Henry A. Warchall
DMS Division of Mathematical Sciences
MPS Directorate for Mathematical & Physical Sciences
Start Date:
April 15, 2003
Expires:
March 31, 2009 (Estimated)
Awarded Amount to Date:
$540000
Investigator(s):
Eric Vanden-Eijnden eve2@cims.nyu.edu (Principal Investigator)
Sponsor:
New York University
70 WASHINGTON SQUARE S
NEW YORK, NY 10012 212/998-2121
NSF Program(s):
COMPUTATIONAL MATHEMATICS, APPLIED MATHEMATICS
Field Application(s):
0000099 Other Applications NEC
Program Reference Code(s):
OTHR, 9263, 1187, 1045, 0000
Program Element Code(s):
1271, 1266
ABSTRACT
Abstract of NSF Proposal 0239625
PI: Eric Vanden-Eijnden, Courant Institute of Mathematical Sciences
Title: Transition pathways in complex systems
The description of complex system driven by rare events, or
conformations, is a major challenge in applied mathematics and
computational sciences. Well-known examples of conformations include
nucleation events during phase transition, conformational changes in
molecules, thermal activated switching of magnetic materials, and
chemical reactions. The disparity between the execution time of the
conformation event and the waiting time between these events is
typically so large that it impossible to simulate the dynamics of
these processes by solving directly the underlying dynamic equations.
This project is a combined theorical and numerical effort to describe
and simulate these rare conformation changes. The theoretical
description of transition pathways in complex systems leads to
challenging problem in probability and stochastic processes theory
which require to go beyond the standard tools of large deviation
theory and extensions thereof. These new theoretical tools will be
developed so as to naturally lead to efficient algorithms, well-suited
for the numerical investigation of the transition pathways required in
realistic complex systems.
Applied mathematics has much to contribute, and much to gain in
understanding via a coordinate program of analysis, simulation, and
education the mechanisms by which rare conformation changes arise in
complex systems. Topics to be addressed include: (a) the development
of appropriate theoretical tools for the description of the transition
pathways in complex systems; (b) the development of efficient
numerical algorithms for the identification of these pathways; and,
(c) the development of courses at undergraduate and graduate levels in
applied stochastic methods which will provide the students with the
necessary background to do research on these topics at the interface
between mathematics, computer science, and the natural sciences.
Successful pursuit of these issues requires a multidisciplinary
effort, drawing expertise from computational sciences, applied
mathematics, in the multiple fields in the natural sciences which
involve complex dynamical systems. The students and postdoctoral
scientists participating this effort will gain flexibility and
perspective through exposure to these many disciplines.
PUBLICATIONS PRODUCED AS A RESULT OF THIS RESEARCH Next
(Showing: 1 - 20 of 35).
A. Ma jda, I. Timofeyev and E Vanden-Eijnden.
"Stochastic models for selected slow variables in large deterministic systems,"
Nonlinearity,
v.19,
2006,
p. 769.
Ariel, G; Vanden-Eijnden, E.
"Testing transition state theory on Kac-Zwanzig model,"
JOURNAL OF STATISTICAL PHYSICS,
v.126,
2007,
p. 43
- 73.
Cyrill Muratov and Eric Vanden-Eijnden.
"Breakup of universality in the generalized spinodal theory,"
Journal of statistical physics,
v.114,
2004,
p. 605.
D. T. Crommelin and E. Vanden-Eijnden.
"Reconstruction of diffusions using spectral data from time-series,"
Comm. Math. Sci.,
v.429,
2006,
p. 651.
D. T. Crommelin and E. Vanden-Eijnden.
"Fitting timeseries by continuous-time Markov chains: A quadratic programming approach,"
J. Comp. Phys.,
v.217,
2006,
p. 782.
Deville, REL; Milewski, PA; Pignol, RJ; Tabak, EG; Vanden-Eijnden, E.
"Nonequilibrium statistics of a reduced model for energy transfer in waves,"
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS,
v.60,
2007,
p. 439
- 461.
DeVille, REL; Vanden-Eijnden, E.
"A nontrivial scaling limit for multiscale Markov chains,"
JOURNAL OF STATISTICAL PHYSICS,
v.126,
2007,
p. 75
- 94.
DeVille, REL; Vanden-Eijnden, E.
"Wavetrain response of an excitable medium to local stochastic forcing,"
NONLINEARITY,
v.20,
2007,
p. 51
- 74.
Deville, REL; Vanden-Eijnden, E.
"Self-induced stochastic resonance for Brownian ratchets under load,"
COMMUNICATIONS IN MATHEMATICAL SCIENCES,
v.5,
2007,
p. 431
- 446.
Doering, CR; Sargsyan, KV; Sander, LM; Vanden-Eijnden, E.
"Asymptotics of rare events in birth-death processes bypassing the exact solutions,"
JOURNAL OF PHYSICS-CONDENSED MATTER,
v.19,
2007,
E, W; Engquist, B; Li, XT; Ren, WQ; Vanden-Eijnden, E.
"Heterogeneous multiscale methods: A review,"
COMMUNICATIONS IN COMPUTATIONAL PHYSICS,
v.2,
2007,
p. 367
- 450.
E, WN; Ren, WQ; Vanden-Eijnden, E.
"Simplified and improved string method for computing the minimum energy paths in barrier-crossing events,"
JOURNAL OF CHEMICAL PHYSICS,
v.126,
2007,
E. Vanden-Eijnden and G. Ciccotti.
"Second-order integrators for Langevin equations with holonomic constraints,"
Chem. Phys. Lett.,
v.429,
2006,
p. 310.
E. Vanden-Eijnden, F. Tal.
"Transition state theory:
Variational formulation, dynamical corrections, and error estimates,"
J. Chem. Phys.,
v.123,
2005,
p. 184103.
F. Tal, E. Vanden-Eijnden.
"Transition state theory and dynamical corrections in ergodic
systems,"
Nonlinearity,
v.19,
2006,
p. 501.
G. Ariel and E. Vanden-Eijnden.
"Testing transition state theory on Kac-Zwanzig model,"
J. Stat. Phys.,
v.126,
2007,
p. 43.
G. Ciccotti, R. Kapral, and E. Vanden-Eijnden.
"Blue Moon sampling, vectorial reaction coordinates, and unbiased constrained dynamics,"
ChemPhysChem,
v.6,
2005,
p. 1809.
Ibrahim Fatkullin and Eric Vanden-Eijnden.
"Statistical description of contact-interacting particles on the line,"
Journal of Statistical Physics,
v.112,
2003,
p. 155.
Kohn, RV; Otto, F; Reznikoff, MG; Vanden-Eijnden, E.
"Action minimization and sharp-interface limits for the stochastic Allen-Cahn equation,"
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS,
v.60,
2007,
p. 393
- 438.
L. Maragliano and E. Vanden-Eijnden.
"A temperature accelerated method for sampling free energy and determining reaction
pathways in rare events simulations,"
Chem. Phys. Lett.,
v.426,
2006,
p. 168.
