufgaben erganzt. Durch die zweifarbige Gestaltung ist der Stoff jetzt noch ubersichtlicher gegliedert.

This book describes an effective framework for setting the right process parameters and new mold design to reduce the current plastic defects in injection molding. It presents a new approach for the optimization of injection molding process via (i) a new mold runner design which leads to 20 percent reduction in scrap rate, 2.5 percent reduction in manufacturing time, and easier ejection of injected part, (ii) a new mold gate design which leads to less plastic defects; and (iii) the introduction of a number of promising alternatives with high moldability indices. Besides presenting important developments of relevance academic research, the book also includes useful information for people working in the injection molding industry, especially in the green manufacturing field.

These papers on Intelligent Data Analysis and Management (IDAM) examine issues related to the research and applications of Artificial Intelligence techniques in data analysis and management across a variety of disciplines. The papers derive from the 2013 IDAM conference in Kaohsiung ,Taiwan. It is an interdisciplinary research field involving academic researchers in information technologies, computer science, public policy, bioinformatics, medical informatics, and social and behavior studies, etc. The techniques studied include (but are not limited to): data visualization, data pre-processing, data engineering, database mining techniques, tools and applications, evolutionary algorithms, machine learning, neural nets, fuzzy logic, statistical pattern recognition, knowledge filtering, and post-processing, etc.

This book provides a self-contained introduction to the theory of infinite-dimensional systems theory and its applications to port-Hamiltonian systems. The textbook starts with elementary known results, then progresses smoothly to advanced topics in current research. Many physical systems can be formulated using a Hamiltonian framework, leading to models described by ordinary or partial differential equations. For the purpose of control and for the interconnection of two or more Hamiltonian systems it is essential to take into account this interaction with the environment. This book is the first textbook on infinite-dimensional port-Hamiltonian systems. An abstract functional analytical approach is combined with the physical approach to Hamiltonian systems. This combined approach leads to easily verifiable conditions for well-posedness and stability. The book is accessible to graduate engineers and mathematicians with a minimal background in functional analysis. Moreover, the theory is illustrated by many worked-out examples.

This book provides a crash course on various methods from the bifurcation theory of Functional Differential Equations (FDEs). FDEs arise very naturally in economics, life sciences and engineering and the study of FDEs has been a major source of inspiration for advancement in nonlinear analysis and infinite dimensional dynamical systems. The book summarizes some practical and general approaches and frameworks for the investigation of bifurcation phenomena of FDEs depending on parameters with chap. This well illustrated book aims to be self contained so the readers will find in this book all relevant materials in bifurcation, dynamical systems with symmetry, functional differential equations, normal forms and center manifold reduction. This material was used in graduate courses on functional differential equations at Hunan University (China) and York University (Canada).