POSTERS ABSTRACTS. Day 2: Tuesday, June 28, Fractional-step kinetic Monte Carlo algorithms and hierarchical parallelization

Size: px

Start display at page:

Download "POSTERS ABSTRACTS. Day 2: Tuesday, June 28, Fractional-step kinetic Monte Carlo algorithms and hierarchical parallelization"

Charlene Hunter
5 years ago
Views:

1 COARSE-GRAINING OF MANY BODY SYSTEMS: ANALYSIS, COMPUTATIONS AND APPLICATIONS JUNE 27-JULY 1, 2011 HERAKLION, CRETE POSTERS ABSTRACTS Day 2: Tuesday, June 28, 2011 Fractional-step kinetic Monte Carlo algorithms and hierarchical parallelization Georgios Arampatzis University of Crete Department of Applied Mathematics, Knossos Ave., GR Heraklion, Greece Abstract: We present a new framework for constructing parallel algorithms for lattice Kinetic Monte Carlo (KMC) simulations. These algorithms have the capacity to simulate a wide range of spatio-temporal scales of spatially distributed, non-equilibrium physiochemical processes with complex chemistry and transport micro-mechanisms, while they can be tailored to specific hierarchical parallel architectures such as clusters of GPUs. The proposed parallel algorithms are controlled approximations of kinetic Monte Carlo algorithms, departing from the predominant paradigm of creating parallel KMC algorithms with exactly the same master equation as the serial one. Instead, our methodology relies on first developing a spatio-temporal decomposition of the Markov operator underlying the KMC algorithm into a hierarchy of operators corresponding to the processors structure in the parallel architecture. Based on this operator decomposition, we formulate Fractional Step Approximation schemes by employing the Trotter Theorem; these schemes, (a) determine the communication schedule between processors, and (b) are run independently on each processor through a serial KMC simulation, on each fractional step time-window. This flexibility and hierarchical structure are key advantages for tailoring our framework to particular parallel architectures with complex memory and processor hierarchies, e.g. clusters of GPUs. Furthermore, the numerical and statistical consistency of the proposed algorithms is rigorously justified, showing the convergence of our approximating schemes to the original serial KMC algorithm. In this presentation we also include detailed benchmarking using available exact solutions, for example, in Ising-type systems and we demonstrate the capabilities of the method to simulate complex spatially distributed reactions at very large scales on GPUs. 1

2 Conditional reversible work method for molecular coarse graining applications Emiliano Brini Center of Smart Interfaces - TU Darmstadt Petersenstrasse 32, Darmstadt, Germany brini@csi.tu-darmstadt.de Abstract: Systematically coarse-grained models for complex fluids usually lack chemical and thermodynamic transferability. Efforts to improve transferability require the development of effective potentials with unequivocal physical significance. The Conditional Reversible Work (CRW) method uses an interaction free energy to describe the pairwise non-bonded interaction between coarse-grained beads, therefore the CRW-method provides a unique and clear thermodynamic meaning of the potentials. The method used to obtain these potentials is straightforward to implement, can be readily extended to compute hydration contributions in implicit-solvent potentials, and is easy to automize. As a first illustration of the method, we present CRW potentials for 3-site models of hexane and toluene. Multilevel coarse graining Monte Carlo methods for stochastic lattice systems Evangelia Kalligiannaki University of Delaware 432 Ewing Hall Department of Mathematical Sciences University of Delaware Newark, Delaware ekalligi@math.udel.edu Abstract: We propose a hierarchy of Monte Carlo methods for sampling dynamic and equilibrium properties of stochastic lattice systems with complex interactions. The method is composed by two properly coupled Monte Carlo steps efficiently coupling coarse and fine state spaces, designed in virtue of coarse graining techniques for lattice systems. Significant reduction of the computational cost of traditional Markov Chain Monte Carlo and kinetic Monte Carlo methods for systems with competing interactions is achieved, while we are capable of providing microscopic information. Adaptive weak approximation of reaction processes by a tau-leap method Jesper Karlsson King Abdullah University of Science and Technology (KAUST) 4700 KAUST, Thuwal , Kingdom of Saudi Arabia jesper.karlsson@kaust.edu.sa Abstract: We present novel weak error estimates for the tau-leap method. These error estimates are used to control the global weak error by an adaptive time-stepping algorithm. Adaptive methods are relevant for efficient numerical simulation and here their impact is in applied fields such as computational chemistry and mathematical biology when modeling complex reactions. To our knowledge no such adaptive method for global error control has previously been developed for the tau-leap method. Finally, we use numerical experiments to show practical computational gains from using the adaptive tau-leap method. 2

3 Blended quasicontinuum energies Brian Van Koten* and Mitchell Luskin University of Minnesota-Twin Cities Vincent Hall, 206 Church St SE, Minneapolis, Minnesota, 55455, USA Abstract: The original quasicontinuum energy (QCE) [2] couples an atomistic model to a finite element continuum model based on the Cauchy-Born strain energy density. The Cauchy-Born strain energy density reproduces the atomistic energy density for a uniformly deformed lattice. The QCE energy also reproduces the atomistic energy density for a uniformly deformed lattice simply by modifying the volume of the tetrahedra within the cut-off radius of the boundary of the atomistic region [2]. It is desirable that a quasicontinuum energy be patch test consistent, i.e., that it reproduce the zero net forces at each atom for a uniformly deformed lattice. The fully atomistic and Cauchy-Born energies are patch test consistent by symmetry, but the symmetry is broken in the QCE atomistic-to-continuum interface and QCE does not in fact satisfy the patch test. Despite several partial solutions, the development of patch test consistent quasicontinuum energies for multi-dimensional crystalline solids modeled by many-body potentials remains a challenge. We propose that by blending the atomistic and continuum models of QCE in an interfacial region with thickness of a small number k of blended atoms, a quasicontinuum energy (BQCE) can be developed that significantly improves the accuracy of QCE. The BQCE energy can be implemented for any decomposition of three-dimensional space into tetrahedra, and a code for the BQCE energy can be obtained simply by suppressing the coarsening in the blending interface of any QCE code. In [3], we give an error analysis of the blended quasicontinuum energy (BQCE) for a periodic one-dimensional chain of atoms with next-nearest neighbor interactions. Our analysis includes the optimization of the blending function for an improved convergence rate.we show that the l 2 strain error for the non-blended QCE energy (QCE), which has low order O(ε 1/2 ) where ε is the atomistic length scale, can be reduced by a factor of k 3/2 for an optimized blending function where k is the number of atoms in the blending region. The QCE energy has been further shown to suffer from a O(1) error in the critical strain at which the lattice loses stability [1]. We prove that the error in the critical strain of BQCE can be reduced by a factor of k 2 for an optimized blending function, thus demonstrating that the BQCE energy for an optimized blending function can give an accurate approximation of the deformation near lattice instabilities such as crack growth. REFERENCES [1] M. Dobson, M. Luskin, and C. Ortner. Accuracy of quasicontinuum approximations near instabilities. Journal of the Mechanics and Physics of Solids, to appear. arxiv: v2. [2] M. Ortiz, R. Phillips, and E. B. Tadmor. Quasicontinuum analysis of defects in solids. Philosophical Magazine A, 73(6): , [3] B. Van Koten and M. Luskin. Analysis of energy-based blended quasicontinuum approximations, 2011.arXiv: v3 [math.na]. Brian Van Koten, Presenting Author*, School of Mathematics, University of Minnesota, 206 Church Street SE, Minneapolis, MN 55455, U.S.A. address: vank0068@umn.edu Mitchell Luskin, School of Mathematics, University of Minnesota, 206 Church Street SE, Minneapolis, MN 55455, U.S.A. address: luskin@umn.edu 3

4 Minimization problem of Allen Cahn action Yuko Nagase Archimedes Center for Modeling, Analysis & Computation (ACMAC) Knossos Avenue, 71409, Heraklion, Crete, Greece nagase/ Abstract: In this poster we present the minimization problem of the Allen Cahn action functional with an equal double well potential. For the stochastic Allen-Cahn equation switching from one stable state to the other rarely occurs. The probability of switching is determined by the minimum of the action functional. We give an explicit description of the minimum and its optimal path in one dimension. A quantitative analysis of stochastic isothermal molecular dynamics methods Emad Noorizadeh NAIS University of Edinburgh 5605, James Clerk Maxwell Building, King s Building, University of Edinburgh, EH9 3JZ, UK e.noorizadeh@ed.ac.uk Abstract: We present a mathematical framework for a quantitative analysis of stochastic thermostat used in molecular dynamics. This is done by defining a term /efficiency/ which relate the rate of equilibration of average kinetic energy to the perturbation introduced by random noises in calculation of time dependent properties such as autocorrelation functions. We study three different thermostats, namely Langevin, a stochastic Nose-Hoover due to Samoletov /et al /(J.Stat.Phys *128*, , 2007) and a generalization of the stochastic scaling method suggested by Bussi /et al/ (J.Chem.Phys *126*, , 2007). In particular, we observe that the equilibration of stochastic Nose-Hoover is best described by a nonlinear system whereas the equilibration of Langevin and the stochastic scaling are described by exponential decay. We find that for stochastic Nose-Hoover and stochastic scaling, the estimated rate of build-up of error in velocity autocorrelation function, is smaller then the equilibration rate by a factor /n/, whereas for standard Langevin the two rates are approximately equal. This suggests stochastic Nose-Hoover and stochastic scaling are more efficient by a factor /n/ for estimating things like autocorrelation functions. Numerical experiments are presented which confirm the theoretical results. This is a joint work with Ben Leimkuhler (University of Edinburgh) and Oliver Penrose (Heriot-Watt University). Controlled-error approximations of surface diffusion of interacting particles with applications to pattern formation Yannis Pantazis University of Massachusetts pantazis@math.umass.edu Abstract: Microscopic processes on surfaces such as adsorption, desorption, diffusion and reaction of interacting particles can be simulated using kinetic Monte Carlo (kmc) 4

5 algorithms. Even though kmc methods are accurate, they are computationally expensive for large-scale systems. Hence approximation algorithms are necessary for simulating physically observable properties. One such approximation method is coarse-graining of the lattice-domain which leads to coarse-grained Monte Carlo (GCMC) methods. Recently, stochastic Langevin approximations of the coarse-grained model were developed for surface diffusion which resulted to further acceleration of the simulations. Another well-known approach of simulating surface processes is to the take the limit of infinite number of particles and obtain mesoscopic equations, either deterministic or stochastic. In this paper, we are interested on simulating surface diffusion for the application of pattern formation using stochastic models whose approximation error is computable not only asymptotically but also for finite-size domains. This can be achieved by developing stochastic models using ideas both from the coarse-grained formulation and the mesoscopic equations. This results not only the same accelerations as in the Langevin approximation but also in the estimation of the approximation error. For the proposed models, detailed balance condition is satisfied thus the long-time errors are controlled by the invariant measure as well by the large deviations while the finite-time errors are controlled by weak-error estimates. Numerical simulation results validate the theoretical findings. Cluster expansion in the canonical ensemble Elena Pulvirenti Universita Roma Tre Via San Leonardo Murialdo 1, Roma Abstract: We consider a system of particles confined in a box interacting via a tempered and stable pair potential. We prove the validity of the cluster expansion for the canonical partition function in the high temperature - low density regime. The convergence is uniform in the volume and in the thermodynamic limit it reproduces Mayer s virial expansion providing an alternative and more direct derivation which avoids the deep combinatorial issues present in the original proof. Hierarchical modeling of protein assemblies at multiple length and time scales Anastassia N. Rissanou 1,2 and Vagelis Harmandaris 1,3 1 Department of Applied Mathematics, University of Crete, GR 71409, Heraklion, Crete, Greece. 2 Institute of Electronic Structure and Laser, Foundation for Research and Technology Hellas, GR Heraklion, Greece. 3 Institute of Applied and Computational Mathematics, Foundation for Research and Technology Hellas, GR Heraklion, Greece. rissanou@tem.uoc.gr Abstract: Numerous supramolecular protein assemblies had been demonstrated to have either physiological or pathological activities. The most significant case of disease associated self-organized structures is that of amyloid fibrils, whose formation is the hallmark of major human disorders. In addition, bioconjugated hybrids belong to a class of materials which are very promising because of their biomedical and technological applications. From the scientific point of view it is necessary to gain a better understanding of the relation between structure and macroscopic properties of such systems. In this aspect, computer simulations 5

6 provide an important opportunity to shed light on the possible supramolecular organization patterns, their stability and the governing interplay of interactions as well as their relation with the molecular structure. Simulation methodologies have the advantage that they can be aimed at either molecular or micro-structural length scales. However to model realistic systems hierarchical modelling schemes that involve more than one simulation levels are critical. Here we propose a novel multi-scale simulation approach that combines atomistic and coarse graining (CG) simulations. Through a rigorous derivation of the effective interaction in the CG description, we are capable to quantitatively predict of the structure and the dynamics of complex biological systems at realistic length and time scales. Currently, the multi-scale approach will be applied on: (a) the diphenylalanine peptide (b) the octapeptide NSGAITIG and (c) their hybrids with polymer molecules (PEO and PNIPAM). In addition we will directly compare the simulation predictions to new experimental data produced in the framework of the present work. Error estimates for molecular dynamics Mattias Sandberg KTH Royal Institute of Technology Computer Science and Communication, Stockholm msandb@kth.se Abstract: Error estimates for Symplectic Euler molecular dynamics approximations compared to quantum mechanics. Self assembly of short peptide sequences from a natural fibrous protein, the adenovirus fiber shaft Phanourios Tamamis University of Cyprus Department of Physics, University of Cyprus, PO20537, CY1678,Cyprus tamamis@ucy.ac.cy Abstract: P. Tamamis, Z. Skotti, D. Terzaki, L. Mastroyannis, A. Mitraki, G.Archontis We investigate by multi-microsecond replica-exchange simulations the self-assembly of an amyloidogenic undecapeptide sequence from the adenovirus fiber shaft, with potential Cabinding properties. We employ the CHARMM22 force-field for the peptide interactions and a generalized Born implicit model for solvent effects. We determine the thermodynamically dominant peptide conformations, construct a plausible structural model of the amyloid-fiber and validate it by explicit-solvent simulations. 6

Advanced sampling. fluids of strongly orientation-dependent interactions (e.g., dipoles, hydrogen bonds)

Advanced sampling. fluids of strongly orientation-dependent interactions (e.g., dipoles, hydrogen bonds) Advanced sampling ChE210D Today's lecture: methods for facilitating equilibration and sampling in complex, frustrated, or slow-evolving systems Difficult-to-simulate systems Practically speaking, one is