Analysis, Modeling and Simulation of Multiscale Problems / edited by Alexander Mielke.

Springer eBooks

Exponential Estimates in Averaging and Homogenisation -- Multiscale Problems in Solidification Processes -- Multiscale Modeling of Epitaxial Growth: From Discrete-Continuum to Continuum Equations -- On Asymptotic Limits of Cahn-Hilliard Systems with Elastic Misfit -- Simulations of Complex Microstructure Formations -- Multiple Scales in Phase Separating Systems with Elastic Misfit -- A General Theory for Elastic Phase Transitions in Crystals -- Relaxation and the Computation of Effective Energies and Microstructures in Solid Mechanics -- Derivation of Elastic Theories for Thin Sheets and the Constraint of Incompressibility -- Domain Walls and Vortices in Thin Ferromagnetic Films -- Wavelet-Based Multiscale Methods for Electronic Structure Calculations -- Multi-Scale Modeling of Quantum Semiconductor Devices -- Electronic States in Semiconductor Nanostructures and Upscaling to Semi-Classical Models -- Shape Optimization of Biomorphic Ceramics with Microstructures by Homogenization Modeling -- Discrete Free Energy Functionals for Elastic Materials with Phase Change -- Continuum Descriptions for the Dynamics in Discrete Lattices: Derivation and Justification -- Wave Trains, Solitons and Modulation Theory in FPU Chains -- On the Effect of Correlations, Fluctuations and Collisions in Ostwald Ripening -- Radiative Friction for Charges Interacting with the Radiation Field: Classical Many-Particle Systems -- Numerical Integrators for Highly Oscillatory Hamiltonian Systems: A Review -- Energy Level Crossings in Molecular Dynamics -- Motion of Electrons in Adiabatically Perturbed Periodic Structures -- Graph Algorithms for Dynamical Systems -- Conditional Averaging for Diffusive Fast-Slow Systems: A Sketch for Derivation.

This book reports recent mathematical developments in the DFG Priority Programme "Analysis, Modeling and Simulation of Multiscale Problems", which started as a German research initiative in 2000. The field of multiscale problems occurs 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. Recently developed tools are described in a comprehensive manner. This book provides the state of the art on the mathematical foundations of the modeling and the efficient numerical treatment of such problems.

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