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At least 127 records · Page 7Linked to original sources

arXiv2010

Numerical Feynman integrals for density operator dynamics using master equation interpolants: faster convergence and significant reduction of computational cost

The Feynman integral is one of the most accurate methods for calculating density operator dynamics in open quantum systems. However, the number of time steps that can realistically be used is always limited, therefore one often obtains an approximation of the density operator at a sparse grid of points in time. Instead of relying only on \textit{ad hoc} interpolation methods such as splines to estimate the system density operator in between these points, I propose a method that uses physical information to assist with this interpolation. This method is tested on a physically significant system, on which its use allows important qualitative features of the density operator dynamics to be captured with as little as 2 time steps in the Feynman integral. This method allows for an enormous reduction in the amount of memory and CPU time required for approximating density operator dynamics within a desired accuracy. Since this method does not change the way the Feynman integral itself is calculated, the value of the density operator approximation at the points in time used to discretize the Feynamn integral will be the same whether or not this method is used, but its approximation in between these points in time is considerably improved by this method.

physics.comp-ph↗

arXiv2010

Fourier Domain Analysis performances of a RESPER probe - Amplitude and Phase inaccuracies due to the Round-Off noise of FFT processors

This report proposes to discuss the Fourier domain analysis performances of a RESPER probe. A uniform ADC, which is characterized by a sensible phase inaccuracy depending on frequency, is connected to a Fast Fourier Transform (FFT) processor, that is especially affected by a round-off amplitude noise linked to both the FFT register length and samples number. If the register length is equal to 32 bits, then the round-off noise is entirely negligible, else, once bits are reduced to 16, a technique of compensation must occur. In fact, oversampling can be employed within a short time window, reaching a compromise between the needs of limiting the phase inaccuracy due to ADC and not raising too much the number of averaged FFT values sufficient to bound the round-off. Finally, the appendix presents an outline of somewhat lengthy demonstrations needed to calculate the amplitude and especially phase inaccuracies due to the round-off noise of FFT processors.

physics.geo-ph↗

arXiv2011

General-purpose molecular dynamics simulations on GPU-based clusters

We present a GPU implementation of LAMMPS, a widely-used parallel molecular dynamics (MD) software package, and show 5x to 13x single node speedups versus the CPU-only version of LAMMPS. This new CUDA package for LAMMPS also enables multi-GPU simulation on hybrid heterogeneous clusters, using MPI for inter-node communication, CUDA kernels on the GPU for all methods working with particle data, and standard LAMMPS C++ code for CPU execution. Cell and neighbor list approaches are compared for best performance on GPUs, with thread-per-atom and block-per-atom neighbor list variants showing best performance at low and high neighbor counts, respectively. Computational performance results of GPU-enabled LAMMPS are presented for a variety of materials classes (e.g. biomolecules, polymers, metals, semiconductors), along with a speed comparison versus other available GPU-enabled MD software. Finally, we show strong and weak scaling performance on a CPU/GPU cluster using up to 128 dual GPU nodes.

cond-mat.mtrl-sci↗

arXiv2011

The Symmetries of Image Formation by Scattering. I. Theoretical Framework

We perceive the world through images formed by scattering. The ability to interpret scattering data mathematically has opened to our scrutiny the constituents of matter, the building blocks of life, and the remotest corners of the universe. Here, we deduce for the first time the fundamental symmetries underlying image formation. Intriguingly, these are similar to those of the anisotropic "Taub universe"' of general relativity, with eigenfunctions closely related to spinning tops in quantum mechanics. This opens the possibility to apply the powerful arsenal of tools developed in two major branches of physics to new problems. We augment these tools with graph-theoretic means to recover the three-dimensional structure of objects from random snapshots of unknown orientation at four orders of magnitude higher complexity than previously demonstrated. Our theoretical framework offers a potential link to recent observations on face perception in higher primates. In a later paper, we demonstrate the recovery of structure and dynamics from ultralow-signal random sightings of systems with no orientational or timing information.

physics.comp-ph↗

arXiv2012

Modified string method for finding minimum energy path

We present an efficient algorithm for calculating the minimum energy path (MEP) and energy barriers between local minima on a multidimensional potential energy surface (PES). Such paths play a central role in the understanding of transition pathways between metastable states. Our method relies on the original formulation of the string method [Phys. Rev. B ${\bf 66}$, 052301 (2002)], i.e. to evolve a smooth curve along a direction normal to the curve. The algorithm works by performing minimization steps on hyperplanes normal to the curve. Therefore the problem of finding MEP on the PES is remodeled as a set of constrained minimization problems. This provides the flexibility of using minimization algorithms faster than the steepest descent method used in the simplified string method [J. Chem. Phys., ${\bf 126}$(16),164103 (2007)]. At the same time, it provides a more direct analog of the finite temperature string method. The applicability of the algorithm is demonstrated using various examples.

physics.comp-ph↗

arXiv2010

Treecode and fast multipole method for N-body simulation with CUDA

Due to the variety and importance of applications of treecodes and FMM, the combination of algorithmic acceleration with hardware acceleration can have tremendous impact. Alas, programming these algorithms efficiently is no piece of cake. In this contribution, we aim to present GPU kernels for treecode and FMM in, as much as possible, an uncomplicated, accessible way. The interested reader should consult some of the copious literature on the subject for a deeper understanding of the algorithms themselves. Here, we will offer the briefest of summaries. We will focus our attention on achieving a GPU implementation that is efficient in its utilization of the architecture, but without applying the most advanced techniques known in the field (which would complicate the presentation).

physics.comp-ph↗

arXiv2010

Lattice SU(2) on GPU's

We discuss the CUDA approach to the simulation of pure gauge Lattice SU(2). CUDA is a hardware and software architecture developed by NVIDIA for computing on the GPU. We present an analysis and performance comparison between the GPU and CPU with single precision. Analysis with single and multiple GPU's, using CUDA and OPENMP, are also presented. In order to obtain a high performance, the code must be optimized for the GPU architecture, i.e., an implementation that exploits the memory hierarchy of the CUDA programming model. Using GPU texture memory and minimizing the data transfers between CPU and GPU, we achieve a speedup of $200\times$ using 2 NVIDIA 295 GTX cards relative to a serial CPU, which demonstrates that GPU's can serve as an efficient platform for scientific computing. With multi-GPU's we are able, in one day computation, to generate 1 000 000 gauge configurations in a $48^4$ lattice with $β=6.0$ and calculate the mean average plaquette. We present results for the mean average plaquette in several lattice sizes for different $β$. Finally we present results for the mean average Polyakov loop at finite temperature.

hep-lat↗

arXiv2010

An Energy Conserving Parallel Hybrid Plasma Solver

We investigate the performance of a hybrid plasma solver on the test problem of an ion beam. The parallel solver is based on cell centered finite differences in space, and a predictor-corrector leapfrog scheme in time. The implementation is done in the FLASH software framework. It is shown that the solver conserves energy well over time, and that the parallelization is efficient (it exhibits weak scaling).

physics.space-ph↗

arXiv2010

Three-Dimensional Lattice Boltzmann Model for High-Speed Compressible Flows

A highly efficient three-dimensional (3D) Lattice Boltzmann (LB) model for high speed compressible flows is proposed. This model is developed from the original one by Kataoka and Tsutahara[Phys. Rev. E 69, 056702 (2004)]. The convection term is discretized by the Non-oscillatory, containing No free parameters and Dissipative (NND) scheme, which effectively damps oscillations at discontinuities. To be more consistent with the kinetic theory of viscosity and to further improve the numerical stability, an additional dissipation term is introduced. Model parameters are chosen in such a way that the von Neumann stability criterion is satisfied. The new model is validated by well-known benchmarks, (i) Riemann problems, including the problem with Lax shock tube and a newly designed shock tube problem with high Mach number; (ii) reaction of shock wave on droplet or bubble. Good agreements are obtained between LB results and exact ones or previously reported solutions. The model is capable of simulating flows from subsonic to supersonic and capturing jumps resulted from shock waves.

cond-mat.stat-mech↗

arXiv2010

Static and dynamic simulation in the classical two-dimensional anisotropic Heisenberg model

By using a simulated annealing approach, Monte Carlo and molecular-dynamics techniques we have studied static and dynamic behavior of the classical two-dimensional anisotropic Heisenberg model. We have obtained numerically that the vortex developed in such a model exhibit two different behaviors depending if the value of the anisotropy $λ$ lies below or above a critical value $λ_c$ . The in-plane and out-of-plane correlation functions ($S^{xx}$ and $S^{zz}$) were obtained numerically for $λ< λ_c$ and $λ> λ_c$ . We found that the out-of-plane dynamical correlation function exhibits a central peak for $λ> λ_c$ but not for $λ< λ_c$ at temperatures above $T_{BKT}$ .

cond-mat.stat-mech↗

arXiv2010

What Determines the Yield Stress in Amorphous Solids?

A crucially important material parameter for all amorphous solids is the yield stress, which is the value of the stress for which the material yields to plastic flow when it is strained quasi-statically at zero temperature. It is difficult in laboratory experiments to determine what parameters of the inter-particle potential effect the value of the yield stress. Here we use the versatility of numerical simulations to study the dependence of the yield stress on the parameters of the inter-particle potential. We find a very simple dependence on the fundamental scales which characterize the repulsive and attractive parts of the potential respectively, and offer a scaling theory that collapses the data for widely different potentials and in different space dimensions.

physics.comp-ph↗

arXiv2010

Staggered fermions simulations on GPUs

We present our implementation of the RHMC algorithm for staggered fermions on Graphics Processing Units using the NVIDIA CUDA programming language. While previous studies exclusively deal with the Dirac matrix inversion problem, our code performs the complete MD trajectory on the GPU. After pointing out the main bottlenecks and how to circumvent them, we discuss the performance of our code.

hep-lat↗

arXiv2011

Thin-shell theory based analysis of radially pressurized multiwall carbon nanotubes

Elastic radial deformation of multiwall carbon nanotubes (MWNTs) under hydrostatic pressure is investigated within the continuum elastic approximation. The thin-shell theory, with accurate elastic constants and interwall couplings, allows us to estimate the critical pressure $p_c$ above which the original circular cross-section transforms into radially corrugated ones. Emphasis is placed on the rigorous formulation of the van der Waals interaction between adjacent walls, which we analyze using two different approaches. Possible consequences of the radial corrugation in the physical properties of pressurized MWNTs are also discussed.

cond-mat.mes-hall↗

arXiv2010

Free energy computations by minimization of Kullback-Leibler divergence: an efficient adaptive biasing potential method for sparse representations

The present paper proposes an adaptive biasing potential for the computation of free energy landscapes. It is motivated by statistical learning arguments and unifies the tasks of biasing the molecular dynamics to escape free energy wells and estimating the free energy function, under the same objective. It offers rigorous convergence diagnostics even though history dependent, non-Markovian dynamics are employed. It makes use of a greedy optimization scheme in order to obtain sparse representations of the free energy function which can be particularly useful in multidimensional cases. It employs embarrassingly parallelizable sampling schemes that are based on adaptive Sequential Monte Carlo and can be readily coupled with legacy molecular dynamics simulators. The sequential nature of the learning and sampling scheme enables the efficient calculation of free energy functions parametrized by the temperature. The characteristics and capabilities of the proposed method are demonstrated in three numerical examples.

math-ph↗

arXiv2010

Improved automated lattice perturbation theory in background field gauge

We present an algorithm to automatically derive Feynman rules for lattice perturbation theory in background field gauge. Vertices with an arbitrary number of both background and quantum legs can be derived automatically from both gluonic and fermionic actions. The algorithm is a generalisation of our earlier algorithm based on prior work by Lüscher and Weisz. We also present techniques allowing for the parallelisation of the evaluation of the often rather complex lattice Feynman rules that should allow for efficient implementation on GPUs, but also give a significant speed-up when calculating the derivatives of Feynman diagrams with respect to external momenta.

hep-lat↗

arXiv2011

Simulation of Equilibrated States via Molecular Monte Carlo Method of Systems Connected to 3 Reservoirs

Metastable structures in macromolecular and colloidal systems are non-equilibrium states that often have long lifetimes and cause difficulties in simulating equilibrium. In order to escape from the long-lived metastable states, we propose a newly devised method, molecular Monte-Carlo simulation of systems connected to 3 reservoirs: chemical potential $μ$, pressure $P$, and temperature $T$. One of these reservoirs is adjusted for the thermodynamic equilibrium condition according to Gibbs-Duhem equation, so that this adjusted 3rd reservoir does not thermodynamically affect phases and states. Additional degrees of freedom, i.e. system volume $V$ and the number of particles $N$, reduce kinetic barriers of non-equilibrium states and facilitate quick equilibration. We show globally-anisotropic defect-free ordered structures, e.g. string-like colloidal assembly, are obtained via our method.

cond-mat.soft↗

arXiv2011

A deterministic numerical model for the nonlinear Boltzmann equation

We propose a new deterministic numerical scheme, based on the discontinuous Galerkin method, for solving the Boltzamnn equation for rarefied gases. The new scheme guarantees the conservation of the mass, momentum and energy. We avoid any stochastic procedures in the treatment of the collision operator of the Boltzmamn equation.

physics.comp-ph↗

arXiv2012

Recombination Lines of CII in the Spectra of Planetary Nebulae

The current report presents the work to investigate the recombination lines of CII in the spectra of planetary nebulae. Two CIII targets were prepared and used to generate theoretical data required in the investigation of recombination lines that arise from collisions between electrons and ions in thin plasma found in planetary nebulae and other astrophysical objects. One of these targets contains 9 atomic terms while the other contains 26 terms. For each one of these targets, theoretical data concerning bound and autoionizing states were generated in the intermediate coupling approximation by R-matrix and Autostructure codes and compared to experimental data. The comparison revealed very good agreement. These theoretical data were then used to generate emissivity data and compare it to the carbon recombination lines found in the observational line list of Zhang et al [2005] on the planetary nebula NGC 7027. The main tool used in this analysis is the `Emissivity' code which is a program developed by the author [2010] in the course of this investigation to calculate the emissivity of transition lines from resonances and subsequent cascade decay. The results of the analysis from both targets using a least-squares optimization technique indicate a temperature of 10200-10500K of the line-emitting region.

physics.atom-ph↗