The goal of my research is to develop a computational tool that can uncover the pathway and the transition states that exist when a molecule changes conformation or when it chemically changes. In many such circumstances, a process must overcome an energy barrier before proceeding to completion. If the size of the barrier is large compared to the available thermal energy, a process must rely on the occurrence of one or more rare events. For such circumstances, one would like to understand the reaction pathways so as to improve yields, or as in the case of protein folding, to understand the intermediate states. Many simple processes have been explored using theoretical tools such as molecular dynamics, where the movements of individual atoms are calculated. However, when the barrier is large, crossing the relevant barrier is indeed a very rare event. Although computer speeds have been doubling every 18 months (a consequence of Moore's law), the exponentially long waiting times necessary for barrier hopping pushes the required computational effort out of the feasibility range for all but the simplest models. To explore these barrier-limited processes, I am working with students and collaborators to develop a novel computational technique to sample the paths themselves in a thermodynamically significant manner.
The bottom of the wells on the x axis are at the potential zero, while the bottom of the well on the y-axis is at a value of 0.25. The potential at the saddles is one.
The temperature is 0.20 in energy units. The time length of the path is 62.5 units. The number of divisions along the path is 2^18.
The path starts in the well on the left and ends in the well on the right but not before it stalls in the third well. Note that the length of the path is short in that it does not allow for multiple transitions.
Patrick Malsom (Ph.D.)
Ernie Ablordeppey (M.S.)
* John F. Clark, Ph.D., 1993.
Thesis: A Study of Short-Range Order in Disordered Alloys
* Dereje Seifu
, Ph.D., 1994.
Thesis: Energy of Ordered and Disordered Copper-Gold Alloys
* Mahdi Sanati,
Thesis: A theoretical study of the omega-phase transformation in metals
* Thomas Maloney, M.S., 2010.
Thesis: Adaptive Array-Gain Spatial Filtering in Magnetoencephalography
N. Bowditch, Harvard University, 1802
B. Peirce, Harvard University, 1829
J. Lovering, Harvard University, 1833
J. Trowbridge, Harvard University, 1873
W. C. Sabine, Harvard University, 1890
P. W. Bridgman, Harvard University, 1908
E. C. Kemble, Harvard University, 1917
E. Feenberg, Harvard University, 1933
C. E. Campbell, Washington University (St. Louis), 1969
F. J. Pinski, University of Minnesota, 1977
Kullback-Leibler Approximation for Probability Measures on Infinite Dimensional Spaces
Frank Pinski, Gideon Simpson, Andrew Stuart, and Hendrik Weber
A Function Space HMC Algorithm With Second Order Langevin Diffusion Limit,
Michela Ottobre, Natesh S. Pillai, Frank J. Pinski, and Andrew M. Stuart
Gamma-Limit for Transition Paths of Maximal Probability, F.J. Pinski, F. Theil and A.M. Stuart, J. Stat. Phys. 146, 955–974 (2012); doi:10.1007/s10955-012-0443-8
Hybrid Monte-Carlo on Hilbert Spaces, A. Beskos, F.J. Pinski, J.-M. Sanz-Serna and A.M.Stuart, Stoch. Proc. Applic. 121, 2201–2230 (2011); doi:10.1016/j.spa.2011.06.003
Transition paths in molecules at finite temperature, F.J. Pinski and A.M. Stuart, J. Chem. Phys. 132, 184104 (2010); doi:10.1063/1.3391160
Talk: ICIAM, 2011 (Vancouver)
Talk: AIMS, 2012 (Orlando)