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The Fermi-Dirac distribution as a model of a thermodynamically ideal liquid. Phase transition of the first kind for neutral gases (corresponding to nonpolar molecules)
Mathematical notes. 2017. Vol. 101. No. 1. P. 100–114.
In this paper, we introduce the notions of enlarged number theory and of thermodynamically ideal liquid and calculate the temperature below which it appears. This temperature is T = 0.84Tc, where Tc is the critical temperature of a gas whose molecules are nonpolar. For such a gas, in a sufficiently wide neighborhood of the binodal, the isotherms of a gas and of a thermodynamically ideal liquid coincide with those of a van der Waals gas for the critical value of the compressibility factor Zc = 3/8. In this sense, for T ≤ 0.84Tc and the particular case Zc = 3/8, the developed theory is a generalization of the van der Waals model. A new phase transition of the second kind at the point of zero activity is described.
Kasapenko N., Orlova T., N. Kondratyuk, Journal of Chemical Physics 2025 Vol. 162 No. 15 Article 154901
Molecular dynamics methods have proven their applicability for the simulation of the structure and properties of liquid crystals. For the reproduction of phase transitions in liquid crystals, many authors have reparameterized the classical force fields. For the first time, we demonstrate that even a general-purpose force field, for example, General AMBER Force Field (GAFF), without ...
Added: August 12, 2025
Chertenkov V., Shchur L., / Series arXiv "math". 2024. No. 2411.13027.
The main question raised in the letter is the applicability of a neural network trained on a spin lattice model in one universality class to test a model in another universality class. The quantities of interest are the critical phase transition temperature and the correlation length exponent. In other words, the question of transfer learning ...
Added: November 21, 2024
Glushak A., Smirnov G., Applied Clay Science 2023 Vol. 243 Article 107072
Friedel’s salt, also known as Cl-Hydrocalumite, (Ca2[Al(OH)6]⋅ Cl⋅2H2O), is one of the calcium aluminates phases (AFm phases). It can accommodate radioactive chlorine isotopes, serving as a potential material in radioactive waste applications. Earlier X-Ray diffraction and nuclear magnetic resonance (NMR) experiments demonstrated the existence of the first-order phase transition between 303 K and 313 K. The ...
Added: July 31, 2023
Gordeev I., Kolotova L., Starikov S., Scripta Materialia 2022 Vol. 210 Article 114481
The mechanism of Al-Si alloy crystallization from an amorphous state is still unclear. Despite the absence of equilibrium compounds for this binary system, there are several experimental evidences confirming the formation of metastable silicide at annealing of amorphous Si mixed with Al. Classification of this metastable structure is a missing puzzle piece in the description ...
Added: January 28, 2022
Starikov S., Gordeev I., Lysogorskiy Y. et al., Computational Materials Science 2020 Vol. 184 Article 109891
Metal-semiconductor nanostructures are key objects for multifunctional electronics and optical design. We report
a new interatomic potential for atomistic simulation of a ternary Si-Au-Al system. The development procedure
was based on the force-matching method that allowed us to create the potential without use of experimental
data at the fitting. Extensive validation including elastic, thermophysical and defect properties
demonstrates a ...
Added: January 28, 2022
Kolotova L., Gordeev I., Crystals 2020 Vol. 10 P. 515
Using molecular dynamics simulations, we studied the structural properties of orthorhombic, monoclinic, and body-centered tetragonal (bct) phases of U–Mo alloys. A sequence of shear transformations between metastable phases takes place upon doping of uranium with molybdenum from pure alpha-U: orthorhombic alpha' -> monoclinic alpha'' -> bct gamma^0 -> body-centered cubic (bcc) with doubled lattice constant gamma^s ...
Added: January 28, 2022
Starikov S. V., Kolotova L., Kuksin A. Y. et al., Journal of Nuclear Materials 2018 Vol. 499 P. 451–463
We studied structure and thermodynamic properties of cubic and tetragonal phases of pure uranium and
U-Mo alloys using atomistic simulations: molecular dynamics and density functional theory. The main
attention was paid to the metastable g0-phase that is formed in U-Mo alloys at low temperature.
Structure of g0-phase is similar to body-centered tetragonal (bct) lattice with displacement of a ...
Added: January 28, 2022
Kolokoltsov V., Transactions of the Moscow Mathematical Society 2021 Vol. 82 No. 1 P. 93–104
Combining intuitive probabilistic assumptions with the basic laws of classical thermodynamics, using
the latter to express probabilistic parameters in terms of the thermodynamic quantities, we get a simple
unified derivation of the fundamental ensembles of statistical physics avoiding any limiting procedures,
quantum hypothesis and even statistical entropy maximization. This point of view leads also to some
related classes of ...
Added: October 29, 2021
Negodin V., Polyachenko Y., Fleita D. et al., Journal of Molecular Liquids 2021 Vol. 322 No. 1-3 Article 114954
The equilibrium and metastable states of the Lennard-Jones vapor, liquid, and crystal, are studied in the vicinity of the phase transition points. Vapor-liquid, liquid-vapor, liquid-crystal, and crystal-liquid transitions are modeled within the molecular dynamics method. As a research tool, a four-point correlation function is used for the qualitative detection of collective motions of atoms in ...
Added: May 14, 2021
Bondarenko D. M., Baskin K., NETSOL: New Trends in Social and Liberal Sciences 2019 Vol. 4 No. 2 P. 1–23
In the book where he coined the term “Axial Age”, Karl Jaspers noted that human history included both “tranquil ages” and “ages of change”. This paper begins with the observation that this oscillation between stable and transformational periods encapsulates the pattern in complexity theory by which systems oscillate between relatively long “stable states” and shorter ...
Added: November 17, 2019
Maslov V. P., Mathematical notes 2018 Vol. 103 No. 6 P. 929–935
It is well known that the formula for the Fermi distribution is obtained from the formula
for the Bose distribution if the argument of the polylogarithm, the activity a, the energy, and the
number of particles change sign. The paper deals with the behavior of the Bose–Einstein distribution
as a → 0; in particular, the neighborhood of the ...
Added: December 8, 2018
Maslov V. P., Mathematical notes 2018 Vol. 103 No. 4 P. 616–620
A relation between the jump of spin and the corresponding jump of energy is derived. This relation is used to determine the binding energy of the nucleus and the “entanglement” energy between two bosons. The latter is shown to be inversely proportional to the area in the two-dimensional case. ...
Added: December 8, 2018
Maslov V. P., Mathematical notes 2017 Vol. 102 No. 4 P. 583–586
Added: November 17, 2018
Maslov V., Теоретическая и математическая физика 2018 Т. 196 № 1 С. 161–166
Since the deep paper by Bohr and Kalckar in 1938, it has been known that the Ramanujan formula in
number theory is related to statistical physics and nuclear theory. From the early 1970s, there have been
attempts to generalize number theory from the space of integers to the space of rational numbers, i.e., to
construct a so-called analytic ...
Added: October 30, 2018
Maslov V. P., Mathematical notes 2017 Vol. 102 No. 2 P. 234–251
It is shown in the paper that the number pN(M) of partitions of a positive integer M
into N positive integer summands coincides with the Bose and Fermi distributions with logarithmic
accuracy if one identifies M with energy and N with the number of particles. We use the Gentile
statistics (a.k.a. parastatistics) to derive self-consistent algebraic equations that ...
Added: October 29, 2018
Maslov V. P., Mathematical notes 2017 Vol. 101 No. 3 P. 488–496
Abstract—Regularization of the Bose–Einstein distribution using a parastatistical correction,
i.e., by means of the Gentile statistics, is carried out. It is shown that the regularization result
asymptotically coincides with the Erdo˝ s formula obtained by using Ramanujan’s formula for the
number of variants of the partition of an integer into summands. TheHartley entropy regarded as the
logarithm of the ...
Added: October 28, 2018
Maslov V., Mathematical notes 2017 Vol. 101 No. 4 P. 660–665
In the paper “The relationship between the Fermi–Dirac distribution and statistical
distributions in languages” (This issue of “Math. Notes”), the Bose–Einstein and Fermi–Dirac
distributions are considered in connectionwith frequency distributions in languages in the context of
the author’s approach to thermodynamics and number theory problems. The present article presents
certain clarifications of certain notions used in that approach, in ...
Added: October 28, 2018
Kalinin N., Shkolnikov M., Discrete and continuous dynamical systems, A 2018 Vol. 38 No. 6 P. 2827–2849
The theory of tropical series, that we develop here, firstly appeared in the study of the growth of pluriharmonic functions. Motivated by waves in sandpile models we introduce a dynamic on the set of tropical series, and it is experimentally observed that this dynamic obeys a power law. So, this paper serves as a compilation of results ...
Added: April 17, 2018
Andreev A. F., Melnikovsky L.A., Journal of Experimental and Theoretical Physics 2017 Vol. 124 No. 6 P. 920–923
The conditions for applicability of the mean field theory for describing the thermodynamics of the surface of 4He crystals are investigated based on analysis of experimental data. It is found that although the faceting phase transition itself is a Berezinsky–Kosterlitz–Thouless phase transition, the thermodynamic potential outside a narrow neighborhood of the transition temperature can be ...
Added: February 23, 2018
Tamm M., Nechaev S. K., Valba O. V., Journal of Statistical Mechanics: Theory and Experiment 2017 Vol. 2017 No. 053301 P. 1–17
We study the asymptotic behavior of the number of paths of length N on several classes of infinite graphs with a single special vertex. This vertex can work as an ‘entropic trap’ for the path, i.e. under certain conditions the dominant part of long paths becomes localized in the vicinity of the special point instead ...
Added: October 19, 2017
Panov V., Statistics and Probability Letters 2017 Vol. 129 P. 379–386
In this paper, we study the fluctuations of sums of random variables with distribution defined as a mixture of light-tail and truncated heavy-tail distributions. We focus on the case when both the mixing coefficient and the truncation level depend on the number of summands. The aim of this research is to characterize the limiting distributions ...
Added: July 10, 2017
Grinin L. E., Korotayev A., Issaev L. et al., / Издательский дом НИУ ВШЭ. Серия IR "International Relations". 2017. № WP BRP 29/IR/2017.
The present working paper analyzes the world order in the past, present and future as well as the main factors, foundations and ideas underlying the maintaining and change of the international and global order. The first two sections investigate the evolution of the world order starting from the ancient times up to the late twentieth ...
Added: April 16, 2017