SNP Meeting/IMA PI Conference:
The Interface between Atomistic and Continuum Theories

We are pleased to acknowledge the support of the following institutions:

The Society for Natural Philosophy, founded in 1963 by the late Clifford Truesdell, nourishes specific research aimed at the unity of mathematical and physical science. It seeks to recognize and promote work of high quality. Additional information about the Society is available at http://www.ms.uky.edu/~snp/.

Continuum theories for the behavior of materials have dominated engineering practice for more than a century. Such theories combine principles of balance with phenomenological constitutive relations to provide field equations for analysis and design. Outside the regime of linear response, the guidelines for choosing constitutive equations are limited to those dictated by thermodynamics, invariance, symmetry, and ad-hoc notions concerning physical relevance. Explicit constitutive relations valid for nonlinear response are therefore rather uncommon. This hindrance has generated efforts, most notably in the field of rheology but also more recently in nonlinear elasticity, to derive continuum-level constitutive equations based on detailed atomistic considerations.

Over the past 20 years, the increasing power and decreasing cost of multiprocessor computers have enabled atomistic simulations based on quantum mechanics and classical molecular dynamics. These simulations include studies of fracture, dislocation dynamics, phase interfaces, electro-osmostic fluid flow in nano- and micro-scale channels, and wetting. At present, computational limitations make it difficult to use such atomistic simulations to describe processes involving length scales larger than a micron or time intervals longer than a millisecond.

Such limitations have led to the development of various hybrid atomistic-continuum schemes, including discrete dislocation dynamics, the quasi-continuum method, and the heterogeneous multiscale method.

Associated with these and other related developments are many important questions that should be of great interest to the science community in general and to the researchers in mechanics in particular:

• What are appropriate generalizations of the Born rule for quasicrystals and other complex materials?
• What is the appropriate definition of stress at the atomistic level?
• How are continuum limits of discrete models affected by the type of averaging technique used?
• How, if at all, do configurational forces arise from the averaging of atomistic models?
• What are meaningful restrictions on atomistic constitutive equations (e.g., on density functionals) and how are those restrictions inherited (in forms familiar to mechanicians) at the continuum level?

• To highlight the most recent advances in developing novel ideas to bridge atomistic and continuum theories;
• To allow for discussions and initiate new collaborations between mechanicians and mathematicians who might otherwise not attend the same conferences, as well as between senior and junior investigators;
• To expose Ph.D. students and postdocs in mechanics, applied mathematics, and materials science and engineering to the forefronts of current research;
• To help shape new directions of research among investigators who share a common interest in developing atomistic-continuum constitutive theories.

List of Confirmed Participants

Papers on topics related to the theme of the meeting are solicited for 30-minute "round-table" presentations. In selecting speakers for the round-table sessions, preference will be given to younger researchers. Colleagues who wish to give a round-table presentation are requested to submit one-page abstracts by September 1^st, 2007 to Yi-chao Chen (chen@uh.edu) and Eliot Fried (efried@me.wustl.edu). Final decisions on speaker selection will be communicated by September 15^th, 2007. The Society will provide some travel and lodging support to young researchers who are selected to speak in the round-table sessions. Prospective speakers who wish to receive such support should so indicate when they submit their abstract.

For the members of the Society for Natural Philosophy*, a registration fee of $50 will be charged to help defray the costs of the banquet and of refreshments at coffee breaks. The registration fee for non-members is $75, which also provides a one year membership with the Society. To facilitate planning, all prospective participants are urged to notify Professor Yi-chao Chen(chen@uh.edu) by e-mail, as soon as possible, their intention to attend this meeting. A check of $50 or $75, made payable to "University of Houston", should be sent to Yi-chao Chen (Department of Mechanical Engineering, University of Houston, N207 Engineering Building 1, Houston, TX 77204-4006, USA) by October 10^th, 2007 .

* For the membership information, see the Society website above. It is noted that the membership dues for students are free.

The Society for Natural Philosophy (SNP), the Institute for Mathematics and its Applications (IMA), and the University of Houston (UH) have pledged funds to support this meeting. Moreover, a grant from the National Science Foundation (NSF) will ensure the availability of support to young researchers. Recent Ph.D.'s and advanced graduate students are strongly encouraged to apply for travel and lodging support. Prospective participants who will have to use their personal funds to attend this meeting are also encouraged to apply for partial support.

This SNP Meeting is co-sponsored by the IMA as an IMA PI Conference. Faculty members, students, and employees of IMA Participating Institutions are eligible to apply for travel support from the IMA PI funds of their home institution. Those interested should direct enquiries to the IMA representative of their home institution.

A block of rooms has been reserved at the JW Marriott Houston (phone: +1-800-228-9290), where the Saturday and Sunday sessions will take place. We strongly encourage participants to make hotel reservations as soon as possible, before the cutoff date of October 4^th, 2007. When making reservations by phone, please mention the group code "SNP" for the special rate ($109 + tax). Reservations can also be made online* at

* The group code is already entered in the appropriate field.