The aim of these notes is to include in a uniform presentation style several topics related to the theory of degenerate nonlinear diffusion equations, treated in the mathematical framework of evolutio
Diffusion Tensor Imaging (DTI) is a variation of diffusion-weighed imaging. Particularly in the neurosciences, this technique has gained tremendous momentum in the past decade, both from a technical p
This book describes the central aspects of diffusion in solids, and goes on to provide easy access to important information about diffusion in metals, alloys, semiconductors, ion-conducting materials,
Reaction-diffusion and excitable media are amongst most intriguing substrates. Despite apparent simplicity of the physical processes involved the media exhibit a wide range of amazing patterns: from t
Recent advances in MR technology permit the application of diffusion MRI outside of the brain. In this book, the authors present cases drawn from daily clinical practice to illustrate the role of dif
This book deals with the physics of cosmic ray diffusion theory, focusing on the physics of nonlinear transport of cosmic rays through turbulent interplanetary or interstellar plasma. The author discu
This book provides an overview of the practical aspects of diffusion tensor imaging (DTI), from understanding the basis of the technique through selection of the right protocols, trouble-shooting data
This book presents the leading models of social network diffusion that are used to demonstrate the spread of disease, ideas, and behavior. It introduces diffusion models from the fields of computer sc
This textbook provides an introduction to changes that occur in solids such as ceramics, mainly at high temperatures, which are diffusion controlled, as well as presenting research data. Such changes
Working in the fractional Laplace framework, this book provides models and theorems related to nonlocal diffusion phenomena. In addition to a simple probabilistic interpretation, some applications to
Schrodinger Equations and Diffusion Theory addresses the question “What is the Schrodinger equation?” in terms of diffusion processes, and shows that the Schrodinger equation and diffusion equations i
Diffusion and growth phenomena abound in the real worldsurrounding us. Someexamples: growth of the world'spopulation, growth rates of humans, public interest in newsevents, growth and decline of cent
Up-to-date research in metric diffusion along compact foliations is presented in this book. Beginning with fundamentals from the optimal transportation theory and the theory of foliations; this book m
The authors give an overview of atomic diffusion as applied to all types of stars, showing where it plays an essential role and how it can be implemented in modelling. Part I describes the tools that
A long time ago I started writing a book about Markov chains, Brownian motion, and diffusion. I soon had two hundred pages of manuscript and my publisher was enthusiastic. Some years and several draft
Surveying a wide variety of mathematical models of diffusion in the ecological context, this book is written with the primary intent of providing scientists, particularly physicists but also biologist
This book on singular perturbation problems - in particular, stationary reaction-convection-diffusion problems exhibiting layer behaviour - is devoted to the construction and analysis of numerical met
This book is devoted to parameter estimation in diffusion models involving fractional Brownian motion and related processes. For many years now, standard Brownian motion has been (and still remains) a
From the reviews: "This book is an excellent presentation of the application of martingale theory to the theory of Markov processes, especially multidimensional diffusions. [...] This monogra
Diffusion processes are a promising instrument for realistically modelling the time-continuous evolution of phenomena not only in the natural sciences but also in finance and economics. Their mathemat
The usefulness of the book to the reader is exposure to many different classes of materials and relaxation phenomena. They are tied together by the universal relaxation and diffusion properties they s
Surveying a wide variety of mathematical models of diffusion in the ecological context, this book is written with the primary intent of providing scientists, particularly physicists but also biologist
This book deals with the optimal control of solutions of fully observable Ito-type stochastic differential equations. The validity of the Bellman differential equation for payoff functions is proved a
"Molecular Sieves - Science and Technology" covers, in a comprehensive manner, the science and technology of zeolites and all related microporous and mesoporous materials. The contributions are groupe
This monograph provides an accessible introduction to the regional analysis of fractional diffusion processes. It begins with background coverage of fractional calculus, functional analysis, distribut
In this book basic and some more advanced thermodynamics and phase as well as stability diagrams relevant for diffusion studies are introduced. Following, Fick’s laws of diffusion, atomic mechanisms,
The present volume is an extensive monograph on the analytic and geometric aspects of Markov diffusion operators. It focuses on the geometric curvature properties of the underlying structure in order
This volume contains a wealth of results and methodologies applicable to a wide range of problems arising in reaction-diffusion theory. The first part is concerned with obtaining the complete structu
This monograph is the first to provide readers with numerical tools for a systematic analysis of bifurcation problems in reaction-diffusion equations. Many examples and figures illustrate analysis of
Product sales, especially for new products, are influenced by many factors. These factors are both internal and external to the selling organization, and are both controllable and uncontrollable. Due
Product sales, especially for new products, are influenced by many factors. These factors are both internal and external to the selling organization, and are both controllable and uncontrollable. Due
This book systematically presents solutions to the linear time-fractional diffusion-wave equation. It introduces the integral transform technique and discusses the properties of the Mittag-Leffler, Wr
This book contains papers presented at the 2014 MICCAI Workshop on Computational Diffusion MRI, CDMRI’14. Detailing new computational methods applied to diffusion magnetic resonance imaging data, it o
This book describes numerical methods for partial differential equations coupling advection, diffusion and reaction terms, encompassing methods for hyperbolic, parabolic and stiff and nonstiff ordinar
This book introduces selected recent findings on the analysis and control of dynamical behaviors for coupled reaction-diffusion neural networks. It presents novel research ideas and essential definiti
This work considers a small random perturbation of alpha-stable jump type nonlinear reaction-diffusion equations with Dirichlet boundary conditions over an interval. It has two stable points whose dom
This book presents the fundamental theory for non-standard diffusion problems in movement ecology. Levy processes and anomalous diffusion have shown to be both powerful and useful tools for qualitativ
Why writing a book about a specialized task of the large topic of complex systems? And who will read it? The answer is simple: The fascination for a didactically valuable point of view, the elegance o
For this edition, a number of typographical errors and minor slip-ups have been corrected. In addition, following the persistent encouragement of Olga Oleinik, I have added a new chapter, Chapter 25,
