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Models of Particles and Moving Media deals with the use of mathematical models to study electrical interactions with moving particles and moving media. Topics covered range from space-time and the Galilean transformation to the Lorentz transformation of time and space and of Maxwell's equations. Forces and wave interaction with uniformly moving circuits and continua are also considered, along with non-uniform motion of charged particles in prescribed electric and magnetic fields. Comprised of seven chapters, this book begins with an overview of some of the ways in which motion can be described, with particular reference to the concept of space-time and the Galilean transformation. The discussion then turns to the Lorentz transformation of time and space, giving emphasis on the transformation of coordinates, time dilation and the Lorentz contraction, and conservation of mass and energy. After an analysis of the Lorentz transformation of Maxwell's equations, forces and wave interaction with uniformly moving circuits and continua are reviewed, along with non-uniform motion of charged particles in prescribed electric and magnetic fields. The book concludes by describing the use of the Lagrangian model and the Eulerian model to determine the motion of many interacting particles and the motion of charged and conducting fluids, respectively. This monograph is written primarily for students and researchers in the fields of mathematics and physics.
Models of Particles and Moving Media ...
Using examples from finance and modern warfare to the flocking of birds and the swarming of bacteria, the collected research in this volume demonstrates the common methodological approaches and tools for modeling and simulating collective behavior. The topics presented point toward new and challenging frontiers of applied mathematics, making the volume a useful reference text for applied mathematicians, physicists, biologists, and economists involved in the modeling of socio-economic systems.
The main purpose of this book is to provide the theoretical background to engineers and scientists engaged in modeling transport phenomena in porous media, in connection with various engineering projects, and to serve as a text for senior and graduate courses on transport phenomena in porous media. Such courses are taught in various disciplines, e. g. , civil engineering, chemical engineering, reservoir engineering, agricultural engineering and soil science. In these disciplines, problems are encountered in which various extensive quantities, e. g. , mass and heat, are transported through a porous material domain. Often the porous material contains several fluid phases, and the various extensive quantities are transported simultaneously throughout the multiphase system. In all these disciplines, management decisions related to a system's development and its operation have to be made. To do so, the 'manager', or the planner, needs a tool that will enable him to forecast the response of the system to the implementation of proposed management schemes. This forecast takes the form of spatial and temporal distributions of variables that describe the future state of the considered system. Pressure, stress, strain, density, velocity, solute concentration, temperature, etc. , for each phase in the system, and sometime for a component of a phase, may serve as examples of state variables. The tool that enables the required predictions is the model. A model may be defined as a simplified version of the real (porous medium) system that approximately simulates the excitation-response relations of the latter.
Most of the natural and biological phenomena such as solute transport in porous media exhibit variability which can not be modeled by using deterministic approaches. There is evidence in natural phenomena to suggest that some of the observations can not be explained by using the models which give deterministic solutions. Stochastic processes have a rich repository of objects which can be used to express the randomness inherent in the system and the evolution of the system over time. The attractiveness of the stochastic differential equations (SDE) and stochastic partial differential equations (SPDE) come from the fact that we can integrate the variability of the system along with the scientific knowledge pertaining to the system. One of the aims of this book is to explaim some useufl concepts in stochastic dynamics so that the scientists and engineers with a background in undergraduate differential calculus could appreciate the applicability and appropriateness of these developments in mathematics. The ideas are explained in an intuitive manner wherever possible with out compromising rigor.The solute transport problem in porous media saturated with water had been used as a natural setting to discuss the approaches based on stochastic dynamics. The work is also motivated by the need to have more sophisticated mathematical and computational frameworks to model the variability one encounters in natural and industrial systems. This book presents the ideas, models and computational solutions pertaining to a single problem: stochastic flow of contaminant transport in the saturated porous media such as that we find in underground aquifers. In attempting to solve this problem using stochastic concepts, different ideas and new concepts have been explored, and mathematical and computational frameworks have been developed in the process. Some of these concepts, arguments and mathematical and computational constructs are discussed in an intuititve manner in this book.
Models for the mechanical behavior of porous media introduced more than 50 years ago are still relied upon today, but more recent work shows that, in some cases, they may violate the laws of thermodynamics. In The Thermophysics of Porous Media, the author shows that physical consistency requires a unique description of dynamic processes that involv
This open access book promotes the idea that all media types are multimodal and that comparing media types, through an intermedial lens, necessarily involves analysing these multimodal traits. The collection includes a series of interconnected articles that illustrate and clarify how the concepts developed in Elleström’s influential article The Modalities of Media: A Model for Understanding Intermedial Relations (Palgrave Macmillan, 2010) can be used for methodical investigation and interpretation of media traits and media interrelations. The authors work with a wide range of old and new media types that are traditionally investigated through limited, media-specific concepts. The publication is a significant contribution to interdisciplinary research, advancing the frontiers of conceptual as well as practical understanding of media interrelations. This is the second of two volumes. It contains a concluding article by Elleström and seven contributions concentrated on the issue of media transformations: how media characteristics are transferred and transfigured among various media products and media types.
In this standard reference of the field, theoretical and experimental approaches to flow, hydrodynamic dispersion, and miscible displacements in porous media and fractured rock are considered. Two different approaches are discussed and contrasted with each other. The first approach is based on the classical equations of flow and transport, called 'continuum models'. The second approach is based on modern methods of statistical physics of disordered media; that is, on 'discrete models', which have become increasingly popular over the past 15 years. The book is unique in its scope, since (1) there is currently no book that compares the two approaches, and covers all important aspects of porous media problems; and (2) includes discussion of fractured rocks, which so far has been treated as a separate subject. Portions of the book would be suitable for an advanced undergraduate course. The book will be ideal for graduate courses on the subject, and can be used by chemical, petroleum, civil, environmental engineers, and geologists, as well as physicists, applied physicist and allied scientists that deal with various porous media problems.
The MBR market continues to experience a massive growth. The best practice in the field is constantly changing and unique quality requirements and management issues are regularly emerging. The second edition of Membrane Biological Reactors: Theory, Modeling, Design, Management and Applications to Wastewater Reuse comprehensively covers the salient features and emerging issues associated with the MBR technology. The book provides thorough coverage starting from biological aspects and fundamentals of membranes, via modeling and design concepts, to practitioners’ perspective and good application examples. In the second edition, the chapters have been updated to cover the recently emerged issues. Particularly, the book presents the current status of the technology including market drivers/ restraints and development trend. Process fundamentals (both the biological and membrane components) have received in-depth coverage in the new edition. A new chapter has been added to provide a stronger focus on reuse applications in general and the decisive role of MBR in the entire reuse chain. The second edition also comes with a new chapter containing practical design problems to complement the concepts communicated throughout the book. Other distinguishing features of the new edition are coverage of novel developments and hybrid processes for specialised wastewaters, energy efficiency and sustainability of the process, aspects of MBR process automation and recent material on case studies. The new edition is a valuable reference to the academic and professional community and suitable for undergraduate and postgraduate teaching in Environmental Engineering, Chemical Engineering and Biotechnology.