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Author: Imtiaz Ahmad Ali Publisher: ISBN: Category : Languages : en Pages : 436
Book Description
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.
Author: Imtiaz Ahmad Ali Publisher: ISBN: Category : Languages : en Pages : 436
Book Description
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.
Author: Andreas Schadschneider Publisher: Elsevier ISBN: 0080560520 Category : Science Languages : en Pages : 585
Book Description
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
Author: Stefania Ugolini Publisher: Springer Nature ISBN: 303087432X Category : Mathematics Languages : en Pages : 273
Book Description
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.
Author: Toshio Mikami Publisher: Springer Nature ISBN: 9811617546 Category : Mathematics Languages : en Pages : 129
Book Description
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.
Author: Stefania Ugolini Publisher: ISBN: 9783030874339 Category : Languages : en Pages : 0
Book Description
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.
Author: Cédric Villani Publisher: Springer Science & Business Media ISBN: 3540710507 Category : Mathematics Languages : en Pages : 970
Book Description
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.
Author: Sergio Albeverio Publisher: Springer ISBN: 3540784934 Category : Mathematics Languages : en Pages : 183
Book Description
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.
Author: Don Kulasiri Publisher: North-Holland ISBN: 9780444511027 Category : Mathematics Languages : en Pages : 239
Book Description
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.
Author: Livio Gibelli Publisher: Springer ISBN: 3030051293 Category : Mathematics Languages : en Pages : 292
Book Description
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.
Author: Marcos Marino Publisher: Springer Science & Business Media ISBN: 3540798137 Category : Mathematics Languages : en Pages : 219
Book Description
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.
Author: Imtiaz Ahmad Ali
Author: Imtiaz Ahmad Ali
Author: Andreas Schadschneider
Author: Stefania Ugolini
Author: Toshio Mikami
Author: Stefania Ugolini
Author: Cédric Villani
Author: Sergio Albeverio
Author: Don Kulasiri
Author: Livio Gibelli
Author: Marcos Marino