There is no fee associated with the workshop, but please register via the ICMS website. There is limited funding to assist with travel/accommodation for early career researchers. Should you wish to apply for this, please complete the relevant section in the registration form.
Complex Multiscale Systems (CMS) play a crucial and wide-ranging role in
daily life; examples include many chemical and biological processes,
mechanical and electrical properties of materials, and many modern
technologies such as micro- and nano-fluidic systems, batteries, fuel
cells, and genetic analysis. A general problem of CMS is that they
represent high dimensional computational problems which (a) are beyond
most standard computational methods and (b) when tractable often show
unfavourable effects such as oscillations, finite time blow-up or
unphysical solutions such as negative densities. Often, available
macroscale models are not sufficiently accurate whilst the corresponding
microscale models are too inefficient and/or result in excessively large
amounts of data. Computational approaches attempt to combine these two
viewpoints in the hope of achieving a reasonable compromise between
accuracy and efficiency.
Prof. Weinan E
currently holds positions at the Department of Mathematics and
Program in Applied and Computational Mathematics at Princeton
University, and at the Beijing International Center for Mathematical
Research at Peking University. Previous to this, he held a professorship
at the Courant Institute, New York University. He is recognised as a
world-leader in a wide range of areas of applied and interdisciplinary
mathematics, including multiscale modelling, density functional theory
for electronic structure analysis, the theory and modelling of rare
events with applications in chemistry and material sciences, stochastic
partial differential equations, and the mathematical theory of solids,
from atomic to macroscopic scales. He has published over 150 scientific
papers and, in 2011, a book on the ‘Principles of Multiscale Modeling’
(CUP). Amongst a number of awards and honours, he received the Feng Kang
Prize in Scientific Computing (1999), the ICIAM Collatz Prize (2003) and
the Ralph E. Kleinman Prize (2009). He was elected as a fellow of
Institute of Physics (2005), a fellow of SIAM (2009), a member of the
Chinese Academy of Sciences (2011), and a fellow of the American
Mathematical Society (2012).
Weinan E (Princeton University) Progresses and challenges in multiscale modeling
Gero Friesecke (TU Munich)
Does the electronic Schrödinger equation explain the chemical behaviour of atoms and molecules? A tale of hidden scales
Ping Lin (University of Dundee) Error estimates for quasi-continuum methods with simple or complex lattice structures
Lucia Scardia (University of Glasgow) Homogenization of dislocations dynamics
Weinan EProgresses and challenges in multiscale modeling
I will try to give a candid assessment of the current status of the
field, discussing both the main successes and the major difficulties.
I will start by reviewing some of the classical methodologies.
I will then discuss the relatively new developments, in theory, algorithms
If time permits, I will also discuss some typical instabilities
and inconsistencies that can arise in multiscale methods.
Lucia ScardiaHomogenization of dislocations dynamics
Dislocations are defects in the crystal structure of a metal, and their collective motion gives rise to permanent deformations of the metal at the macroscopic scale.
Although good models for dislocations are available at the level of the atomic lattice, it is not well-understood how to incorporate the effect of their presence and motion in a model at the macroscopic, engineering scale. Since the number of dislocations even in a small portion of metal is very high, it is natural to take a sequence of systems with an increasing number of dislocations, and to derive an effective description in terms of a dislocation density. This micro-to-macro upscaling can be performed rigorously using Gamma-convergence, a variational convergence that has been successfully applied to a variety of problems in materials science.
In this talk I will give an overview of my contribution to this field and discuss some recent progress in modelling dislocation interactions and dynamics.
This is based on work in collaboration with Marc Geers, Ron Peerlings, Mark Peletier, Maria Giovanna Mora, Stefan Mueller and Caterina Zeppieri.
Gero FrieseckeDoes the electronic Schrödinger equation explain the chemical behaviour of atoms and molecules? A tale of hidden scales
Molecular quantum chemistry can be viewed as a huge 'natural laboratory'
for multiscale methods. However, whereas in classical multiscale problems
the degrees of freedom and the scale parameters appear explicitly in the
governing equations, in quantum chemistry both the essential variables and
the scales are emergent, or 'hidden'. Even for small systems they have to
be unearthed by a combination of empiricism, physical considerations, and
careful modelling and computation of subsystems.
After a general introduction I will discuss three examples in more detail:
the binding energies of the dimers He2, Li2, Be2,
N2 (atomic number 2,
3, 4, 7) which are approximately in the ratio 0.001 : 10 : 1 : 100; level
splittings of atoms governing the emergent total atomic spin which is
crucial for chemical behaviour, mispredicted for transition metals by even
the best density functional theory models, but can be understood via a
multiscale perspective (joint work with Ben Goddard and Christian Mendl);
and pair density oscillations at given single-particle density whose
understanding, as we will argue, will be an important step towards future
density functionals with improved accuracy (joint work with Huajie Chen,
Codina Cotar, Claudia Klueppelberg, Christian Mendl, Brendan Pass).
Multiscale Computational Methods in Materials Modelling (MCM3), Edinburgh, 16th-20th June 2014