Simple Brownian Diffusion PDF Download

Author: Daniel Thomas Gillespie
Publisher: Oxford University Press, USA
ISBN: 0199664501
Category : Science
Languages : en
Pages : 288

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Book Description
Brownian diffusion, the motion of large molecules in a sea of very many much smaller molecules, is topical because it is one of the ways in which biologically important molecules move about inside living cells. This book presents the mathematical physics that underlies the four simplest models of Brownian diffusion.

Author: Daniel Thomas Gillespie
Publisher: OUP Oxford
ISBN: 0191641537
Category : Science
Languages : en
Pages : 336

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Book Description
Brownian diffusion is the motion of one or more solute molecules in a sea of very many, much smaller solvent molecules. Its importance today owes mainly to cellular chemistry, since Brownian diffusion is one of the ways in which key reactant molecules move about inside a living cell. This book focuses on the four simplest models of Brownian diffusion: the classical Fickian model, the Einstein model, the discrete-stochastic (cell-jumping) model, and the Langevin model. The authors carefully develop the theories underlying these models, assess their relative advantages, and clarify their conditions of applicability. Special attention is given to the stochastic simulation of diffusion, and to showing how simulation can complement theory and experiment. Two self-contained tutorial chapters, one on the mathematics of random variables and the other on the mathematics of continuous Markov processes (stochastic differential equations), make the book accessible to researchers from a broad spectrum of technical backgrounds.

Author: Peter Mörters
Publisher: Cambridge University Press
ISBN: 1139486578
Category : Mathematics
Languages : en
Pages :

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Book Description
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.

Author: Kiyosi Itô
Publisher: Springer Science & Business Media
ISBN: 3642620256
Category : Mathematics
Languages : en
Pages : 341

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Book Description
Since its first publication in 1965 in the series Grundlehren der mathematischen Wissenschaften this book has had a profound and enduring influence on research into the stochastic processes associated with diffusion phenomena. Generations of mathematicians have appreciated the clarity of the descriptions given of one- or more- dimensional diffusion processes and the mathematical insight provided into Brownian motion. Now, with its republication in the Classics in Mathematics it is hoped that a new generation will be able to enjoy the classic text of Itô and McKean.

Author: Jean-Louis Barrat
Publisher: Cambridge University Press
ISBN: 9780521789530
Category : Science
Languages : en
Pages : 410

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Book Description
Presenting a unified approach, this book focusses on the concepts and theoretical methods that are necessary for an understanding of the physics and chemistry of the fluid state. The authors do not attempt to cover the whole field in an encyclopedic manner. Instead, important ideas are presented in a concise and rigorous style, and illustrated with examples from both simple molecular liquids and more complex soft condensed matter systems such as polymers, colloids, and liquid crystals.

Author: Albert Einstein
Publisher: Courier Corporation
ISBN: 9780486603049
Category : Science
Languages : en
Pages : 148

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Book Description
Five early papers evolve theory that won Einstein a Nobel Prize: "Movement of Small Particles Suspended in a Stationary Liquid Demanded by the Molecular-Kinetic Theory of Heat"; "On the Theory of the Brownian Movement"; "A New Determination of Molecular Dimensions"; "Theoretical Observations on the Brownian Motion"; and "Elementary Theory of the Brownian Motion."

Author: Ron Milo
Publisher: Garland Science
ISBN: 1317230698
Category : Science
Languages : en
Pages : 399

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Book Description
A Top 25 CHOICE 2016 Title, and recipient of the CHOICE Outstanding Academic Title (OAT) Award. How much energy is released in ATP hydrolysis? How many mRNAs are in a cell? How genetically similar are two random people? What is faster, transcription or translation?Cell Biology by the Numbers explores these questions and dozens of others provid

Author: Federico Toschi
Publisher: Springer Nature
ISBN: 3030233707
Category : Science
Languages : en
Pages : 313

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Book Description
This open access book, published in the Soft and Biological Matter series, presents an introduction to selected research topics in the broad field of flowing matter, including the dynamics of fluids with a complex internal structure -from nematic fluids to soft glasses- as well as active matter and turbulent phenomena. Flowing matter is a subject at the crossroads between physics, mathematics, chemistry, engineering, biology and earth sciences, and relies on a multidisciplinary approach to describe the emergence of the macroscopic behaviours in a system from the coordinated dynamics of its microscopic constituents. Depending on the microscopic interactions, an assembly of molecules or of mesoscopic particles can flow like a simple Newtonian fluid, deform elastically like a solid or behave in a complex manner. When the internal constituents are active, as for biological entities, one generally observes complex large-scale collective motions. Phenomenology is further complicated by the invariable tendency of fluids to display chaos at the large scales or when stirred strongly enough. This volume presents several research topics that address these phenomena encompassing the traditional micro-, meso-, and macro-scales descriptions, and contributes to our understanding of the fundamentals of flowing matter. This book is the legacy of the COST Action MP1305 “Flowing Matter”.

Author: Dimitri D Vvedensky
Publisher: Morgan & Claypool Publishers
ISBN: 1643276204
Category : Science
Languages : en
Pages : 184

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Book Description
Phase transformations are among the most intriguing and technologically useful phenomena in materials, particularly with regard to controlling microstructure. After a review of thermodynamics, this book has chapters on Brownian motion and the diffusion equation, diffusion in solids based on transition-state theory, spinodal decomposition, nucleation and growth, instabilities in solidification, and diffusionless transformations. Each chapter includes exercises whose solutions are available in a separate manual. This book is based on the notes from a graduate course taught in the Centre for Doctoral Training in the Theory and Simulation of Materials. The course was attended by students with undergraduate degrees in physics, mathematics, chemistry, materials science, and engineering. The notes from this course, and this book, were written to accommodate these diverse backgrounds.

Author: Radek Erban
Publisher: Cambridge University Press
ISBN: 1108572995
Category : Mathematics
Languages : en
Pages : 322

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Book Description
This practical introduction to stochastic reaction-diffusion modelling is based on courses taught at the University of Oxford. The authors discuss the essence of mathematical methods which appear (under different names) in a number of interdisciplinary scientific fields bridging mathematics and computations with biology and chemistry. The book can be used both for self-study and as a supporting text for advanced undergraduate or beginning graduate-level courses in applied mathematics. New mathematical approaches are explained using simple examples of biological models, which range in size from simulations of small biomolecules to groups of animals. The book starts with stochastic modelling of chemical reactions, introducing stochastic simulation algorithms and mathematical methods for analysis of stochastic models. Different stochastic spatio-temporal models are then studied, including models of diffusion and stochastic reaction-diffusion modelling. The methods covered include molecular dynamics, Brownian dynamics, velocity jump processes and compartment-based (lattice-based) models.