Structure Factor and Radial Distribution Function for Liquid Argon at 85 °K

Yarnell, J. L.; Katz, M. J.; Wenzel, R. G.; Koenig, Seymour H.

doi:10.1103/physreva.7.2130

Cited by 466 publications

(182 citation statements)

References 16 publications

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“…The presen' study refers to the silver-germanium alloy. Thi [6] correction is developed by Yarnell [7] and consists in an evaluation of this inelasticity effect. We also estimated following Blech [10].…”

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confidence: 99%

Neutron diffraction studies of liquid silver and liquid Ag-Ge alloys

et al. 1976

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confidence: 99%

Neutron diffraction studies of liquid silver and liquid Ag-Ge alloys

et al. 1976

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“…Furthermore, for such bases, g M (r) converges to g(r) uniformly in M [19]. 4 This implies that in principle, the maximum error in g M (r) is controlled through M . However, Monte Carlo sampling also introduces uncertainty in a j , which can be estimated via…”

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confidence: 88%

“…In simulations of condensed matter systems, one can barely overstate the importance of the radial distribution function (RDF) g(r). To name only a few applications, g(r) is used to (i) link thermodynamic properties to microscopic details [1-3]; (ii) compute structure factors for comparison with X-ray diffraction [4,5]; and more recently, (iii) calibrate interparticle forces for coarse-grained (CG) molecular dynamics (MD) [6][7][8][9][10][11]. Indeed, the RDF is such a key property that in the past few years, much work has been devoted to estimating g(r) via parallel processing on GPUs [12].…”

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Beyond histograms: Efficiently estimating radial distribution functions via spectral Monte Carlo

Patrone

Rosch

2017

The Journal of Chemical Physics

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Despite more than 40 years of research in condensed-matter physics, state-of-the-art approaches for simulating the radial distribution function (RDF) g(r) still rely on binning pair-separations into a histogram. Such methods suffer from undesirable properties, including subjectivity, high uncertainty, and slow rates of convergence. Moreover, such problems go undetected by the metrics often used to assess RDFs. To address these issues, we propose (I) a spectral Monte Carlo (SMC) method that yields g(r) as an analytical series expansion; and (II) a Sobolev norm that assesses the quality of RDFs by quantifying their fluctuations. Using the latter, we show that, relative to histogram-based approaches, SMC reduces by orders of magnitude both the noise in g(r) and the number of pair separations needed for acceptable convergence. Moreover, SMC reduces subjectivity and yields simple, differentiable formulas for the RDF, which are useful for tasks such as coarse-grained force-field calibration via iterative Boltzmann inversion. In simulations of condensed matter systems, one can barely overstate the importance of the radial distribution function (RDF) g(r). To name only a few applications, g(r) is used to (i) link thermodynamic properties to microscopic details [1-3]; (ii) compute structure factors for comparison with X-ray diffraction [4,5]; and more recently, (iii) calibrate interparticle forces for coarse-grained (CG) molecular dynamics (MD) [6][7][8][9][10][11]. Indeed, the RDF is such a key property that in the past few years, much work has been devoted to estimating g(r) via parallel processing on GPUs [12]. Given these observations, it is thus surprising that state-of-the-art techniques still construct g(r) by binning simulated pair-separations into histograms, with little thought given to developing more efficient methods [3,13].In this letter, we address this issue by proposing a spectral Monte Carlo (SMC) method for computing simulated RDFs. The key idea behind our approach is to express g(r) in an appropriate basis set and determine the mode coefficients via Monte Carlo estimates. Relative to binning, we show that this approach decreases subjectivity of the analysis, thereby reducing both the noise in g(r) and the number of pair separations needed to generate useful RDFs. To support these claims, we also discuss how traditional L 2 (or sum-of-squares) metrics are insufficient for assessing convergence of g(r) and propose a Sobolev norm [14] as an appropriate alternative.The motivation for this work stems from the fact that g(r) is increasingly being used in settings in which the details of its functional form play a critical role. For example, scientists now routinely simulate untested materials in an effort to tailor their structural properties without the need for expensive experiments [15,16]; in such applications, objectively computing RDFs is a key task. Along * paul.patrone@nist.gov related lines, structural properties are increasingly being used to calibrate coarse-grained force-fields [6][7][8][9][10][...

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“…Suite à l'interaction entre le faisceau de neutrons incidents et la matière de l'échantillon, l'échantillon se comporte comme une source et produit une onde diffusée : ilk'r-2ev'l) r (14) où l'amplitude de diffusion, avec la dimension d'une longueur, caractérise la force de l'interaction neutron-matière. A grande distance de la cible, l'onde diffusée pourra être considérée comme une onde plane, de vecteur d'onde k'.…”

Section: 3 Diffusion Des Neutronsunclassified

“…Un exemple en est donné sur la figure 26 pour l'argon liquide [14]. La figure montre aussi la fonction de paires G (r), obtenue à partir de la courbe précédente par transformée de Fourier.…”

Section: Neutrons Et Matériauxunclassified

Neutrons et matériaux : introduction

Schweizer

2003

J. Phys. IV France

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Structure Factor and Radial Distribution Function for Liquid Argon at 85 °K

Cited by 466 publications

References 16 publications

Neutron diffraction studies of liquid silver and liquid Ag-Ge alloys

Neutron diffraction studies of liquid silver and liquid Ag-Ge alloys

Beyond histograms: Efficiently estimating radial distribution functions via spectral Monte Carlo

Neutrons et matériaux : introduction

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