Multiscale Problems in Science and Technology: Challenges to Mathematical Analysis and Perspectives

ISBN-13: 9783540435846 / Angielski / Miękka / 2002 / 316 str.

Nenad Antonic; C. J. Van Duijin; Willi Jager

Opis

The International conference on Multiscale problems in science and technol ogy; Challenges to mathematical analysis and applications brought together mathematicians working on multiscale techniques (homogenisation, singular perturbation) and specialists from applied sciences who use these techniques. Our idea was that mathematicians could contribute to solving problems in the emerging applied disciplines usually overlooked by them and that specialists from applied sciences could pose new challenges for multiscale problems. Numerous problems in natural sciences contain multiple scales: flows in complex heterogeneous media, many particles systems, composite media, etc. Mathematically, we are led to study of singular homogenisation limits and the procedure is called upscaling or homogenisation. The processes to be up scaled are usually described by differential equations. For simple cases, when the differential equation is linear and the heterogeneities are periodic some progress has been made. However, most natural phenomena are described by nonlinear differential equations in a random nonhomogeneous medium and, despite an intensive development in recent years, there are many open problems. The objective of the conference was to bring together leading special ists from Europe and the United States and to discuss new challenges in this quickly developing field. Topics of the conference were Nonlinear Partial Differential Equations and Applied Analysis, with direct applications to the modeling in Material Sciences, Petroleum Engineering and Hydrodynamics."

Spis treści

Mathematical Tools for Studying Oscillations and Concentrations: from Young Measures to H-Measures and Their Variants.- Statistical Mechanics of Violent Relaxation in Stellar Systems.- On the Role of Interface Energies in the Description of Material Behavior.- Projection Generated Homogenization.- Derivation of the Diphasic Biot’s Law.- Mesoscopic Models of Reaction-Diffusion Processes with Exclusion Mechanism.- Two-Scale Models for Liquid-Solid Phase Transitions in Binary Material with Equiaxed Microstructure.- Asymptotic Behaviour of the Incompressible Newtonian Flow Through Thin Constricted Fracture.- Finite Dimensional Approximations for Elliptic Problems with Rapidly Oscillating Coefficients.- The Failure of Uniform Exponential Decay for Boundary Layers.- Homogenization of Random Nonstationary Convection-Diffusion Problem.- Remarks on ?-Convergence of Penalized Functionals of Ginzburg-Landau Type in One Dimension.- Homogenization of a Free Boundary Problem: the no-Slip Condition.- Radiative Transfer with Many Spectral Lines.- PageNumber="307">Selected abstracts.