This thesis is concerned with flows through cascades, i.e. periodic arrays of obstacles. Such geometries are relevant to a range of physical scenarios, chiefly the aerodynamics and aeroacoustics of turbomachinery flows. Despite the fact that turbomachinery is of paramount importance to a number of industries, many of the underlying mechanisms in cascade flows remain opaque. In order to clarify the function of different physical parameters, the author considers six separate problems. For example, he explores the significance of realistic blade geometries in predicting turbomachinery performance, and the possibility that porous blades can achieve noise reductions. In order to solve these challenging problems, the author deploys and indeed develops techniques from across the spectrum of complex analysis: the Wiener-Hopf method, Riemann-Hilbert problems, and the Schottky-Klein prime function all feature prominently. These sophisticated tools are then used to elucidate the underlying mathematical and physical structures present in cascade flows. The ensuing solutions greatly extend previous works and offer new avenues for future research. The results are not of simply academic value but are also useful for aircraft designers seeking to balance aeroacoustic and aerodynamic effects.

The XIIIth Bialowieza Summer Workshop was held from July 9 to 15, 1994. While still within the general framework of Differential Geometric Methods in Physics, the XnIth Workshop was expanded in scope to include quantum groups, q-deformations and non-commutative geometry. It is expected that lectures on these topics will now become an integral part of future workshops. In the more traditional areas, lectures were devoted to topics in quantization, field theory, group representations, coherent states, complex and Poisson structures, the Berry phase, graded contractions and some infinite-dimensional systems. Those of us who have taken part in the evolution of the workshops over the years, feel a good measure of satisfaction with the excellent quality of the papers presented, in particular the mathematical rigour and novelty. Each year a significant number of new results are presented and future directions of research are discussed. Their freshness and immediacy inevitably leads to intense discussions and an exchange of ideas in an informal and physically charming environment. The present workshop also had a higher attendance than its predecessors, with ap proximately 65 registered participants. As usual, there was a large number of graduate students and young researchers among them."

The book reviews a large number of 1- and 2-dimensional equations that describe nonlinear phenomena in various areas of modern theoretical and mathematical physics. It is meant, above all, for physicists who specialize in the field theory and physics of elementary particles and plasma, for mathe maticians dealing with nonlinear differential equations, differential geometry, and algebra, and the theory of Lie algebras and groups and their representa tions, and for students and post-graduates in these fields. We hope that the book will be useful also for experts in hydrodynamics, solid-state physics, nonlinear optics electrophysics, biophysics and physics of the Earth. The first two chapters of the book present some results from the repre sentation theory of Lie groups and Lie algebras and their counterpart on supermanifolds in a form convenient in what follows. They are addressed to those who are interested in integrable systems but have a scanty vocabulary in the language of representation theory. The experts may refer to the first two chapters only occasionally. As we wanted to give the reader an opportunity not only to come to grips with the problem on the ideological level but also to integrate her or his own concrete nonlinear equations without reference to the literature, we had to expose in a self-contained way the appropriate parts of the representation theory from a particular point of view."

The objective of this book is to construct a rigorous mathematical approach to linear hereditary problems of wave propagation theory and demonstrate the efficiency of mathematical theorems in hereditary mechanics. By using both real end complex Tauberian techniques for the Laplace transform, a classification of near-front asymptotics of solutions to considered equations is given-depending on the singularity character of the memory function. The book goes on to derive the description of the behavior of these solutions and demonstrates the importance of nonlinear Laplace transform in linear hereditary elasticity. This book is of undeniable value to researchers working in areas of mathematical physics and related fields.

Fortran remains one of the principal programming languages used in high-performance scientific, numerical, and engineering computing. A series of significant revisions to the standard versions of the language have progressively enhanced its capabilities and the latest standard, Fortran 2008, includes many modern features, such as object orientation, coarrays for parallel programming, interoperability with C and various other enhancements.
Modern Fortran Explained expands on its predecessor, Fortran 95/2003 Explained. The opening chapters contain a complete description of Fortran 95, extended by Fortran 2003 allocatable array features. Coverage of the other additional features of Fortran 2003 follows, before new chapters on coarrays and the many other enhancements of Fortran 2008. The distinction between the three language levels is maintained throughout, allowing readers to understand and amend legacy code as well as the new features.
Authored by three experts in the field, two of whom have actively contributed to Fortran 2008, this is a complete and authoritative description of Fortran in its modern form. It is intended for new and existing users of the language and for all those involved in scientific and numerical computing. It is suitable as a textbook for teaching and, with its extensive Appendices and an Index, as a handy reference for practitioners.

Nail your next physics exam and prepare yourself for the next level of physics education Physics isn't the easiest part of high school, but it doesn't have to be pull-your-hair-out hard. In Physics I Workbook For Dummies, you get practical guidance to reinforce what you already know and master new physics concepts. You'll gain confidence in critical subject areas like motion, thermodynamics, and electromagnetism while setting yourself up for success in college- and university-level physics courses. This book offers hands-on practice exercises in the book and on an online test bank that come with plain-English answers and step-by-step explanations so you can see what you did right and where you need practice. The perfect combination of instruction and application, Physics I Workbook For Dummies also provides: Understandable explanations of central physics concepts and the techniques you need to solve common problems Practice questions with complete answer explanations to test your knowledge as you progress Highlights of the ten most common pitfalls and traps that students encounter in physics assignments and exams and how to avoid them A collection of the ten most useful online physics resources, along with free, 1-year access to online chapter quizzes Whether you're planning to tackle the MCAT one day or just want to improve your performance on your next physics test, Physics I Workbook For Dummies offers you an opportunity to master a rewarding and challenging subject that unlocks countless educational and career opportunities.

This book reports on current challenges in bridge engineering faced by professionals around the globe, giving a special emphasis to recently developed techniques and methods for bridge design, construction and monitoring. Based on extended and revised papers selected from outstanding presentation at the Istanbul Bridge Conference 2018, held from November 5 - 6, 2018, in Istanbul, Turkey, and by highlighting major bridge studies, spanning from numerical and modeling studies to the applications of new construction techniques and monitoring systems, this book is intended to promote high standards in modern bridge engineering. It offers a timely reference to both academics and professionals in this field.

This textbook provides a thorough overview of mathematical physics, highlighting classical topics as well as recent developments. Readers will be introduced to a variety of methods that reflect current trends in research, including the Bergman kernel approach for solving boundary value and spectral problems for PDEs with variable coefficients. With its careful treatment of the fundamentals as well as coverage of topics not often encountered in textbooks, this will be an ideal text for both introductory and more specialized courses. The first five chapters present standard material, including the classification of PDEs, an introduction to boundary value and initial value problems, and an introduction to the Fourier method of separation of variables. More advanced material and specialized treatments follow, including practical methods for solving direct and inverse Sturm-Liouville problems; the theory of parabolic equations, harmonic functions, potential theory, integral equations and the method of non-orthogonal series. Methods of Mathematical Physics is ideal for undergraduate students and can serve as a textbook for a regular course in equations of mathematical physics as well as for more advanced courses on selected topics.

In Search of a Theory of Everything takes readers on an adventurous journey through space and time on a quest for a unified "theory of everything" by means of a rare and agile interplay between the natural philosophies of influential ancient Greek thinkers and the laws of modern physics. By narrating a history and a philosophy of science, theoretical physicist Demetris Nicolaides logically connects great feats of critical mind and unbridled human imagination in their ambitious quest for the theory that will ultimately explain all the phenomena of nature via a single immutable overarching law. This comparative study of the universe tells the story of physics through philosophy, of the current via the forgotten, in a balanced way. Nicolaides begins each chapter with a relatively easier analysis of nature-one conceived by a major natural philosopher of antiquity-easing readers gradually into the more complex views of modern physics, by intertwining finely the two, the ancient with the new. Those philosophers' rigorous scientific inquiry of the universe includes ideas that resonate with aspects of modern science, puzzles about nature that still baffle, and clever philosophical arguments that are used today to reassess competing principles of modern physics and speculate about open physics problems. In Search of a Theory of Everything is a new kind of sight, a philosophical insight of modern physics that has long been left unexamined.

Most of the many books on finite elements are devoted either to mathematical theory or to engineering applications, but not to both. This book seeks to bridge the gap by presenting the main theoretical ideas of the finite element method and the analysis of its errors in an accessible way. At the same time it presents computed numbers which not only illustrate the theory but can only be analysed using the theory. This approach, both dual and interacting between theory and computation makes this book unique.
Much research is currently being done into reliability in computational modelling, involving both validation of the mathematical models and verification of the numerical schemes. By treating finite element error analysis in this way this book is a significant contribution to the verification process of finite element modelling in the context of reliability.

A compendium representing the current state of the art in the modelling, simulation and physics of the interaction of hydrogen and helium with plasma facing materials in fusion reactors. This is the topic that will determine the success of the production of energy by future Tokamak reactors and it is here discussed by the world's experts. Topics covered are recycling of hydrogen isotopes; wall fuelling and wall pumping; active control of hydrogen recycling; hydrogen and helium behaviour in solids and liquid metals; and databases for recycling.

This book presents the results of a European-Chinese collaborative research project, Manipulation of Reynolds Stress for Separation Control and Drag Reduction (MARS), including an analysis and discussion of the effects of a number of active flow control devices on the discrete dynamic components of the turbulent shear layers and Reynolds stress. From an application point of view, it provides a positive and necessary step to control individual structures that are larger in scale and lower in frequency compared to the richness of the temporal and spatial scales in turbulent separated flows.

Based on courses given at the CRM Banff summer school in 1999, this volume provides a snapshot of topics engaging theoretical physicists at the end of the twentieth century and the beginning of the twenty-first. Young physicists will find in these chapters pedagogical introductions to subjects currently active in theoretical physics, and more seasoned physicists will find a chance to share the excitement of fields outside their immediate research interests.

This book addresses recent developments in mathematical analysis and computational methods for solving direct and inverse problems for Maxwell's equations in periodic structures. The fundamental importance of the fields is clear, since they are related to technology with significant applications in optics and electromagnetics. The book provides both introductory materials and in-depth discussion to the areas in diffractive optics that offer rich and challenging mathematical problems. It is also intended to convey up-to-date results to students and researchers in applied and computational mathematics, and engineering disciplines as well.

This volume is a basic introduction to certain aspects of elliptic functions and elliptic integrals. Primarily, the elliptic functions stand out as closed solutions to a class of physical and geometrical problems giving rise to nonlinear differential equations. While these nonlinear equations may not be the types of greatest interest currently, the fact that they are solvable exactly in terms of functions about which much is known makes up for this. The elliptic functions of Jacobi, or equivalently the Weierstrass elliptic functions, inhabit the literature on current problems in condensed matter and statistical physics, on solitons and conformal representations, and all sorts of famous problems in classical mechanics. The lectures on elliptic functions have evolved as part of the first semester of a course on theoretical and mathematical methods given to first and second year graduate students in physics and chemistry at the University of North Dakota. They are for graduate students or for researchers who want an elementary introduction to the subject that nevertheless leaves them with enough of the details to address real problems. The style is supposed to be informal. The intention is to introduce the subject as a moderate extension of ordinary trigonometry in which the reference circle is replaced by an ellipse. This entre depends upon fewer tools and has seemed less intimidating that other typical introductions to the subject that depend on some knowledge of complex variables. The first three lectures assume only calculus, including the chain rule and elementary knowledge of differential equations. In the later lectures, the complex analytic properties are introduced naturally so that a more complete study becomes possible.

Stochastic differential equations have many applications in the natural sciences. Besides, the employment of probabilistic representations together with the Monte Carlo technique allows us to reduce solution of multi-dimensional problems for partial differential equations to integration of stochastic equations. This approach leads to powerful computational mathematics that is presented in the treatise. The authors propose many new special schemes, some published here for the first time. In the second part of the book they construct numerical methods for solving complicated problems for partial differential equations occurring in practical applications, both linear and nonlinear. All the methods are presented with proofs and hence founded on rigorous reasoning, thus giving the book textbook potential. An overwhelming majority of the methods are accompanied by the corresponding numerical algorithms which are ready for implementation in practice. The book addresses researchers and graduate students in numerical analysis, physics, chemistry, and engineering as well as mathematical biology and financial mathematics.

This book highlights cutting-edge research in the field of network science, offering scientists, researchers, students, and practitioners a unique update on the latest advances in theory and a multitude of applications. It presents the peer-reviewed proceedings of the Eighth International Conference on Complex Networks and their Applications (COMPLEX NETWORKS 2019), which took place in Lisbon, Portugal, on December 10-12, 2019. The carefully selected papers cover a wide range of theoretical topics such as network models and measures; community structure, and network dynamics; diffusion, epidemics, and spreading processes; resilience and control as well as all the main network applications, including social and political networks; networks in finance and economics; biological and neuroscience networks; and technological networks.

This proceedings volume contains a selection of papers presented at the Fourth International Conference on High Performance Scientific Computing held at the Hanoi Institute of Mathematics, Vietnamese Academy of Science and Technology (VAST), March 2-6, 2009. The conference was organized by the Hanoi Institute of Mathematics, the Interdisciplinary Center for Scientific Computing (IWR), Heidelberg, and its Heidelberg Graduate School of Mathematical and Computational Methods for the Sciences, and Ho Chi Minh City University of Technology. The contributions cover the broad interdisciplinary spectrum of scientific computing and present recent advances in theory, development of methods, and applications in practice. Subjects covered are mathematical modelling, numerical simulation, methods for optimization and control, parallel computing, software development, applications of scientific computing in physics, mechanics, biology and medicine, engineering, hydrology problems, transport, communication networks, production scheduling, industrial and commercial problems.

This volume collects recent contributions on the contemporary trends in the mathematics of quantum mechanics, and more specifically in mathematical problems arising in quantum many-body dynamics, quantum graph theory, cold atoms, unitary gases, with particular emphasis on the developments of the specific mathematical tools needed, including: linear and non-linear Schroedinger equations, topological invariants, non-commutative geometry, resonances and operator extension theory, among others. Most of contributors are international leading experts or respected young researchers in mathematical physics, PDE, and operator theory. All their material is the fruit of recent studies that have already become a reference in the community. Offering a unified perspective of the mathematics of quantum mechanics, it is a valuable resource for researchers in the field.

This is an agenda-setting and high-profile book that presents an authoritative and cutting-edge analysis of nanoscience and technology. The Oxford Handbook of Nanoscience and Technology provides a comprehensive and accessible overview of the major achievements in different aspects of this field.
The Handbook comprises 3 volumes, structured thematically, with 25 chapters each. Volume I presents fundamental issues of basic physics, chemistry, biochemistry, tribology etc. of nanomaterials. Volume II focuses on the progress made with host of nanomaterials including DNA and protein based nanostructures. Volume III highlights engineering and related developments, with a focus on frontal application areas. All chapters are written by noted international experts in the field. The book should be useful for final year undergraduates specializing in the field. It should prove indispensable to graduate students, and serious researchers from academic and industrial sectors working in the field of Nanoscience and Technology from different disciplines including Physics, Chemistry, Biochemistry, Biotechnology, Medicine, Materials Science, Metallurgy, Ceramics, Information Technology as well as Electrical, Electronic and Computational Engineering.

Introduction to Mathematical Modeling helps students master the processes used by scientists and engineers to model real-world problems, including the challenges posed by space exploration, climate change, energy sustainability, chaotic dynamical systems and random processes. Primarily intended for students with a working knowledge of calculus but minimal training in computer programming in a first course on modeling, the more advanced topics in the book are also useful for advanced undergraduate and graduate students seeking to get to grips with the analytical, numerical, and visual aspects of mathematical modeling, as well as the approximations and abstractions needed for the creation of a viable model.

This is an agenda-setting and high-profile book that presents an authoritative and cutting-edge analysis of nanoscience and technology. The Oxford Handbook of Nanoscience and Technology provides a comprehensive and accessible overview of the major achievements in different aspects of this field.
The Handbook comprises 3 volumes, structured thematically, with 25 chapters each. Volume I presents fundamental issues of basic physics, chemistry, biochemistry, tribology etc. of nanomaterials. Volume II focuses on the progress made with host of nanomaterials including DNA and protein based nanostructures. Volume III highlights engineering and related developments, with a focus on frontal application areas. All chapters are written by noted international experts in the field. The book should be useful for final year undergraduates specializing in the field. It should prove indispensable to graduate students, and serious researchers from academic and industrial sectors working in the field of Nanoscience and Technology from different disciplines including Physics, Chemistry, Biochemistry, Biotechnology, Medicine, Materials Science, Metallurgy, Ceramics, Information Technology as well as Electrical, Electronic and Computational Engineering.