# Multiscale methods

People: |
Yuen Au Yeung |

Marco Cicalese | |

Gero Friesecke | |

Alice Mikikits-Leitner | |

Sarah Rathbauer |

- atomic-to-continuum limits in solid mechanics (including effective theories for thin films, crystallisation, shape prediction, fracture, elasticity)
- effective models for shape, interaction and long time evolution of coherent modes in lattice systems
- bridging of time scales in molecular dynamics simulations.

# Recent workshop

Development and Analysis of Multiscale Methods^{}

IMA Annual Program Year Workshop,

University of Minnesota, USA, November 3-7, 2008

**Organizers:**

Frank L. H. Brown, Chemistry and Biochemistry, University of California

Anne M. Chaka, National Institute of Standards and Technology

Gero Friesecke, Mathematics, TU Munich

Kurt Kremer, Max Planck Institute for Polymer Research, Mainz

Yousef Saad, Computer Science and Engineering, University of Minnesota

Gregory A. Voth, Theoretical and Physical Chemistry, University of Utah

# Publications

- G. Friesecke, O. Junge, P. Koltai, Mean field approximation in conformation dynamics, Multiscale Model. Simul. Vol. 8 No. 1, 254-268, 2009 Article
^{}Preprint^{} - B. Schmidt, Qualitative properties of a continuum theory for thin films,
*Annales de l'I.H.P. - Analyse non linéaire*25, 43 - 75, 2008 - B. Schmidt, A derivation of continuum nonlinear plate theory from atomistic models,
*SIAM Mult. Model. Simul.*5, 664-694, 2006 - J. Giannoulis, A. Mielke, Dispersive evolution of pulses in oscillator chains with general interaction potentials,
*Discrete Contin. Dyn. Syst.*Ser. B. 6, 493-523, 2006 - J. Giannoulis, A. Mielke, The nonlinear Schr"odinger equation as a macroscopic limit for an oscillator chain with cubic nonlinearities,
*Nonlinearity*17, 551-565, 2004 - G. Friesecke, R. D. James, A Scheme for the Passage from Atomic to Continuum Theory for Thin Films, Nanotubes and Nanorods,
*J. Mech. Phys. Solids*48, 1519-1540, 2000 - G. Friesecke, R. L. Pego, Solitary waves on FPU lattices I: qualitative properties, renormalization and continuum limit, with R. L. Pego,
*Nonlinearity*12, 1601-1627, 1999