Bulletin of the American Physical Society
APS March Meeting 2013
Volume 58, Number 1
Monday–Friday, March 18–22, 2013; Baltimore, Maryland
Session N25: Focus Session: Modeling of Rare Events II |
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Sponsoring Units: DCOMP Chair: Eric Vanden-Eijnden, New York University Room: 327 |
Wednesday, March 20, 2013 11:15AM - 11:51AM |
N25.00001: TBD Invited Speaker: Eric Vanden-Eijnden |
Wednesday, March 20, 2013 11:51AM - 12:27PM |
N25.00002: ABSTRACT WITHDRAWN |
Wednesday, March 20, 2013 12:27PM - 12:39PM |
N25.00003: Temperature and rate sensitivity of melting in Cu Amit Samanta, Tang-Qing Yu, Weinan E The nature of melting of a crystal is a long standing topic of interest in materials science. Using advanced simulation techniques such as finite temperature string method and temperature accelerated molecular dynamics, we trace the minimum free energy path (MFEP) for a transition from solid to liquid phase at different temperatures in copper. Analysis of the configurations along the MFEP reveals that the rate determining transition state and the ensuing melting mechanisms are a function of temperature of the system. Close to equilibrium melting temperatures, the saddle point is determined by the critical size of the liquid nucleus, however, at higher temperatures, we find that the saddle structure consists of defect clusters from which the liquid nucleus is formed. [Preview Abstract] |
Wednesday, March 20, 2013 12:39PM - 12:51PM |
N25.00004: Efficient minimum mode finding in transition states calculations Weiguo Gao, Jing Leng, Cheng Shang, Zhi-Pan Liu Transition states are fundamental to understanding the reaction dynamics qualitatively in chemical physics. To date various methods of first principle location of the transition states have been developed. In the absence of the knowledge of the final structure, the minimum-mode following method climbs up to a transition state without calculating the Hessian matrix. One weakness of this kind of approaches is that the number of rotations to determine the minimum mode is usually unpredictable. In this work, we propose a locally optimal search direction finding algorithm which is an extension of the traditional conjugate gradient method without additional calculations of the forces. We also show that the translation of forces improves the numerical stability. Experiments for the Baker test system show that the proposed algorithm is much faster than the original dimer conjugate gradient method. [Preview Abstract] |
Wednesday, March 20, 2013 12:51PM - 1:03PM |
N25.00005: Extension of the string method for saddle points search Weiqing Ren The string method was designed for finding minimum energy paths between two minima of a potential (or free) energy. It evolves a continuous curve in the path space by steepest descent dynamics. In this talk, we discuss how the string method can be modified for saddle point search. Compared to the existing algorithms, the new method has the advantage that the computed saddle points are guaranteed to be directly connected to the minima. We will also discuss how the convergence can be accelerated using an inexact Newton method. [Preview Abstract] |
Wednesday, March 20, 2013 1:03PM - 1:15PM |
N25.00006: On extreme value statistics of correlated random variables Maxime Clusel, Jean-Yves Fortin The statistics of extreme values of a set on independent and identically distributed random variables is a well established mathematical theory that can be traced back to the late 1920s, with pioneering work by Fisher and Tippett. While efforts have been made to go beyond the uncorrelated case, little is known about the extremes of strongly correlated variables. Notable exceptions are the distribution of extreme eigenvalues of random matrices (Tracy and Widom 1994), the Airy law for one-dimensional random walks (Majumdar and Comtet 2005), and random variables with logarithmic interactions (Fyodorov and Bouchaud 2008). We propose to adapt the equivalence between extremes and sums (Bertin and Clusel 2006) to obtain asymptotic distributions of correlated random variables. We will show how this approach works in the logarithmic case, before extending it to power-law correlations and beyond. We will eventually illustrate these cases with a simple model, a one-dimensional gas of interacting particles. [Preview Abstract] |
Wednesday, March 20, 2013 1:15PM - 1:27PM |
N25.00007: Study of the diffusion of points defects in crystalline silicon using the kinetic ART method Mickael Trochet, Peter Brommer, Laurent-Karim Beland, Jean-Francois Joly, Normand Mousseau Because of the long-time scale involved, the activated diffusion of point defects is often studied in standard molecular dynamics at high temperatures only, making it more difficult to characterize complex diffusion mechanisms. Here, we turn to the study of point defect diffusion in crystalline silicon using kinetic ART (kART)[1-2], an off-lattice kinetic Monte Carlo method with on-the-fly catalog building based on the activation-relaxation technique (ART nouveau). By generating catalogs of diffusion mechanisms and fully incorporating elastic and off-lattice effects, kART is a unique tool for characterizing this problem. More precisely, using kART with the standard Stillinger-Weber potential we consider the evolution of crystalline cells with 1 to 4 vacancies and 1 to 4 interstitials at various temperatures and to provide a detailed picture of both the atomistic diffusion mechanisms and overall kinetics in addition to identifying special configurations such as a 2-interstitial super-diffuser. \\[4pt] [1] F. El-Mellouhi, N. Mousseau and L.J. Lewis, Phys. Rev. B. 78, 153202 (2008)\\[0pt] [2] L. K. B\'eland, P. Brommer, F. El-Mellouhi, J.-F. Joly and N. Mousseau, Phys. Rev. E 84, 046704 (2011). [Preview Abstract] |
Wednesday, March 20, 2013 1:27PM - 1:39PM |
N25.00008: An iterative action minimizing method for computing optimal paths in stochastic dynamical systems Brandon Lindley, Ira Schwartz We present a numerical method for computing optimal transition pathways and transition rates in systems of stochastic differential equations (SDEs). In particular, we compute the most probable transition path of stochastic equations by minimizing the effective action in a corresponding deterministic Hamiltonian system. The numerical method presented here involves using an iterative scheme for solving a two-point boundary value problem for the Hamiltonian system. We validate our method by applying it to both continuous stochastic systems, such as nonlinear oscillators governed by the Duffing equation, and finite discrete systems, such as epidemic problems, which are governed by a set of master equations. Furthermore, we demonstrate that this method is capable of dealing with stochastic systems of delay differential equations. [Preview Abstract] |
Wednesday, March 20, 2013 1:39PM - 1:51PM |
N25.00009: The stability of vacancy-like defects in amorphous silicon Jean-Francois Joly, Normand Mousseau The contribution of vacancy-like defects to the relaxation of amorphous silicon (a-Si) has been a matter of debate for a long time. Due to their disordered nature, there is a large number local environments in which such a defect can exists. Previous numerical studies the vacancy in a-Si have been limited to small systems and very short timescales. Here we use kinectic ART (k-ART), an off-lattice kinetic Monte-Carlo simulation method with on-the-fly catalog building [1,2] to study the time evolution of 1000 different single vacancy configurations in a well-relaxed a-Si model. Our results show that most of the vacancies are annihlated quickly. In fact, while 16\% of the 1000 isolated vacancies survive for more than 1 ns of simulated time, 0.043\% remain after 1 ms and only 6 of them survive longer than 0.1 second. Diffusion of the full vacancy is only seen in 19\% of the configurations and diffusion usually leads directly to the annihilation of the defect. The actual annihilation event, in which one of the defective atoms fills the vacancy, is usually similar in all the configurations but local bonding environment heavily influence its activation barrier and relaxation energy. \\[4pt] [1] El-Mellouhi et al,Phys. Rev B. 78, (2008)\\[0pt] [2] Beland et al., Phys. Rev. E. 84, (2011) [Preview Abstract] |
Wednesday, March 20, 2013 1:51PM - 2:03PM |
N25.00010: Ga Surface Diffusion on GaAs(001) $\beta$ 2(2 $\times$ 4): An ab initio Local Superbasin Kinetic Monte Carlo Study Yangzheng Lin, Kristen Fichthorn We use first-principles density functional theory to characterize the diffusion of a Ga adatom on GaAs(01) $\beta$ 2(2 $\times$ 4). Beginning with previously identified potential energy minima on this surface, we used the climbing-image nudged elastic band method to identify transition states and delineate diffusion pathways. These studies led to the discovery of eight new binding sites for Ga, which more than doubles the number that had been previously identified. The diffusion pathways for hopping between these minima involve energy barriers that vary significantly in magnitude, such that minima are spatially arranged in groups connected by low barriers and separated from each other by high barriers. Thus, the diffusion process is significantly more complex than was previously believed. To resolve the diffusion, we applied our recently developed local superbasin kinetic Monte Carlo method, which efficiently resolves the long-time dynamics of this complex process. [Preview Abstract] |
Wednesday, March 20, 2013 2:03PM - 2:15PM |
N25.00011: Physical Point Consequences Alfred Phillips Jr. We have considered a physical point, and accordingly we have made a distinction between a physical derivative and a mathematical derivative. We trace how this consideration impacts spacetime, general relativity (the so-called cosmological constant problem), quantum mechanics, and their one hundred twenty orders-of-magnitude discrepancy in vacuum energy. [Preview Abstract] |
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