Advection and Diffusion in Random Media PDF Download

Author: Leonid Piterbarg
Publisher: Springer Science & Business Media
ISBN: 1475744587
Category : Mathematics
Languages : en
Pages : 334

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Book Description
This book originated from our interest in sea surface temperature variability. Our initial, though entirely pragmatic, goal was to derive adequate mathemat ical tools for handling certain oceanographic problems. Eventually, however, these considerations went far beyond oceanographic applications partly because one of the authors is a mathematician. We found that many theoretical issues of turbulent transport problems had been repeatedly discussed in fields of hy drodynamics, plasma and solid matter physics, and mathematics itself. There are few monographs concerned with turbulent diffusion in the ocean (Csanady 1973, Okubo 1980, Monin and Ozmidov 1988). While selecting material for this book we focused, first, on theoretical issues that could be helpful for understanding mixture processes in the ocean, and, sec ond, on our own contribution to the problem. Mathematically all of the issues addressed in this book are concentrated around a single linear equation: the stochastic advection-diffusion equation. There is no attempt to derive universal statistics for turbulent flow. Instead, the focus is on a statistical description of a passive scalar (tracer) under given velocity statistics. As for applications, this book addresses only one phenomenon: transport of sea surface temperature anomalies. Hopefully, however, our two main approaches are applicable to other subjects.

Author: Jack Xin
Publisher: Springer Science & Business Media
ISBN: 0387876839
Category : Mathematics
Languages : en
Pages : 165

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Book Description
This book aims to give a user friendly tutorial of an interdisciplinary research topic (fronts or interfaces in random media) to senior undergraduates and beginning grad uate students with basic knowledge of partial differential equations (PDE) and prob ability. The approach taken is semiformal, using elementary methods to introduce ideas and motivate results as much as possible, then outlining how to pursue rigor ous theorems, with details to be found in the references section. Since the topic concerns both differential equations and probability, and proba bility is traditionally a quite technical subject with a heavy measure theoretic com ponent, the book strives to develop a simplistic approach so that students can grasp the essentials of fronts and random media and their applications in a self contained tutorial. The book introduces three fundamental PDEs (the Burgers equation, Hamilton– Jacobi equations, and reaction–diffusion equations), analysis of their formulas and front solutions, and related stochastic processes. It builds up tools gradually, so that students are brought to the frontiers of research at a steady pace. A moderate number of exercises are provided to consolidate the concepts and ideas. The main methods are representation formulas of solutions, Laplace meth ods, homogenization, ergodic theory, central limit theorems, large deviation princi ples, variational principles, maximum principles, and Harnack inequalities, among others. These methods are normally covered in separate books on either differential equations or probability. It is my hope that this tutorial will help to illustrate how to combine these tools in solving concrete problems.

Author: Yvan Saint-Aubin
Publisher: Springer Science & Business Media
ISBN: 1475736711
Category : Science
Languages : en
Pages : 646

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Book Description
Based on courses given at the CRM Banff summer school in 1999, this volume provides a snapshot of topics engaging theoretical physicists at the end of the twentieth century and the beginning of the twenty-first. Young physicists will find in these chapters pedagogical introductions to subjects currently active in theoretical physics, and more seasoned physicists will find a chance to share the excitement of fields outside their immediate research interests.

Author: Dongxiao Zhang
Publisher: Elsevier
ISBN: 0080517773
Category : Mathematics
Languages : en
Pages : 371

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Book Description
Stochastic Methods for Flow in Porous Media: Coping with Uncertainties explores fluid flow in complex geologic environments. The parameterization of uncertainty into flow models is important for managing water resources, preserving subsurface water quality, storing energy and wastes, and improving the safety and economics of extracting subsurface mineral and energy resources. This volume systematically introduces a number of stochastic methods used by researchers in the community in a tutorial way and presents methodologies for spatially and temporally stationary as well as nonstationary flows. The author compiles a number of well-known results and useful formulae and includes exercises at the end of each chapter. - Balanced viewpoint of several stochastic methods, including Greens' function, perturbative expansion, spectral, Feynman diagram, adjoint state, Monte Carlo simulation, and renormalization group methods - Tutorial style of presentation will facilitate use by readers without a prior in-depth knowledge of Stochastic processes - Practical examples throughout the text - Exercises at the end of each chapter reinforce specific concepts and techniques - For the reader who is interested in hands-on experience, a number of computer codes are included and discussed

Author: David W. Hendricks
Publisher: CRC Press
ISBN: 1420003437
Category : Technology & Engineering
Languages : en
Pages : 1266

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Book Description
The unit process approach, common in the field of chemical engineering, was introduced about 1962 to the field of environmental engineering. An understanding of unit processes is the foundation for continued learning and for designing treatment systems. The time is ripe for a new textbook that delineates the role of unit process principles in environmental engineering. Suitable for a two-semester course, Water Treatment Unit Processes: Physical and Chemical provides the grounding in the underlying principles of each unit process that students need in order to link theory to practice. Bridging the gap between scientific principles and engineering practice, the book covers approaches that are common to all unit processes as well as principles that characterize each unit process. Integrating theory into algorithms for practice, Professor Hendricks emphasizes the fundamentals, using simple explanations and avoiding models that are too complex mathematically, allowing students to assimilate principles without getting sidelined by excess calculations. Applications of unit processes principles are illustrated by example problems in each chapter. Student problems are provided at the end of each chapter; the solutions manual can be downloaded from the CRC Press Web site. Excel spreadsheets are integrated into the text as tables designated by a "CD" prefix. Certain spreadsheets illustrate the idea of "scenarios" that emphasize the idea that design solutions depend upon assumptions and the interactions between design variables. The spreadsheets can be downloaded from the CRC web site. The book has been designed so that each unit process topic is self-contained, with sidebars and examples throughout the text. Each chapter has subheadings, so that students can scan the pages and identify important topics with little effort. Problems, references, and a glossary are found at the end of each chapter. Most chapters contain downloadable Excel spreadsheets integrated into the text and appendices with additional information. Appendices at the end of the book provide useful reference material on various topics that support the text. This design allows students at different levels to easily navigate through the book and professors to assign pertinent sections in the order they prefer. The book gives your students an understanding of the broader aspects of one of the core areas of the environmental engineering curriculum and knowledge important for the design of treatment systems.

Author: David Hendricks
Publisher: CRC Press
ISBN: 1439895090
Category : Technology & Engineering
Languages : en
Pages : 930

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Book Description
Carefully designed to balance coverage of theoretical and practical principles, Fundamentals of Water Treatment Unit Processes delineates the principles that support practice, using the unit processes approach as the organizing concept. The author covers principles common to any kind of water treatment, for example, drinking water, municipal wastew

Author: Nicolae Suciu
Publisher: Springer
ISBN: 303015081X
Category : Mathematics
Languages : en
Pages : 276

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Book Description
This book presents, in an accessible and self-consistent way, the theory of diffusion in random velocity fields, together with robust numerical simulation approaches. The focus is on transport processes in natural porous media, with applications to contaminant transport in groundwater. Starting from basic information on stochastic processes, more challenging issues are subsequently addressed, such as the correlation structure of the diffusion process in random fields, the relation between memory effects and ergodic properties, derivation and parameterizations of evolution equations for probability densities, and the relation between measurements and spatio-temporal upscaling. Written for readers with a background in applied mathematics, engineering, physics or geophysics, the book offers an essential basis for further research in the stochastic modeling of groundwater systems.

Author: Henri Berestycki
Publisher: Springer Science & Business Media
ISBN: 9781402009723
Category : Mathematics
Languages : en
Pages : 554

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Book Description
Nonlinear partial differential equations abound in modern physics. The problems arising in these fields lead to fascinating questions and, at the same time, progress in understanding the mathematical structures is of great importance to the models. Nevertheless, activity in one of the approaches is not always sufficiently in touch with developments in the other field. The book presents the joint efforts of mathematicians and physicists involved in modelling reactive flows, in particular superconductivity and superfluidity. Certain contributions are fundamental to an understanding of such cutting-edge research topics as rotating Bose-Einstein condensates, Kolmogorov-Zakharov solutions for weak turbulence equations, and the propagation of fronts in heterogeneous media.

Author: Robert Adler
Publisher: Springer Science & Business Media
ISBN: 1461224306
Category : Mathematics
Languages : en
Pages : 473

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Book Description
The study of the ocean is almost as old as the history of mankind itself. When the first seafarers set out in their primitive ships they had to understand, as best they could, tides and currents, eddies and vortices, for lack of understanding often led to loss of live. These primitive oceanographers were, of course, primarily statisticians. They collected what empirical data they could, and passed it down, ini tially by word of mouth, to their descendants. Data collection continued throughout the millenia, and although data bases became larger, more re liable, and better codified, it was not really until surprisingly recently that mankind began to try to understand the physics behind these data, and, shortly afterwards, to attempt to model it. The basic modelling tool of physical oceanography is, today, the partial differential equation. Somehow, we all 'know" that if only we could find the right set of equations, with the right initial and boundary conditions, then we could solve the mysteries of ocean dynamics once and for all.

Author: Jens Feder
Publisher: Cambridge University Press
ISBN: 1108996361
Category : Science
Languages : en
Pages : 361

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Book Description
An invaluable reference for graduate students and academic researchers, this book introduces the basic terminology, methods and theory of the physics of flow in porous media. Geometric concepts, such as percolation and fractals, are explained and simple simulations are created, providing readers with both the knowledge and the analytical tools to deal with real experiments. It covers the basic hydrodynamics of porous media and how complexity emerges from it, as well as establishing key connections between hydrodynamics and statistical physics. Covering current concepts and their uses, this book is of interest to applied physicists and computational/theoretical Earth scientists and engineers seeking a rigorous theoretical treatment of this topic. Physics of Flow in Porous Media fills a gap in the literature by providing a physics-based approach to a field that is mostly dominated by engineering approaches.