Local density corrected three-body distribution functions for probing local structure reorganization in liquids

2008 ◽  
Vol 10 (44) ◽  
pp. 6653 ◽  
Author(s):  
Anirban Bhattacharjee ◽  
Thomas S. Hofer ◽  
Bernd M. Rode
Keyword(s):  
Local Structure ◽  
Local Density ◽  
Distribution Functions ◽  
Body Distribution ◽  
Three Body

scholarly journals Do galactic bars depend on environment?: an information theoretic analysis of Galaxy Zoo 2

2020 ◽  
Vol 501 (1) ◽  
pp. 994-1001
Author(s):  
Suman Sarkar ◽  
Biswajit Pandey ◽  
Snehasish Bhattacharjee
Keyword(s):  
Spatial Distribution ◽  
Mutual Information ◽  
Local Density ◽  
Statistical Significance ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Host Galaxy ◽  
Data Sets ◽  
Data Set ◽  
Information Theoretic

ABSTRACT We use an information theoretic framework to analyse data from the Galaxy Zoo 2 project and study if there are any statistically significant correlations between the presence of bars in spiral galaxies and their environment. We measure the mutual information between the barredness of galaxies and their environments in a volume limited sample (Mr ≤ −21) and compare it with the same in data sets where (i) the bar/unbar classifications are randomized and (ii) the spatial distribution of galaxies are shuffled on different length scales. We assess the statistical significance of the differences in the mutual information using a t-test and find that both randomization of morphological classifications and shuffling of spatial distribution do not alter the mutual information in a statistically significant way. The non-zero mutual information between the barredness and environment arises due to the finite and discrete nature of the data set that can be entirely explained by mock Poisson distributions. We also separately compare the cumulative distribution functions of the barred and unbarred galaxies as a function of their local density. Using a Kolmogorov–Smirnov test, we find that the null hypothesis cannot be rejected even at $75{{\ \rm per\ cent}}$ confidence level. Our analysis indicates that environments do not play a significant role in the formation of a bar, which is largely determined by the internal processes of the host galaxy.

A three-body Gaussian model of solid helium

1984 ◽  
Vol 62 (7) ◽  
pp. 683-687 ◽  
Author(s):  
Douglas P. Locke
Keyword(s):  
Ground State ◽  
Reasonable Agreement ◽  
Particle Distribution ◽  
Solid Helium ◽  
Gaussian Model ◽  
Distribution Functions ◽  
Liquid Transition ◽  
Wide Range ◽  
Three Body ◽  
Ground State Energies

A simple, analytic set of three-body models is used to calculate ground state energies and single-particle distribution functions for solid 3He and 4He. Reasonable agreement with other models and experiments over a wide range of molar bolumes (10 cm3 to the liquid transition) is demonstrated.

scholarly journals Low-order many-body interactions determine the local structure of liquid water

2019 ◽  
Vol 10 (35) ◽  
pp. 8211-8218 ◽  
Author(s):  
Marc Riera ◽  
Eleftherios Lambros ◽  
Thuong T. Nguyen ◽  
Andreas W. Götz ◽  
Francesco Paesani
Keyword(s):  
Liquid Water ◽  
Local Structure ◽  
Quantum Effects ◽  
Many Body ◽  
Three Body ◽  
Many Body Interactions ◽  
Nuclear Quantum Effects ◽  
Structure Of Liquid ◽  
Low Order

Two-body and three-body energies, modulated by higher-body terms and nuclear quantum effects, determine the structure of liquid water and require sub-chemical accuracy that is achieved by the MB-pol model but not by existing DFT functionals.

Investigations using wide-angle electron diffraction on pair ordering mechanisms in FeTb alloys by thermal annealing

1994 ◽  
Vol 52 ◽  
pp. 660-661
Author(s):  
M. Tewes ◽  
J. Zweck ◽  
H. Hoffmann
Keyword(s):  
Electron Diffraction ◽  
Short Range ◽  
Local Density ◽  
Coordination Shell ◽  
Density Fluctuations ◽  
Distribution Functions ◽  
Atomic Scale ◽  
Short Range Ordering ◽  
Isotropic Structure ◽  
Pair Distribution Functions

In our recent work we have shown that electron diffraction is a suitable and precise method to observe short range ordering in various amorphous FeTb alloys by calculating pair distribution functions (PDFs) from these data by means of a fourier inversion. A PDF g(r) is an autocorrelation function of the specimen’s density fluctuations: g(r) = 4πr(ϱ(r) - ϱo) with ϱ(r): autocorrelation of the local density in a distance r, and ϱo macroscopic density of the specimen. The spatial resolution that can be achieved is better than 0.02 nm, and the fine structure of the first coordination shell of the short range order has been described quantitatively with an isotropic structure model. The deviation between calculated and measured PDFs has been about 2%.However, the origin of the uniaxial perpendicular anisotropy in rare earth / transition metal amorphous alloys like FeTb is in general attributed to small anisotropic concentration fluctuations on an atomic scale as introduced in pair ordering, band orientation or stress induced anisotropy models.

Applications of Neural Network Fitting of Potential-Energy Surfaces

2012 ◽  
Author(s):  
Lionel Raff ◽  
Ranga Komanduri ◽  
Martin Hagan ◽  
Satish Bukkapatnam
Keyword(s):  
Potential Energy ◽  
Density Functional ◽  
Local Density ◽  
Reaction Dynamics ◽  
Local Environment ◽  
Potential Surfaces ◽  
Empirical Potential ◽  
Hidden Layer ◽  
Experimental Values ◽  
Three Body

In this chapter, several examples of NN fitting of databases obtained using either ab initio electronic structure methods or an empirical potential will be discussed. The objective of this presentation is not to provide a complete and comprehensive review of the field nor is it to acquaint the reader with the details of the reaction dynamics of the particular systems employed as examples. It is rather to provide a clear picture of the power and limitations of NN methods for the investigation of reaction dynamics. We begin with a brief overview of the literature in the field. Neural networks provide a powerful method to effect the fitting of an ensemble of potential energy points in a database. In 1993, Blank et al. employed an NN to fit data derived from an empirical potential model for CO chemisorbed on a Ni(111) surface. Two years later, these same investigators also examined the interaction potential of H2 on a Si(100)-2 × 1 surface using a data set comprising 750 energies computed using local density functional theory. To the best of our knowledge, these were the first two examples in which NNs were employed to provide the PES for a dynamics study. Hobday et al. have investigated the energies of C-H systems by using a Tersoff potential form in which the three-body term is replaced by an NN comprising five input nodes, one hidden layer with six nodes, and an output layer. In this work, the five input elements are computed by consideration of the bond type, i.e., C-C or C-H, the three-body bond angle θ, which is input to the NN in the form (1 + cos θ)2, the connectivity of the local environment, and the second neighbor information. The method was applied to carbon clusters and a wide variety of alkanes, alkenes, alkynes, aromatics, and radicals. Comparison of the atomization energies obtained using the NN potential surfaces with experimental values showed the errors for 12 alkanes, 13 alkenes, 4 alkynes, 7 aromatics, and 12 radicals to lie in the ranges zero to 0.3 eV (alkanes), 0.1 to 1.5 eV (alkenes), 0 to 0.5 eV (alkynes), zero to 1.0 eV (aromatics), and zero to 2.8 eV (radicals).

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