Bulletin of the American Physical Society
APS March Meeting 2013
Volume 58, Number 1
Monday–Friday, March 18–22, 2013; Baltimore, Maryland
Session M25: Focus Session: Modeling of Rare Events I |
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Sponsoring Units: DCOMP Chair: Amit Samanta, Princeton University Room: 327 |
Wednesday, March 20, 2013 8:00AM - 8:36AM |
M25.00001: Local Hyperdynamics Invited Speaker: Arthur Voter We present a new formulation of the hyperdynamics method in which the biasing effect is local, making it suitable for large systems. In standard hyperdynamics, the requirement that the bias potential be zero everywhere on the dividing surface bounding the state has the consequence that for large systems the boost factor decays to unity, regardless of the form of the bias potential. In the new method, the bias force on each atom is obtained by differentiating a local bias energy that depends only on the coordinates of atoms within a finite range D of this atom. This bias force is thus independent of the bias force in distant parts of the system, providing a method that gives a constant boost factor, independent of the system size. Although the resulting dynamics are no longer conservative, we show that for a homogeneous system (all atoms equivalent) using a simplifed bond-boost bias potential, the bias forces in any local region are equivalent to those in a system accelerated by a specific boost factor, except for additional error forces that balance in a time average. We also argue that even for inhomogeneous systems, the errors relative to an exactly accelerated dynamics should should decay roughly as 1/D. We demonstrate for some realistic atomistic systems that the method gives escape rates in excellent agreement with direct molecular dynamics simulations. [Preview Abstract] |
Wednesday, March 20, 2013 8:36AM - 8:48AM |
M25.00002: A Local Superbasin Kinetic Monte Carlo Method Kristen Fichthorn, Yangzheng Lin A ubiquitous problem in atomic-scale simulation of materials is the small-barrier problem, in which the free-energy landscape presents ``superbasins'' with low intra-basin energy barriers relative to the inter-basin barriers. Rare-event simulation methods, such as kinetic Monte Carlo (KMC) and accelerated molecular dynamics, are inefficient for such systems because considerable effort is spent simulating short-time, intra-basin motion without evolving the system significantly. We developed an adaptive local-superbasin KMC algorithm (LSKMC) for treating fast, intra-basin motion using a Master-equation / Markov-chain approach and long-time evolution using KMC. Our algorithm is designed to identify local superbasins in an on-the-fly search during conventional KMC, construct the rate matrix, compute the mean exit time and its distribution, obtain the probability to exit to each of the superbasin border (absorbing) states, and integrate superbasin exits with non-superbasin moves. We demonstrate various aspects of the method in several examples, which also highlight the efficiency of the method. [Preview Abstract] |
Wednesday, March 20, 2013 8:48AM - 9:00AM |
M25.00003: Free energy calculation from umbrella sampling using Bayesian inference Noam Bernstein, Thomas Stecher, G\'abor Cs\'anyi Using simulations to obtain information about the free energy of a system far from its free energy minima requires biased sampling, for example using a series of harmonic umbrella confining potentials to scan over a range of collective variable values. One fundamental distinction between existing methods that use this approach is in what quantities are measured and how they are used: histograms of the system's probability distribution in WHAM, or gradients of the potential of mean force for umbrella integration (UI) and the single-sweep radial basis function (RBF) approach. Here we present a method that reconstructs the free energy from umbrella sampling data using Bayesian inference that effectively uses all available information from multiple umbrella windows. We show that for a single collective variable, our method can use histograms, gradients, or both, to match or outperform WHAM and UI in the accuracy of free energy for a given amount of total simulation time. In higher dimensions, our method can effectively use gradient information to reconstruct the multidimensional free energy surface. We test our method for the alanine polypeptide model system, and show that it is more accurate than a RBF reconstruction for sparse data, and more stable for abundant data. [Preview Abstract] |
Wednesday, March 20, 2013 9:00AM - 9:12AM |
M25.00004: Characterization of the relation between energy landscape and the time evolution of complex materials using kinetic ART Kokou Gawonou N'tsouaglo, Jean-Francois Joly, Laurent Karim Beland, Peter Brommer, Normand Mousseau In the last two decades, there has been a considerable interest in the development of accelerated numerical methods for sampling the energy landscape of complex materials. Many of these methods are based on the kinetic Monte Carlo (KMC) algorithm introduced 40 years ago. This is the case of kinetic ART, for example, which uses a very efficient transition-state searching method, ART nouveau, coupled with a topological tool, NAUTY, to offer an off-lattice KMC method with on-the-fly catalog building to study complex systems, such as ion-bombarded and amorphous materials, on timescales of a second or more. Looking at two systems, vacancy aggregation in Fe and energy relaxation in ion-bombarded c-Si, we characterize the changes in the energy landscape and the relation to its time evolution with kinetic ART and its correspondence with the well-known Bell-Evans-Polanyi principle used in chemistry. [Preview Abstract] |
Wednesday, March 20, 2013 9:12AM - 9:24AM |
M25.00005: Atomistic simulations of melting and solidification using temperature accelerated molecular dynamics Tang-Qing Yu, Amit Samanta, Weinan E, Mark Tuckerman, Eric Vanden-Eijnden A detailed understanding of melting/solidification mechanisms in metals remains obscure, though over the years many simulations and experiments have been performed for clarifying it. We have applied the enhanced-sampling method, Temperature-Accelerated Molecular Dynamics, to study the melting/solidification of FCC metals like copper, nickel under the constant temperature and pressure conditions. Free energy surfaces along Steinhardt order parameters and local density are obtained and minimum free energy path (MFEP) between the metastable states are calculated. An analysis of the atomic structure along the MFEP, reveals that an interplay between orientation ordering and positional ordering governs this phase transition. [Preview Abstract] |
Wednesday, March 20, 2013 9:24AM - 9:36AM |
M25.00006: An Algorithm to Compute Statistics of Stochastic Paths on Complex Landscapes Michael Manhart, Alexandre V. Morozov Many systems in physics, chemistry, and biology can be modeled as a random walk on a network subject to a potential landscape. There is great interest in understanding the statistical properties of pathways on these landscapes, especially their times, lengths, and distributions in space. The complexity of the networks and landscapes arising in many models makes them difficult to solve by traditional analytical and computational tools. Moreover, standard methods do not always provide the most relevant information for characterizing these pathways. We develop an explicitly path-based formalism for studying these problems, which we implement using a numerical dynamic programming algorithm. It is especially well-suited to studying first-passage problems and rare transitions between metastable states. This method is valid for arbitrary networks and landscapes, as well as semi-Markovian processes with non-exponential waiting-time distributions. We explore this method on a variety of simple models including regular lattices, fractals, and protein sequence evolution. [Preview Abstract] |
Wednesday, March 20, 2013 9:36AM - 9:48AM |
M25.00007: ABSTRACT WITHDRAWN |
Wednesday, March 20, 2013 9:48AM - 10:00AM |
M25.00008: An Efficient Kernel Polynomial Method for Calculating Transition Rates in Large-Scale Materials Chen Huang, Arthur Voter, Danny Perez We present an efficient method for calculating transition rates in large-scale materials using harmonic transition state theory. In this method, we first reformulate the prefactor of the transition rates in terms of the density of states (DOS) of Hessian matrices. The DOS are then efficiently calculated with the kernel polynomial method. The scaling of our method is discussed in detail. We demonstrate our approach by calculating the prefactors for vacancy hopping and Frenkel pair formation in silver. Very good agreement between the KPM approach and exact diagonalization is observed. [Preview Abstract] |
Wednesday, March 20, 2013 10:00AM - 10:12AM |
M25.00009: Reaching extended length-scales with temperature-accelerated dynamics Jacques G. Amar, Yunsic Shim In temperature-accelerated dynamics (TAD) a high-temperature molecular dynamics (MD) simulation is used to accelerate the search for the next low-temperature activated event. While TAD has been quite successful in extending the time-scales of simulations of non-equilibrium processes, due to the fact that the computational work scales approximately as the cube of the number of atoms, until recently only simulations of relatively small systems have been carried out. Recently, we have shown that by combining spatial decomposition with our synchronous sublattice algorithm, significantly improved scaling is possible. However, in this approach the size of activated events is limited by the processor size while the dynamics is not exact. Here we discuss progress in developing an alternate approach in which high-temperature parallel MD along with localized saddle-point (LSAD) calculations, are used to carry out TAD simulations without restricting the size of activated events while keeping the dynamics ``exact'' within the context of harmonic transition-state theory. In tests of our LSAD method applied to Ag/Ag(100) annealing and Cu/Cu(100) growth simulations we find significantly improved scaling of TAD, while maintaining a negligibly small error in the energy barriers. [Preview Abstract] |
Wednesday, March 20, 2013 10:12AM - 10:24AM |
M25.00010: Switching time distributions and scaling behavior in a bistable tunnel diode circuit with adjustable noise intensity Steven J. Jones, Yu Bomze, S.W. Teitsworth We report the measurement of first-passage time distributions associated with electrical current switching in a tunnel diode circuit that is driven by a noise generator with adjustable noise intensity $D$. The tunnel diode circuit is biased with a voltage $V_{\mathrm{f}}$ that is set in a range of bistability which terminates at the upper end in a saddle-node bifurcation at voltage $V_{\mathrm{th}}$. We employ a high bandwidth technique that permits measurement of stochastically-varying switching times over a very large dynamic range [1], with measured times ranging from 1 $\mu $s to several seconds. The dependence of both the form of the distribution and extracted mean switching time $\tau $ are also studied as a function of reduced voltage $V_{\mathrm{th}} - V_{\mathrm{f}}$ and $D$. Switching time distributions are generally found to possess exponential tails at long times, consistent with a picture of noise-induced escape via a single saddle point. Also, parameter regimes are identified in which the mean switching time scales as reduced voltage to the 3/2 power and linearly with inverse noise intensity. [1] Yu. Bomze, R. Hey, H. T. Grahn, and S. W. Teitsworth, Phys. Rev. Lett. \textbf{109}, 026801 (2012). [Preview Abstract] |
Wednesday, March 20, 2013 10:24AM - 10:36AM |
M25.00011: Dependence of switching path distributions on relative noise intensities for a two-dimensional model of electrical conduction in a tunnel diode circuit Paul H. Dannenberg, J.C. Neu, S.W. Teitsworth The incorporation of negative differential resistance elements such as tunnel diodes into electronic circuits often leads to bistability, i.e., distinct co-existing states of current for a given applied voltage. Such systems are generally far-from-equilibrium and non-gradient. We discuss a model of electrical conduction in a tunnel diode circuit in the form of a two-dimensional dynamical system, and use a geometric minimum action method (gMAM) [1] to study the dependence of the most probable escape paths (MPEPs) and associated actions on the ratio of the noise amplitudes associated with the two variables. We find that the MPEP follows the time-reversed path (i.e., a saddle-node trajectory) for a unique value of noise amplitude ratio; however, in general, MPEPs follow distinct paths that vary significantly as the noise amplitude ratio is varied. Additionally, we find good agreement between the computed MPEPs and actions and numerically generated switching path distributions and mean first-passage times, respectively. \\[4pt] [1] M. Heymann and E. Vanden-Eijnden, Phys. Rev. Lett. \textbf{100}, 140601 (2008). [Preview Abstract] |
Wednesday, March 20, 2013 10:36AM - 10:48AM |
M25.00012: Kinetics of droplet wetting-mode transitions on grooved surfaces: Forward flux sampling Azar Shahraz, Ali Borhan, Kristen Fichthorn Liquid droplets on rough surfaces typically exhibit either the Cassie wetting mode, in which the droplet resides on top of the roughness, or the Wenzel mode, in which the droplet penetrates into the roughness. For a fixed surface topology and droplet size, one of these modes is the global free-energy minimum. However, the other state is often metastable and long-lived due a free-energy barrier that hinders the transition between the two wetting states. Metastable wetting states have been observed experimentally and we also observe them in molecular dynamics (MD) simulations of a droplet on a grooved surface. Using forward flux sampling, we study the kinetics of the Cassie-Wenzel transition. The global-minimum wetting states that emerge from our nanoscale MD approach are consistent with those predicted by a macroscopic model for the free energy. We find that the free-energy barrier for this transition depends on the droplet size and surface topology. A committor analysis indicates that the transition-state ensemble consists of droplets that are on the verge of initiating/breaking contact with the substrate below the grooves. [Preview Abstract] |
Wednesday, March 20, 2013 10:48AM - 11:00AM |
M25.00013: Diffusion of small Ni and Cu clusters on Ni (111): Application of SLKMC-II* Syed Islamuddin Shah, Giridhar Nandipati, Talat S. Rahman We have examined the diffusion of small Ni and Cu islands (consisting of up to 10 atoms) on the Ni(111) surface using a self-learning kinetic Monte Carlo (SLKMC-II) [1] method with an improved pattern-recognition scheme that allows inclusion of both fcc and hcp sites in the simulations. In an SLKMC simulation [2] a database holds information about the local neighborhood of an atom and associated processes that is accumulated on-the-fly, as the simulation proceeds. The activation energy barriers for the identified diffusion processes were calculated using semi-empirical interaction potential based on the embedded-atom method. Although a variety of concerted, multi-atom and single-atom processes were automatically revealed in our simulations, we found that these small islands diffuse primarily via concerted motion. We report diffusion coefficients for each island size at several temperatures, and from the Arrhenius plot extract the size-dependent effective diffusion barrier for these islands. Our evaluation of the occurrence frequency of processes most responsible for the diffusion of island of a specific size reveal several that are not accessible in SLKMC-I [2] or in short time-scale MD simulations. We also provide results of extending SLKMC-II to examine epitaxial growth in these systems. [1] S. Islamuddin Shah, et al., J. Phys.: Condens. Matter 24, 354004 (2012). [2] O. Trushin, et al., Phys. Rev. B 72, 115401 (2005). [Preview Abstract] |
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