Stochastic Pdes And Modelling Of Multiscale Complex System

Author : Wang Wei,Chen Xiaopeng,Lv Yan
Publisher : World Scientific
Page : 240 pages
File Size : 50,6 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 : Xiaoying Han,Peter Kloeden
Publisher : World Scientific
Page : 381 pages
File Size : 53,8 Mb
Release : 2023-03-14
Category : Mathematics
ISBN : 9789811267772

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Dissipative Lattice Dynamical Systems by Xiaoying Han,Peter Kloeden Pdf

There is an extensive literature in the form of papers (but no books) on lattice dynamical systems. The book focuses on dissipative lattice dynamical systems and their attractors of various forms such as autonomous, nonautonomous and random. The existence of such attractors is established by showing that the corresponding dynamical system has an appropriate kind of absorbing set and is asymptotically compact in some way.There is now a very large literature on lattice dynamical systems, especially on attractors of all kinds in such systems. We cannot hope to do justice to all of them here. Instead, we have focused on key areas of representative types of lattice systems and various types of attractors. Our selection is biased by our own interests, in particular to those dealing with biological applications. One of the important results is the approximation of Heaviside switching functions in LDS by sigmoidal functions.Nevertheless, we believe that this book will provide the reader with a solid introduction to the field, its main results and the methods that are used to obtain them.

Author : Peter Kloeden,Meihua Yang
Publisher : World Scientific
Page : 157 pages
File Size : 43,7 Mb
Release : 2020-11-25
Category : Mathematics
ISBN : 9789811228674

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An Introduction To Nonautonomous Dynamical Systems And Their Attractors by Peter Kloeden,Meihua Yang Pdf

The nature of time in a nonautonomous dynamical system is very different from that in autonomous systems, which depend only on the time that has elapsed since starting rather than on the actual time itself. Consequently, limiting objects may not exist in actual time as in autonomous systems. New concepts of attractors in nonautonomous dynamical system are thus required.In addition, the definition of a dynamical system itself needs to be generalised to the nonautonomous context. Here two possibilities are considered: two-parameter semigroups or processes and the skew product flows. Their attractors are defined in terms of families of sets that are mapped onto each other under the dynamics rather than a single set as in autonomous systems. Two types of attraction are now possible: pullback attraction, which depends on the behaviour from the system in the distant past, and forward attraction, which depends on the behaviour of the system in the distant future. These are generally independent of each other.The component subsets of pullback and forward attractors exist in actual time. The asymptotic behaviour in the future limit is characterised by omega-limit sets, in terms of which form what are called forward attracting sets. They are generally not invariant in the conventional sense, but are asymptotically invariant in general and, if the future dynamics is appropriately uniform, also asymptotically negatively invariant.Much of this book is based on lectures given by the authors in Frankfurt and Wuhan. It was written mainly when the first author held a 'Thousand Expert' Professorship at the Huazhong University of Science and Technology in Wuhan.

Author : Panagiotis D. Christofides,Antonios Armaou,Yiming Lou,Amit Varshney
Publisher : Springer Science & Business Media
Page : 247 pages
File Size : 51,8 Mb
Release : 2008-10-28
Category : Science
ISBN : 9780817647933

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Control and Optimization of Multiscale Process Systems by Panagiotis D. Christofides,Antonios Armaou,Yiming Lou,Amit Varshney Pdf

This book—the first of its kind—presents general methods for feedback controller synthesis and optimization of multiscale systems, illustrating their application to thin-film growth, sputtering processes, and catalytic systems of industrial interest. The authors demonstrate the advantages of the methods presented for control and optimization through extensive simulations. Included in the work are new techniques for feedback controller design and optimization of multiscale process systems that are not included in other books. The book also contains a rich collection of new research topics and references to significant recent work.

Author : A. J. Roberts
Publisher : SIAM
Page : 760 pages
File Size : 51,5 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 : Alexander N. Gorban,Nikolas Kazantzis,I. G. Kevrekidis,Hans Christian Öttinger,Konstantinos Theodoropoulos
Publisher : Springer Science & Business Media
Page : 554 pages
File Size : 49,7 Mb
Release : 2006-09-22
Category : Science
ISBN : 9783540358886

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Model Reduction and Coarse-Graining Approaches for Multiscale Phenomena by Alexander N. Gorban,Nikolas Kazantzis,I. G. Kevrekidis,Hans Christian Öttinger,Konstantinos Theodoropoulos Pdf

Model reduction and coarse-graining are important in many areas of science and engineering. How does a system with many degrees of freedom become one with fewer? How can a reversible micro-description be adapted to the dissipative macroscopic model? These crucial questions, as well as many other related problems, are discussed in this book. All contributions are by experts whose specialities span a wide range of fields within science and engineering.

Author : Jinqiao Duan,Wei Wang
Publisher : Elsevier
Page : 283 pages
File Size : 55,7 Mb
Release : 2014-03-06
Category : Mathematics
ISBN : 9780128012697

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Effective Dynamics of Stochastic Partial Differential Equations by Jinqiao Duan,Wei Wang Pdf

Effective Dynamics of Stochastic Partial Differential Equations focuses on stochastic partial differential equations with slow and fast time scales, or large and small spatial scales. The authors have developed basic techniques, such as averaging, slow manifolds, and homogenization, to extract effective dynamics from these stochastic partial differential equations. The authors’ experience both as researchers and teachers enable them to convert current research on extracting effective dynamics of stochastic partial differential equations into concise and comprehensive chapters. The book helps readers by providing an accessible introduction to probability tools in Hilbert space and basics of stochastic partial differential equations. Each chapter also includes exercises and problems to enhance comprehension. New techniques for extracting effective dynamics of infinite dimensional dynamical systems under uncertainty Accessible introduction to probability tools in Hilbert space and basics of stochastic partial differential equations Solutions or hints to all Exercises

Author : Jerome Noailly,Stephane Avril,Peter Pivonka,Stefan Scheiner
Publisher : Frontiers Media SA
Page : 317 pages
File Size : 40,5 Mb
Release : 2022-03-11
Category : Science
ISBN : 9782889746620

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Multiscale Modeling to Tackle the Complexity of Load-Bearing Organ and Tissue Regulation by Jerome Noailly,Stephane Avril,Peter Pivonka,Stefan Scheiner Pdf

Author : Somnath Ghosh,Dennis Dimiduk
Publisher : Springer Science & Business Media
Page : 669 pages
File Size : 54,5 Mb
Release : 2010-11-17
Category : Science
ISBN : 9781441906434

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Computational Methods for Microstructure-Property Relationships by Somnath Ghosh,Dennis Dimiduk Pdf

Computational Methods for Microstructure-Property Relationships introduces state-of-the-art advances in computational modeling approaches for materials structure-property relations. Written with an approach that recognizes the necessity of the engineering computational mechanics framework, this volume provides balanced treatment of heterogeneous materials structures within the microstructural and component scales. Encompassing both computational mechanics and computational materials science disciplines, this volume offers an analysis of the current techniques and selected topics important to industry researchers, such as deformation, creep and fatigue of primarily metallic materials. Researchers, engineers and professionals involved with predicting performance and failure of materials will find Computational Methods for Microstructure-Property Relationships a valuable reference.

Author : Weinan E
Publisher : Cambridge University Press
Page : 485 pages
File Size : 52,6 Mb
Release : 2011-07-07
Category : Mathematics
ISBN : 9781107096547

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Principles of Multiscale Modeling by Weinan E Pdf

A systematic discussion of the fundamental principles, written by a leading contributor to the field.

Author : Christian Kuehn
Publisher : SIAM
Page : 260 pages
File Size : 45,6 Mb
Release : 2019-04-10
Category : Mathematics
ISBN : 9781611975659

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PDE Dynamics by Christian Kuehn Pdf

This book provides an overview of the myriad methods for applying dynamical systems techniques to PDEs and highlights the impact of PDE methods on dynamical systems. Also included are many nonlinear evolution equations, which have been benchmark models across the sciences, and examples and techniques to strengthen preparation for research. PDE Dynamics: An Introduction is intended for senior undergraduate students, beginning graduate students, and researchers in applied mathematics, theoretical physics, and adjacent disciplines. Structured as a textbook or seminar reference, it can be used in courses titled Dynamics of PDEs, PDEs 2, Dynamical Systems 2, Evolution Equations, or Infinite-Dimensional Dynamics.

Author : National Research Council,Division on Engineering and Physical Sciences,Board on Mathematical Sciences and Their Applications,Committee on Mathematical Foundations of Verification, Validation, and Uncertainty Quantification
Publisher : National Academies Press
Page : 144 pages
File Size : 55,9 Mb
Release : 2012-07-26
Category : Mathematics
ISBN : 9780309256346

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Assessing the Reliability of Complex Models by National Research Council,Division on Engineering and Physical Sciences,Board on Mathematical Sciences and Their Applications,Committee on Mathematical Foundations of Verification, Validation, and Uncertainty Quantification Pdf

Advances in computing hardware and algorithms have dramatically improved the ability to simulate complex processes computationally. Today's simulation capabilities offer the prospect of addressing questions that in the past could be addressed only by resource-intensive experimentation, if at all. Assessing the Reliability of Complex Models recognizes the ubiquity of uncertainty in computational estimates of reality and the necessity for its quantification. As computational science and engineering have matured, the process of quantifying or bounding uncertainties in a computational estimate of a physical quality of interest has evolved into a small set of interdependent tasks: verification, validation, and uncertainty of quantification (VVUQ). In recognition of the increasing importance of computational simulation and the increasing need to assess uncertainties in computational results, the National Research Council was asked to study the mathematical foundations of VVUQ and to recommend steps that will ultimately lead to improved processes. Assessing the Reliability of Complex Models discusses changes in education of professionals and dissemination of information that should enhance the ability of future VVUQ practitioners to improve and properly apply VVUQ methodologies to difficult problems, enhance the ability of VVUQ customers to understand VVUQ results and use them to make informed decisions, and enhance the ability of all VVUQ stakeholders to communicate with each other. This report is an essential resource for all decision and policy makers in the field, students, stakeholders, UQ experts, and VVUQ educators and practitioners.

Author : Center for Turbulence Research (U.S.)
Publisher : Unknown
Page : 486 pages
File Size : 42,8 Mb
Release : 2009
Category : Turbulence
ISBN : UCAL:B5619117

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Annual Research Briefs ... by Center for Turbulence Research (U.S.) Pdf

Author : Andrew J. Majda,Samuel N. Stechmann,Shengqian Chen,H. Reed Ogrosky,Sulian Thual
Publisher : Springer Nature
Page : 123 pages
File Size : 49,8 Mb
Release : 2019-09-24
Category : Mathematics
ISBN : 9783030222475

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Tropical Intraseasonal Variability and the Stochastic Skeleton Method by Andrew J. Majda,Samuel N. Stechmann,Shengqian Chen,H. Reed Ogrosky,Sulian Thual Pdf

In this text, modern applied mathematics and physical insight are used to construct the simplest and first nonlinear dynamical model for the Madden-Julian oscillation (MJO), i.e. the stochastic skeleton model. This model captures the fundamental features of the MJO and offers a theoretical prediction of its structure, leading to new detailed methods to identify it in observational data. The text contributes to understanding and predicting intraseasonal variability, which remains a challenging task in contemporary climate, atmospheric, and oceanic science. In the tropics, the Madden-Julian oscillation (MJO) is the dominant component of intraseasonal variability. One of the strengths of this text is demonstrating how a blend of modern applied mathematical tools, including linear and nonlinear partial differential equations (PDEs), simple stochastic modeling, and numerical algorithms, have been used in conjunction with physical insight to create the model. These tools are also applied in developing several extensions of the model in order to capture additional features of the MJO, including its refined vertical structure and its interactions with the extratropics. This book is of interest to graduate students, postdocs, and senior researchers in pure and applied mathematics, physics, engineering, and climate, atmospheric, and oceanic science interested in turbulent dynamical systems as well as other complex systems.

Author : Nicola Bellomo
Publisher : MDPI
Page : 118 pages
File Size : 41,6 Mb
Release : 2020-05-29
Category : Business & Economics
ISBN : 9783039288793

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Kinetic Theory and Swarming Tools to Modeling Complex Systems—Symmetry problems in the Science of Living Systems by Nicola Bellomo Pdf

This MPDI book comprises a number of selected contributions to a Special Issue devoted to the modeling and simulation of living systems based on developments in kinetic mathematical tools. The focus is on a fascinating research field which cannot be tackled by the approach of the so-called hard sciences—specifically mathematics—without the invention of new methods in view of a new mathematical theory. The contents proposed by eight contributions witness the growing interest of scientists this field. The first contribution is an editorial paper which presents the motivations for studying the mathematics and physics of living systems within the framework an interdisciplinary approach, where mathematics and physics interact with specific fields of the class of systems object of modeling and simulations. The different contributions refer to economy, collective learning, cell motion, vehicular traffic, crowd dynamics, and social swarms. The key problem towards modeling consists in capturing the complexity features of living systems. All articles refer to large systems of interaction living entities and follow, towards modeling, a common rationale which consists firstly in representing the system by a probability distribution over the microscopic state of the said entities, secondly, in deriving a general mathematical structure deemed to provide the conceptual basis for the derivation of models and, finally, in implementing the said structure by models of interactions at the microscopic scale. Therefore, the modeling approach transfers the dynamics at the low scale to collective behaviors. Interactions are modeled by theoretical tools of stochastic game theory. Overall, the interested reader will find, in the contents, a forward look comprising various research perspectives and issues, followed by hints on to tackle these.