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Chkhartishvili, Levan

doi:10.1023/a:1010295711303

Cited by 17 publications

(9 citation statements)

References 4 publications

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“…Finding an analytical equation for α solid for q > 0.15 is more difficult since already accounting for the overlap of three depletion zones is mathematically laborious. 56 However, it is possible to find an equation for the free volume available in an fcc crystal, or any other given (binary) crystal structure, accounting for multiple overlaps with a numerical approach. One way to do this is using Wolfram Mathematica's built-in Region functions.…”

Section: Fluid Phasementioning

confidence: 99%

Phase behavior of binary hard-sphere mixtures: Free volume theory including reservoir hard-core interactions

Opdam

Schelling

Tuinier

2021

The Journal of Chemical Physics

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Section: Fluid Phasementioning

confidence: 99%

Phase behavior of binary hard-sphere mixtures: Free volume theory including reservoir hard-core interactions

Opdam

Schelling

Tuinier

2021

The Journal of Chemical Physics

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“…When QCTS is based on the semi-classical parameterization of constituent atoms [38][39][40], electric charge density and electric field potential distributions in atoms are represented by radial step-like functions. Carrying out electronic structure calculations using this method requires the resolution of some special geometric and algebraic problems [41][42][43][44][45][46][47]. Mathematical aspects of the approach have been summarized in the monograph [46].…”

Section: Discussionmentioning

confidence: 99%

On Semi-Classical Approach to Materials Electronic Structure

Chkhartishvili

2021

J. Mater. Sci. Technol. Res.

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Materials atomic structure, ground-state and physical properties as well as their chemical reactivity mainly are determined by electronic structure. When first-principles methods of studying the electronic structure acquire good predictive power, the best approach would be to design new functional materials theoretically and then check experimentally only most perspective ones. In the paper, the semi-classical model of multi-electron atom is constructed, which makes it possible to calculate analytically (in special functions) the electronic structure of atomic particles themselves and materials as their associated systems. Expected relative accuracy makes a few percent, what is quite acceptable for materials science purposes.

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“…[40] Chkhartishvili (2001) also reported a formula for computing the volume of the intersection of three spheres with different radii. [41] Naiman and Wynn (1992) generalized Kratky's observation to arbitrary dimensions: they found that the union of d-dimensional balls could be computed by the inclusion-exclusion formula containing only at most the intersection terms among d + 1 balls if a simplicial complex which conveyed the intersection information among all balls was available. [42] They explicitly stated that the Delaunay triangulation was such a simplicial complex in the particular case of identically sized balls.…”

Section: Inclusion-exclusion Principlementioning

confidence: 99%

Beta‐decomposition for the volume and area of the union of three‐dimensional balls and their offsets

et al. 2012

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Given a set of spherical balls, called atoms, in three-dimensional space, its mass properties such as the volume and the boundary area of the union of the atoms are important for many disciplines, particularly for computational chemistry/biology and structural molecular biology. Despite many previous studies, this seemingly easy problem of computing mass properties has not been well-solved. If the mass properties of the union of the offset of the atoms are to be computed as well, the problem gets even harder. In this article, we propose algorithms that compute the mass properties of both the union of atoms and their offsets both correctly and efficiently. The proposed algorithms employ an approach, called the Beta-decomposition, based on the recent theory of the beta-complex. Given the beta-complex of an atom set, these algorithms decompose the target mass property into a set of primitives using the simplexes of the beta-complex. Then, the molecular mass property is computed by appropriately summing up the mass property corresponding to each simplex. The time complexity of the proposed algorithm is O(m) in the worst case where m is the number of simplexes in the beta-complex that can be efficiently computed from the Voronoi diagram of the atoms. It is known in ℝ(3) that m = O(n) on average for biomolecules and m = O(n(2)) in the worst case for general spheres where n is the number of atoms. The theory is first introduced in ℝ(2) and extended to ℝ(3). The proposed algorithms were implemented into the software BetaMass and thoroughly tested using molecular structures available in the Protein Data Bank. BetaMass is freely available at the Voronoi Diagram Research Center web site.

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Untitled

Cited by 17 publications

References 4 publications

Phase behavior of binary hard-sphere mixtures: Free volume theory including reservoir hard-core interactions

Phase behavior of binary hard-sphere mixtures: Free volume theory including reservoir hard-core interactions

On Semi-Classical Approach to Materials Electronic Structure

Beta‐decomposition for the volume and area of the union of three‐dimensional balls and their offsets

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