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Keywords = Wigner-Seitz cell

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19 pages, 694 KiB  
Article
Nuclear Matter and Finite Nuclei: Relativistic Thomas–Fermi Approximation Versus Relativistic Mean-Field Approach
by Shuying Li, Hong Shen and Jinniu Hu
Universe 2025, 11(8), 255; https://doi.org/10.3390/universe11080255 (registering DOI) - 1 Aug 2025
Viewed by 33
Abstract
The Thomas–Fermi approximation is a powerful method that has been widely used to describe atomic structures, finite nuclei, and nonuniform matter in supernovae and neutron-star crusts. Nonuniform nuclear matter at subnuclear density is assumed to be composed of a lattice of heavy nuclei [...] Read more.
The Thomas–Fermi approximation is a powerful method that has been widely used to describe atomic structures, finite nuclei, and nonuniform matter in supernovae and neutron-star crusts. Nonuniform nuclear matter at subnuclear density is assumed to be composed of a lattice of heavy nuclei surrounded by dripped nucleons, and the Wigner–Seitz cell is commonly introduced to simplify the calculations. The self-consistent Thomas–Fermi approximation can be employed to study both a nucleus surrounded by nucleon gas in the Wigner–Seitz cell and an isolated nucleus in the nuclide chart. A detailed comparison is made between the self-consistent Thomas–Fermi approximation and the relativistic mean-field approach for the description of finite nuclei, based on the same nuclear interaction. These results are then examined using experimental data from the corresponding nuclei. Full article
(This article belongs to the Special Issue Advances in Nuclear Astrophysics)
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9 pages, 2042 KiB  
Communication
Structure of Argon Solid Phases Formed from the Liquid State at Different Isobaric Cooling Rates
by Eugeny I. German, Shulun B. Tsydypov, Michael I. Ojovan and Migmar V. Darmaev
Appl. Sci. 2024, 14(3), 1295; https://doi.org/10.3390/app14031295 - 4 Feb 2024
Cited by 2 | Viewed by 1838
Abstract
By the method of molecular dynamics, computer simulation of the processes of isobaric cooling of argon particle systems under initial conditions with a temperature of 150 K at pressure values from 0.1 to 4 MPa to a temperature of 40 K with cooling [...] Read more.
By the method of molecular dynamics, computer simulation of the processes of isobaric cooling of argon particle systems under initial conditions with a temperature of 150 K at pressure values from 0.1 to 4 MPa to a temperature of 40 K with cooling rates of 108, 109, 1010, 1011 and 1012 K/s was performed. As a result of a computer experiment, coordinate arrays of particles were obtained, which were subjected to the procedure of three-dimensional Voronoi partitioning to identify and calculate the number of elementary cells of the crystal structure. Analysis of the structure of argon solid phases formed during isobaric cooling allowed us to deduce an estimated pattern between the concentration of FCC (face-centered cubic) cells in solid argon and the cooling rate from the liquid state. The evaluation of the orientation of the axes of translation of crystal cells in the array of particle coordinates made it possible to classify the solid phases formed as a result of cooling as single crystals, glassy media with the inclusion of clusters and single cells of FCC structures. It was revealed that during isobaric cooling at a rate not exceeding 108 K/s, argon completely crystallizes, at isobaric cooling rates of 109–1010 K/s, the union of elementary cells of the crystal structure into clusters is observed in glassy argon, and at rates of 1011 K/s and higher at pressures of 1 MPa and lower, solid vitreous phases of argon are formed in which no crystal structure cells are detected. Full article
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16 pages, 6238 KiB  
Article
Numerical Study on Effect of Contact and Interfacial Resistance on Thermal Conductivity of Dispersed Composites
by Atsushi Kondo, Hiroshi Matsuura and Yoshiharu Ito
Materials 2023, 16(2), 517; https://doi.org/10.3390/ma16020517 - 5 Jan 2023
Cited by 2 | Viewed by 1525
Abstract
A series of finite element analyses were conducted to clarify the effect of contact and interfacial resistance between constituents on effective thermal conductivities of dispersed composites. Equally dispersed fillers in FCC (face-centered cubic) and BCC (body-centered cubic) material systems were extracted from cyclic [...] Read more.
A series of finite element analyses were conducted to clarify the effect of contact and interfacial resistance between constituents on effective thermal conductivities of dispersed composites. Equally dispersed fillers in FCC (face-centered cubic) and BCC (body-centered cubic) material systems were extracted from cyclic microstructures as unit cell models. In addition to spherical fillers, a polyhedron called the Wigner–Seitz cell that can realize a fully packed microstructure was chosen as the shape of the filler to investigate the effect of contact between the high volumetric fraction of fillers. The effective thermal conductivities of the resulting composites were calculated based on the FEA results and compared to the theoretical results for various volume fractions of the fillers including the maximum packing fraction. The following conclusions were obtained from the present study: 1. The effect of the contact depending on the shape and configuration of the fillers has more of a significant influence on the effective thermal conductivity than the influence of the increase in the volume fraction of the fillers. 2. When the contact occurred, the effective thermal conductivity became more than double that without contact. 3. Interfacial thermal resistance must be less than the order of 10−4 m2 K/W to obtain improvement in the effective thermal conductivity by compounding the fillers. Full article
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13 pages, 433 KiB  
Article
Debye-Hückel Free Energy of an Electric Double Layer with Discrete Charges Located at a Dielectric Interface
by Guilherme Volpe Bossa and Sylvio May
Membranes 2021, 11(2), 129; https://doi.org/10.3390/membranes11020129 - 14 Feb 2021
Cited by 8 | Viewed by 3228
Abstract
Poisson–Boltzmann theory provides an established framework to calculate properties and free energies of an electric double layer, especially for simple geometries and interfaces that carry continuous charge densities. At sufficiently small length scales, however, the discreteness of the surface charges cannot be neglected. [...] Read more.
Poisson–Boltzmann theory provides an established framework to calculate properties and free energies of an electric double layer, especially for simple geometries and interfaces that carry continuous charge densities. At sufficiently small length scales, however, the discreteness of the surface charges cannot be neglected. We consider a planar dielectric interface that separates a salt-containing aqueous phase from a medium of low dielectric constant and carries discrete surface charges of fixed density. Within the linear Debye-Hückel limit of Poisson–Boltzmann theory, we calculate the surface potential inside a Wigner–Seitz cell that is produced by all surface charges outside the cell using a Fourier-Bessel series and a Hankel transformation. From the surface potential, we obtain the Debye-Hückel free energy of the electric double layer, which we compare with the corresponding expression in the continuum limit. Differences arise for sufficiently small charge densities, where we show that the dominating interaction is dipolar, arising from the dipoles formed by the surface charges and associated counterions. This interaction propagates through the medium of a low dielectric constant and alters the continuum power of two dependence of the free energy on the surface charge density to a power of 2.5 law. Full article
(This article belongs to the Special Issue Electrostatics in Cell Membranes and in Artificial Membrane Models)
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9 pages, 2900 KiB  
Article
Molecular Dynamics Simulations of Vacancy Generation and Migration near a Monocrystalline Silicon Surface during Energetic Cluster Ion Implantation
by Guoying Liang, Haowen Zhong, Yinong Wang, Shijian Zhang, Mofei Xu, Shicheng Kuang, Jianhui Ren, Nan Zhang, Sha Yan, Xiao Yu, Gennady Efimovich Remnev and Xiaoyun Le
Coatings 2020, 10(2), 146; https://doi.org/10.3390/coatings10020146 - 5 Feb 2020
Cited by 3 | Viewed by 3421
Abstract
The process of ion implantation often involves vacancy generation and migration. The vacancy generation and migration near a monocrystalline silicon surface during three kinds of energetic Si35 cluster ion implantations were investigated by molecular dynamics simulations in the present work. The patterns [...] Read more.
The process of ion implantation often involves vacancy generation and migration. The vacancy generation and migration near a monocrystalline silicon surface during three kinds of energetic Si35 cluster ion implantations were investigated by molecular dynamics simulations in the present work. The patterns of vacancy generation and migration, as well as the implantation-induced amorphous structure, were analyzed according to radial distribution function, Wigner–Seitz cell, and identify diamond structure analytical methods. A lot of vacancies rapidly generate and migrate in primary directions and form an amorphous structure in the first two picoseconds. The cluster with higher incident kinetic energy can induce the generation and migration of more vacancies and a deeper amorphous structure. Moreover, boundaries have a loading–unloading effect, where interstitial atoms load into the boundary, which then acts as a source, emitting interstitial atoms to the target and inducing the generation of vacancies again. These results provide more insight into doping silicon via ion implantation. Full article
(This article belongs to the Special Issue Plasma Surface Engineering)
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15 pages, 2424 KiB  
Article
Transverse Density Fluctuations around the Ground State Distribution of Counterions near One Charged Plate: Stochastic Density Functional View
by Hiroshi Frusawa
Entropy 2020, 22(1), 34; https://doi.org/10.3390/e22010034 - 25 Dec 2019
Cited by 10 | Viewed by 3152
Abstract
We consider the Dean–Kawasaki (DK) equation of overdamped Brownian particles that forms the basis of the stochastic density functional theory. Recently, the linearized DK equation has successfully reproduced the full Onsager theory of symmetric electrolyte conductivity. In this paper, the linear DK equation [...] Read more.
We consider the Dean–Kawasaki (DK) equation of overdamped Brownian particles that forms the basis of the stochastic density functional theory. Recently, the linearized DK equation has successfully reproduced the full Onsager theory of symmetric electrolyte conductivity. In this paper, the linear DK equation is applied to investigate density fluctuations around the ground state distribution of strongly coupled counterions near a charged plate, focusing especially on the transverse dynamics along the plate surface. Consequently, we find a crossover scale above which the transverse density dynamics appears frozen and below which diffusive behavior of counterions can be observed on the charged plate. The linear DK equation provides a characteristic length of the dynamical crossover that is similar to the Wigner–Seitz radius used in equilibrium theory for the 2D one-component plasma, which is our main result. Incidentally, general representations of longitudinal dynamics vertical to the plate further suggest the existence of advective and electrical reverse-flows; these effects remain to be quantitatively investigated. Full article
(This article belongs to the Special Issue Recent Developments in Dissipative Phenomena)
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18 pages, 6168 KiB  
Article
Prototiles and Tilings from Voronoi and Delone Cells of the Root Lattice An
by Nazife Ozdes Koca, Abeer Al-Siyabi, Mehmet Koca and Ramazan Koc
Symmetry 2019, 11(9), 1082; https://doi.org/10.3390/sym11091082 - 28 Aug 2019
Cited by 4 | Viewed by 5413
Abstract
The orthogonal projections of the Voronoi and Delone cells of root lattice A n onto the Coxeter plane display various rhombic and triangular prototiles including thick and thin rhombi of Penrose, Amman–Beenker tiles, Robinson triangles, and Danzer triangles to name a few. We [...] Read more.
The orthogonal projections of the Voronoi and Delone cells of root lattice A n onto the Coxeter plane display various rhombic and triangular prototiles including thick and thin rhombi of Penrose, Amman–Beenker tiles, Robinson triangles, and Danzer triangles to name a few. We point out that the symmetries representing the dihedral subgroup of order 2 h involving the Coxeter element of order h = n + 1 of the Coxeter–Weyl group a n play a crucial role for h -fold symmetric tilings of the Coxeter plane. After setting the general scheme we give samples of patches with 4-, 5-, 6-, 7-, 8-, and 12-fold symmetries. The face centered cubic (f.c.c.) lattice described by the root lattice A 3 , whose Wigner–Seitz cell is the rhombic dodecahedron projects, as expected, onto a square lattice with an h = 4 -fold symmetry. Full article
(This article belongs to the Special Issue Mathematical Crystallography 2019)
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