This book presents the various algebraic techniques for solving partial differential equations to yield exact solutions, techniques developed by the author in recent years and with emphasis on physical equations such as: the Maxwell equations, the Dirac equations, the KdV equation, the KP equation, the nonlinear Schrodinger equation, the Davey and Stewartson equations, the Boussinesq equations in geophysics, the Navier-Stokes equations and the boundary layer problems. In order to solve them, I have employed the grading technique, matrix differential operators, stable-range of nonlinear terms, moving frames, asymmetric assumptions, symmetry transformations, linearization techniques and special functions. The book is self-contained and requires only a minimal understanding of calculus and linear algebra, making it accessible to a broad audience in the fields of mathematics, the sciences and engineering. Readers may find the exact solutions and mathematical skills needed in their own research.

This book presents a consistent development of the Kohn-Nirenberg type global quantization theory in the setting of graded nilpotent Lie groups in terms of their representations. It contains a detailed exposition of related background topics on homogeneous Lie groups, nilpotent Lie groups, and the analysis of Rockland operators on graded Lie groups together with their associated Sobolev spaces. For the specific example of the Heisenberg group the theory is illustrated in detail. In addition, the book features a brief account of the corresponding quantization theory in the setting of compact Lie groups. The monograph is the winner of the 2014 Ferran Sunyer i Balaguer Prize.

This book features a selection of articles based on the XXXIV Bialowieza Workshop on Geometric Methods in Physics, 2015. The articles presented are mathematically rigorous, include important physical implications and address the application of geometry in classical and quantum physics. Special attention deserves the session devoted to discussions of Gerard Emch's most important and lasting achievements in mathematical physics. The Bialowieza workshops are among the most important meetings in the field and gather participants from mathematics and physics alike. Despite their long tradition, the Workshops remain at the cutting edge of ongoing research. For the past several years, the Bialowieza Workshop has been followed by a School on Geometry and Physics, where advanced lectures for graduate students and young researchers are presented. The unique atmosphere of the Workshop and School is enhanced by the venue, framed by the natural beauty of the Bialowieza forest in eastern Poland.

Bioenergy Options for a Cleaner Environment describes the biomass resource and its delivery. A panel of international experts describe the range of conversion technologies both commercially available and under development, and explore the technical, environmental and socio-economic barriers and benefits of using biomass in both developed and developing countries.
*Covers a number of perspectives, taking the reader through the whole process from the bioenergy resource through conversion to fuel, to policy issues.
*World class Editor and contributors
*Accessible and useful to those working in agriculture, forestry and planning, as well as energy researchers.

Throughout history, people have tried to construct 'theories of everything': highly ambitious attempts to understand nature in its totality. This account presents these theories in their historical contexts, from little known hypotheses from the past to modern developments such as the theory of superstrings, the anthropic principle and ideas of many universes, and uses them to problematize the limits of scientific knowledge. Do claims to theories of everything belong to science at all? Which are the epistemic standards on which an alleged scientific theory of the universe - or the multiverse - is to be judged?
Such questions are currently being discussed by physicists and cosmologists, but rarely within a historical perspective. This book argues that these questions have a history and that knowledge of the historical development of 'higher speculations' may inform and qualify the current debate of the nature and limits of scientific explanation.

This book provides readers with modern computational techniques for solving variety of problems from electrical, mechanical, civil and chemical engineering. Mathematical methods are presented in a unified manner, so they can be applied consistently to problems in applied electromagnetics, strength of materials, fluid mechanics, heat and mass transfer, environmental engineering, biomedical engineering, signal processing, automatic control and more.

This book describes the development of a system dynamics-based model that can capture the future trajectories of housing energy and carbon emissions. It approaches energy and carbon emissions in the housing sector as a complex socio-technical problem involving the analysis of intrinsic interrelationships among dwellings, occupants and the environment. Based on an examination of the UK housing sector but with relevance worldwide, the book demonstrates how the systems dynamics simulation can be used as a learning laboratory regarding future trends in housing energy and carbon emissions. The authors employ a pragmatic research strategy, involving the collection of both qualitative and quantitative data to develop a model. The book enriches readers' understanding of the complexity involved in housing energy and carbon emissions from a systems-thinking perspective. As such, it will be of interest to researchers in the fields of architectural engineering, housing studies and climate change, while also appealing to industry practitioners and policymakers specializing in housing energy.

This book and companion DVD provide a comprehensive set of modeling methods for data and uncertainty analysis, taking readers beyond mainstream methods and focusing on techniques with a broad range of real-world applications. The companion DVD contains tutorials, sample code, and software packages with demonstrations, enabling readers to test and use tools presented in the book.

The book will be useful as a textbook for graduate students, or as a training manual in the fields of calibration and testing. The work may also serve as a reference for metrologists, mathematicians, statisticians, software engineers, chemists, and other practitioners with a general interest in measurement science.

For most cases of interest, exact solutions to nonlinear equations describing stochastic dynamical systems are not available. This book details the relatively simple and popular linearization techniques available, covering theory as well as application. It examines models with continuous external and parametric excitations, those that cover the majority of known approaches.

This book is an introduction into stochastic processes for physicists, biologists and financial analysts. Using an informal approach, all the necessary mathematical tools and techniques are covered, including the stochastic differential equations, mean values, probability distribution functions, stochastic integration and numerical modeling. Numerous examples of practical applications of the stochastic mathematics are considered in detail, ranging from physics to the financial theory. A reader with basic knowledge of the probability theory should have no difficulty in accessing the book content.

This new book on Mathematical Methods In Physics is intended to be used for a 2-semester course for first year MA or PhD physics graduate students, or senior undergraduates majoring in physics, engineering or other technically related fields.Emphasis has been placed on physics applications, included where appropriate, to complement basic theories. Applications include moment of inertia in "Tensor Analysis"; Maxwell's equations, magnetostatic, stress tensor, continuity equation and heat flow in "fields"; special and spherical harmonics in "Hilbert Space"; electrostatics, hydrodynamics and Gamma function in "Complex Variable Theory"; vibrating string, vibrating membrane and harmonic oscillator in "Ordinary Differential Equations"; age of the earth and temperature variation of the earth's surface in "Heat Conduction"; and field due to a moving point charge (Lienard-Wiechart potentials) in "Wave Equations".Subject not usually found in standard mathematical physics texts include Theory of Curves in Space in "Vector Analysis", and Retarded and Advanced D-Functions in "Wave Equations".Lastly, problem solving techniques are presented by way of appendices, comprising 75 pages of problems with their solutions. These problems provide applications as well as extensions to the theory.A useful compendium, with such excellent features, will surely make it a key reference text.

This book presents a systematic methodology for the development of parallel multi-physics models and its implementation in geophysical and biomedical applications. The methodology includes conservative discretization methods for partial differential equations on general meshes, as well as data structures and algorithms for organizing parallel simulations on general meshes. The structures and algorithms form the core of the INMOST (Integrated Numerical Modelling Object-oriented Supercomputing Technologies) platform for the development of parallel models on general meshes. The authors consider applications for addressing specific geophysical and biomedical challenges, including radioactive contaminant propagation with subsurface waters, reservoir simulation, and clot formation in blood flows. The book gathers all the components of this methodology, from algorithms and numerical methods to the open-source software, as well as examples of practical applications, in a single source, making it a valuable asset for applied mathematicians, computer scientists, and engineers alike.

This Edited Volume engages with concepts of gender and identity as they are mobilized in research to understand the experiences of learners, teachers and practitioners of physics. The focus of this collection is on extending theoretical understandings of identity as a means to explore the construction of gender in physics education research. This collection expands an understanding of gendered participation in physics from a binary gender deficit model to a more complex understanding of gender as performative and intersectional with other social locations (e.g., race, class, LGBT status, ability, etc). This volume contributes to a growing scholarship using sociocultural frameworks to understand learning and participation in physics, and that seeks to challenge dominant understandings of who does physics and what counts as physics competence. Studying gender in physics education research from a perspective of identity and identity construction allows us to understand participation in physics cultures in new ways. We are able to see how identities shape and are shaped by inclusion and exclusion in physics practices, discourses that dominate physics cultures, and actions that maintain or challenge structures of dominance and subordination in physics education. The chapters offered in this book focus on understanding identity and its usefulness in various contexts with various learner or practitioner populations. This scholarship collectively presents us with a broad picture of the complexity inherent in doing physics and doing gender.

Fifty years ago, a new approach to reaction kinetics began to emerge: one based on mathematical models of reaction kinetics, or formal reaction kinetics. Since then, there has been a rapid and accelerated development in both deterministic and stochastic kinetics, primarily because mathematicians studying differential equations and algebraic geometry have taken an interest in the nonlinear differential equations of kinetics, which are relatively simple, yet capable of depicting complex behavior such as oscillation, chaos, and pattern formation. The development of stochastic models was triggered by the fact that novel methods made it possible to measure molecules individually. Now it is high time to make the results of the last half-century available to a larger audience: students of chemistry, chemical engineering and biochemistry, not to mention applied mathematics. Based on recent papers, this book presents the most important concepts and results, together with a wealth of solved exercises. The book is accompanied by the authors' Mathematica package, ReactionKinetics, which helps both students and scholars in their everyday work, and which can be downloaded from http://extras.springer.com/ and also from the authors' websites. Further, the large set of unsolved problems provided may serve as a springboard for individual research.

This thesis studies collider phenomenology of physics beyond the Standard Model at the Large Hadron Collider (LHC). It also explores in detail advanced topics related to Higgs boson and supersymmetry - one of the most exciting and well-motivated streams in particle physics. In particular, it finds a very large enhancement of multiple Higgs boson production in vector-boson scattering when Higgs couplings to gauge bosons differ from those predicted by the Standard Model. The thesis demonstrates that due to the loss of unitarity, the very large enhancement for triple Higgs boson production takes place. This is a truly novel finding. The thesis also studies the effects of supersymmetric partners of top and bottom quarks on the Higgs production and decay at the LHC, pointing for the first time to non-universal alterations for two main production processes of the Higgs boson at the LHC-vector boson fusion and gluon-gluon fusion. Continuing the exploration of Higgs boson and supersymmetry at the LHC, the thesis extends existing experimental analysis and shows that for a single decay channel the mass of the top quark superpartner below 175 GeV can be completely excluded, which in turn excludes electroweak baryogenesis in the Minimal Supersymmetric Model. This is a major new finding for the HEP community. This thesis is very clearly written and the introduction and conclusions are accessible to a wide spectrum of readers.

This thesis investigates the sound generated by solid bodies in steady subsonic flows with unsteady perturbations, as is typically used when determining the noise generated by turbulent interactions. The focus is predominantly on modelling the sound generated by blades within an aircraft engine, and the solutions are presented as asymptotic approximations. Key analytical techniques, such as the Wiener-Hopf method, and the matched asymptotic expansion method are clearly detailed. The results allow for the effect of variations in the steady flow or blade shape on the noise generated to be analysed much faster than when solving the problem numerically or considering it experimentally.

Learn how to quickly solve electromagnetic scattering problems using the Moment Method with this unique book.

Software Included! Accompanying software featuring FORTRAN source code allows you to modify the book's examples and understand how simple and complex shapes scatter waves. One 3.5" IBM PC-compatible diskette.

The latest state of simulation techniques to model plasticity and fracture in crystalline materials on the nano- and microscale is presented. Discrete dislocation mechanics and the neighbouring fields molecular dynamics and crystal plasticity are central parts. The physical phenomena, the theoretical basics, their mathematical description and the simulation techniques are introduced and important problems from the formation of dislocation structures to fatigue and fracture from the nano- to microscale as well as it 's impact on the macro behaviour are considered.

Boris Pavlov (1936-2016), to whom this volume is dedicated, was a prominent specialist in analysis, operator theory, and mathematical physics. As one of the most influential members of the St. Petersburg Mathematical School, he was one of the founders of the Leningrad School of Non-self-adjoint Operators. This volume collects research papers originating from two conferences that were organized in memory of Boris Pavlov: "Spectral Theory and Applications", held in Stockholm, Sweden, in March 2016, and "Operator Theory, Analysis and Mathematical Physics - OTAMP2016" held at the Euler Institute in St. Petersburg, Russia, in August 2016. The volume also includes water-color paintings by Boris Pavlov, some personal photographs, as well as tributes from friends and colleagues.