Session X25: Focus Session: Modeling of Rare Events: Methods and Applications II

Accelerated Molecular Dynamics of Rare Events with the Bond-Boost Method

A continuing challenge in materials simulation is to conduct long time and large length simulations of structural evolution, while accurately retaining atomic detail. For many materials, dynamical evolution occurs through a series of ``rare events,'' in which the system spends a long-time period in one free-energy minimum before escaping and moving on to another. To address the rare-event problem for materials evolution, we developed the bond-boost method, which is a variant of hyperdynamics. We will introduce the bond-boost method and demonstrate several applications of it to thin-film growth and surface kinetics. A significant problem that plagues rare-event simulations is the ``small barrier problem'' and we will discuss how this problem can be addressed within the bond-boost method. We will also discuss our recent efforts to combine this method with kinetic Monte Carlo simulations.   

Generalizations of the string method

Generalizations of the string method will be presented that permit to identify the saddle points by which the process escapes the basin of attraction of a minimum of the potential due to thermal noise, or to map out the volume of this basin. These methods will be illustrated via examples such as thermal reorganization of Lennard-Jones clusters and packings of soft-spheres.   

String method for the computation of minimum energy paths and saddle points

Many problems arising from applied sciences can be abstractly formulated as a system that navigates over a complex energy landscape of high or infinite dimensions. The system is confined in metastable states for long times before making important transitions from one metastable state to another. For gradient systems driven by small noise, the transitions follow the minimum energy path, i.e. the heteroclinic orbit connecting the metastable states. I will talk about the zero-temperature string method for computing the minimum energy paths and the saddle points.   

Rare events in viscoelastic escape dynamics and subdiffusive transport

Anomalously slow relaxation, escape and transport processes become increasingly important in many research domains. This talk is focused on a profound question: Does anomalously slow subdiffusive dynamics imply rare events with a divergent mean time separating such events in multistable potentials? The answer depends on the underlying physical mechanism. It is shown that the subdiffusive dynamics originated due to the medium's viscoelasticity and described by a power law memory kernel within the non-Markovian generalized Langevin equation (GLE) approach does not imply such anomalously rare events [1]. Based on a Markovian multidimensional embedding of the GLE dynamics it is shown that the kinetics of subdiffusive Kramers escape is asymptotically stretched exponential for intermediate barriers. It is characterized by a finite mean escape time, and all the higher moments are also finite. Moreover, it approaches normal exponential kinetics for very high barriers which coexists with anomalously slow subdiffusion and transport in washboard potentials [1]. Rare escape events for such subdiffusive dynamics are not presenting the transport limiting step. \\[4pt] [1] I. Goychuk, Phys. Rev. E 80, 046125 (2009); Adv. Chem. Phys. 150 (2012, in press).   

Non-axisymmetric Deformations of Monovalent Metallic Nanowires: A Stochastic Field Theory Approach

A stochastic Ginzburg-Landau field theory is used to describe the noise-induced transition of monovalent metallic nanowires. Here the transition consists of the nanowire changing from one locally stable radius to another (and thereby changing its conductance as well). The lifetime of a specific wire configuration is obtained from the Kramers rate formula in the limit of of weak noise. We found a ``phase transition'' in the saddle state under general conditions, and have constructed a phase diagram of the activated transition. To study the transition process further, we employed a numerical approach called the string method in order to obtain in detail the complete transition path, crucial to solving the dynamics of wire deformation and transition under noise. We also discuss several interesting applications to lifetime calculations for real nanowires.   

Study of Evaporation Rate of Water in Hydrophobic Confinement using Forward Flux Sampling

Drying of hydrophobic cavities is of interest in understanding biological self assembly, protein stability and opening and closing of ion channels. Liquid-to-vapor transition of water in confinement is associated with large kinetic barriers which preclude its study using conventional simulation techniques. Using forward flux sampling to study the kinetics of the transition between two hydrophobic surfaces, we show that a) the free energy barriers to evaporation scale linearly with the distance between the two surfaces, d; b) the evaporation rates increase as the lateral size of the surfaces, L increases, and c) the transition state to evaporation for sufficiently large L is a cylindrical vapor cavity connecting the two hydrophobic surfaces. Finally, we decouple the effects of confinement geometry and surface chemistry on the evaporation rates.   

Reaching extended length-scales with accelerated dynamics

While temperature-accelerated dynamics (TAD) has been quite successful in extending the time-scales for non-equilibrium simulations of small systems, the computational time increases rapidly with system size. One possible solution to this problem, which we refer to as parTAD$^1$ is to use spatial decomposition combined with our previously developed semi-rigorous synchronous sublattice algorithm$^2$. However, while such an approach leads to significantly better scaling as a function of system-size, it also artificially limits the size of activated events and is not completely rigorous. Here we discuss progress we have made in developing an alternative approach in which localized saddle-point searches are combined with parallel GPU-based molecular dynamics in order to improve the scaling behavior. By using this method, along with the use of an adaptive method to determine the optimal high-temperature$^3$, we have been able to significantly increase the range of time- and length-scales over which accelerated dynamics simulations may be carried out. [1] Y. Shim et al, Phys. Rev. B {\bf 76}, 205439 (2007); ibid, Phys. Rev. Lett. {\bf 101}, 116101 (2008). [2] Y. Shim and J.G. Amar, Phys. Rev. B {\bf 71}, 125432 (2005). [3] Y. Shim and J.G. Amar, J. Chem. Phys. 134, 054127 (2011).   

A computational atomistic study of the relaxation of ion-bombarded \emph{c}-Si on experimental time-scales: an application of the kinetic Activation Relaxation Technique

The kinetic activation relaxation technique (kinetic ART) method, an off-lattice, self-learning kinetic Monte Carlo (KMC) algorithm with on-the-fly event search,\footnote{L. K. B\'{e}land, P. Brommer, F. El-Mellouhi, J.-F. Joly and N. Mousseau, Phys. Rev. E \textbf{84}, 046704 (2011).} is used to study the relaxation of \emph{c}-Si after Si$^-$ bombardment at 3 keV. We describe the evolution of the damaged areas at room-temperature and above for periods of the order of seconds, treating long-range elastic deformations exactly. We assess the stability of the nanoscale structures formed by the damage cascade and the mechanisms that govern post-implantation annealing.   

Dislocation Cross-slip Mechanisms in Aluminum

We have systematically studied dislocation cross-slip in Al at zero temperature by atomistic simulations, focusing on the dependence of the transition paths and energy barriers on dislocation length and position. We find that for a short dislocation segment, the cross-slip follows the uniform Fleischer (FL) mechanism. For a longer dislocation segment, we have identified two different cross-slip mechanisms depending on the initial and final positions of the dislocation. If the initial and final positions are symmetric relative to the intersection of the primary and cross-slip planes, the dislocation cross-slips via the Friedel-Escaig (FE) mechanism. However, when the initial and final positions are asymmetric, the dislocation cross-slips via a combination of the FL and FE mechanisms. The leading partial folds over to the cross-slip plane first, forming a stair-rod dislocation at the intersection with which the trailing partial then merges via the FL mechanism. Afterwards, constrictions appear asymmetrically and move away from each other to complete the cross-slip via the FE mechanism.   

The Effects of Hydrogen on the Potential-Energy Surface of Amorphous Silicon

Hydrogenated amorphous silicon (a-Si:H) is an important semiconducting material used in many applications from solar cells to transistors. In 2010, Houssem et al. [1], using the open-ended saddle-point search method, ART nouveau, studied the characteristics of the potential energy landscape of a-Si as a function of relaxation. Here, we extend this study and follow the impact of hydrogen doping on the same a-Si models as a function of doping level. Hydrogen atoms are first attached to dangling bonds, then are positioned to relieve strained bonds of fivefold coordinated silicon atoms. Once these sites are saturated, further doping is achieved with a Monte-Carlo bond switching method that preserves coordination and reduces stress [2]. Bonded interactions are described with a modified Stillinger-Weber potential and non-bonded Si-H and H-H interactions with an adapted Slater-Buckingham potential. Large series of ART nouveau searches are initiated on each model, resulting in an extended catalogue of events that characterize the evolution of potential energy surface as a function of H-doping. \\[4pt] [1] Houssem et al., Phys Rev. Lett., 105, 045503 (2010)\\[0pt] [2] Mousseau et al., Phys Rev. B, 41, 3702 (1990)   

Order-order Nucleation in Copolymers: A String Method Approach

The mechanism of nucleation in order-order phase transitions of block copolymers is an interesting problem presenting both theoretical and numerical challenges. In this talk we will introduce our recent work of applying the string method to the order-order nucleation in diblock copolymer. We use the self-consistent field model, and search for the saddle point of the free energy functional by solving a variational problem. We will also talk about a study of the epitaxial relation between ordered phases (work by Wang Chu et al.), which verifies one of the assumptions taken by the numerical method beforehand.