Analysis, Modeling and Simulation of Multiscale Problems

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Alexander Mielke
Springer Science & Business Media, Oct 14, 2006 - Mathematics - 697 pages
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This book reports recent mathematical developments in the Programme "Analysis, Modeling and Simulation of Multiscale Problems", which started as a German research initiative in 2006. Multiscale problems occur in many fields of science, such as microstructures in materials, sharp-interface models, many-particle systems and motions on different spatial and temporal scales in quantum mechanics or in molecular dynamics. The book presents current mathematical foundations of modeling, and proposes efficient numerical treatment.

 

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Contents

Exponential Estimates in Averaging and Homogenisation
1
Petrova Torben Swart
2
Stephan Luckhaus Luca Mugnai
10
Multiscale Problems in Solidification Processes
21
Sergio Conti
22
Hongjun
30
Michael Dellnitz WeierstraßInstitut für Angewandte
39
On Asymptotic Limits of CahnHilliard Systems
86
Electronic States in Semiconductor Nanostructures
365
Shape Optimization of Biomorphic Ceramics with
395
Discrete Free Energy Functionals for Elastic Materials
425
Leipzig Carsten Carstensen
435
Wave Trains Solitons and Modulation Theory in FPU Chains
463
Analysis und Stochastik Facultad de Matemáticas
499
On the Effect of Correlations Fluctuations and Collisions
501
Radiative Friction for Charges Interacting with
531

Simulations of Complex Microstructure Formations
113
Multiple Scales in Phase Separating Systems
153
A General Theory for Elastic Phase Transitions in Crystals
179
Relaxation and the Computation of Effective Energies
197
Derivation of Elastic Theories for Thin Sheets
225
Domain Walls and Vortices in Thin Ferromagnetic Films
248
Matthias Kurzke Christof Melcher Roger Moser 249
299
MultiScale Modeling of Quantum Semiconductor Devices
331
Motion of Electrons in Adiabatically Perturbed
551
Numerical Integrators for Highly Oscillatory Hamiltonian
552
David Cohen Tobias Jahnke Katina Lorenz Christian Lubich 553
577
Gianluca Panati Herbert Spohn Stefan Teufel
595
Graph Algorithms for Dynamical Systems
619
Colored Plates
683
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