A Note on the Averaging Approach for the Random Linear Transport Equation PDF Download

Author: Fábio A. Dorini
Publisher:
ISBN:
Category : Averaging method (Differential equations)
Languages : en
Pages : 18

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Author: Dia Zeidan
Publisher: Springer Nature
ISBN: 9811696659
Category : Technology & Engineering
Languages : en
Pages : 323

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Book Description
This book contains select invited chapters on the latest research in numerical fluid dynamics and applications. The book aims at discussing the state-of-the-art developments and improvements in numerical fluid dynamics. All the chapters are presented for approximating and simulating how these methods and computations interact with different topics such as shock waves, non-equilibrium single and two-phase flows, elastic human-airway, and global climate. In addition to the fundamental research involving novel types of mathematical sciences, the book presents theoretical and numerical developments in fluid dynamics. The contributions by well-established global experts in fluid dynamics have brought different features of numerical fluid dynamics in a single book. The book serves as a useful resource for high-impact advances involving computational fluid dynamics, including recent developments in mathematical modelling, numerical methods such as finite volume, finite difference and finite element, symbolic computations, and open numerical programs such as OpenFOAM software. The book addresses interdisciplinary topics in industrial mathematics that lie at the forefront of research into new types of mathematical sciences, including theory and applications. This book will be beneficial to industrial and academic researchers, as well as graduate students, working in the fields of natural and engineering sciences. The book will provide the reader highly successful materials and necessary research in the field of fluid dynamics.

Author: Gerald C. Pomraning
Publisher: World Scientific
ISBN: 9789810208448
Category : Science
Languages : en
Pages : 260

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Book Description
This book deals with neutral particle flow in a stochastic mixture consisting of two or more immiscible fluids. After giving an introduction to linear kinetic theory and particle transport in a nonstochastic setting, it discusses recent formulations for particle flow through a background material whose properties are only known in a statistical sense. The mixing descriptions considered are both Markovian and renewal statistics. Various models and exact results are presented for the ensemble average of the intensity in such stochastic mixtures. In the Markovian case, the underlying kinetic description is the integro-differential transport equation, whereas for renewal statistics the natural starting point is the purely integral formulation of transport theory.

Author: Paul Nelson
Publisher: CRC Press
ISBN: 1000946541
Category : Mathematics
Languages : en
Pages : 479

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Book Description
This book includes seminal papers on technical subjects—transport theory, invariant imbedding, and integral equations—presented as contributions to honour George Milt Wing in celebration of his 65th birth anniversary in 1988.

Author: Jeffery Lewins
Publisher: Springer Science & Business Media
ISBN: 0306478110
Category : Science
Languages : en
Pages : 328

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Book Description
Some countries have moved beyond the design and operation of nuclear electricity generating systems to confronting the issue of nuclear waste disposal, whole others are still committed to further nuclear facility construction. Volume 24 chronicles these key developments and examines nuclear reactor accidents at Chernobyl, Bhopal, and TMI. The text also analyzes current international knowledge of neutron interactions; deterministic methods based on mean values for assessing radiation distributions; practical applications of the TIBERE models to explicit computation of leakage terms in realistic reactor geometry; and a technique to deal with the issues of finance, risk assessment, and public perception.

Author: Gregory F. Lawler
Publisher: American Mathematical Soc.
ISBN: 0821848291
Category : Mathematics
Languages : en
Pages : 170

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Book Description
The heat equation can be derived by averaging over a very large number of particles. Traditionally, the resulting PDE is studied as a deterministic equation, an approach that has brought many significant results and a deep understanding of the equation and its solutions. By studying the heat equation and considering the individual random particles, however, one gains further intuition into the problem. While this is now standard for many researchers, this approach is generally not presented at the undergraduate level. In this book, Lawler introduces the heat equations and the closely related notion of harmonic functions from a probabilistic perspective. The theme of the first two chapters of the book is the relationship between random walks and the heat equation. This first chapter discusses the discrete case, random walk and the heat equation on the integer lattice; and the second chapter discusses the continuous case, Brownian motion and the usual heat equation. Relationships are shown between the two. For example, solving the heat equation in the discrete setting becomes a problem of diagonalization of symmetric matrices, which becomes a problem in Fourier series in the continuous case. Random walk and Brownian motion are introduced and developed from first principles. The latter two chapters discuss different topics: martingales and fractal dimension, with the chapters tied together by one example, a random Cantor set. The idea of this book is to merge probabilistic and deterministic approaches to heat flow. It is also intended as a bridge from undergraduate analysis to graduate and research perspectives. The book is suitable for advanced undergraduates, particularly those considering graduate work in mathematics or related areas.

Author: Hans Petter Langtangen
Publisher: Springer Science & Business Media
ISBN: 3642182372
Category : Mathematics
Languages : en
Pages : 676

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Book Description
A gentle introduction to advanced topics such as parallel computing, multigrid methods, and special methods for systems of PDEs. The goal of all chapters is to ‘compute’ solutions to problems, hence algorithmic and software issues play a central role. All software examples use the Diffpack programming environment - some experience with Diffpack is required. There are also some chapters covering complete applications, i.e., the way from a model, expressed as systems of PDEs, through to discretization methods, algorithms, software design, verification, and computational examples. Suitable for readers with a background in basic finite element and finite difference methods for partial differential equations.

Author: H. Germano Pavão
Publisher:
ISBN:
Category : Fourier analysis
Languages : en
Pages : 14

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Author: Stanislaw Ryszard Massel
Publisher: World Scientific
ISBN: 9814502286
Category : Technology & Engineering
Languages : en
Pages : 509

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Book Description
New Edition: Ocean Surface Waves: Their Physics and Prediction (3rd Edition)This book is intended as a handbook for professionals and researchers in the areas of Physical Oceanography, Ocean and Coastal Engineering and as a text for graduate students in these fields.It presents a comprehensive study on surface ocean waves induced by wind, including basic mathematical principles, physical description of the observed phenomena, practical forecasting techniques of various wave parameters and applications in ocean and coastal engineering, all from the probabilistic and spectral points of view.The book commences with a description of mechanisms of surface wave generation by wind and its modern modeling techniques. The stochastic and probabilistic terminology is introduced and the basic statistical and spectral properties of ocean waves are developed and discussed in detail.The bulk of material deals with the prediction techniques for waves in deep and coastal waters for simple and complex ocean basins and complex bathymetry. The various prediction methods, currently used in oceanography and ocean engineering, are described and the examples of practical calculations illustrate the basic text.An appendix provides a description of the modern methods of wave measurement, including the remote sensing techniques. Also the wave simulation methods and random data analysis techniques are discussed. In the book a lot of discoveries of the Russian and East European scientists, largely unknown in the Western literature due to the language barrier, are referred to.

Author: Rao S. Govindaraju
Publisher: Springer Science & Business Media
ISBN: 1402057520
Category : Science
Languages : en
Pages : 298

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Book Description
This book deals with the concept of moments, and how they find application in subsurface hydrologic problems-particularly those dealing with solute transport. Both temporal and spatial moments are dealt with in some detail for a wide variety of problems. Several examples using experimental data, both from laboratory columns and field experiments, are provided to give the readers a clear idea about the scope of this method.