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Stochastic Transport In Complex And Dynamic Geometries
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Book Synopsis Stochastic Transport in Complex and Dynamic Geometries by : Imtiaz Ahmad Ali
Download or read book Stochastic Transport in Complex and Dynamic Geometries written by Imtiaz Ahmad Ali and published by . This book was released on 2021 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic transport is a widely studied phenomenon among physicists. This includes diffusive processes like Brownian motion which have helped describe numerous systems ranging from the spreading of dye molecules in a liquid to the spreading of human populations. Transport behavior can be affected by properties such as the local curvature of a surface or the dynamics of a network on which the transport takes place. A quantitative characterization of these factors is critical for a deeper understanding of transport in such cases and is of much interest to the study of random walk theory, stochastic processes, and anomalous diffusion in general. In this dissertation, we aim to accomplish this aim by focusing on two specific cases - (i) anomalous diffusion of a random walker on curved surfaces and (ii) transport of cargo on dynamic filament networks. Levy walks are a class of anomalous diffusion studied in Euclidean space. In many cases of interest, transport takes place on surfaces with non-zero Gaussian curvature. We take the first steps towards studying how surface curvature affects anomalous transport described by Levy walk statistics. We develop a computational model to simulate Levy walks along geodesics in Euclidean, spherical, and hyperbolic spaces. By comparing our numerical results to a Taylor expansion of the mean-squared displacement (MSD) in powers of curvature around the Euclidean case, we can establish the validity of a generalized expression for MSD of anomalous diffusion with curvature corrections. The transport of cargo within cells is a critical physiological process. Many new studies consider the impact on transport of the morphology of the networks of filaments. One aspect that has received less attention is the growth/shrinkage and dynamic turnover of these networks. We study transport of cargo carried by myosin motors on dynamic actin network. Use a stochastic simulation model accounting for both active and passive transport and incorporate the dynamics of the actin network. We show how treadmilling speed of actin filament affect cargo transport, motor attachment/detachment rates and network density. We show the existence of filament dynamics in physiological regimes that optimize cargo transport and how it can be tuned.
Book Synopsis Stochastic Transport in Complex Systems by : Andreas Schadschneider
Download or read book Stochastic Transport in Complex Systems written by Andreas Schadschneider and published by Elsevier. This book was released on 2010-10-01 with total page 585 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first part of the book provides a pedagogical introduction to the physics of complex systems driven far from equilibrium. In this part we discuss the basic concepts and theoretical techniques which are commonly used to study classical stochastic transport in systems of interacting driven particles. The analytical techniques include mean-field theories, matrix product ansatz, renormalization group, etc. and the numerical methods are mostly based on computer simulations. In the second part of the book these concepts and techniques are applied not only to vehicular traffic but also to transport and traffic-like phenomena in living systems ranging from collective movements of social insects (for example, ants) on trails to intracellular molecular motor transport. These demonstrate the conceptual unity of the fundamental principles underlying the apparent diversity of the systems and the utility of the theoretical toolbox of non-equilibrium statistical mechanics in interdisciplinary research far beyond the traditional disciplinary boundaries of physics. Leading industry experts provide a broad overview of the interdisciplinary nature of physics Presents unified descriptions of intracellular, ant, and vehicular traffic from a physics point of view Applies theoretical methods in practical everyday situations Reference and guide for physicists, engineers and graduate students
Book Synopsis Geometry and Invariance in Stochastic Dynamics by : Stefania Ugolini
Download or read book Geometry and Invariance in Stochastic Dynamics written by Stefania Ugolini and published by Springer Nature. This book was released on 2022-02-09 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Stochastic Optimal Transportation by : Toshio Mikami
Download or read book Stochastic Optimal Transportation written by Toshio Mikami and published by Springer Nature. This book was released on 2021-06-15 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, the optimal transportation problem (OT) is described as a variational problem for absolutely continuous stochastic processes with fixed initial and terminal distributions. Also described is Schrödinger’s problem, which is originally a variational problem for one-step random walks with fixed initial and terminal distributions. The stochastic optimal transportation problem (SOT) is then introduced as a generalization of the OT, i.e., as a variational problem for semimartingales with fixed initial and terminal distributions. An interpretation of the SOT is also stated as a generalization of Schrödinger’s problem. After the brief introduction above, the fundamental results on the SOT are described: duality theorem, a sufficient condition for the problem to be finite, forward–backward stochastic differential equations (SDE) for the minimizer, and so on. The recent development of the superposition principle plays a crucial role in the SOT. A systematic method is introduced to consider two problems: one with fixed initial and terminal distributions and one with fixed marginal distributions for all times. By the zero-noise limit of the SOT, the probabilistic proofs to Monge’s problem with a quadratic cost and the duality theorem for the OT are described. Also described are the Lipschitz continuity and the semiconcavity of Schrödinger’s problem in marginal distributions and random variables with given marginals, respectively. As well, there is an explanation of the regularity result for the solution to Schrödinger’s functional equation when the space of Borel probability measures is endowed with a strong or a weak topology, and it is shown that Schrödinger’s problem can be considered a class of mean field games. The construction of stochastic processes with given marginals, called the marginal problem for stochastic processes, is discussed as an application of the SOT and the OT.
Book Synopsis Geometry and Invariance in Stochastic Dynamics by : Stefania Ugolini
Download or read book Geometry and Invariance in Stochastic Dynamics written by Stefania Ugolini and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Stochastic Geometry by : David Coupier
Download or read book Stochastic Geometry written by David Coupier and published by Springer. This book was released on 2019-04-09 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume offers a unique and accessible overview of the most active fields in Stochastic Geometry, up to the frontiers of recent research. Since 2014, the yearly meeting of the French research structure GDR GeoSto has been preceded by two introductory courses. This book contains five of these introductory lectures. The first chapter is a historically motivated introduction to Stochastic Geometry which relates four classical problems (the Buffon needle problem, the Bertrand paradox, the Sylvester four-point problem and the bicycle wheel problem) to current topics. The remaining chapters give an application motivated introduction to contemporary Stochastic Geometry, each one devoted to a particular branch of the subject: understanding spatial point patterns through intensity and conditional intensities; stochastic methods for image analysis; random fields and scale invariance; and the theory of Gibbs point processes. Exposing readers to a rich theory, this book will encourage further exploration of the subject and its wide applications.
Book Synopsis Stochastic Dynamics. Modeling Solute Transport in Porous Media by : Don Kulasiri
Download or read book Stochastic Dynamics. Modeling Solute Transport in Porous Media written by Don Kulasiri and published by Elsevier. This book was released on 2002-11-22 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most of the natural and biological phenomena such as solute transport in porous media exhibit variability which can not be modeled by using deterministic approaches. There is evidence in natural phenomena to suggest that some of the observations can not be explained by using the models which give deterministic solutions. Stochastic processes have a rich repository of objects which can be used to express the randomness inherent in the system and the evolution of the system over time. The attractiveness of the stochastic differential equations (SDE) and stochastic partial differential equations (SPDE) come from the fact that we can integrate the variability of the system along with the scientific knowledge pertaining to the system. One of the aims of this book is to explaim some useufl concepts in stochastic dynamics so that the scientists and engineers with a background in undergraduate differential calculus could appreciate the applicability and appropriateness of these developments in mathematics. The ideas are explained in an intuitive manner wherever possible with out compromising rigor. The solute transport problem in porous media saturated with water had been used as a natural setting to discuss the approaches based on stochastic dynamics. The work is also motivated by the need to have more sophisticated mathematical and computational frameworks to model the variability one encounters in natural and industrial systems. This book presents the ideas, models and computational solutions pertaining to a single problem: stochastic flow of contaminant transport in the saturated porous media such as that we find in underground aquifers. In attempting to solve this problem using stochastic concepts, different ideas and new concepts have been explored, and mathematical and computational frameworks have been developed in the process. Some of these concepts, arguments and mathematical and computational constructs are discussed in an intuititve manner in this book.
Book Synopsis Stochastic Transport Processes in Discrete Biological Systems by : Eckart Frehland
Download or read book Stochastic Transport Processes in Discrete Biological Systems written by Eckart Frehland and published by Springer Science & Business Media. This book was released on 2013-03-13 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes are in part based on a course for advanced students in the applications of stochastic processes held in 1978 at the University of Konstanz. These notes contain the results of re cent studies on the stochastic description of ion transport through biological membranes. In particular, they serve as an introduction to an unified theory of fluctuations in complex biological transport systems. We emphasize that the subject of this volume is not to introduce the mathematics of stochastic processes but to present a field of theoretical biophysics in which stochastic methods are important. In the last years the study of membrane noise has become an important method in biophysics. Valuable information on the ion transport mechanisms in membranes can be obtained from noise analysis. A number of different processes such as the opening and closing of ion channels have been shown to be sources of the measured current or voltage fluctuations. Bio logical 'transport systems can be complex. For example, the transport process can be coupled to other processes such as chemical reactions and take place in discontinuous structures of molecular dimensions. Furthermore, since there are strong electric fields or high concentration gradients across biological membranes ion transport processes of biological relevance are mostly processes far from equilibrium. For these reasons the development of new theoretical concepts has been necessary. The concept of transport in discrete systems has turned out to be more appropriate than continuum models.
Book Synopsis Stochastic Processes, Physics and Geometry: New Interplays. I by : Sergio Albeverio
Download or read book Stochastic Processes, Physics and Geometry: New Interplays. I written by Sergio Albeverio and published by American Mathematical Soc.. This book was released on 2000 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume and "IStochastic Processes, Physics and Geometry: New Interplays II" present state-of-the-art research currently unfolding at the interface between mathematics and physics. Included are select articles from the international conference held in Leipzig (Germany) in honor of Sergio Albeverio's sixtieth birthday. The theme of the conference, "Infinite Dimensional (Stochastic) Analysis and Quantum Physics", was chosen to reflect Albeverio's wide-ranging scientific interests. The articles in these books reflect that broad range of interests and provide a detailed overview highlighting the deep interplay among stochastic processes, mathematical physics, and geometry. The contributions are written by internationally recognized experts in the fields of stochastic analysis, linear and nonlinear (deterministic and stochastic) PDEs, infinite dimensional analysis, functional analysis, commutative and noncommutative probability theory, integrable systems, quantum and statistical mechanics, geometric quantization, and neural networks. Also included are applications in biology and other areas. Most of the contributions are high-level research papers. However, there are also some overviews on topics of general interest. The articles selected for publication in these volumes were specifically chosen to introduce readers to advanced topics, to emphasize interdisciplinary connections, and to stress future research directions. Volume I contains contributions from invited speakers; Volume II contains additional contributed papers. Members of the Canadian Mathematical Society may order at the AMS member price.
Book Synopsis Optimal Transport by : Cédric Villani
Download or read book Optimal Transport written by Cédric Villani and published by Springer Science & Business Media. This book was released on 2008-10-26 with total page 970 pages. Available in PDF, EPUB and Kindle. Book excerpt: At the close of the 1980s, the independent contributions of Yann Brenier, Mike Cullen and John Mather launched a revolution in the venerable field of optimal transport founded by G. Monge in the 18th century, which has made breathtaking forays into various other domains of mathematics ever since. The author presents a broad overview of this area, supplying complete and self-contained proofs of all the fundamental results of the theory of optimal transport at the appropriate level of generality. Thus, the book encompasses the broad spectrum ranging from basic theory to the most recent research results. PhD students or researchers can read the entire book without any prior knowledge of the field. A comprehensive bibliography with notes that extensively discuss the existing literature underlines the book’s value as a most welcome reference text on this subject.
Book Synopsis Modeling Complex Living Systems by : N. Bellomo
Download or read book Modeling Complex Living Systems written by N. Bellomo and published by Springer Science & Business Media. This book was released on 2008 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: Develops different mathematical methods and tools to model living systems. This book presents material that can be used in such real-world applications as immunology, transportation engineering, and economics. It is of interest to those involved in modeling complex social systems and living matter in general.
Book Synopsis Symplectic 4-Manifolds and Algebraic Surfaces by : Denis Auroux
Download or read book Symplectic 4-Manifolds and Algebraic Surfaces written by Denis Auroux and published by Springer Science & Business Media. This book was released on 2008-04-17 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern approaches to the study of symplectic 4-manifolds and algebraic surfaces combine a wide range of techniques and sources of inspiration. Gauge theory, symplectic geometry, pseudoholomorphic curves, singularity theory, moduli spaces, braid groups, monodromy, in addition to classical topology and algebraic geometry, combine to make this one of the most vibrant and active areas of research in mathematics. It is our hope that the five lectures of the present volume given at the C.I.M.E. Summer School held in Cetraro, Italy, September 2-10, 2003 will be useful to people working in related areas of mathematics and will become standard references on these topics. The volume is a coherent exposition of an active field of current research focusing on the introduction of new methods for the study of moduli spaces of complex structures on algebraic surfaces, and for the investigation of symplectic topology in dimension 4 and higher.
Book Synopsis Enumerative Invariants in Algebraic Geometry and String Theory by : Marcos Marino
Download or read book Enumerative Invariants in Algebraic Geometry and String Theory written by Marcos Marino and published by Springer Science & Business Media. This book was released on 2008-08-22 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: Starting in the middle of the 80s, there has been a growing and fruitful interaction between algebraic geometry and certain areas of theoretical high-energy physics, especially the various versions of string theory. Physical heuristics have provided inspiration for new mathematical definitions (such as that of Gromov-Witten invariants) leading in turn to the solution of problems in enumerative geometry. Conversely, the availability of mathematically rigorous definitions and theorems has benefited the physics research by providing the required evidence in fields where experimental testing seems problematic. The aim of this volume, a result of the CIME Summer School held in Cetraro, Italy, in 2005, is to cover part of the most recent and interesting findings in this subject.
Book Synopsis Geometry and Topology in Hamiltonian Dynamics and Statistical Mechanics by : Marco Pettini
Download or read book Geometry and Topology in Hamiltonian Dynamics and Statistical Mechanics written by Marco Pettini and published by Springer Science & Business Media. This book was released on 2007-06-14 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers a new explanation of the origin of Hamiltonian chaos and its quantitative characterization. The author focuses on two main areas: Riemannian formulation of Hamiltonian dynamics, providing an original viewpoint about the relationship between geodesic instability and curvature properties of the mechanical manifolds; and a topological theory of thermodynamic phase transitions, relating topology changes of microscopic configuration space with the generation of singularities of thermodynamic observables. The book contains numerous illustrations throughout and it will interest both mathematicians and physicists.
Book Synopsis Crowd Dynamics, Volume 1 by : Livio Gibelli
Download or read book Crowd Dynamics, Volume 1 written by Livio Gibelli and published by Springer. This book was released on 2019-01-22 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume explores the complex problems that arise in the modeling and simulation of crowd dynamics in order to present the state-of-the-art of this emerging field and contribute to future research activities. Experts in various areas apply their unique perspectives to specific aspects of crowd dynamics, covering the topic from multiple angles. These include a demonstration of how virtual reality may solve dilemmas in collecting empirical data; a detailed study on pedestrian movement in smoke-filled environments; a presentation of one-dimensional conservation laws with point constraints on the flux; a collection of new ideas on the modeling of crowd dynamics at the microscopic scale; and others. Applied mathematicians interested in crowd dynamics, pedestrian movement, traffic flow modeling, urban planning, and other topics will find this volume a valuable resource. Additionally, researchers in social psychology, architecture, and engineering may find this information relevant to their work.
Book Synopsis SPDE in Hydrodynamics: Recent Progress and Prospects by : Sergio Albeverio
Download or read book SPDE in Hydrodynamics: Recent Progress and Prospects written by Sergio Albeverio and published by Springer Science & Business Media. This book was released on 2008-04-14 with total page 183 pages. Available in PDF, EPUB and Kindle. Book excerpt: Of the three lecture courses making up the CIME summer school on Fluid Dynamics at Cetraro in 2005 reflected in this volume, the first, due to Sergio Albeverio describes deterministic and stochastic models of hydrodynamics. In the second course, Franco Flandoli starts from 3D Navier-Stokes equations and ends with turbulence. Finally, Yakov Sinai, in the 3rd course, describes some rigorous mathematical results for multidimensional Navier-Stokes systems and some recent results on the one-dimensional Burgers equation with random forcing.
Book Synopsis Noncommutative Geometry by : Alain Connes
Download or read book Noncommutative Geometry written by Alain Connes and published by Springer. This book was released on 2003-12-15 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: Noncommutative Geometry is one of the most deep and vital research subjects of present-day Mathematics. Its development, mainly due to Alain Connes, is providing an increasing number of applications and deeper insights for instance in Foliations, K-Theory, Index Theory, Number Theory but also in Quantum Physics of elementary particles. The purpose of the Summer School in Martina Franca was to offer a fresh invitation to the subject and closely related topics; the contributions in this volume include the four main lectures, cover advanced developments and are delivered by prominent specialists.
