Noise-Induced Phenomena in Slow-Fast Dynamical Systems

2006-02-07
Noise-Induced Phenomena in Slow-Fast Dynamical Systems

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  • Author: Nils Berglund
  • Publisher: Springer Science & Business Media
  • ISBN: 1846281865
  • Category : Mathematics
  • Languages : en
  • Pages : 283

Stochastic Differential Equations have become increasingly important in modelling complex systems in physics, chemistry, biology, climatology and other fields. This book examines and provides systems for practitioners to use, and provides a number of case studies to show how they can work in practice.

Noise-Driven Phenomena in Hysteretic Systems

2013-11-04
Noise-Driven Phenomena in Hysteretic Systems

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  • Author: Mihai Dimian
  • Publisher: Springer Science & Business Media
  • ISBN: 1461413745
  • Category : Technology & Engineering
  • Languages : en
  • Pages : 233

Noise-Driven Phenomena in Hysteretic Systems provides a general approach to nonlinear systems with hysteresis driven by noisy inputs, which leads to a unitary framework for the analysis of various stochastic aspects of hysteresis. This book includes integral, differential and algebraic models that are used to describe scalar and vector hysteretic nonlinearities originating from various areas of science and engineering. The universality of the authors approach is also reflected by the diversity of the models used to portray the input noise, from the classical Gaussian white noise to its impulsive forms, often encountered in economics and biological systems, and pink noise, ubiquitous in multi-stable electronic systems. The book is accompanied by HysterSoft© - a robust simulation environment designed to perform complex hysteresis modeling – that can be used by the reader to reproduce many of the results presented in the book as well as to research both disruptive and constructive effects of noise in hysteretic systems.

Handbook of Dynamic Data Driven Applications Systems

2018-11-13
Handbook of Dynamic Data Driven Applications Systems

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  • Author: Erik Blasch
  • Publisher: Springer
  • ISBN: 3319955047
  • Category : Computers
  • Languages : en
  • Pages : 750

The Handbook of Dynamic Data Driven Applications Systems establishes an authoritative reference of DDDAS, pioneered by Dr. Darema and the co-authors for researchers and practitioners developing DDDAS technologies. Beginning with general concepts and history of the paradigm, the text provides 32 chapters by leading experts in10 application areas to enable an accurate understanding, analysis, and control of complex systems; be they natural, engineered, or societal: Earth and Space Data Assimilation Aircraft Systems Processing Structures Health Monitoring Biological Data Assessment Object and Activity Tracking Embedded Control and Coordination Energy-Aware Optimization Image and Video Computing Security and Policy Coding Systems Design The authors explain how DDDAS unifies the computational and instrumentation aspects of an application system, extends the notion of Smart Computing to span from the high-end to the real-time data acquisition and control, and manages Big Data exploitation with high-dimensional model coordination.

Stochastic Pdes And Modelling Of Multiscale Complex System

2019-05-07
Stochastic Pdes And Modelling Of Multiscale Complex System

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  • Author: Wang Wei
  • Publisher: World Scientific
  • ISBN: 981120036X
  • Category : Mathematics
  • Languages : en
  • Pages : 240

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.

Handbook of Dynamic Data Driven Applications Systems

2022-05-11
Handbook of Dynamic Data Driven Applications Systems

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  • Author: Erik P. Blasch
  • Publisher: Springer Nature
  • ISBN: 3030745686
  • Category : Computers
  • Languages : en
  • Pages : 753

The Handbook of Dynamic Data Driven Applications Systems establishes an authoritative reference of DDDAS, pioneered by Dr. Darema and the co-authors for researchers and practitioners developing DDDAS technologies. Beginning with general concepts and history of the paradigm, the text provides 32 chapters by leading experts in ten application areas to enable an accurate understanding, analysis, and control of complex systems; be they natural, engineered, or societal: The authors explain how DDDAS unifies the computational and instrumentation aspects of an application system, extends the notion of Smart Computing to span from the high-end to the real-time data acquisition and control, and manages Big Data exploitation with high-dimensional model coordination. The Dynamically Data Driven Applications Systems (DDDAS) paradigm inspired research regarding the prediction of severe storms. Specifically, the DDDAS concept allows atmospheric observing systems, computer forecast models, and cyberinfrastructure to dynamically configure themselves in optimal ways in direct response to current or anticipated weather conditions. In so doing, all resources are used in an optimal manner to maximize the quality and timeliness of information they provide. Kelvin Droegemeier, Regents’ Professor of Meteorology at the University of Oklahoma; former Director of the White House Office of Science and Technology Policy We may well be entering the golden age of data science, as society in general has come to appreciate the possibilities for organizational strategies that harness massive streams of data. The challenges and opportunities are even greater when the data or the underlying system are dynamic - and DDDAS is the time-tested paradigm for realizing this potential. Sangtae Kim, Distinguished Professor of Mechanical Engineering and Distinguished Professor of Chemical Engineering at Purdue University

Stochastic Methods in Neuroscience

2010
Stochastic Methods in Neuroscience

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  • Author: Carlo Laing
  • Publisher: Oxford University Press
  • ISBN: 0199235074
  • Category : Mathematics
  • Languages : en
  • Pages : 399

Computational or mathematical neuroscience is a research area currently of great interest, due to, amongst other factors, rapid increases in computing power, increases in the ability to record large amounts of neurophysiological data, and a realisation amongst both neuroscientists and mathematicians that each can benefit from collaborating with the other. Suitable for graduates and researchers in computational neuroscience, stochastic systems, and neuroscientists seeking to learn more about recent advances in the modelling and analysis of noisy neural systems, this text presents an overview of neuroscience and the role of noise via a series of self-contained chapters on major aspects, written by experts in their particular field. These range over Markov chain models for ion channel release, stochastically forced single neurons and population of neurons, statistical methods for parameter estimation, and the numerical approximation these models. Each chapter will give an overview of a particular topic, including its history, important results in the area, and future challenges.

Coupled Mathematical Models for Physical and Biological Nanoscale Systems and Their Applications

2018-06-20
Coupled Mathematical Models for Physical and Biological Nanoscale Systems and Their Applications

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  • Author: Luis L. Bonilla
  • Publisher: Springer
  • ISBN: 331976599X
  • Category : Mathematics
  • Languages : en
  • Pages : 314

This volume gathers selected contributions from the participants of the Banff International Research Station (BIRS) workshop Coupled Mathematical Models for Physical and Biological Nanoscale Systems and their Applications, who explore various aspects of the analysis, modeling and applications of nanoscale systems, with a particular focus on low dimensional nanostructures and coupled mathematical models for their description. Due to the vastness, novelty and complexity of the interfaces between mathematical modeling and nanoscience and nanotechnology, many important areas in these disciplines remain largely unexplored. In their efforts to move forward, multidisciplinary research communities have come to a clear understanding that, along with experimental techniques, mathematical modeling and analysis have become crucial to the study, development and application of systems at the nanoscale. The conference, held at BIRS in autumn 2016, brought together experts from three different communities working in fields where coupled mathematical models for nanoscale and biosystems are especially relevant: mathematicians, physicists (both theorists and experimentalists), and computational scientists, including those dealing with biological nanostructures. Its objectives: summarize the state-of-the-art; identify and prioritize critical problems of major importance that require solutions; analyze existing methodologies; and explore promising approaches to addressing the challenges identified. The contributions offer up-to-date introductions to a range of topics in nano and biosystems, identify important challenges, assess current methodologies and explore promising approaches. As such, this book will benefit researchers in applied mathematics, as well as physicists and biologists interested in coupled mathematical models and their analysis for physical and biological nanoscale systems that concern applications in biotechnology and medicine, quantum information processing and optoelectronics.

Effective Dynamics of Stochastic Partial Differential Equations

2014-03-06
Effective Dynamics of Stochastic Partial Differential Equations

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  • Author: Jinqiao Duan
  • Publisher: Elsevier
  • ISBN: 0128012692
  • Category : Mathematics
  • Languages : en
  • Pages : 282

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

Data Assimilation

2015-09-05
Data Assimilation

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  • Author: Kody Law
  • Publisher: Springer
  • ISBN: 3319203258
  • Category : Mathematics
  • Languages : en
  • Pages : 242

This book provides a systematic treatment of the mathematical underpinnings of work in data assimilation, covering both theoretical and computational approaches. Specifically the authors develop a unified mathematical framework in which a Bayesian formulation of the problem provides the bedrock for the derivation, development and analysis of algorithms; the many examples used in the text, together with the algorithms which are introduced and discussed, are all illustrated by the MATLAB software detailed in the book and made freely available online. The book is organized into nine chapters: the first contains a brief introduction to the mathematical tools around which the material is organized; the next four are concerned with discrete time dynamical systems and discrete time data; the last four are concerned with continuous time dynamical systems and continuous time data and are organized analogously to the corresponding discrete time chapters. This book is aimed at mathematical researchers interested in a systematic development of this interdisciplinary field, and at researchers from the geosciences, and a variety of other scientific fields, who use tools from data assimilation to combine data with time-dependent models. The numerous examples and illustrations make understanding of the theoretical underpinnings of data assimilation accessible. Furthermore, the examples, exercises and MATLAB software, make the book suitable for students in applied mathematics, either through a lecture course, or through self-study.

Geometry and Invariance in Stochastic Dynamics

2022-02-09
Geometry and Invariance in Stochastic Dynamics

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  • Author: Stefania Ugolini
  • Publisher: Springer Nature
  • ISBN: 303087432X
  • Category : Mathematics
  • Languages : en
  • Pages : 273

This book grew out of the Random Transformations and Invariance in Stochastic Dynamics conference held in Verona from the 25th to the 28th of March 2019 in honour of Sergio Albeverio. It presents the new area of studies concerning invariance and symmetry properties of finite and infinite dimensional stochastic differential equations.This area constitutes a natural, much needed, extension of the theory of classical ordinary and partial differential equations, where the reduction theory based on symmetry and invariance of such classical equations has historically proved to be very important both for theoretical and numerical studies and has given rise to important applications. The purpose of the present book is to present the state of the art of the studies on stochastic systems from this point of view, present some of the underlying fundamental ideas and methods involved, and to outline the main lines for future developments. The main focus is on bridging the gap between deterministic and stochastic approaches, with the goal of contributing to the elaboration of a unified theory that will have a great impact both from the theoretical point of view and the point of view of applications. The reader is a mathematician or a theoretical physicist. The main discipline is stochastic analysis with profound ideas coming from Mathematical Physics and Lie’s Group Geometry. While the audience consists essentially of academicians, the reader can also be a practitioner with Ph.D., who is interested in efficient stochastic modelling.