Bulletin of the American Physical Society
2005 APS March Meeting
Monday–Friday, March 21–25, 2005; Los Angeles, CA
Session A32: Focus Session: Novel Computational Algorithms: From Materials to the Universe I |
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Sponsoring Units: DCOMP Chair: Mark Novotny, Mississippi State Room: LACC 507 |
Monday, March 21, 2005 8:00AM - 8:36AM |
A32.00001: The Geometric Cluster Algorithm: Rejection-Free Monte Carlo Simulation of Complex Fluids Invited Speaker: The study of complex fluids is an area of intense research activity, in which exciting and counter-intuitive behavior continue to be uncovered. Ironically, one of the very factors responsible for such interesting properties, namely the presence of multiple relevant time and length scales, often greatly complicates accurate theoretical calculations and computer simulations that could explain the observations. We have recently developed a new Monte Carlo simulation method\footnote{J. Liu and E. Luijten, Phys.\ Rev.\ Lett.\textbf{92}, 035504 (2004); see also Physics Today, March 2004, pp.\ 25--27.} that overcomes this problem for several classes of complex fluids. Our approach can accelerate simulations by orders of magnitude by introducing nonlocal, collective moves of the constituents. Strikingly, these cluster Monte Carlo moves are proposed in such a manner that the algorithm is rejection-free. The identification of the clusters is based upon geometric symmetries and can be considered as the off-latice generalization of the widely-used Swendsen--Wang and Wolff algorithms for lattice spin models. While phrased originally for complex fluids that are governed by the Boltzmann distribution, the geometric cluster algorithm can be used to efficiently sample configurations from an arbitrary underlying distribution function and may thus be applied in a variety of other areas. In addition, I will briefly discuss various extensions of the original algorithm, including methods to influence the size of the clusters that are generated and ways to introduce density fluctuations. [Preview Abstract] |
Monday, March 21, 2005 8:36AM - 8:48AM |
A32.00002: Efficient Cluster Algorithm for Resistively Shunted Josephson Junctions Philipp Werner, Matthias Troyer We present a cluster algorithm for resistively shunted Josephson junctions which dramatically improves sampling efficiency. The algorithm combines local updates in Fourier space with rejection-free cluster updates which exploit the symmetries of the Josephson coupling energy. As an application, we consider the superconductor-to-insulator transition in a single junction and the phase diagram of a recently proposed two-junction model with charge relaxation. [Preview Abstract] |
Monday, March 21, 2005 8:48AM - 9:00AM |
A32.00003: Schrodinger eigenstates for surface-confinement problems Morten Willatzen, Jens Gravesen, Lok C. Lew Yan Voon The theory of a quantum-mechanical particle confined to a surface is described using differential geometry arguments including the simplification of the three-dimensional Schr\"{o}dinger problem into three ordinary differential equations in curved coordinates for the case of an arbitrary surface of revolution. These equations are solved - in terms of eigenvalues and eigenstates - either completely analytically or by use of a simple one-dimensional finite-difference scheme for the cases of a cylinder, a cone, an elliptic torus, a sinusoidal-shaped surface of revolution, and a catenoid. A comparison with an exact three-dimensional treatment of the hollow cylinder problem shows that the surface-confinement approximation (corresponding to assuming zero thickness of the particle domain perpendicular to the surface) is excellent in cases where the (hollow) cylinder thickness is less than approximately 10{\%} of the cylinder radius, hence justifying the rationale in employing a similar analysis for the other (above-mentioned) more complicated surface-confinement problems. Symmetry properties of the various eigenstates are finally discussed and compared. [Preview Abstract] |
Monday, March 21, 2005 9:00AM - 9:12AM |
A32.00004: Global optimization in surface structure determination by electron diffraction using generalized pattern search methods Zhengji Zhao, Juan Meza, Michel Van Hove Low energy electron diffraction (LEED) is the most commonly used method for detailed surface structure determination. This method can be formulated as an inverse problem, by attempting to fit dynamically calculated LEED intensities to experimental data. As with any such method, it faces a challenging global optimization. We discuss the use of generalized pattern search (GPS) methods for this global optimization, using the complex Ni(001)-(5x5)-Li structure as an example. We present numerical results for one particular GPS method (NOMAD) and compare its performance to previously used genetic algorithm methods. [Preview Abstract] |
Monday, March 21, 2005 9:12AM - 9:24AM |
A32.00005: Reciprocal space approach to finite size error in many-body simulations Simone Chiesa, David Ceperley, Richard Martin, Markus Holzmann A scheme for the correction of the finite size error in the potential energy occuring in the quantum Monte Carlo simulation of the bulk materials is presented. It is based on the fact that the potential energy can be written as a sum over the static structure factor, S(k), and on the assumption that S(k) does not depend on the simulation cell size. The error in the potential energy is then an integration error and corrected by an improved integration scheme. This also leads to an understanding of the scaling of the error with system size. Applications to the electron gas and to a novel nitrogen structure are presented. [Preview Abstract] |
Monday, March 21, 2005 9:24AM - 9:36AM |
A32.00006: Quantum spin glass and Sourlas codes Jun-ichi Inoue Quantum version of Sourlas error-correcting codes are investigated from statistical mechanical point of view. Our problems are equivalent to those of quantum Ising spin glasses with $p$-body interactions. According to Ruj$\acute{\rm a}$n, we assume that information of the correct bits should be obtained from the equilibrium states of the Hamiltonian and the performance of the decoding results is estimated by the overlap between the original information bit and the sign of the local magnetization. We introduce the transverse field as a quantum fluctuation into the Hamiltonian and adjust this to the optimal value so that the overlap takes its maximum. At low temperature and small transverse field, we find analytically that the retrieval quality is dramatically improved. This analytical results are supported by quantum Monte Carlo simulations. [Preview Abstract] |
Monday, March 21, 2005 9:36AM - 9:48AM |
A32.00007: Comparison of energy minimization and variance minimization methods for optimizing variational parameters in many body wave functions C.J. Umrigar, Claudia Filippi The variance minimization method has become the standard method for optimizing many body wave functions for quantum Monte Carlo because it is far more efficient that performing a straightforward energy minimization. We have modified two recent energy minimization methods to make energy minimization highly efficient. First, we have modified the straightforward Newton method used by Lin, Zhang and Rappe, \emph{J. Chem. Phys.}. \textbf{112}, 2659 (2000) to reduce the statistical fluctuations by more than two orders of magnitude. Tests on a flexible Jastrow that includes 3-body electron-electron-nucleus correlation terms show that it is very efficient. Second, we have extended the generalized eigenvalue method of Nightingale and Melik-Alaverdian \emph{Phys. Rev. Lett}. \textbf{87}, 043401 (2001), for linear parameters, to nonlinear parameters, and are currently testing this method. [Preview Abstract] |
Monday, March 21, 2005 9:48AM - 10:00AM |
A32.00008: Monte Carlo Summation Technique Wenduo Zhou, R. Robinson, B. Sch\"uttler The extended Hubbard model is a frequently used model to describe strongly correlated electron systems. The Green's function of this model can be calculated by perturbation theory associated with Feynman diagrams. In order to fully understand this model, larger lattices and perturbation expansions to higher order are essential. However, the current computing power limits both the sizes of physical systems and the maximum orders of perturbation expansions by brute force summation. In order to overcome this obstacle, we have developed a novel technique to do the summation by a Monte Carlo algorithm. We have applied this technique to the 2-D extended Hubbard Model in momentum space, and computed its Green's function $G(k)$ and self-energy $\Sigma(k)$ by a \emph{self-consistent} algorithm, combined with the corresponding \emph{irreducible} Feynman diagrams. Results for the (nearly) half-filled band case close to the Mott-Hubbard transition will be discussed. \\ \\ $^*$This research was supported by NSF Grant DMR-0081789 [Preview Abstract] |
Monday, March 21, 2005 10:00AM - 10:12AM |
A32.00009: Simple geometry optimization with Variational Quantum Monte Carlo method Dan Nissenbaum, B. Barbiellini, A. Bansil Stochastic optimization methods may be combined with Quantum Monte Carlo (QMC) integration to obtain a computational scheme for treating many body wavefunctions suitable for addressing modern problems in nanoscale physics. In this connection, we are investigating the range of applicability of the Stochastic Gradient Approximation (SGA) technique [1]. The SGA possesses the important advantage that the updating of the electronic variational parameters and the nuclear coordinates can be carried out simultaneously and without an explicit determination of the total energy for each geometry. We present illustrative results using simple variational functions for describing the hydrogen molecule, the lithium dimer, and the neutral and charged Li$_4$ clusters. We computed highly accurate potential energy surfaces on a fine grid in order to test the efficacy of the SGA in locating the energy minima in the parameter space. Work supported in part by the USDOE.\\ $\mbox{[1]}$ A. Harju, B. Barbiellini, S. Siljam\"aki, R.M. Nieminen, and G. Ortiz, Phys. Rev. Lett. {\bf 79}, 1173 (1997). [Preview Abstract] |
Monday, March 21, 2005 10:12AM - 10:24AM |
A32.00010: Accuracy and applicability of the finite temperature quasicontinuum method Laurent Dupuy, Ellad B. Tadmor, R. Miller, Rob Phillips The quasicontinuum method is a mixed continuum and atomistic approach for simulating the mechanical response of polycrystalline materials. It allows large-scale atomistic calculations to be performed on moderately small computers. This method was rencently extended to study the behavior of defects at finite temperature. In this talk, we focus on the accuracy and applicability of this method. Possible shortcomings such as mesh-dependence and ghost-forces are discussed. [Preview Abstract] |
Monday, March 21, 2005 10:24AM - 10:36AM |
A32.00011: Electronic structure code based on existing parallel AMR infrastructure Jean-Luc Fattebert, Rich Hornung, Andy Wissink, Francois Gygi Following the first developments in real-space methods for electronic structure calculations, various efforts have been carried out in the past ten years to improve efficiency using local adaptive mesh refinement (AMR), in particular for finite physical systems. So far, the complexity of AMR codes has limited these efforts to serial calculations of relatively small problems. One way of overcoming this barrier is to build a code based on an existing parallel AMR infrastructure. We will report our progress in developing a parallel Finite Element electronic structure code based on the C++ SAMRAI (Structured Adaptive Mesh Refinement Application Infrastructure) library developed at Lawrence Livermore National Laboratory (www.llnl.gov/casc/SAMRAI). [Preview Abstract] |
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A32.00012: Fine-Lattice Discretization for Fluid Simulations: Convergence of Critical Parameters. Young C. Kim, Michael E. Fisher In simulating continuum fluids with long-range interactions, such as plasmas and electrolytes, that undergo phase separation and criticality, it is computationally advantageous to confine the particles to the sites of a lattice of fine spacing, $a_{0} $, relative to their size, $a$.$^{1,2}$ But, how does the discretization parameter, $\zeta\equiv a/a_{0}$ (typically,$^ {1} \geq 5$) affect the values of the critical temperature and density, etc.? A heuristic argument,$^{2}$ essentially exact in $d=1$ and $2$ dimensions, shows that for models with hard-core potentials, both $T_{c}(\zeta)$ and $\rho_{c}(\zeta)$ converge to their continuum limits as $1/\zeta^{(d+1)/2}$ for $d\leq 3$ when $\zeta\rightarrow\infty$. However, the behavior of the error for $d\geq 2$ (related to a classical problem in number theory) is highly erratic. Exact results for $d=1$ illuminate the issues and reveal that optimal choices for $\zeta$ can improve the rate of convergence by factors of $1/\zeta$.$^{2}$ For $d\geq 2$, the convergence of the {\em second virial coefficients} to their continuum values exhibit similar erratic behavior which transfers to $T_{c}$ and $\rho_{c}$. This can be used in to enhance extrapolation to $\zeta\rightarrow\infty$. Data for the hard-core or {\em restricted primitive model} electrolyte have thereby been used to establish that (contrary to recent suggestions) the criticality is of Ising-type --- as against classical, XY, etc.\\ 1. Y.\ C.\ Kim and M.\ E.\ Fisher, Phys.\ Rev.\ Lett.\ {\bf 92}, 185703 (2004).\\ 2. S.\ Moghaddam, Y.\ C.\ Kim and M.\ E.\ Fisher, J.\ Phys.\ Chem.\ B (2005) $~~~~$[in press]. [Preview Abstract] |
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A32.00013: Thermodynamically accurate particle-based mesodynamics Alejandro Strachan, Brad Holian Particle-based mesoscopic approaches, where groups of atoms are represented by a single \textit{mesoparticle}, are widely used to achieve length- and time-scales beyond what is possible with atomistic modeling. I will present \textbf{a new mesodynamical approach that describes the energy exchange between mesoparticles and their internal degrees of freedom} in a thermodynamically accurate way. In our approach, energy exchange is done through particle coordinates, rather than momenta, resulting in Galilean invariant equations of motion; the total linear momentum as well as total energy (including the internal energy of the mesoparticles) are conserved and no coupling occurs when a mesoparticle is in free flight.The parameters entering our mesodynamics are easily obtained from first-principles and its results are in excellent agreement with all-atom simulations. Furthermore, our approach enables for a quantum mechanical description of the thermal properties of the implicit degrees of freedom (all-atom MD is always classical) and is generally applicable to many problems of materials science, chemistry, and biology. [Preview Abstract] |
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