Multiple scale methods

Thursday, November 6, 2008 - 2:45pm - 3:30pm
Mark Robbins (Johns Hopkins University)
Many multiscale algorithms focus on the bulk. The rapid changes in composition and properties at interfaces between materials make them more challenging. The talk will address three strategies to incorporating interfacial behavior. The first section considers interfaces between a solid and a binary fluid mixture. Molecular simulations of binary fluid mixtures are fit to general flow boundary conditions for mesoscopic and sharp interface continuum models.
Thursday, November 6, 2008 - 4:00pm - 4:45pm
Toshihiro Kawakatsu (Tohoku University)
We present the results of our recent developments of
multiscale modelling on dynamics of phase separation and
phase transition in multiphase dense polymeric systems.
Our modeling is based on density functional theories of
polymeric systems, such as the self-consistent field (SCF)
theory and the Ginzburg-Landau (GL) theory.
We combine these theories with flow dynamics, diffusion
dynamics, and the effects of external fields such as
a flow field, electric field, and confinements.
Friday, November 7, 2008 - 11:15am - 12:00pm
Bjorn Engquist (The University of Texas at Austin)
An advantage with the framework of the heterogeneous multiscale method is that the full knowledge of an effective or macroscale equation is not required for the numerical approximation of a homogenized or averaged solution. A higher fidelity microscale model is used to supply the missing data. The efficiency is gained by only applying the microscale model in sub domains. The structure of the macroscale equation must however be known.
Sunday, November 2, 2008 - 2:00pm - 3:30pm
Weinan E (Princeton University)
Joint work with Eric Vanden-Eijnden.

In many problems of multiscale modeling,
we are interested in capturing the macroscale behavior of the system
with the help of some accurate microscale models, bypassing the need
of using empirical macroscale models.
This paper gives an overview of the recent efforts on establishing
general strategies for designing such algorithms.
After reviewing some important classical examples, the Car-Parrinello
molecular dynamics, the quasicontinuum method for modeling the deformation
Friday, November 7, 2008 - 10:30am - 11:15am
Rafael Delgado-Buscalioni (Autonomous University of Madrid)
The final goal of multiscale methods based on domain decomposition, is
to retain full atomistic
detail only where needed (within a region of interest), while using
a coarse-grained model to introduce the essential information about the
surroundings dynamics. Importantly, the atomistic region becomes an open
which exchanges mass, momentum and energy with the exterior. The
hydrodynamics of flux exchange can be
solved using an hybrid molecular-continuum description (hybrid MD)
Thursday, November 6, 2008 - 2:00pm - 2:45pm
Wilma Olson (Rutgers, The State University of New Jersey)
Encoded in the strings of DNA bases that make up the genomes of living species are codes that regulate, control, and describe all sorts of biological processes. The underpinnings of these codes lie in the base sequence-dependent micromechanical properties of DNA, which determine the degree to which the long, threadlike molecule fluctuates and how it responds to the proteins that control its processing and govern its packaging.
Thursday, November 6, 2008 - 11:45am - 12:30pm
Florence Tama (University of Arizona)
Multipronged approaches have recently gained interest for tackling structural problems related to large biological complexes. Structural dynamical information is often obtained by low-resolution experimental techniques, such as Cryo Electron Microscopy (cryo-EM), Small Angle X-ray Scattering (SAXS) and Fluorescence Resonance Energy Transfer (FRET). Each of these techniques offers different advantages and meet with different pitfalls, artifacts and limitations.
Wednesday, November 5, 2008 - 10:30am - 11:15am
Eric Vanden-Eijnden (New York University)
I will present a new general framework for designing multiscale methods. Compared with previous work such as Brandt’s systematic up-scaling, the heterogeneous multiscale method and the “equation-free” approach, this new framework has the distinct feature that it does not require reinitializing the microscale model at each macro time step or each macro iteration step. In the new strategy, the macro- and micro-models evolve simultaneously using different time steps (and therefore different clocks), and they exchange data at every step. The micro-model uses its own
Tuesday, November 4, 2008 - 9:15am - 10:00am
Teresa Head-Gordon (University of California, Berkeley)
I will describe two coarse-grained models and a multiscale
model relevant in the context of molecular or langevin dynamics
of bulk liquids and macromolecules. We have recently achieved a
fundamental result in deriving an analytical solution for
computing the screened electrostatic interaction between
arbitrary numbers of proteins of arbitrarily complex charge
distributions, assuming they are well described by spherical
low dielectric cavities in a higher dielectric salty medium
Sunday, October 31, 2010 - 10:00am - 11:30am
Thomas Hou (California Institute of Technology)
A broad range of scientific and engineering problems involve multiple scales. Traditional approaches have been known to be valid for limited spatial and temporal scales. Multiple scales dominate simulation efforts wherever large disparities in spatial and temporal scales are encountered. Such disparities appear in virtually all areas of modern science and engineering, for example, composite materials, porous media, turbulent transport in high Reynolds number flows, and so on.


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