1,371 research outputs found
Reformulation of the Stochastic Potential Switching Algorithm and a Generalized Fourtuin-Kasteleyn Representation
A new formulation of the stochastic potential switching algorithm is
presented. This reformulation naturally leads us to a generalized
Fourtuin-Kasteleyn representation of the partition function Z. A formula for
internal energy E and that of heat capacity C are derived from derivatives of
the partition function. We also derive a formula for the exchange probability
in the replica exchange Monte Carlo method. By combining the formulae with the
Stochastic Cutoff method, we can greatly reduce the computational time to
perform internal energy and heat capacity measurements and the replica exchange
Monte Carlo method in long-range interacting systems. Numerical simulations in
three dimensional magnetic dipolar systems show the validity and efficiency of
the method.Comment: 11 pages, 6 figures, to appear in PR
Persistence in systems with algebraic interaction
Persistence in coarsening 1D spin systems with a power law interaction
is considered. Numerical studies indicate that for sufficiently
large values of the interaction exponent ( in our
simulations), persistence decays as an algebraic function of the length scale
, . The Persistence exponent is found to be
independent on the force exponent and close to its value for the
extremal () model, . For smaller
values of the force exponent (), finite size effects prevent the
system from reaching the asymptotic regime. Scaling arguments suggest that in
order to avoid significant boundary effects for small , the system size
should grow as .Comment: 4 pages 4 figure
Fast multipole networks
Two prerequisites for robotic multiagent systems are mobility and
communication. Fast multipole networks (FMNs) enable both ends within a unified
framework. FMNs can be organized very efficiently in a distributed way from
local information and are ideally suited for motion planning using artificial
potentials. We compare FMNs to conventional communication topologies, and find
that FMNs offer competitive communication performance (including higher network
efficiency per edge at marginal energy cost) in addition to advantages for
mobility
How can a 22-pole ion trap exhibit 10 local minima in the effective potential?
The column density distribution of trapped OH ions in a 22-pole ion trap
is measured for different trap parameters. The density is obtained from
position-dependent photodetachment rate measurements. Overall, agreement is
found with the effective potential of an ideal 22-pole. However, in addition we
observe 10 distinct minima in the trapping potential, which indicate a breaking
of the 22-fold symmetry. Numerical simulations show that a displacement of a
subset of the radiofrequency electrodes can serve as an explanation for this
symmetry breaking
High Performance Algorithms for Counting Collisions and Pairwise Interactions
The problem of counting collisions or interactions is common in areas as
computer graphics and scientific simulations. Since it is a major bottleneck in
applications of these areas, a lot of research has been carried out on such
subject, mainly focused on techniques that allow calculations to be performed
within pruned sets of objects. This paper focuses on how interaction
calculation (such as collisions) within these sets can be done more efficiently
than existing approaches. Two algorithms are proposed: a sequential algorithm
that has linear complexity at the cost of high memory usage; and a parallel
algorithm, mathematically proved to be correct, that manages to use GPU
resources more efficiently than existing approaches. The proposed and existing
algorithms were implemented, and experiments show a speedup of 21.7 for the
sequential algorithm (on small problem size), and 1.12 for the parallel
proposal (large problem size). By improving interaction calculation, this work
contributes to research areas that promote interconnection in the modern world,
such as computer graphics and robotics.Comment: Accepted in ICCS 2019 and published in Springer's LNCS series.
Supplementary content at https://mjsaldanha.com/articles/1-hpc-ssp
Eliminating artificial boundary conditions in time-dependent density functional theory using Fourier contour deformation
We present an efficient method for propagating the time-dependent Kohn-Sham equations in free space, based on the recently introduced Fourier contour deformation (FCD) approach. For potentials which are constant outside a bounded domain, FCD yields a high-order accurate numerical solution of the time-dependent Schrodinger equation directly in free space, without the need for artificial boundary conditions. Of the many existing artificial boundary condition schemes, FCD is most similar to an exact nonlocal transparent boundary condition, but it works directly on Cartesian grids in any dimension, and runs on top of the fast Fourier transform rather than fast algorithms for the application of nonlocal history integral operators. We adapt FCD to time-dependent density functional theory (TDDFT), and describe a simple algorithm to smoothly and automatically truncate long-range Coulomb-like potentials to a time-dependent constant outside of a bounded domain of interest, so that FCD can be used. This approach eliminates errors originating from the use of artificial boundary conditions, leaving only the error of the potential truncation, which is controlled and can be systematically reduced. The method enables accurate simulations of ultrastrong nonlinear electronic processes in molecular complexes in which the inteference between bound and continuum states is of paramount importance. We demonstrate results for many-electron TDDFT calculations of absorption and strong field photoelectron spectra for one and two-dimensional models, and observe a significant reduction in the size of the computational domain required to achieve high quality results, as compared with the popular method of complex absorbing potentials
Stochastic Cutoff Method for Long-Range Interacting Systems
A new Monte-Carlo method for long-range interacting systems is presented.
This method consists of eliminating interactions stochastically with the
detailed balance condition satisfied. When a pairwise interaction of a
-particle system decreases with the distance as ,
computational time per one Monte Carlo step is for
and for , where is the spatial
dimension. We apply the method to a two-dimensional magnetic dipolar system.
The method enables us to treat a huge system of spins with reasonable
computational time, and reproduces a circular order originated from long-range
dipolar interactions.Comment: 18 pages, 9 figures, 1 figure and 1 reference are adde
An Adaptive Fast Multipole Boundary Element Method for Poisson−Boltzmann Electrostatics
The numerical solution of the Poisson−Boltzmann (PB) equation is a useful but a computationally demanding tool for studying electrostatic solvation effects in chemical and biomolecular systems. Recently, we have described a boundary integral equation-based PB solver accelerated by a new version of the fast multipole method (FMM). The overall algorithm shows an order N complexity in both the computational cost and memory usage. Here, we present an updated version of the solver by using an adaptive FMM for accelerating the convolution type matrix-vector multiplications. The adaptive algorithm, when compared to our previous nonadaptive one, not only significantly improves the performance of the overall memory usage but also remarkably speeds the calculation because of an improved load balancing between the local- and far-field calculations. We have also implemented a node-patch discretization scheme that leads to a reduction of unknowns by a factor of 2 relative to the constant element method without sacrificing accuracy. As a result of these improvements, the new solver makes the PB calculation truly feasible for large-scale biomolecular systems such as a 30S ribosome molecule even on a typical 2008 desktop computer
Coulomb Interactions via Local Dynamics: A Molecular--Dynamics Algorithm
We derive and describe in detail a recently proposed method for obtaining
Coulomb interactions as the potential of mean force between charges which are
dynamically coupled to a local electromagnetic field. We focus on the Molecular
Dynamics version of the method and show that it is intimately related to the
Car--Parrinello approach, while being equivalent to solving Maxwell's equations
with freely adjustable speed of light. Unphysical self--energies arise as a
result of the lattice interpolation of charges, and are corrected by a
subtraction scheme based on the exact lattice Green's function. The method can
be straightforwardly parallelized using standard domain decomposition. Some
preliminary benchmark results are presented.Comment: 8 figure
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