| Homogenization and Porous Media Softcover Repri Edition Contributor(s): Hornung, Ulrich (Editor) |
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ISBN: 1461273390 ISBN-13: 9781461273394 Publisher: Springer OUR PRICE: $104.49 Product Type: Paperback - Other Formats Published: September 2012 |
| Additional Information |
| BISAC Categories: - Mathematics | Mathematical Analysis - Science | Physics - Mathematical & Computational - Mathematics | Applied |
| Dewey: 515 |
| Series: Interdisciplinary Applied Mathematics |
| Physical Information: 0.63" H x 6.14" W x 9.21" (0.94 lbs) 279 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: For several decades developments in porous media have taken place in almost independent areas. In civilengineering, many papers were publisheddealing with the foundations offlow and transport through porous media. The method used in most cases is called averaging, and the notion ofa representative elementary vol- ume(REV)playsanimportantrole. Inchemicalengineering, papersonconceptual models were written on the theory ofmixtures. Intheoretical physics and stochas- tic analysis, percolation theory has emerged, providing probabilistic models for systems where theconnectedness propertiesofsomecomponentdominatethebe- havior. In mathematics, atheoryhasbeendevelopedcalled homogenizationwhich deals with partial differential equations having rapidly oscillating coefficients. Early work in these and related areas was - among others - done by the fol- lowing scientists: Maxwell Max81] and Rayleigh Ray92] studied the effective conductivity of media with small concentrations of randomly and periodically, respectively, arranged inclusions. Einstein Ein06] investigated the effective vis- cosityofsuspensions with hard spherical particles in compressible viscous fluids. Marchenko and Khrouslov MK64] looked at the asymptotic nature of homog- enization; they introduced a general approach of averaging based on asymptotic tools which can handle a variety ofdifferent physical problems. Unfortunately, up to now, little efforthas been made to bridge the gap between these different fields of research. Consequently, many results were and are dis- covered independently, and scientists are almost unable to understand each other because the respective languages have been developing in different directions. |