Discrete to Continuum Systems (Seminar)
Abstract
In the last decades there has been quite some interest in the derivation of continuous models from discrete ones. Examples are in nonlinear elasticity, dislocation energies in crystals, surface energies in spin models, phase transitions, fracture mechanics, stochastic homogenization and many more. The mathematical tools used are formal asymptotics, homogenization techniques, Γ-convergence, geometric measure theory and large deviations. Depending on the interest of the participants, we would like to give an overview of some of the relevant results in the vast literature. There will be weekly presentations on selected papers.
Selected topics:
- Validity and failure of Cauchy-Born rule for derivation of elastic energies.
- Non-zero temperature case and free energy derivation.
- Higher order limits and derivation of surface energies in multiphase problems.
- Limit of dilute dislocations in crystals.
- Discrete models for fracture and image processing.
- Stochastic homogenization
- Motion and depinning of random interfaces.
- Numerical schemes for atomistic to continuum coupling.
Date and time info
Monday 11:15 - 12:45, MPI MIS, A 01
Keywords
Homogenization, Phase Transitions, Discrete Interfaces
Prerequisites
Analysis I-III, basic probability theory
Audience
MSc students, PhD students, Postdocs
Language
English
