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Asymptotic Methods for Investigating Quasiwave Equations of Hyperbolic Type (Mathematics and Its Applications #402)
by Yuri A. Mitropolsky G. Khoma M. GromyakThe theory of partial differential equations is a wide and rapidly developing branch of contemporary mathematics. Problems related to partial differential equations of order higher than one are so diverse that a general theory can hardly be built up. There are several essentially different kinds of differential equations called elliptic, hyperbolic, and parabolic. Regarding the construction of solutions of Cauchy, mixed and boundary value problems, each kind of equation exhibits entirely different properties. Cauchy problems for hyperbolic equations and systems with variable coefficients have been studied in classical works of Petrovskii, Leret, Courant, Gording. Mixed problems for hyperbolic equations were considered by Vishik, Ladyzhenskaya, and that for general two dimensional equations were investigated by Bitsadze, Vishik, Gol'dberg, Ladyzhenskaya, Myshkis, and others. In last decade the theory of solvability on the whole of boundary value problems for nonlinear differential equations has received intensive development. Significant results for nonlinear elliptic and parabolic equations of second order were obtained in works of Gvazava, Ladyzhenskaya, Nakhushev, Oleinik, Skripnik, and others. Concerning the solvability in general of nonlinear hyperbolic equations, which are connected to the theory of local and nonlocal boundary value problems for hyperbolic equations, there are only partial results obtained by Bronshtein, Pokhozhev, Nakhushev.
Asymptotic Methods for Relaxation Oscillations and Applications (Applied Mathematical Sciences #63)
by Johan GrasmanIn various fields of science, notably in physics and biology, one is con fronted with periodic phenomena having a remarkable temporal structure: it is as if certain systems are periodically reset in an initial state. A paper of Van der Pol in the Philosophical Magazine of 1926 started up the investigation of this highly nonlinear type of oscillation for which Van der Pol coined the name "relaxation oscillation". The study of relaxation oscillations requires a mathematical analysis which differs strongly from the well-known theory of almost linear oscillations. In this monograph the method of matched asymptotic expansions is employed to approximate the periodic orbit of a relaxation oscillator. As an introduction, in chapter 2 the asymptotic analysis of Van der Pol's equation is carried out in all detail. The problem exhibits all features characteristic for a relaxation oscillation. From this case study one may learn how to handle other or more generally formulated relaxation oscillations. In the survey special attention is given to biological and chemical relaxation oscillators. In chapter 2 a general definition of a relaxation oscillation is formulated.
Asymptotic Methods for the Fokker-Planck Equation and the Exit Problem in Applications (Springer Series in Synergetics)
by Johan Grasman Onno A., HerwaardenAsymptotic methods are of great importance for practical applications, especially in dealing with boundary value problems for small stochastic perturbations. This book deals with nonlinear dynamical systems perturbed by noise. It addresses problems in which noise leads to qualitative changes, escape from the attraction domain, or extinction in population dynamics. The most likely exit point and expected escape time are determined with singular perturbation methods for the corresponding Fokker-Planck equation. The authors indicate how their techniques relate to the Itô calculus applied to the Langevin equation. The book will be useful to researchers and graduate students.
Asymptotic Methods in Electromagnetics
by Daniel Bouche Frederic Molinet Raj MittraNumerically rigorous techniques for the computation of electromagnetic fields diffracted by an object become computationally intensive, if not impractical to handle, at high frequencies and one must resort to asymptotic methods to solve the scattering problem at short wavelengths. The asymptotic methods provide closed form expansions for the diffracted fields and are also useful for eliciting physical interpretations of the various diffraction phenomena. One of the principal objectives of this book is to discuss the different asymptotic methods in a unified manner. Although the book contains explicit formulas for computing the field diffracted by conducting or dielectric-coated objects, it also provides the mathematical foundations of the different methods and explains how they are interrelated.
Asymptotic Methods in Quantum Mechanics: Application to Atoms, Molecules and Nuclei (Springer Series in Chemical Physics #64)
by S.H. Patil K.T. TangQuantum mechanics and the Schrodinger equation are the basis for the de scription of the properties of atoms, molecules, and nuclei. The development of reliable, meaningful solutions for the energy eigenfunctions of these many is a formidable problem. The usual approach for obtaining particle systems the eigenfunctions is based on their variational extremum property of the expectation values of the energy. However the complexity of these variational solutions does not allow a transparent, compact description of the physical structure. There are some properties of the wave functions in some specific, spatial domains, which depend on the general structure of the Schrodinger equation and the electromagnetic potential. These properties provide very useful guidelines in developing simple and accurate solutions for the wave functions of these systems, and provide significant insight into their physical structure. This point, though of considerable importance, has not received adequate attention. Here we present a description of the local properties of the wave functions of a collection of particles, in particular the asymptotic properties when one of the particles is far away from the others. The asymptotic behaviour of this wave function depends primarily on the separation energy of the outmost particle. The universal significance of the asymptotic behaviour of the wave functions should be appreciated at both research and pedagogic levels. This is the main aim of our presentation here.
Asymptotic Modeling of Atmospheric Flows
by Radyadour Kh. ZeytounianThe present work is not exactly a "course", but rather is presented as a monograph in which the author has set forth what are, for the most part, his own results; this is particularly true of Chaps. 7-13. Many of the problems dealt with herein have, since the school year 1975-76, been the subject of a series of graduate lectures at the "Universire des Sciences et Techniques de Lille I" for students preparing for the "Diplome d'Etudes Ap profondies de Mecanique (option fluides)". The writing of this book was thus strongly influenced by the author's own conception of meteorology as a fluid mechanics discipline which is in a privi leged area for the application of singular perturbation techniques. It goes without saying that the modeling of atmospheric flows is a vast and complex problem which is presently the focal point of many research projects. The enonnity of the topic explains why many important questions have not been taken up in this work, even among those which are closely related to the subject treated herein. Nonetheless, the author thought it worthwhile for the development of future research on the modeling of atmospheric flows (from the viewpoint of theoretical fluid mechanics) to bring forth a book specifying the problems which have already been resolved in this field and those which are, as yet, unsolved.
Asymptotic Perturbation Methods: For Nonlinear Differential Equations in Physics
by Attilio MaccariAsymptotic Perturbation Methods Cohesive overview of powerful mathematical methods to solve differential equations in physics Asymptotic Perturbation Methods for Nonlinear Differential Equations in Physics addresses nonlinearity in various fields of physics from the vantage point of its mathematical description in the form of nonlinear partial differential equations and presents a unified view on nonlinear systems in physics by providing a common framework to obtain approximate solutions to the respective nonlinear partial differential equations based on the asymptotic perturbation method. Aside from its complete coverage of a complicated topic, a noteworthy feature of the book is the emphasis on applications. There are several examples included throughout the text, and, crucially, the scientific background is explained at an elementary level and closely integrated with the mathematical theory to enable seamless reader comprehension. To fully understand the concepts within this book, the prerequisites are multivariable calculus and introductory physics. Written by a highly qualified author with significant accomplishments in the field, Asymptotic Perturbation Methods for Nonlinear Differential Equations in Physics covers sample topics such as: Application of the various flavors of the asymptotic perturbation method, such as the Maccari method to the governing equations of nonlinear system Nonlinear oscillators, limit cycles, and their bifurcations, iterated nonlinear maps, continuous systems, and nonlinear partial differential equations (NPDEs) Nonlinear systems, such as the van der Pol oscillator, with advanced coverage of plasma physics, quantum mechanics, elementary particle physics, cosmology, and chaotic systems Infinite-period bifurcation in the nonlinear Schrodinger equation and fractal and chaotic solutions in NPDEs Asymptotic Perturbation Methods for Nonlinear Differential Equations in Physics is ideal for an introductory course at the senior or first year graduate level. It is also a highly valuable reference for any professional scientist who does not possess deep knowledge about nonlinear physics.
Asymptotic Perturbation Methods: For Nonlinear Differential Equations in Physics
by Attilio MaccariAsymptotic Perturbation Methods Cohesive overview of powerful mathematical methods to solve differential equations in physics Asymptotic Perturbation Methods for Nonlinear Differential Equations in Physics addresses nonlinearity in various fields of physics from the vantage point of its mathematical description in the form of nonlinear partial differential equations and presents a unified view on nonlinear systems in physics by providing a common framework to obtain approximate solutions to the respective nonlinear partial differential equations based on the asymptotic perturbation method. Aside from its complete coverage of a complicated topic, a noteworthy feature of the book is the emphasis on applications. There are several examples included throughout the text, and, crucially, the scientific background is explained at an elementary level and closely integrated with the mathematical theory to enable seamless reader comprehension. To fully understand the concepts within this book, the prerequisites are multivariable calculus and introductory physics. Written by a highly qualified author with significant accomplishments in the field, Asymptotic Perturbation Methods for Nonlinear Differential Equations in Physics covers sample topics such as: Application of the various flavors of the asymptotic perturbation method, such as the Maccari method to the governing equations of nonlinear system Nonlinear oscillators, limit cycles, and their bifurcations, iterated nonlinear maps, continuous systems, and nonlinear partial differential equations (NPDEs) Nonlinear systems, such as the van der Pol oscillator, with advanced coverage of plasma physics, quantum mechanics, elementary particle physics, cosmology, and chaotic systems Infinite-period bifurcation in the nonlinear Schrodinger equation and fractal and chaotic solutions in NPDEs Asymptotic Perturbation Methods for Nonlinear Differential Equations in Physics is ideal for an introductory course at the senior or first year graduate level. It is also a highly valuable reference for any professional scientist who does not possess deep knowledge about nonlinear physics.
Asymptotic Representation of Relaxation Oscillations in Lasers (Understanding Complex Systems)
by Elena V. Grigorieva Sergey A. KaschenkoIn this book we analyze relaxation oscillations in models of lasers with nonlinear elements controlling light dynamics. The models are based on rate equations taking into account periodic modulation of parameters, optoelectronic delayed feedback, mutual coupling between lasers, intermodal interaction and other factors. With the aim to study relaxation oscillations we present the special asymptotic method of integration for ordinary differential equations and differential-difference equations. As a result, they are reduced to discrete maps. Analyzing the maps we describe analytically such nonlinear phenomena in lasers as multistability of large-amplitude relaxation cycles, bifurcations of cycles, controlled switching of regimes, phase synchronization in an ensemble of coupled systems and others. The book can be fruitful for students and technicians in nonlinear laser dynamics and in differential equations.
Asymptotic Solutions of Strongly Nonlinear Systems of Differential Equations (Springer Monographs in Mathematics)
by Valery V. Kozlov Stanislav D. FurtaThe book is dedicated to the construction of particular solutions of systems of ordinary differential equations in the form of series that are analogous to those used in Lyapunov’s first method. A prominent place is given to asymptotic solutions that tend to an equilibrium position, especially in the strongly nonlinear case, where the existence of such solutions can’t be inferred on the basis of the first approximation alone. The book is illustrated with a large number of concrete examples of systems in which the presence of a particular solution of a certain class is related to special properties of the system’s dynamic behavior. It is a book for students and specialists who work with dynamical systems in the fields of mechanics, mathematics, and theoretical physics.
Asymptotic Stability of Steady Compressible Fluids (Lecture Notes in Mathematics #2024)
by Mariarosaria PadulaThis volume introduces a systematic approach to the solution of some mathematical problems that arise in the study of the hyperbolic-parabolic systems of equations that govern the motions of thermodynamic fluids. It is intended for a wide audience of theoretical and applied mathematicians with an interest in compressible flow, capillarity theory, and control theory. The focus is particularly on recent results concerning nonlinear asymptotic stability, which are independent of assumptions about the smallness of the initial data. Of particular interest is the loss of control that sometimes results when steady flows of compressible fluids are upset by large disturbances. The main ideas are illustrated in the context of three different physical problems: (i) A barotropic viscous gas in a fixed domain with compact boundary. The domain may be either an exterior domain or a bounded domain, and the boundary may be either impermeable or porous. (ii) An isothermal viscous gas in a domain with free boundaries. (iii) A heat-conducting, viscous polytropic gas.
Asymptotic Structure of Space-Time
by F. EspositoThe Symposium on Asymptotic Structure of Space-Time (SOASST) was held at the University of Cincinnati, June 14-18, 1976. We had been thinking of organizing a symposium on the properties of "in finity" for several years. The subject had reached a stage of maturity and had also formed a basis for important current investi gations. It was felt that a symposium, together with a publication of the proceedings, would review, summarize, and consolidate, the more mature aspects of the field and serve as an appropriate intro duction to an expanding body of research. We had from the first the enthusiastic support and encouragement of many colleagues; with their cooperation and advice, the Symposium acquired its final form. These proceedings will attest to the value of the Symposium. The Symposium consisted of thirty lectures and had an attendance of approximately one hundred and thirty. The final impetus to our decision to go forward was the Bicen tennial Anniversary of the independence of our country. A most appropriate celebration on a University Campus surely is an intel lectual Symposium which pays honor to the histories and traditional purposes of a University. The Symposium was supported financially by the University of Cincinnatl Bicentennial Committee, the National Science Foundation, the Gravity Research Foundation, and by Armand Knoblaugh, Professor Emeritus of Physics of the University of Cincinnati.
Asymptotics beyond All Orders (Nato Science Series B: #284)
by Harvey Segur Saleh Tanveer Herbert J. LevineAn asymptotic expansion is a series that provides a sequence of increasingly accurate approximations to a function in a particular limit. The formal definition, given by Poincare (1886, Acta Math. 8:295), is as follows. Given a function,
Asymptotics for Dissipative Nonlinear Equations (Lecture Notes in Mathematics #1884)
by Nakao Hayashi Elena I. Kaikina Pavel Naumkin Ilya A. ShishmarevThis is the first book in world literature giving a systematic development of a general asymptotic theory for nonlinear partial differential equations with dissipation. Many typical well-known equations are considered as examples, such as: nonlinear heat equation, KdVB equation, nonlinear damped wave equation, Landau-Ginzburg equation, Sobolev type equations, systems of equations of Boussinesq, Navier-Stokes and others.
Asymptotics in Dynamics, Geometry and PDEs; Generalized Borel Summation: Proceedings of the conference held in CRM Pisa, 12-16 October 2009, Vol. I (Publications of the Scuola Normale Superiore #12.1)
by Édéric Menous David Sauzin Ovidiu Costin Édéric FauvetThese are the proceedings of a one-week international conference centered on asymptotic analysis and its applications. They contain major contributions dealing with - mathematical physics: PT symmetry, perturbative quantum field theory, WKB analysis, - local dynamics: parabolic systems, small denominator questions, - new aspects in mould calculus, with related combinatorial Hopf algebras and application to multizeta values, - a new family of resurgent functions related to knot theory.
Asymptotics in Dynamics, Geometry and PDEs; Generalized Borel Summation: Proceedings of the conference held in CRM Pisa, 12-16 October 2009, Vol. II (Publications of the Scuola Normale Superiore #12.2)
by Édéric Menous David Sauzin Ovidiu Costin Édéric FauvetThese are the proceedings of a one-week international conference centered on asymptotic analysis and its applications. They contain major contributions dealing with: mathematical physics: PT symmetry, perturbative quantum field theory, WKB analysis, local dynamics: parabolic systems, small denominator questions, new aspects in mould calculus, with related combinatorial Hopf algebras and application to multizeta values, a new family of resurgent functions related to knot theory.
Asymptotics of Elliptic and Parabolic PDEs: and their Applications in Statistical Physics, Computational Neuroscience, and Biophysics (Applied Mathematical Sciences #199)
by David Holcman Zeev SchussThis is a monograph on the emerging branch of mathematical biophysics combining asymptotic analysis with numerical and stochastic methods to analyze partial differential equations arising in biological and physical sciences. In more detail, the book presents the analytic methods and tools for approximating solutions of mixed boundary value problems, with particular emphasis on the narrow escape problem. Informed throughout by real-world applications, the book includes topics such as the Fokker-Planck equation, boundary layer analysis, WKB approximation, applications of spectral theory, as well as recent results in narrow escape theory. Numerical and stochastic aspects, including mean first passage time and extreme statistics, are discussed in detail and relevant applications are presented in parallel with the theory. Including background on the classical asymptotic theory of differential equations, this book is written for scientists of various backgrounds interested in deriving solutions to real-world problems from first principles.
At Home (Be an Eco Hero #1)
by Susan BarracloughFind out how you can be an eco hero at home! Learn how to save energy and water, and how to reduce, reuse and recycle your waste. This colourful book for children features large photographs and engaging superhero children characters that are illustrated in a cartoon style.
At The Kitchen Table: Simple, low-waste recipes for family and friends
by Megan DaviesWant to eat well, reduce food and packaging waste and save some money? Home Bird is here to help, going back to basics with seasonal, bold and wholesome recipes that are not only better for the environment but also your well-being and budget.Influenced by nostalgic meals and cooking for loved ones, Megan Davies has written this book for the eco-minded home cook. She includes invaluable tips on how to make ingredients stretch; from potato peel crisps to pickled cucumber and beetroot. Megan also features ways to turn leftovers into a new meal, such as a Roasted Fennel, Chive and Dill Pasta Bake or Frittata, both from a leftover Raw Fennel, Chive and Dill Salad. Recipes include multi-tasking brunch or late-night dishes such as Bircher Pancakes or Sweet Potato Baked Eggs. Suppers for Sharing that can be scaled up to feed a crowd or down for a more intimate occasion range from Roasted Squash with Almonds and Tarragon to the best Roast Chicken recipe with Pan Pastry Croutons (plus, of course, ways to use up any uneaten chicken!). From On the Side accompaniments and stunning Sweet Things such as Pot Luck Tarte Tatin this collection of delicious and ingenious recipes will have all the inspiration you need to run a more sustainable home kitchen, reduce your carbon footprint and make the sort of small changes at home that can make a big difference to our world.
At Nature’s Edge: The Global Present and Long-Term History
by Gunnel Cederlöf Mahesh RangarajanIn an epoch when environmental issues make the headlines, this is a work that goes beyond the everyday. Ecologies as diverse as the Himalayas and the Indian Ocean coast, the Negev desert and the former military bases of Vietnam, or the Namib desert and the east African savannah all have in common a long-time human presence and the many ways people have modified nature. With research covering countries from Asia, Africa, and Australia, the authors come together to ask how and why human impacts on nature have grown in scale and pace from a long pre-history. The chapters in this volume illumine specific patterns and responses across time, going beyond an overt centring of the European experience. The tapestry of life and the human reshaping of environments evoke both concern and hope, making it vital to understand when, why, and how we came to this particular turn in the road. Eschewing easy labels and questioning eurocentrism in today’s climate vocabulary, this is a volume that will stimulate rethinking among scholars and citizens alike.
At One with Nature: Advances in Ecological Architecture in the Work of Ken Yeang
by Ken Yeang Edwina Threipland"At One with Nature is an inspiring collection of the latest work of Ken Yeang that further advances sustainable architecture and design. This collection features recent projects as he explores how we can achieve harmony between the natural and our built environments to create a better planet by design. Each project features and highlights not only the systems and devices adopted, but also outlines the intentions and ecological considerations demonstrating best practices for how we can proceed moving forward. The book role models our living Earth and shows how we can behave as stewards of our planet."--Cassia Patel, Oceanic Global Foundation At One with Nature showcases Ken Yeang's latest ideas, built projects designs, research work and advances in the field of designing with nature, a topic that Yeang has pioneered and developed over many decades since receiving his doctorate in ecological design and planning from Cambridge University. His ideas and work are even more pertinent today with the current state of devastation of Earth's natural systems and a biogeochemical cycle that has been extensively and severely impacted by human society. The global environment today is in a state of crisis, but what can society do to address the issues? Yeang's recent projects are presented with instructive diagrams that provide a basis for action for architects, planners, designers, engineers, and anyone whose daily work impinges on the natural environment. Offered in a highly visual, annotated format, with instructive illustrations of Yeang's theoretical books on the topic, At One with Nature is an invaluable resource that students and academics interested in designing with nature will find both informative and relevant.
At Risk: Natural Hazards, People's Vulnerability and Disasters (PDF)
by Piers Blaikie Terry Cannon Ian Davis Ben WisnerThe term 'natural disaster' is often used to refer to natural events such as earthquakes, hurricanes or floods. However, the phrase 'natural disaster' suggests an uncritical acceptance of a deeply engrained ideological and cultural myth. At Risk questions this myth and argues that extreme natural events are not disasters until a vulnerable group of people is exposed. The updated new edition confronts a further ten years of ever more expensive and deadly disasters and discusses disaster not as an aberration, but as a signal failure of mainstream 'development'. Two analytical models are provided as tools for understanding vulnerability. One links remote and distant 'root causes' to 'unsafe conditions' in a 'progression of vulnerability'. The other uses the concepts of 'access' and 'livelihood' to understand why some households are more vulnerable than others. Examining key natural events and incorporating strategies to create a safer world, this revised edition is an important resource for those involved in the fields of environment and development studies.
At Risk: Natural Hazards, People's Vulnerability and Disasters
by Piers Blaikie Terry Cannon Ian Davis Ben WisnerThe term 'natural disaster' is often used to refer to natural events such as earthquakes, hurricanes or floods. However, the phrase 'natural disaster' suggests an uncritical acceptance of a deeply engrained ideological and cultural myth. At Risk questions this myth and argues that extreme natural events are not disasters until a vulnerable group of people is exposed. The updated new edition confronts a further ten years of ever more expensive and deadly disasters and discusses disaster not as an aberration, but as a signal failure of mainstream 'development'. Two analytical models are provided as tools for understanding vulnerability. One links remote and distant 'root causes' to 'unsafe conditions' in a 'progression of vulnerability'. The other uses the concepts of 'access' and 'livelihood' to understand why some households are more vulnerable than others. Examining key natural events and incorporating strategies to create a safer world, this revised edition is an important resource for those involved in the fields of environment and development studies.
At Risk: Natural Hazards, People's Vulnerability and Disasters
by Piers Blaikie Terry Cannon Ian Davis Ben WisnerThe term 'natural disaster' is often used to refer to natural events such as earthquakes, hurricanes or floods. However, the phrase 'natural disaster' suggests an uncritical acceptance of a deeply engrained ideological and cultural myth. At Risk questions this myth and argues that extreme natural events are not disasters until a vulnerable group of people is exposed. The updated new edition confronts a further ten years of ever more expensive and deadly disasters and discusses disaster not as an aberration, but as a signal failure of mainstream 'development'. Two analytical models are provided as tools for understanding vulnerability. One links remote and distant 'root causes' to 'unsafe conditions' in a 'progression of vulnerability'. The other uses the concepts of 'access' and 'livelihood' to understand why some households are more vulnerable than others. Examining key natural events and incorporating strategies to create a safer world, this revised edition is an important resource for those involved in the fields of environment and development studies.
At Risk
by Ben Wisner Piers Blaikie Terry Cannon Ian DavisThe term 'natural disaster' is often used to refer to natural events such as earthquakes, hurricanes or floods. However, the phrase 'natural disaster' suggests an uncritical acceptance of a deeply engrained ideological and cultural myth. At Risk questions this myth and argues that extreme natural events are not disasters until a vulnerable group of people is exposed. The updated new edition confronts a further ten years of ever more expensive and deadly disasters and discusses disaster not as an aberration, but as a signal failure of mainstream 'development'. Two analytical models are provided as tools for understanding vulnerability. One links remote and distant 'root causes' to 'unsafe conditions' in a 'progression of vulnerability'. The other uses the concepts of 'access' and 'livelihood' to understand why some households are more vulnerable than others. Examining key natural events and incorporating strategies to create a safer world, this revised edition is an important resource for those involved in the fields of environment and development studies.