Progress in Computational Physics is a new e-book series devoted to recent research trends in computational physics. It contains chapters contributed by outstanding experts of modeling of physical problems. The series focuses on interdisciplinary computational perspectives of current physical challenges, new numerical techniques for the solution of mathematical wave equations and describes certain real-world applications. With the help of powerful computers and sophisticated methods of numerical mathematics it is possible to simulate many ultramodern devices, e.g. photonic crystals structures, semiconductor nanostructures or fuel cell stacks devices, thus preventing expensive and longstanding design and optimization in the laboratories. In this book series, research manuscripts are shortened as single chapters and focus on one hot topic per volume. Engineers, physicists, meteorologists, etc. and applied mathematicians can benefit from the series content. Readers will get a deep and active insight into state-of-the art modeling and simulation techniques of ultra-modern devices and problems. Periodic structure problems arise quite often in many modern application areas like semiconductor nanostructures (e.g. quantum dots and nanocrystals), semiconductor superlattices, photonic crystals structures, meta materials or Bragg gratings of surface plasmon polariton waveguides. This first volume treats both mathematical analysis of periodic structure problems and state-of-the art numerical techniques, such as frequency domain methods, beam propagation methods and eigenmode expansion methods. Several chapters are devoted to concrete applications of periodic media simulation. The book is a useful resource for individuals interested in complex wave mechanics of unique physical structures.

Progress in Computational Physics is a new e-book series devoted to recent research trends in computational physics. It contains chapters contributed by outstanding experts of modeling of physical problems. The series focuses on interdisciplinary computational perspectives of current physical challenges, new numerical techniques for the solution of mathematical wave equations and describes certain real-world applications. With the help of powerful computers and sophisticated methods of numerical mathematics it is possible to simulate many ultramodern devices, e.g. photonic crystals structures, semiconductor nanostructures or fuel cell stacks devices, thus preventing expensive and longstanding design and optimization in the laboratories. In this book series, research manuscripts are shortened as single chapters and focus on one hot topic per volume. Engineers, physicists, meteorologists, etc. and applied mathematicians can benefit from the series content. Readers will get a deep and active insight into state-of-the art modeling and simulation techniques of ultra-modern devices and problems. The second volume of this series, titled Coupled Fluid Flow in Energy, Biology and Environmental Research covers the following scientific topics in the fields of modeling, numerical methods and applications: • Coupling between free and porous media flow • Coupling of flow and transport models • Coupling of atmospheric and ground water models This second volume contains both, the mathematical analysis of the coupling between fluid flow and porous media flow and state-of-the art numerical techniques, like tailor-made finite element and finite volume methods. Finally, readers will come across articles devoted to concrete applications of these models in the field of energy, biology and environmental research.

Progress in Computational Physics is an e-book series devoted to recent research trends in computational physics. It contains chapters contributed by outstanding experts of modeling of physical problems. The series focuses on interdisciplinary computational perspectives of current physical challenges, new numerical techniques for the solution of mathematical wave equations and describes certain real-world applications. With the help of powerful computers and sophisticated methods of numerical mathematics it is possible to simulate many ultramodern devices, e.g. photonic crystals structures, semiconductor nanostructures or fuel cell stacks devices, thus preventing expensive and longstanding design and optimization in the laboratories. In this book series, research manuscripts are shortened as single chapters and focus on one hot topic per volume. Engineers, physicists, meteorologists, etc. and applied mathematicians can benefit from the series content. Readers will get a deep and active insight into state-of-the art modeling and simulation techniques of ultra-modern devices and problems. The third volume - Novel Trends in Lattice Boltzmann Methods - Reactive Flow, Physicochemical Transport and Fluid-Structure Interaction - contains 09 chapters devoted to mathematical analysis of different issues related to the lattice Boltzmann methods, advanced numerical techniques for physico-chemical flows, fluid structure interaction and practical applications of these phenomena to real world problems.

The ebook introduces undergraduate students to the basic skills required to use non-relativistic quantum mechanics for bound and scattering problems in atomic, molecular and nuclear physics. Initial emphasis is on problems that admit analytic solutions. These results are then used in conjunction with symmetry to develop approximation methods for both bound and scattering problems. The text concentrates on the application of computational problems to introduce the basic concepts of quantum mechanics. These are then used to study more complex problems that can be reduced to one-body problems.

This book details the development of techniques and ideas from the radial basis function. It begins with a mathematical description of the basic concept of radial function method with chapters progressively delving into the derivation and construction of radial basis functions for large-scale wave propagation problems including singularity problems, high-frequency wave problems and large-scale computation problems. This reference, written by experts in numerical analysis, demonstrates how the functions arise naturally in mathematical analyses of structures responding to external loads. Readers are also equipped with mathematical knowledge about the radial basis function for understanding key algorithms required for practical solutions. Key features: - Introduces basic concepts of radial basis function methods - Provides detailed derivations of several radial basis functions - Explains complex problems using simple language - Contains a wide range of numerical examples to demonstrate applications of relevant functions - Combines the radial basis function with other known numerical methods (boundary element methods and differential equations). - Includes references and appropriate chapter appendices - Includes MATLAB codes for origin intensity factors and nearly singular factors for radial basis calculations The book is designed to make information about radial basis function methods more accessible to research scientists, professional engineers and postgraduate students, with a specific focus on large-scale wave propagation problems.

Radiation Processes In Crystal Solid Solutions is a monograph explaining processes occurring in two classes of crystal solids (metal alloys and doped alkali halides) under irradiation by various types of radiation (alpha, beta, gamma, X-radiations, ions). While metal alloys may differ in high radiation stability, solid solutions based on alkali halides are very radiation-sensitive materials. Radiation defect production mechanisms, intrinsic and extrinsic radiation defects, a role of complexes an impurity-radiation defect which explain distinction in radiating stability of the specified classes of solid solutions are discussed in this e-book. To describe radiation induced phase transformations, two approaches are highlighted: kinetic and thermodynamic. This e-book also includes research on the effect of small radiation doses in a structurally solid phase state of a solution along with a semi-quantitative estimation of radiation effects with respect to temperature changes. This e-book should be a useful reference for advanced readers interested in the physics of radiation and solid state physics.

Since the first description by John Scott Russel in 1834, the solitary wave phenomenon has attracted considerable interests from scientists. The most interesting discovery since then has been the ability to integrate most of the nonlinear wave equations which govern solitary waves, from the Korteweg-de Vries equation to the nonlinear Schrödinger equation, in the 1960's. From that moment, a huge amount of theoretical works can be found on solitary waves. Due to the fact that many physical phenomena can be described by a soliton model, applications have followed each other, in telecommunications first, where the propagation of solitons in fiber optics helps in increasing transmission capacity, thanks to their inherent stability, which make long-distance transmission possible without the use of repeaters. The aim of this book is to present a state of the art theoretical study of solitary waves. Prominent actual works on solitary waves are described.

Scientific Natural Philosophy explains the nature and content of scientific natural philosophy, particularly qualitative modeling, and updates scientific methodology by providing details of the mathematics involved. The book presents a total view of our universe, from the fractal superstring to its destiny as black holes back in to dark matter, and to the timeless and boundless ‘Universe’ where our universe is a local super, super galaxy. It stresses the various levels of complementarity between qualitative and quantitative modeling where the former solves and answers questions the latter could not and duality between quantum and macro gravity. It highlights new information from the Grand Unification Theory (GUT) missing in previous philosophical works such as the indestructible generalized nested fractal superstring, brain waves as common medium of the brain and gene for their functions. Moreover, it points to a new technological epoch brought about by the GUT based on utilization of dark matter towards elevating the quality of life. This comprehensive book provides an exciting perspective on this fascinating field to the reader. explains the nature and content of scientific natural philosophy, particularly qualitative modeling, and updates scientific methodology by providing details of the mathematics involved. The book presents a total view of our universe, from the fractal superstring to its destiny as black holes back in to dark matter, and to the timeless and boundless ‘Universe’ where our universe is a local super, super galaxy. It stresses the various levels of complementarity between qualitative and quantitative modeling where the former solves and answers questions the latter could not and duality between quantum and macro gravity. It highlights new information from the Grand Unification Theory (GUT) missing in previous philosophical works such as the indestructible generalized nested fractal superstring, brain waves as common medium of the brain and gene for their functions. Moreover, it points to a new technological epoch brought about by the GUT based on utilization of dark matter towards elevating the quality of life. This comprehensive book provides an exciting perspective on this fascinating field to the reader. explains the nature and content of scientific natural philosophy, particularly qualitative modeling, and updates scientific methodology by providing details of the mathematics involved. The book presents a total view of our universe, from the fractal superstring to its destiny as black holes back in to dark matter, and to the timeless and boundless ‘Universe’ where our universe is a local super, super galaxy. It stresses the various levels of complementarity between qualitative and quantitative modeling where the former solves and answers questions the latter could not and duality between quantum and macro gravity. It highlights new information from the Grand Unification Theory (GUT) missing in previous philosophical works such as the indestructible generalized nested fractal superstring, brain waves as common medium of the brain and gene for their functions. Moreover, it points to a new technological epoch brought about by the GUT based on utilization of dark matter towards elevating the quality of life. This comprehensive book provides an exciting perspective on this fascinating field to the reader.

In recent times the idea of cloaking has become very popular. After radar and sonar were discovered, problems of "visibility" reduction for physical bodies in air (by electromagnetic waves) or in water (by acoustical waves) have immediately become serious areas of research in physics. New technologies (sensors, actuators) of high spatial-temporal resolution, metamaterials and new computers with fast and accurate calculations, in combination with nontraditional versions of solutions to these boundary problems, have allowed physicists to obtain successful results in some cases. This e-book presents a rare attempt to understand the cloaking problem as a whole. The book should be useful for readers with a strong interest in contemporary problem solving approaches in the physics of waves.

How do things work? What makes up matter? How large is the universe? The answer to these questions lies in understanding physical phenomena: mechanics, electricity, magnetism, optics and many other phenomena can be explained through theories in physics. Indeed, progress in physics has been crucial for mankind’s technological progress. Theories and Theorems is an introductory handbook that gives readers a simple explanation of the laws of physics and presents these concepts in a way that stimulates people to think about the how-and-why of this physical world, in which we live.