Ebook: Multiscale Problems in Science and Technology: Challenges to Mathematical Analysis and Perspectives
- Tags: Appl.Mathematics/Computational Methods of Engineering, Applications of Mathematics, Mathematical Modeling and Industrial Mathematics, Computational Science and Engineering, Mathematics of Computing, Partial Differential Equations
- Year: 2002
- Publisher: Springer-Verlag Berlin Heidelberg
- Edition: 1
- Language: English
- pdf
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.
These are the proceedings of the conference "Multiscale Problems in Science and Technology" held in Dubrovnik, Croatia, 3-9 September 2000. The objective of the conference was to bring together mathematicians working on multiscale techniques (homogenisation, singular pertubation) and specialists from the applied sciences who need these techniques and to discuss new challenges in this quickly developing field. The 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 the multiscale problems. 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.
These are the proceedings of the conference "Multiscale Problems in Science and Technology" held in Dubrovnik, Croatia, 3-9 September 2000. The objective of the conference was to bring together mathematicians working on multiscale techniques (homogenisation, singular pertubation) and specialists from the applied sciences who need these techniques and to discuss new challenges in this quickly developing field. The 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 the multiscale problems. 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.
Content:
Front Matter....Pages I-XII
Mathematical Tools for Studying Oscillations and Concentrations: from Young Measures to H-Measures and Their Variants....Pages 1-84
Statistical Mechanics of Violent Relaxation in Stellar Systems....Pages 85-116
On the Role of Interface Energies in the Description of Material Behavior....Pages 117-128
Projection Generated Homogenization....Pages 129-150
Derivation of the Diphasic Biot’s Law for an Elastic Solid Matrix Containing Isolated Fluid Drops....Pages 151-160
Mesoscopic Models of Reaction-Diffusion Processes with Exclusion Mechanism....Pages 161-173
Two-Scale Models for Liquid-Solid Phase Transitions in Binary Material with Equiaxed Microstructure....Pages 175-187
Asymptotic Behaviour of the Incompressible Newtonian Flow Through Thin Constricted Fracture....Pages 189-202
Finite Dimensional Approximations for Elliptic Problems with Rapidly Oscillating Coefficients....Pages 203-242
The Failure of Uniform Exponential Decay for Boundary Layers....Pages 243-250
Homogenization of Random Nonstationary Convection-Diffusion Problem....Pages 251-270
Remarks on ?-Convergence of Penalized Functionals of Ginzburg-Landau Type in One Dimension....Pages 271-282
Homogenization of a Free Boundary Problem: The no-Slip Condition....Pages 283-290
Radiative Transfer with Many Spectral Lines....Pages 291-306
Back Matter....Pages 307-313
These are the proceedings of the conference "Multiscale Problems in Science and Technology" held in Dubrovnik, Croatia, 3-9 September 2000. The objective of the conference was to bring together mathematicians working on multiscale techniques (homogenisation, singular pertubation) and specialists from the applied sciences who need these techniques and to discuss new challenges in this quickly developing field. The 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 the multiscale problems. 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.
Content:
Front Matter....Pages I-XII
Mathematical Tools for Studying Oscillations and Concentrations: from Young Measures to H-Measures and Their Variants....Pages 1-84
Statistical Mechanics of Violent Relaxation in Stellar Systems....Pages 85-116
On the Role of Interface Energies in the Description of Material Behavior....Pages 117-128
Projection Generated Homogenization....Pages 129-150
Derivation of the Diphasic Biot’s Law for an Elastic Solid Matrix Containing Isolated Fluid Drops....Pages 151-160
Mesoscopic Models of Reaction-Diffusion Processes with Exclusion Mechanism....Pages 161-173
Two-Scale Models for Liquid-Solid Phase Transitions in Binary Material with Equiaxed Microstructure....Pages 175-187
Asymptotic Behaviour of the Incompressible Newtonian Flow Through Thin Constricted Fracture....Pages 189-202
Finite Dimensional Approximations for Elliptic Problems with Rapidly Oscillating Coefficients....Pages 203-242
The Failure of Uniform Exponential Decay for Boundary Layers....Pages 243-250
Homogenization of Random Nonstationary Convection-Diffusion Problem....Pages 251-270
Remarks on ?-Convergence of Penalized Functionals of Ginzburg-Landau Type in One Dimension....Pages 271-282
Homogenization of a Free Boundary Problem: The no-Slip Condition....Pages 283-290
Radiative Transfer with Many Spectral Lines....Pages 291-306
Back Matter....Pages 307-313
....