Stochastic Equations For Complex Systems

Author : A.V. Skorohod
Publisher : Springer Science & Business Media
Page : 202 pages
File Size : 52,7 Mb
Release : 1987-11-30
Category : Mathematics
ISBN : 9027724083

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Stochastic Equations for Complex Systems by A.V. Skorohod Pdf

Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the tinal question. G. K. Chesterton. The Scandal oj Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics, However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches, It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related, Further. the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces, And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes, They draw upon widely different sections of mathematics.

Author : Stefan Heinz,Hakima Bessaih
Publisher : Springer
Page : 192 pages
File Size : 40,8 Mb
Release : 2015-05-06
Category : Mathematics
ISBN : 9783319182063

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Stochastic Equations for Complex Systems by Stefan Heinz,Hakima Bessaih Pdf

Mathematical analyses and computational predictions of the behavior of complex systems are needed to effectively deal with weather and climate predictions, for example, and the optimal design of technical processes. Given the random nature of such systems and the recognized relevance of randomness, the equations used to describe such systems usually need to involve stochastics. The basic goal of this book is to introduce the mathematics and application of stochastic equations used for the modeling of complex systems. A first focus is on the introduction to different topics in mathematical analysis. A second focus is on the application of mathematical tools to the analysis of stochastic equations. A third focus is on the development and application of stochastic methods to simulate turbulent flows as seen in reality. This book is primarily oriented towards mathematics and engineering PhD students, young and experienced researchers, and professionals working in the area of stochastic differential equations and their applications. It contributes to a growing understanding of concepts and terminology used by mathematicians, engineers, and physicists in this relatively young and quickly expanding field.

Author : A.V. Skorohod
Publisher : Springer
Page : 0 pages
File Size : 51,7 Mb
Release : 1987-12-14
Category : Mathematics
ISBN : 9400937679

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Stochastic Equations for Complex Systems by A.V. Skorohod Pdf

Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the tinal question. G. K. Chesterton. The Scandal oj Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics, However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches, It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related, Further. the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces, And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes, They draw upon widely different sections of mathematics.

Author : Paolo Sibani,Henrik Jeldtoft Jensen
Publisher : World Scientific Publishing Company
Page : 300 pages
File Size : 53,7 Mb
Release : 2013-02-20
Category : Mathematics
ISBN : 9781848169951

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Stochastic Dynamics of Complex Systems by Paolo Sibani,Henrik Jeldtoft Jensen Pdf

Dynamical evolution over long time scales is a prominent feature of all the systems we intuitively think of as complex — for example, ecosystems, the brain or the economy. In physics, the term ageing is used for this type of slow change, occurring over time scales much longer than the patience, or indeed the lifetime, of the observer. The main focus of this book is on the stochastic processes which cause ageing, and the surprising fact that the ageing dynamics of systems which are very different at the microscopic level can be treated in similar ways. The first part of this book provides the necessary mathematical and computational tools and the second part describes the intuition needed to deal with these systems. Some of the first few chapters have been covered in several other books, but the emphasis and selection of the topics reflect both the authors' interests and the overall theme of the book. The second part contains an introduction to the scientific literature and deals in some detail with the description of complex phenomena of a physical and biological nature, for example, disordered magnetic materials, superconductors and glasses, models of co-evolution in ecosystems and even of ant behaviour. These heterogeneous topics are all dealt with in detail using similar analytical techniques. This book emphasizes the unity of complex dynamics and provides the tools needed to treat a large number of complex systems of current interest. The ideas and the approach to complex dynamics it presents have not appeared in book form until now.

Author : Lynn Nadel,Daniel I. Stein
Publisher : CRC Press
Page : 588 pages
File Size : 51,7 Mb
Release : 2018-10-08
Category : Mathematics
ISBN : 9780429972126

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1990 Lectures In Complex Systems by Lynn Nadel,Daniel I. Stein Pdf

An excellent series presenting top lecturers from the best institute for complex systems. Topics covered include: stochastic processes; fluid flow; pattern formation; information-based complexity; motor system problems; and the nature of adaptive change.

Author : Wang Wei,Chen Xiaopeng,Lv Yan
Publisher : World Scientific
Page : 240 pages
File Size : 48,5 Mb
Release : 2019-05-07
Category : Mathematics
ISBN : 9789811200366

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Stochastic Pdes And Modelling Of Multiscale Complex System by Wang Wei,Chen Xiaopeng,Lv Yan Pdf

This volume is devoted to original research results and survey articles reviewing recent developments in reduction for stochastic PDEs with multiscale as well as application to science and technology, and to present some future research direction. This volume includes a dozen chapters by leading experts in the area, with a broad audience in mind. It should be accessible to graduate students, junior researchers and other professionals who are interested in the subject. We also take this opportunity to celebrate the contributions of Professor Anthony J Roberts, an internationally leading figure on the occasion of his 60th years birthday in 2017.

Author : Valery I. Klyatskin
Publisher : Springer
Page : 423 pages
File Size : 45,5 Mb
Release : 2014-07-14
Category : Technology & Engineering
ISBN : 9783319075877

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Stochastic Equations: Theory and Applications in Acoustics, Hydrodynamics, Magnetohydrodynamics, and Radiophysics, Volume 1 by Valery I. Klyatskin Pdf

This monograph set presents a consistent and self-contained framework of stochastic dynamic systems with maximal possible completeness. Volume 1 presents the basic concepts, exact results, and asymptotic approximations of the theory of stochastic equations on the basis of the developed functional approach. This approach offers a possibility of both obtaining exact solutions to stochastic problems for a number of models of fluctuating parameters and constructing various asymptotic buildings. Ideas of statistical topography are used to discuss general issues of generating coherent structures from chaos with probability one, i.e., almost in every individual realization of random parameters. The general theory is illustrated with certain problems and applications of stochastic mathematical physics in various fields such as mechanics, hydrodynamics, magnetohydrodynamics, acoustics, optics, and radiophysics.

Author : M. Reza Rahimi Tabar
Publisher : Springer
Page : 280 pages
File Size : 55,5 Mb
Release : 2019-07-04
Category : Science
ISBN : 9783030184728

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Analysis and Data-Based Reconstruction of Complex Nonlinear Dynamical Systems by M. Reza Rahimi Tabar Pdf

This book focuses on a central question in the field of complex systems: Given a fluctuating (in time or space), uni- or multi-variant sequentially measured set of experimental data (even noisy data), how should one analyse non-parametrically the data, assess underlying trends, uncover characteristics of the fluctuations (including diffusion and jump contributions), and construct a stochastic evolution equation? Here, the term "non-parametrically" exemplifies that all the functions and parameters of the constructed stochastic evolution equation can be determined directly from the measured data. The book provides an overview of methods that have been developed for the analysis of fluctuating time series and of spatially disordered structures. Thanks to its feasibility and simplicity, it has been successfully applied to fluctuating time series and spatially disordered structures of complex systems studied in scientific fields such as physics, astrophysics, meteorology, earth science, engineering, finance, medicine and the neurosciences, and has led to a number of important results. The book also includes the numerical and analytical approaches to the analyses of complex time series that are most common in the physical and natural sciences. Further, it is self-contained and readily accessible to students, scientists, and researchers who are familiar with traditional methods of mathematics, such as ordinary, and partial differential equations. The codes for analysing continuous time series are available in an R package developed by the research group Turbulence, Wind energy and Stochastic (TWiSt) at the Carl von Ossietzky University of Oldenburg under the supervision of Prof. Dr. Joachim Peinke. This package makes it possible to extract the (stochastic) evolution equation underlying a set of data or measurements.

Author : Elbert Hendricks,Ole Jannerup,Paul Haase Sørensen
Publisher : Springer Science & Business Media
Page : 555 pages
File Size : 48,5 Mb
Release : 2008-10-13
Category : Technology & Engineering
ISBN : 9783540784869

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Linear Systems Control by Elbert Hendricks,Ole Jannerup,Paul Haase Sørensen Pdf

Modern control theory and in particular state space or state variable methods can be adapted to the description of many different systems because it depends strongly on physical modeling and physical intuition. The laws of physics are in the form of differential equations and for this reason, this book concentrates on system descriptions in this form. This means coupled systems of linear or nonlinear differential equations. The physical approach is emphasized in this book because it is most natural for complex systems. It also makes what would ordinarily be a difficult mathematical subject into one which can straightforwardly be understood intuitively and which deals with concepts which engineering and science students are already familiar. In this way it is easy to immediately apply the theory to the understanding and control of ordinary systems. Application engineers, working in industry, will also find this book interesting and useful for this reason. In line with the approach set forth above, the book first deals with the modeling of systems in state space form. Both transfer function and differential equation modeling methods are treated with many examples. Linearization is treated and explained first for very simple nonlinear systems and then more complex systems. Because computer control is so fundamental to modern applications, discrete time modeling of systems as difference equations is introduced immediately after the more intuitive differential equation models. The conversion of differential equation models to difference equations is also discussed at length, including transfer function formulations. A vital problem in modern control is how to treat noise in control systems. Nevertheless this question is rarely treated in many control system textbooks because it is considered to be too mathematical and too difficult in a second course on controls. In this textbook a simple physical approach is made to the description of noise and stochastic disturbances which is easy to understand and apply to common systems. This requires only a few fundamental statistical concepts which are given in a simple introduction which lead naturally to the fundamental noise propagation equation for dynamic systems, the Lyapunov equation. This equation is given and exemplified both in its continuous and discrete time versions. With the Lyapunov equation available to describe state noise propagation, it is a very small step to add the effect of measurements and measurement noise. This gives immediately the Riccati equation for optimal state estimators or Kalman filters. These important observers are derived and illustrated using simulations in terms which make them easy to understand and easy to apply to real systems. The use of LQR regulators with Kalman filters give LQG (Linear Quadratic Gaussian) regulators which are introduced at the end of the book. Another important subject which is introduced is the use of Kalman filters as parameter estimations for unknown parameters. The textbook is divided into 7 chapters, 5 appendices, a table of contents, a table of examples, extensive index and extensive list of references. Each chapter is provided with a summary of the main points covered and a set of problems relevant to the material in that chapter. Moreover each of the more advanced chapters (3 - 7) are provided with notes describing the history of the mathematical and technical problems which lead to the control theory presented in that chapter. Continuous time methods are the main focus in the book because these provide the most direct connection to physics. This physical foundation allows a logical presentation and gives a good intuitive feel for control system construction. Nevertheless strong attention is also given to discrete time systems. Very few proofs are included in the book but most of the important results are derived. This method of presentation makes the text very readable and gives a good foundation for reading more rigorous texts. A complete set of solutions is available for all of the problems in the text. In addition a set of longer exercises is available for use as Matlab/Simulink ‘laboratory exercises’ in connection with lectures. There is material of this kind for 12 such exercises and each exercise requires about 3 hours for its solution. Full written solutions of all these exercises are available.

Author : E. Tirapegui,Javier Martínez,Rolando Tiemann
Publisher : Springer Science & Business Media
Page : 404 pages
File Size : 52,5 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789401142472

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Instabilities and Nonequilibrium Structures VI by E. Tirapegui,Javier Martínez,Rolando Tiemann Pdf

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.

Author : Vidyadhar Mandrekar,Barbara Rüdiger
Publisher : Springer
Page : 213 pages
File Size : 45,6 Mb
Release : 2014-12-03
Category : Mathematics
ISBN : 9783319128535

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Stochastic Integration in Banach Spaces by Vidyadhar Mandrekar,Barbara Rüdiger Pdf

Considering Poisson random measures as the driving sources for stochastic (partial) differential equations allows us to incorporate jumps and to model sudden, unexpected phenomena. By using such equations the present book introduces a new method for modeling the states of complex systems perturbed by random sources over time, such as interest rates in financial markets or temperature distributions in a specific region. It studies properties of the solutions of the stochastic equations, observing the long-term behavior and the sensitivity of the solutions to changes in the initial data. The authors consider an integration theory of measurable and adapted processes in appropriate Banach spaces as well as the non-Gaussian case, whereas most of the literature only focuses on predictable settings in Hilbert spaces. The book is intended for graduate students and researchers in stochastic (partial) differential equations, mathematical finance and non-linear filtering and assumes a knowledge of the required integration theory, existence and uniqueness results and stability theory. The results will be of particular interest to natural scientists and the finance community. Readers should ideally be familiar with stochastic processes and probability theory in general, as well as functional analysis and in particular the theory of operator semigroups. ​

Author : Stephan Dahlke,Wolfgang Dahmen,Michael Griebel,Wolfgang Hackbusch,Klaus Ritter,Reinhold Schneider,Christoph Schwab,Harry Yserentant
Publisher : Springer
Page : 446 pages
File Size : 48,6 Mb
Release : 2014-11-13
Category : Mathematics
ISBN : 9783319081595

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Extraction of Quantifiable Information from Complex Systems by Stephan Dahlke,Wolfgang Dahmen,Michael Griebel,Wolfgang Hackbusch,Klaus Ritter,Reinhold Schneider,Christoph Schwab,Harry Yserentant Pdf

In April 2007, the Deutsche Forschungsgemeinschaft (DFG) approved the Priority Program 1324 “Mathematical Methods for Extracting Quantifiable Information from Complex Systems.” This volume presents a comprehensive overview of the most important results obtained over the course of the program. Mathematical models of complex systems provide the foundation for further technological developments in science, engineering and computational finance. Motivated by the trend toward steadily increasing computer power, ever more realistic models have been developed in recent years. These models have also become increasingly complex, and their numerical treatment poses serious challenges. Recent developments in mathematics suggest that, in the long run, much more powerful numerical solution strategies could be derived if the interconnections between the different fields of research were systematically exploited at a conceptual level. Accordingly, a deeper understanding of the mathematical foundations as well as the development of new and efficient numerical algorithms were among the main goals of this Priority Program. The treatment of high-dimensional systems is clearly one of the most challenging tasks in applied mathematics today. Since the problem of high-dimensionality appears in many fields of application, the above-mentioned synergy and cross-fertilization effects were expected to make a great impact. To be truly successful, the following issues had to be kept in mind: theoretical research and practical applications had to be developed hand in hand; moreover, it has proven necessary to combine different fields of mathematics, such as numerical analysis and computational stochastics. To keep the whole program sufficiently focused, we concentrated on specific but related fields of application that share common characteristics and as such, they allowed us to use closely related approaches.

Author : Raúl Toral,Pere Colet
Publisher : John Wiley & Sons
Page : 518 pages
File Size : 52,5 Mb
Release : 2014-06-26
Category : Science
ISBN : 9783527683123

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Stochastic Numerical Methods by Raúl Toral,Pere Colet Pdf

Stochastic Numerical Methods introduces at Master level the numerical methods that use probability or stochastic concepts to analyze random processes. The book aims at being rather general and is addressed at students of natural sciences (Physics, Chemistry, Mathematics, Biology, etc.) and Engineering, but also social sciences (Economy, Sociology, etc.) where some of the techniques have been used recently to numerically simulate different agent-based models. Examples included in the book range from phase-transitions and critical phenomena, including details of data analysis (extraction of critical exponents, finite-size effects, etc.), to population dynamics, interfacial growth, chemical reactions, etc. Program listings are integrated in the discussion of numerical algorithms to facilitate their understanding. From the contents: Review of Probability Concepts Monte Carlo Integration Generation of Uniform and Non-uniform Random Numbers: Non-correlated Values Dynamical Methods Applications to Statistical Mechanics Introduction to Stochastic Processes Numerical Simulation of Ordinary and Partial Stochastic Differential Equations Introduction to Master Equations Numerical Simulations of Master Equations Hybrid Monte Carlo Generation of n-Dimensional Correlated Gaussian Variables Collective Algorithms for Spin Systems Histogram Extrapolation Multicanonical Simulations

Author : A. J. Roberts
Publisher : SIAM
Page : 760 pages
File Size : 49,7 Mb
Release : 2014-12-18
Category : Mathematics
ISBN : 9781611973563

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Model Emergent Dynamics in Complex Systems by A. J. Roberts Pdf

Arising out of the growing interest in and applications of modern dynamical systems theory, this book explores how to derive relatively simple dynamical equations that model complex physical interactions. The author?s objectives are to use sound theory to explore algebraic techniques, develop interesting applications, and discover general modeling principles. Model Emergent Dynamics in Complex Systems unifies into one powerful and coherent approach the many varied extant methods for mathematical model reduction and approximation. Using mathematical models at various levels of resolution and complexity, the book establishes the relationships between such multiscale models and clarifying difficulties and apparent paradoxes and addresses model reduction for systems, resolves initial conditions, and illuminates control and uncertainty. The basis for the author?s methodology is the theory and the geometric picture of both coordinate transforms and invariant manifolds in dynamical systems; in particular, center and slow manifolds are heavily used. The wonderful aspect of this approach is the range of geometric interpretations of the modeling process that it produces?simple geometric pictures inspire sound methods of analysis and construction. Further, pictures drawn of state spaces also provide a route to better assess a model?s limitations and strengths. Geometry and algebra form a powerful partnership and coordinate transforms and manifolds provide a powerfully enhanced and unified view of a swathe of other complex system modeling methodologies such as averaging, homogenization, multiple scales, singular perturbations, two timing, and WKB theory.

Author : Roberto Serra
Publisher : Unknown
Page : 248 pages
File Size : 50,6 Mb
Release : 1986
Category : Mathematics
ISBN : UOM:39015032940853

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Introduction to the Physics of Complex Systems by Roberto Serra Pdf