Mathematical Tools for Changing Scale in the Analysis of Physical Systems PDF Download

Author: William G. Gray
Publisher: CRC Press
ISBN: 1000722775
Category : Mathematics
Languages : en
Pages : 260

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Book Description
Mathematical Tools for Changing Scale in the Analysis of Physical Systems presents a new systematic approach to changing the spatial scale of the differential equations describing science and engineering problems. It defines vectors, tensors, and differential operators in arbitrary orthogonal coordinate systems without resorting to conceptually difficult Riemmann-Christoffel tensor and contravariant and covariant base vectors. It reveals the usefulness of generalized functions for indicating curvilineal, surficial, or spatial regions of integration and for transforming among these integration regions. These powerful mathematical tools are harnessed to provide 128 theorems in tabular format (most not previously available in the literature) that transform time-derivative and del operators of a function at one scale to the corresponding operators acting on the function at a larger scale. Mathematical Tools for Changing Scale in the Analysis of Physical Systems also provides sample applications of the theorems to obtain continuum balance relations for arbitrary surfaces, multiphase systems, and problems of reduced dimensionality. The mathematical techniques and tabulated theorems ensure the book will be an invaluable analysis tool for practitioners and researchers studying balance equations for systems encountered in the fields of hydraulics, hydrology, porous media physics, structural analysis, chemical transport, heat transfer, and continuum mechanics.

Author: Kambiz Vafai
Publisher: CRC Press
ISBN: 1439885575
Category : Science
Languages : en
Pages : 946

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Book Description
Handbook of Porous Media, Third Edition offers a comprehensive overview of the latest theories on flow, transport, and heat-exchange processes in porous media. It also details sophisticated porous media models which can be used to improve the accuracy of modeling in a variety of practical applications. Featuring contributions from leading experts i

Author: Peter Bastian
Publisher: Walter de Gruyter
ISBN: 3110282240
Category : Mathematics
Languages : en
Pages : 222

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Book Description
Subsurface flow problems are inherently multiscale in space due to the large variability of material properties and in time due to the coupling of many different physical processes, such as advection, diffusion, reaction and phase exchange. Subsurface flow models still need considerable development. For example, nonequilibrium effects, entrapped air, anomalous dispersion and hysteresis effects can still not be adequately described. Moreover, parameters of the models are diffcult to access and often uncertain. Computational issues in subsurface flows include the treatment of strong heterogeneities and anisotropies in the models, the effcient solution of transport-reaction problems with many species, treatment of multiphase-multicomponent flows and the coupling of subsurface flow models to surface flow models given by shallow water or Stokes equations. With respect to energy and the environment, in particular the modelling and simulation of radioactive waste management and sequestration of CO2 underground have gained high interest in the community in recent years. Both applications provide unique challenges ranging from modelling of clay materials to treating very large scale models with high-performance computing. This book brings together key numerical mathematicians whose interest is in the analysis and computation of multiscale subsurface flow and practitioners from engineering and industry whose interest is in the applications of these core problems.

Author:
Publisher: Academic Press
ISBN: 0128028661
Category : Technology & Engineering
Languages : en
Pages : 460

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Book Description
Advances in Heat Transfer fills the information gap between regularly scheduled journals and university-level textbooks by providing in-depth review articles over a broader scope than in traditional journals or texts. The articles, which serve as a broad review for experts in the field are also of great interest to non-specialists who need to keep up-to-date with the results of the latest research. This serial is essential reading for all mechanical, chemical, and industrial engineers working in the field of heat transfer, or in graduate schools or industry. Compiles the expert opinions of leaders in the industry Fills the information gap between regularly scheduled journals and university-level textbooks by providing in-depth review articles over a broader scope than in traditional journals or texts Essential reading for all mechanical, chemical, and industrial engineers working in the field of heat transfer, or in graduate schools or industry

Author: Marc B. Parlange
Publisher: Oxford University Press, USA
ISBN: 0195109902
Category : Electronic books
Languages : en
Pages : 473

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Book Description
The vadose zone is the region between ground level and the upper limits of soil fully saturated with water. Hydrology in the zone is complex: nonlinear physical, chemical, and biological interactions all affect the transfer of heat, mass, and momentum between the atmosphere and the water table. This book takes an interdisciplinary approach to vadose zone hydrology, bringing together insights from soil science, hydrology, biology, chemistry, physics, and instrumentation design. The chapters present state-of-the-art research, focusing on new frontiers in theory, experiment, and management of soils. The collection addresses the full range of processes, from the pore-scale to field and landscape scales.

Author: Faruk Civan
Publisher: John Wiley & Sons
ISBN: 1118086805
Category : Technology & Engineering
Languages : en
Pages : 443

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Book Description
The book that makes transport in porous media accessible to students and researchers alike Porous Media Transport Phenomena covers the general theories behind flow and transport in porous media a solid permeated by a network of pores filled with fluid which encompasses rocks, biological tissues, ceramics, and much more. Designed for use in graduate courses in various disciplines involving fluids in porous materials, and as a reference for practitioners in the field, the text includes exercises and practical applications while avoiding the complex math found in other books, allowing the reader to focus on the central elements of the topic. Covering general porous media applications, including the effects of temperature and particle migration, and placing an emphasis on energy resource development, the book provides an overview of mass, momentum, and energy conservation equations, and their applications in engineered and natural porous media for general applications. Offering a multidisciplinary approach to transport in porous media, material is presented in a uniform format with consistent SI units. An indispensable resource on an extremely wide and varied topic drawn from numerous engineering fields, Porous Media Transport Phenomena includes a solutions manual for all exercises found in the book, additional questions for study purposes, and PowerPoint slides that follow the order of the text.

Author: Willi Freeden
Publisher: Springer Science & Business Media
ISBN: 364201545X
Category : Mathematics
Languages : en
Pages : 1371

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Book Description
During the last three decades geosciences and geo-engineering were influenced by two essential scenarios: First, the technological progress has changed completely the observational and measurement techniques. Modern high speed computers and satellite based techniques are entering more and more all geodisciplines. Second, there is a growing public concern about the future of our planet, its climate, its environment, and about an expected shortage of natural resources. Obviously, both aspects, viz. efficient strategies of protection against threats of a changing Earth and the exceptional situation of getting terrestrial, airborne as well as spaceborne data of better and better quality explain the strong need of new mathematical structures, tools, and methods. Mathematics concerned with geoscientific problems, i.e., Geomathematics, is becoming increasingly important. The ‘Handbook Geomathematics’ as a central reference work in this area comprises the following scientific fields: (I) observational and measurement key technologies (II) modelling of the system Earth (geosphere, cryosphere, hydrosphere, atmosphere, biosphere) (III) analytic, algebraic, and operator-theoretic methods (IV) statistical and stochastic methods (V) computational and numerical analysis methods (VI) historical background and future perspectives.

Author:
Publisher:
ISBN:
Category : Mechanics, Applied
Languages : en
Pages : 724

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Book Description

Author:
Publisher: Academic Press
ISBN: 9780080922928
Category : Technology & Engineering
Languages : en
Pages : 496

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Book Description
The cross-fertilization of physico-chemical and mathematical ideas has a long historical tradition. This volume of Advances in Chemical Engineering is almost completely dedicated to a conference on “Mathematics in Chemical Kinetics and Engineering (MaCKiE-2007), which was held in Houston in February 2007, bringing together about 40 mathematicians, chemists, and chemical engineers from 10 countries to discuss the application and development of mathematical tools in their respective fields. * Updates and informs the reader on the latest research findings using original reviews * Written by leading industry experts and scholars * Reviews and analyzes developments in the field

Author: Hans Petter Langtangen
Publisher: Springer
ISBN: 3319327267
Category : Mathematics
Languages : en
Pages : 149

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Book Description
The book serves both as a reference for various scaled models with corresponding dimensionless numbers, and as a resource for learning the art of scaling. A special feature of the book is the emphasis on how to create software for scaled models, based on existing software for unscaled models. Scaling (or non-dimensionalization) is a mathematical technique that greatly simplifies the setting of input parameters in numerical simulations. Moreover, scaling enhances the understanding of how different physical processes interact in a differential equation model. Compared to the existing literature, where the topic of scaling is frequently encountered, but very often in only a brief and shallow setting, the present book gives much more thorough explanations of how to reason about finding the right scales. This process is highly problem dependent, and therefore the book features a lot of worked examples, from very simple ODEs to systems of PDEs, especially from fluid mechanics. The text is easily accessible and example-driven. The first part on ODEs fits even a lower undergraduate level, while the most advanced multiphysics fluid mechanics examples target the graduate level. The scientific literature is full of scaled models, but in most of the cases, the scales are just stated without thorough mathematical reasoning. This book explains how the scales are found mathematically. This book will be a valuable read for anyone doing numerical simulations based on ordinary or partial differential equations.