NSF Org:	DMS Division Of Mathematical Sciences
Recipient:	THE TRUSTEES OF PRINCETON UNIVERSITY
Initial Amendment Date:	August 20, 2004
Latest Amendment Date:	August 20, 2004
Award Number:	0407866
Award Instrument:	Standard Grant
Program Manager:	Junping Wang jwang@nsf.gov  (703)292-4488 DMS  Division Of Mathematical Sciences MPS  Directorate for Mathematical and Physical Sciences
Start Date:	September 1, 2004
End Date:	August 31, 2007 (Estimated)
Total Intended Award Amount:	$333,181.00
Total Awarded Amount to Date:	$333,181.00
Funds Obligated to Date:	FY 2004 = $333,181.00
History of Investigator:	Weinan E (Principal Investigator)
Recipient Sponsored Research Office:	Princeton University 1 NASSAU HALL PRINCETON NJ  US  08544-2001 (609)258-3090
Sponsor Congressional District:	12
Primary Place of Performance:	Princeton University 1 NASSAU HALL PRINCETON NJ  US  08544-2001
Primary Place of Performance Congressional District:	12
Unique Entity Identifier (UEI):	NJ1YPQXQG7U5
Parent UEI:
NSF Program(s):	COMPUTATIONAL MATHEMATICS, CONDENSED MATTER & MAT THEORY
Primary Program Source:	app-0104
Program Reference Code(s):	0000, 1271, 7237, 7303, 9263, OTHR
Program Element Code(s):	127100, 176500
Award Agency Code:	4900
Fund Agency Code:	4900
Assistance Listing Number(s):	47.049

ABSTRACT

The PI proposes to develope theoretical models of crystalline solids
that are based on the positions of the atoms that make up the crystal.
As a first step, the PI proposes to study (large) elastic deformation
of perfect crystals. This will help us to understand the critical strain that
the material can sustain before defects form. The PI then proposes to
study the formation, structure, energetics and dynamics of defects in crystals.
Understanding defects in crystals is crucial since defects control the
response and failure of the material, as in, e.g. nano-devices
and semi-conductor thin films. By understanding the interplay between
loading and failure mechanisms as well as their microscopic origin, the PI
hopes to give guidelines fordesigning materials that avoid certain modes of failure.
To obtain simplified models that can be readily linked with traditional
theories of continuum mechanics, the PI also proposes to develop
continuum models in the form of nonlinear elasticity theory
that are derived directly from the atomistic models. Such a theory gives
a much simplified description for the material properties and are
therefore easier to use.

As applications, the PI proposes to study the mechanical properties of
carbon nano-tubes. Nano-tubes are very good examples for this project
since they can sustain very large elastic deformation before failure. In fact
they are the strongest fiber known to us. The PI proposes to study large
(therefore nonlinear) deformations of nano-tubes, their modes of failure,
as well as properties of nano-tube-reinforced materials.

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