Correlation functions in statistical mechanics and astrophysics

Liboff, Richard L.

doi:10.1103/physreva.39.4098

Cited by 3 publications

(2 citation statements)

References 8 publications

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“…Radial distribution functions calculated from systems of several hundred thousand to one million atoms have also been useful in studies of radiation damage in nuclear waste [8] and long-range order in self-assembled alkanethiol monolayers [9]. The RDF is also widely used in astrophysics, where stars replace atoms and the function is typically known as the two-point correlation function [10]. …”

Section: Introductionmentioning

confidence: 99%

Fast analysis of molecular dynamics trajectories with graphics processing units—Radial distribution function histogramming

Levine

Stone

Kohlmeyer

2011

Journal of Computational Physics

237

126

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The calculation of radial distribution functions (RDFs) from molecular dynamics trajectory data is a common and computationally expensive analysis task. The rate limiting step in the calculation of the RDF is building a histogram of the distance between atom pairs in each trajectory frame. Here we present an implementation of this histogramming scheme for multiple graphics processing units (GPUs). The algorithm features a tiling scheme to maximize the reuse of data at the fastest levels of the GPU’s memory hierarchy and dynamic load balancing to allow high performance on heterogeneous configurations of GPUs. Several versions of the RDF algorithm are presented, utilizing the specific hardware features found on different generations of GPUs. We take advantage of larger shared memory and atomic memory operations available on state-of-the-art GPUs to accelerate the code significantly. The use of atomic memory operations allows the fast, limited-capacity on-chip memory to be used much more efficiently, resulting in a fivefold increase in performance compared to the version of the algorithm without atomic operations. The ultimate version of the algorithm running in parallel on four NVIDIA GeForce GTX 480 (Fermi) GPUs was found to be 92 times faster than a multithreaded implementation running on an Intel Xeon 5550 CPU. On this multi-GPU hardware, the RDF between two selections of 1,000,000 atoms each can be calculated in 26.9 seconds per frame. The multi-GPU RDF algorithms described here are implemented in VMD, a widely used and freely available software package for molecular dynamics visualization and analysis.

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Section: Introductionmentioning

confidence: 99%

Fast analysis of molecular dynamics trajectories with graphics processing units—Radial distribution function histogramming

Levine

Stone

Kohlmeyer

2011

Journal of Computational Physics

237

126

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“…Methods for spatial structure studies of many-body systems have been developed and extensively applied in physics of condensed matter [14,15]. Similar techniques are employed to understand the associations of galaxies and the large scale structures of the Universe [16,17]. The main spatial structure function in the study of liquids is the pair distribution function (PDF).…”

Section: Introductionmentioning

confidence: 99%

Conditional pair distributions in many-body systems: Exact results for Poisson ensembles

Rohrmann

Zurbriggen

2012

Phys. Rev. E

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We introduce a conditional pair distribution function (CPDF) which characterizes the probability density of finding an object (e.g., a particle in a fluid) to within a certain distance of each other, with each of these two having a nearest neighbor to a fixed but otherwise arbitrary distance. This function describes special four-body configurations, but also contains contributions due to the so-called mutual nearest neighbor (two-body) and shared neighbor (three-body) configurations. The CPDF is introduced to improve a Helmholtz free energy method based on space partitions. We derive exact expressions of the CPDF and various associated quantities for randomly distributed, noninteracting points at Euclidean spaces of one, two, and three dimensions. Results may be of interest in many diverse scientific fields, from fluid physics to social and biological sciences.

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Ultrafast scalable parallel algorithm for the radial distribution function histogramming using MPI maps

2016

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Correlation functions in statistical mechanics and astrophysics

Cited by 3 publications

References 8 publications

Fast analysis of molecular dynamics trajectories with graphics processing units—Radial distribution function histogramming

Fast analysis of molecular dynamics trajectories with graphics processing units—Radial distribution function histogramming

Conditional pair distributions in many-body systems: Exact results for Poisson ensembles

Ultrafast scalable parallel algorithm for the radial distribution function histogramming using MPI maps

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