Instabilities And Nonequilibrium Structures Iv

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Instabilities And Nonequilibrium Structures Iv

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Author : E. Tirapegui
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Instabilities And Nonequilibrium Structures Iv written by E. Tirapegui and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

We have classified the articles presented here in two Sections according to their general content. In Part I we have included papers which deal with statistical mechanics, math ematical aspects of dynamical systems and sthochastic effects in nonequilibrium systems. Part II is devoted mainly to instabilities and self-organization in extended nonequilibrium systems. The study of partial differential equations by numerical and analytic methods plays a great role here and many works are related to this subject. Most recent developments in this fascinating and rapidly growing area are discussed. PART I STATISTICAL MECHANICS AND RELATED TOPICS NONEQUILIBRIUM POTENTIALS FOR PERIOD DOUBLING R. Graham and A. Hamm Fachbereich Physik, Universitiit Gesamthochschule Essen D4300 Essen 1 Germany ABSTRACT. In this lecture we consider the influence of weak stochastic perturbations on period doubling using nonequilibrium potentials, a concept which is explained in section 1 and formulated for the case of maps in section 2. In section 3 nonequilibrium potentials are considered for the family of quadratic maps (a) at the Feigenbaum 'attractor' with Gaussian noise, (b) for more general non Gaussian noise, and (c) for the case of a strange repeller. Our discussion will be informal. A more detailed account of this and related material can be found in our papers [1-3] and in the reviews [4, 5], where further references to related work are also given. 1.

Instabilities And Nonequilibrium Structures Vi

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Author : E. Tirapegui
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Instabilities And Nonequilibrium Structures Vi written by E. Tirapegui and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.

This book contains two introductory papers on important topics of nonlinear physics. The first one, by M. San Miguel et al., refers to the effect of noise in nonequilibrium systems. The second, by M.E. Brachet, is a modern introduction to turbulence in fluids. The material can be very useful for short courses and is presented accordingly. The authors have made their texts self-contained. The volume also contains a selection of the invited seminars given at the Sixth International Workshop on Instabilities and Nonequilibrium Structures. Audience: This book should be of interest to graduate students and scientists interested in the fascinating problems of nonlinear physics.

Collective Beings

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Author : Gianfranco Minati
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-12-26

Collective Beings written by Gianfranco Minati and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-12-26 with Science categories.

Microscopic models 226 The intrinsic limitations of the theory of phase transitions 229 5. 3 Quantum Field Theory 230 5. 4 Spontaneous Symmetry Breaking 239 5. 5 Non-ideal models of emergence 249 5. 5. 1 Neural networks 250 5. 5. 2 Cellular Automata 261 5. 5. 3 Artificial Life 265 5. 6 The role of noise 273 5. 7 The relationships between traditional and non-traditional models 279 Chapter 6. The Role of Ergodicity 291 6. 1 Some definitions related to ergodicity 293 6. 1. 1 Ergodic 293 6. 1. 2 Disciplinary definitions 293 6. 2 Ergodicity and stationarity 300 6. 3 Ergodicity in Collective Beings 302 6. 4 Emergence, Collective Beings, and Ergodicity 306 6. 5 Further considerations 309 6. 6 Some remarks and possible lines of research 313 Chapter 7. Applications to Social Systems (1): growth, development, sustainable development and ethics 321 7. 1 Growth, Development and Sustainable Development 323 7. 1. 1 Representing Growth 324 7. 1. 2 Development 326 7. 1. 3 Managing for development 334 7. 2 Ethics 336 7. 2. 1 Ethics and Quality 340 7. 2. 2 Effectiveness and advantages of Ethics 342 7. 2. 3 Ethics for quality and effectiveness 343 7. 2. 4 Ethics and Globalization 346 viii Contents Chapter 8. Applications to Social Systems (2): systems archetypes, virtual systems, knowledge management, organizational learning, industrial districts 353 8. 1 Systems archetypes and collective beings 353 8. 2 Virtual systems 359 8. 2.

Dynamics Of Spatio Temporal Cellular Structures

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Author : Innocent Mutabazi
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-12-15

Dynamics Of Spatio Temporal Cellular Structures written by Innocent Mutabazi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-12-15 with Science categories.

The impact of Benard's discovery on 20th century physics is crucial to any modern research area such as fluid dynamics, nonlinear dynamics, and non-equilibrium thermodynamics, just to name a few. This centenary review shows the broad scope and development including modern applications, edited and written by experts in the field.

Quantum Chaos And Mesoscopic Systems

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Author : N.E. Hurt
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-02-28

Quantum Chaos And Mesoscopic Systems written by N.E. Hurt and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-02-28 with Mathematics categories.

4. 2 Variance of Quantum Matrix Elements. 125 4. 3 Berry's Trick and the Hyperbolic Case 126 4. 4 Nonhyperbolic Case . . . . . . . 128 4. 5 Random Matrix Theory . . . . . 128 4. 6 Baker's Map and Other Systems 129 4. 7 Appendix: Baker's Map . . . . . 129 5 Error Terms 133 5. 1 Introduction. . . . . . . . . . . . . . . . . . . . . . . 133 5. 2 The Riemann Zeta Function in Periodic Orbit Theory 135 5. 3 Form Factor for Primes . . . . . . . . . . . . . . . . . 137 5. 4 Error Terms in Periodic Orbit Theory: Co-compact Case. 138 5. 5 Binary Quadratic Forms as a Model . . . . . . . . . . . . 139 6 Co-Finite Model for Quantum Chaology 141 6. 1 Introduction. . . . . . . . 141 6. 2 Co-finite Models . . . . . 141 6. 3 Geodesic Triangle Spaces 144 6. 4 L-Functions. . . . . . . . 145 6. 5 Zelditch's Prime Geodesic Theorem. 146 6. 6 Zelditch's Pseudo Differential Operators 147 6. 7 Weyl's Law Generalized 148 6. 8 Equidistribution Theory . . . . . . . . . 150 7 Landau Levels and L-Functions 153 7. 1 Introduction. . . . . . . . . . . . . . . . . . . . . . . 153 7. 2 Landau Model: Mechanics on the Plane and Sphere. 153 7. 3 Landau Model: Mechanics on the Half-Plane 155 7. 4 Selberg's Spectral Theorem . . . . . . . . . . . 157 7. 5 Pseudo Billiards . . . . . . . . . . . . . . . . . 158 7. 6 Landau Levels on a Compact Riemann Surface 159 7. 7 Automorphic Forms . . . . . 160 7. 8 Maass-Selberg Trace Formula 162 7. 9 Degeneracy by Selberg. . . . 163 7. 10 Hecke Operators . . . . . . . 163 7. 11 Selberg Trace Formula for Hecke Operators 167 7. 12 Eigenvalue Statistics on X . . . . 169 7. 13 Mesoscopic Devices. . . . . . . . 170 7. 14 Hall Conductance on Leaky Tori 170 7.

Optimal Filtering

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Author : V.N. Fomin
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Optimal Filtering written by V.N. Fomin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

This book is devoted to an investigation of some important problems of mod ern filtering theory concerned with systems of 'any nature being able to per ceive, store and process an information and apply it for control and regulation'. (The above quotation is taken from the preface to [27]). Despite the fact that filtering theory is l'argely worked out (and its major issues such as the Wiener-Kolmogorov theory of optimal filtering of stationary processes and Kalman-Bucy recursive filtering theory have become classical) a development of the theory is far from complete. A great deal of recent activity in this area is observed, researchers are trying consistently to generalize famous results, extend them to more broad classes of processes, realize and justify more simple procedures for processing measurement data in order to obtain more efficient filtering algorithms. As to nonlinear filter ing, it remains much as fragmentary. Here much progress has been made by R. L. Stratonovich and his successors in the area of filtering of Markov processes. In this volume an effort is made to advance in certain of these issues. The monograph has evolved over many years, coming of age by stages. First it was an impressive job of gathering together the bulk of the impor tant contributions to estimation theory, an understanding and moderniza tion of some of its results and methods, with the intention of applying them to recursive filtering problems.

Many Particle Dynamics And Kinetic Equations

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Author : C. Cercignani
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Many Particle Dynamics And Kinetic Equations written by C. Cercignani and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.

As our title suggests, there are two aspects in the subject of this book. The first is the mathematical investigation of the dynamics of infinite systems of in teracting particles and the description of the time evolution of their states. The second is the rigorous derivation of kinetic equations starting from the results of the aforementioned investigation. As is well known, statistical mechanics started in the last century with some papers written by Maxwell and Boltzmann. Although some of their statements seemed statistically obvious, we must prove that they do not contradict what me chanics predicts. In some cases, in particular for equilibrium states, it turns out that mechanics easily provides the required justification. However things are not so easy, if we take a step forward and consider a gas is not in equilibrium, as is, e.g., the case for air around a flying vehicle. Questions of this kind have been asked since the dawn of the kinetic theory of gases, especially when certain results appeared to lead to paradoxical conclu sions. Today this matter is rather well understood and a rigorous kinetic theory is emerging. The importance of these developments stems not only from the need of providing a careful foundation of such a basic physical theory, but also to exhibit a prototype of a mathematical construct central to the theory of non-equilibrium phenomena of macroscopic size.

Evolution Processes And The Feynman Kac Formula

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Author : Brian Jefferies
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

Evolution Processes And The Feynman Kac Formula written by Brian Jefferies and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.

This book is an outgrowth of ideas originating from 1. Kluvanek. Unfortunately, Professor Kluvanek did not live to contribute to the project of writing up in a systematic form, the circle of ideas to which the present work is devoted. It is more than likely that with his input, the approach and areas of emphasis of the resulting exposition would have been quite different from what we have here. Nevertheless, the stamp of Kluvanek's thought and philosophy (but not necessarily his approval) abounds throughout this book. Although the title gives no indication, integration theory in vector spaces is a cen tral topic of this work. However, the various notions of integration developed here are intimately connected with a specific application-the representation of evolutions by func tional integrals. The representation of a perturbation to the heat semigroup in terms of Wiener measure is known as the Feynman-Kac formula, but the term has a wider meaning in the present work. Traditionally, such representations have been used to obtain analytic information about perturbations to free evolutions as an alternative to arguments with a more operator-theoretic flavour. No applications of this type are given here. It is an un derlying assumption of the presentation of this material that representations of the nature of the Feynman-Kac formula are worth obtaining, and in the process of obtaining them, we may be led to new, possibly fertile mathematical structures-a view largely motivated by the pervasive use of path integrals in quantum physics.

Feynman Integral And Random Dynamics In Quantum Physics

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Author : Z. Haba
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-11

Feynman Integral And Random Dynamics In Quantum Physics written by Z. Haba and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-11 with Science categories.

The Feynman integral is considered as an intuitive representation of quantum mechanics showing the complex quantum phenomena in a language comprehensible at a classical level. It suggests that the quantum transition amplitude arises from classical mechanics by an average over various interfering paths. The classical picture suggested by the Feynman integral may be illusory. By most physicists the path integral is usually treated as a convenient formal mathematical tool for a quick derivation of useful approximations in quantum mechanics. Results obtained in the formalism of Feynman integrals receive a mathematical justification by means of other (usually much harder) methods. In such a case the rigour is achieved at the cost of losing the intuitive classical insight. The aim of this book is to formulate a mathematical theory of the Feynman integral literally in the way it was expressed by Feynman, at the cost of complexifying the configuration space. In such a case the Feynman integral can be expressed by a probability measure. The equations of quantum mechanics can be formulated as equations of random classical mechanics on a complex configuration space. The opportunity of computer simulations shows an immediate advantage of such a formulation. A mathematical formulation of the Feynman integral should not be considered solely as an academic question of mathematical rigour in theoretical physics.

The Theory Of Anisotropic Elastic Plates

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Author : T.S. Vashakmadze
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-27

The Theory Of Anisotropic Elastic Plates written by T.S. Vashakmadze and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-27 with Science categories.

The main purpose of this work is construction of the mathematical theory of elastic plates and shells, by means of which the investigation of basic boundary value problems of the spatial theory of elasticity in the case of cylindrical do mains reduces to the study of two-dimensional boundary value problems (BVP) of comparatively simple structure. In this respect in sections 2-5 after the introductory material, methods of re duction, known in the literature as usually being based on simplifying hypotheses, are studied. Here, in contradiction to classical methods, the problems, connected with construction of refined theories of anisotropic nonhomogeneous plates with variable thickness without the assumption of any physical and geometrical re strictions, are investigated. The comparative analysis of such reduction methods was carried out, and, in particular, in section 5, the following fact was established: the error transition, occuring with substitution of a two-dimensional model for the initial problem on the class of assumed solutions is restricted from below. Further, in section 6, Vekua's method of reduction, containing regular pro cess of study of three-dimensional problem, is investigated. In this direction, the problems, connected with solvability, convergence of processes, and construction of effective algorithms of approximate solutions are studied.