Analysis and Stochastics of Growth Processes and Interface Models

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Publisher : OUP Oxford
ISBN 13 : 019155359X
Total Pages : 348 pages
Book Rating : 4.1/5 (915 download)

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Book Synopsis Analysis and Stochastics of Growth Processes and Interface Models by : Peter Mörters

Download or read book Analysis and Stochastics of Growth Processes and Interface Models written by Peter Mörters and published by OUP Oxford. This book was released on 2008-07-24 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of topical survey articles by leading researchers in the fields of applied analysis and probability theory, working on the mathematical description of growth phenomena. Particular emphasis is on the interplay of the two fields, with articles by analysts being accessible for researchers in probability, and vice versa. Mathematical methods discussed in the book comprise large deviation theory, lace expansion, harmonic multi-scale techniques and homogenisation of partial differential equations. Models based on the physics of individual particles are discussed alongside models based on the continuum description of large collections of particles, and the mathematical theories are used to describe physical phenomena such as droplet formation, Bose-Einstein condensation, Anderson localization, Ostwald ripening, or the formation of the early universe. The combination of articles from the two fields of analysis and probability is highly unusual and makes this book an important resource for researchers working in all areas close to the interface of these fields.

Stochastic Processes, Multiscale Modeling, and Numerical Methods for Computational Cellular Biology

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Publisher : Springer
ISBN 13 : 3319626272
Total Pages : 377 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Stochastic Processes, Multiscale Modeling, and Numerical Methods for Computational Cellular Biology by : David Holcman

Download or read book Stochastic Processes, Multiscale Modeling, and Numerical Methods for Computational Cellular Biology written by David Holcman and published by Springer. This book was released on 2017-10-04 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on the modeling and mathematical analysis of stochastic dynamical systems along with their simulations. The collected chapters will review fundamental and current topics and approaches to dynamical systems in cellular biology. This text aims to develop improved mathematical and computational methods with which to study biological processes. At the scale of a single cell, stochasticity becomes important due to low copy numbers of biological molecules, such as mRNA and proteins that take part in biochemical reactions driving cellular processes. When trying to describe such biological processes, the traditional deterministic models are often inadequate, precisely because of these low copy numbers. This book presents stochastic models, which are necessary to account for small particle numbers and extrinsic noise sources. The complexity of these models depend upon whether the biochemical reactions are diffusion-limited or reaction-limited. In the former case, one needs to adopt the framework of stochastic reaction-diffusion models, while in the latter, one can describe the processes by adopting the framework of Markov jump processes and stochastic differential equations. Stochastic Processes, Multiscale Modeling, and Numerical Methods for Computational Cellular Biology will appeal to graduate students and researchers in the fields of applied mathematics, biophysics, and cellular biology.

New Trends in Stochastic Analysis and Related Topics

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Publisher : World Scientific
ISBN 13 : 9814360910
Total Pages : 458 pages
Book Rating : 4.8/5 (143 download)

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Book Synopsis New Trends in Stochastic Analysis and Related Topics by : Huaizhong Zhao

Download or read book New Trends in Stochastic Analysis and Related Topics written by Huaizhong Zhao and published by World Scientific. This book was released on 2012 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: The volume is dedicated to Professor David Elworthy to celebrate his fundamental contribution and exceptional influence on stochastic analysis and related fields. Stochastic analysis has been profoundly developed as a vital fundamental research area in mathematics in recent decades. It has been discovered to have intrinsic connections with many other areas of mathematics such as partial differential equations, functional analysis, topology, differential geometry, dynamical systems, etc. Mathematicians developed many mathematical tools in stochastic analysis to understand and model random phenomena in physics, biology, finance, fluid, environment science, etc. This volume contains 12 comprehensive review/new articles written by world leading researchers (by invitation) and their collaborators. It covers stochastic analysis on manifolds, rough paths, Dirichlet forms, stochastic partial differential equations, stochastic dynamical systems, infinite dimensional analysis, stochastic flows, quantum stochastic analysis and stochastic Hamilton Jacobi theory. Articles contain cutting edge research methodology, results and ideas in relevant fields. They are of interest to research mathematicians and postgraduate students in stochastic analysis, probability, partial differential equations, dynamical systems, mathematical physics, as well as to physicists, financial mathematicians, engineers, etc.

Directed Polymers in Random Environments

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Publisher : Springer
ISBN 13 : 3319504878
Total Pages : 210 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Directed Polymers in Random Environments by : Francis Comets

Download or read book Directed Polymers in Random Environments written by Francis Comets and published by Springer. This book was released on 2017-01-26 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analyzing the phase transition from diffusive to localized behavior in a model of directed polymers in a random environment, this volume places particular emphasis on the localization phenomenon. The main questionis: What does the path of a random walk look like if rewards and penalties are spatially randomly distributed?This model, which provides a simplified version of stretched elastic chains pinned by random impurities, has attracted much research activity, but it (and its relatives) still holds many secrets, especially in high dimensions. It has non-gaussian scaling limits and it belongs to the so-called KPZ universality class when the space is one-dimensional. Adopting a Gibbsian approach, using general and powerful tools from probability theory, the discrete model is studied in full generality. Presenting the state-of-the art from different perspectives, and written in the form of a first course on the subject, this monograph is aimed at researchers in probability or statistical physics, but is also accessible to masters and Ph.D. students.

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Author :
Publisher : World Scientific
ISBN 13 :
Total Pages : 1131 pages
Book Rating : 4./5 ( download)

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Book Synopsis by :

Download or read book written by and published by World Scientific. This book was released on with total page 1131 pages. Available in PDF, EPUB and Kindle. Book excerpt:

From Collective Beings to Quasi-Systems

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Publisher : Springer
ISBN 13 : 1493975811
Total Pages : 396 pages
Book Rating : 4.4/5 (939 download)

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Book Synopsis From Collective Beings to Quasi-Systems by : Gianfranco Minati

Download or read book From Collective Beings to Quasi-Systems written by Gianfranco Minati and published by Springer. This book was released on 2018-01-29 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book outlines a possible future theoretical perspective for systemics, its conceptual morphology and landscape while the Good-Old-Fashioned-Systemics (GOFS) era is still under way. The change from GOFS to future systemics can be represented, as shown in the book title, by the conceptual change from Collective Beings to Quasi-systems. With the current advancements, problems and approaches occurring in contemporary science, systemics are moving beyond the traditional frameworks used in the past. From Collective Beings to Coherent Quasi-Systems outlines a conceptual morphology and landscape for a new theoretical perspective for systemics introducing the concept of Quasi-systems. Advances in domains such as theoretical physics, philosophy of science, cell biology, neuroscience, experimental economics, network science and many others offer new concepts and technical tools to support the creation of a fully transdisciplinary General Theory of Change. This circumstance requires a deep reformulation of systemics, without forgetting the achievements of established conventions. The book is divided into two parts. Part I, examines classic systemic issues from new theoretical perspectives and approaches. A new general unified framework is introduced to help deal with topics such as dynamic structural coherence and Quasi-systems. This new theoretical framework is compared and contrasted with the traditional approaches. Part II focuses on the process of translation into social culture of the theoretical principles, models and approaches introduced in Part I. This translation is urgent in post-industrial societies where emergent processes and problems are still dealt with by using the classical or non-systemic knowledge of the industrial phase.

Erdös Centennial

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Publisher : Springer Science & Business Media
ISBN 13 : 3642392865
Total Pages : 714 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis Erdös Centennial by : László Lovász

Download or read book Erdös Centennial written by László Lovász and published by Springer Science & Business Media. This book was released on 2014-01-24 with total page 714 pages. Available in PDF, EPUB and Kindle. Book excerpt: Paul Erdös was one of the most influential mathematicians of the twentieth century, whose work in number theory, combinatorics, set theory, analysis, and other branches of mathematics has determined the development of large areas of these fields. In 1999, a conference was organized to survey his work, his contributions to mathematics, and the far-reaching impact of his work on many branches of mathematics. On the 100th anniversary of his birth, this volume undertakes the almost impossible task to describe the ways in which problems raised by him and topics initiated by him (indeed, whole branches of mathematics) continue to flourish. Written by outstanding researchers in these areas, these papers include extensive surveys of classical results as well as of new developments.

Random Operators

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Publisher : American Mathematical Soc.
ISBN 13 : 1470419130
Total Pages : 343 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Random Operators by : Michael Aizenman

Download or read book Random Operators written by Michael Aizenman and published by American Mathematical Soc.. This book was released on 2015-12-11 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the mathematical theory of disorder effects on quantum spectra and dynamics. Topics covered range from the basic theory of spectra and dynamics of self-adjoint operators through Anderson localization--presented here via the fractional moment method, up to recent results on resonant delocalization. The subject's multifaceted presentation is organized into seventeen chapters, each focused on either a specific mathematical topic or on a demonstration of the theory's relevance to physics, e.g., its implications for the quantum Hall effect. The mathematical chapters include general relations of quantum spectra and dynamics, ergodicity and its implications, methods for establishing spectral and dynamical localization regimes, applications and properties of the Green function, its relation to the eigenfunction correlator, fractional moments of Herglotz-Pick functions, the phase diagram for tree graph operators, resonant delocalization, the spectral statistics conjecture, and related results. The text incorporates notes from courses that were presented at the authors' respective institutions and attended by graduate students and postdoctoral researchers.

Spectral Approach to Transport Problems in Two-Dimensional Disordered Lattices

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Publisher : Springer
ISBN 13 : 3030022129
Total Pages : 114 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis Spectral Approach to Transport Problems in Two-Dimensional Disordered Lattices by : Evdokiya Georgieva Kostadinova

Download or read book Spectral Approach to Transport Problems in Two-Dimensional Disordered Lattices written by Evdokiya Georgieva Kostadinova and published by Springer. This book was released on 2018-12-11 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the spectral approach to transport problems in infinite disordered systems characterized by Anderson-type Hamiltonians. The spectral approach determines (with probability one) the existence of extended states for nonzero disorder in infinite lattices of any dimension and geometry. Here, the author focuses on the critical 2D case, where previous numerical and experimental results have shown disagreement with theory. Not being based on scaling theory, the proposed method avoids issues related to boundary conditions and provides an alternative approach to transport problems where interaction with various types of disorder is considered. Beginning with a general overview of Anderson-type transport problems and their relevance to physical systems, it goes on to discuss in more detail the most relevant theoretical, numerical, and experimental developments in this field of research. The mathematical formulation of the innovative spectral approach is introduced together with a physical interpretation and discussion of its applicability to physical systems, followed by a numerical study of delocalization in the 2D disordered honeycomb, triangular, and square lattices. Transport in the 2D honeycomb lattice with substitutional disorder is investigated employing a spectral analysis of the quantum percolation problem. Next, the applicability of the method is extended to the classical regime, with an examination of diffusion of lattice waves in 2D disordered complex plasma crystals, along with discussion of proposed future developments in the study of complex transport problems using spectral theory.

Random Polymers

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Publisher : Springer
ISBN 13 : 3642003338
Total Pages : 271 pages
Book Rating : 4.6/5 (42 download)

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Book Synopsis Random Polymers by : Frank den Hollander

Download or read book Random Polymers written by Frank den Hollander and published by Springer. This book was released on 2009-04-09 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: Polymer chains that interact with themselves and/or with their environment are fascinating objects, displaying a range of interesting physical and chemical phenomena. The focus in this monograph is on the mathematical description of some of these phenomena, with particular emphasis on phase transitions as a function of interaction parameters, associated critical behavior and space-time scaling. Topics include: self-repellent polymers, self-attracting polymers, polymers interacting with interfaces, charged polymers, copolymers near linear or random selective interfaces, polymers interacting with random substrate and directed polymers in random environment. Different techniques are exposed, including the method of local times, large deviations, the lace expansion, generating functions, the method of excursions, ergodic theory, partial annealing estimates, coarse-graining techniques and martingales. Thus, this monograph offers a mathematical panorama of polymer chains, which even today holds plenty of challenges.

Random Walks, Random Fields, and Disordered Systems

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Publisher : Springer
ISBN 13 : 3319193392
Total Pages : 254 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Random Walks, Random Fields, and Disordered Systems by : Anton Bovier

Download or read book Random Walks, Random Fields, and Disordered Systems written by Anton Bovier and published by Springer. This book was released on 2015-09-21 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focusing on the mathematics that lies at the intersection of probability theory, statistical physics, combinatorics and computer science, this volume collects together lecture notes on recent developments in the area. The common ground of these subjects is perhaps best described by the three terms in the title: Random Walks, Random Fields and Disordered Systems. The specific topics covered include a study of Branching Brownian Motion from the perspective of disordered (spin-glass) systems, a detailed analysis of weakly self-avoiding random walks in four spatial dimensions via methods of field theory and the renormalization group, a study of phase transitions in disordered discrete structures using a rigorous version of the cavity method, a survey of recent work on interacting polymers in the ballisticity regime and, finally, a treatise on two-dimensional loop-soup models and their connection to conformally invariant systems and the Gaussian Free Field. The notes are aimed at early graduate students with a modest background in probability and mathematical physics, although they could also be enjoyed by seasoned researchers interested in learning about recent advances in the above fields.

Analysis and Stochastics of Growth Processes and Interface Models

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Author :
Publisher : Oxford University Press, USA
ISBN 13 : 0199239258
Total Pages : 347 pages
Book Rating : 4.1/5 (992 download)

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Book Synopsis Analysis and Stochastics of Growth Processes and Interface Models by : Peter Mörters

Download or read book Analysis and Stochastics of Growth Processes and Interface Models written by Peter Mörters and published by Oxford University Press, USA. This book was released on 2008-07-24 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a collection of topical survey articles by researchers in the fields of applied analysis and probability theory, working on the mathematical description of growth phenomena. Particular emphasis is given to the interplay of the usually separate fields of applied analysis and probability theory.

Statistical Mechanics of Classical and Disordered Systems

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Publisher : Springer Nature
ISBN 13 : 3030290778
Total Pages : 281 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis Statistical Mechanics of Classical and Disordered Systems by : Véronique Gayrard

Download or read book Statistical Mechanics of Classical and Disordered Systems written by Véronique Gayrard and published by Springer Nature. This book was released on 2019-09-15 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: These proceedings of the conference Advances in Statistical Mechanics, held in Marseille, France, August 2018, focus on fundamental issues of equilibrium and non-equilibrium dynamics for classical mechanical systems, as well as on open problems in statistical mechanics related to probability, mathematical physics, computer science, and biology. Statistical mechanics, as envisioned more than a century ago by Boltzmann, Maxwell and Gibbs, has recently undergone stunning twists and developments which have turned this old discipline into one of the most active areas of truly interdisciplinary and cutting-edge research. The contributions to this volume, with their rather unique blend of rigorous mathematics and applications, outline the state-of-the-art of this success story in key subject areas of equilibrium and non-equilibrium classical and quantum statistical mechanics of both disordered and non-disordered systems. Aimed at researchers in the broad field of applied modern probability theory, this book, and in particular the review articles, will also be of interest to graduate students looking for a gentle introduction to active topics of current research.

Stochastic Processes, Finance And Control: A Festschrift In Honor Of Robert J Elliott

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Publisher : World Scientific
ISBN 13 : 9814483915
Total Pages : 605 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Stochastic Processes, Finance And Control: A Festschrift In Honor Of Robert J Elliott by : Samuel N Cohen

Download or read book Stochastic Processes, Finance And Control: A Festschrift In Honor Of Robert J Elliott written by Samuel N Cohen and published by World Scientific. This book was released on 2012-08-10 with total page 605 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of a series of new, peer-reviewed papers in stochastic processes, analysis, filtering and control, with particular emphasis on mathematical finance, actuarial science and engineering. Paper contributors include colleagues, collaborators and former students of Robert Elliott, many of whom are world-leading experts and have made fundamental and significant contributions to these areas.This book provides new important insights and results by eminent researchers in the considered areas, which will be of interest to researchers and practitioners. The topics considered will be diverse in applications, and will provide contemporary approaches to the problems considered. The areas considered are rapidly evolving. This volume will contribute to their development, and present the current state-of-the-art stochastic processes, analysis, filtering and control.Contributing authors include: H Albrecher, T Bielecki, F Dufour, M Jeanblanc, I Karatzas, H-H Kuo, A Melnikov, E Platen, G Yin, Q Zhang, C Chiarella, W Fleming, D Madan, R Mamon, J Yan, V Krishnamurthy.

Applied Mechanics Reviews

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Publisher :
ISBN 13 :
Total Pages : 540 pages
Book Rating : 4.3/5 (243 download)

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Book Synopsis Applied Mechanics Reviews by :

Download or read book Applied Mechanics Reviews written by and published by . This book was released on 1978 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Brownian Motion

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Publisher : Cambridge University Press
ISBN 13 : 1139486578
Total Pages : pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Brownian Motion by : Peter Mörters

Download or read book Brownian Motion written by Peter Mörters and published by Cambridge University Press. This book was released on 2010-03-25 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This eagerly awaited textbook covers everything the graduate student in probability wants to know about Brownian motion, as well as the latest research in the area. Starting with the construction of Brownian motion, the book then proceeds to sample path properties like continuity and nowhere differentiability. Notions of fractal dimension are introduced early and are used throughout the book to describe fine properties of Brownian paths. The relation of Brownian motion and random walk is explored from several viewpoints, including a development of the theory of Brownian local times from random walk embeddings. Stochastic integration is introduced as a tool and an accessible treatment of the potential theory of Brownian motion clears the path for an extensive treatment of intersections of Brownian paths. An investigation of exceptional points on the Brownian path and an appendix on SLE processes, by Oded Schramm and Wendelin Werner, lead directly to recent research themes.

Journal of the Royal Society, Interface

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Publisher :
ISBN 13 :
Total Pages : 590 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Journal of the Royal Society, Interface by :

Download or read book Journal of the Royal Society, Interface written by and published by . This book was released on 2008 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: