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## Thermodynamic equations of state with three defining constants

Mathematical notes. 2010. Vol. 87. No. 5. P. 728-737.

The well-known empiric Van der Waals equation contains two constants characterizing a given gas, so that, in general, it depends on the characteristic interaction of particles of the given gas. In this paper, equations depending on three defining constants, are constructed on the basis of he mathematically rigorous results obtained by the author in recent papers.

Keywords: Bose condensatefractal dimensionnumber of degrees of freedomequations of statetheory of imperfect gasesinteraction potential of particlesIrving Fisher lawБозе конденсатфрактальная размерностьчисло степеней свободыуравнения состояниятеория идеальных газовпотенциал взаимодействия частицзакон Ирвинга-Фишера

Duality of critical interfaces in Potts model: numerical check / Cornell University. Series "Working papers by Cornell University". 2010. No. 1008.3573.

We report on numerical investigation of fractal properties of critical interfaces in two-dimensional Potts models. Algorithms for finding percolating interfaces of Fortuin-Kasteleyn clusters, their external perimeters and interfaces of spin clusters are presented. Fractal dimensions are measured and compared to exact theoretical predictions. ...

Added: March 7, 2016

Mathematical notes 2012 Vol. 91 No. 5 P. 697-703

We study the case where the values of random variables increase without bound. ...

Added: January 17, 2013

Теоретическая и математическая физика 2020 Т. 202 № 3 С. 458-473

In the framework of the Gross-Pitaevsky equation, we consider the problem of the expansion of quantum gases into vacuum, for which the chemical potential μ depends on the density n in a power manner with the index v =2/D, where D is the dimension of space. For gas condensates of Bose-atoms at temperatures T → 0 the main ...

Added: February 4, 2020

Mathematical notes 2013 Vol. 93 No. 1-2 P. 102-136

In this paper we systematically present a new approach to classical thermodynamics, using asymptotic distribution from number theory and generalizing the Bose-Einstein distribution. The phase transition from gas to liquid, the thermodynamics of fluids, as well as the behavior of liquids under negative pressure are elucidated. ...

Added: April 1, 2013

Oxford: Elsevier, 2014

This Reference Module contains trusted, peer-reviewed, comprehensive content from our reference works as curated by our world-class editorial board led by Editor-in-Chief, Scott A. Elias. It is designed for faster, more relevant browsing within the subject and beyond, with topic pages for quick, clear overviews, subject hierarchies to put everything in context, and guidance to ...

Added: March 26, 2014

Mathematical notes 2013 Vol. 94 No. 5 P. 722-813

In the present paper, we describe an approach to thermodynamics that does not involve Bogolyubov chains or Gibbs ensembles. We present isotherms, isochores, and isobars of various pure gases, as well as binodals, i.e., lines along which gas becomes liquid, and spinodals (endpoints of isotherms). We study supercritical phenomena for values of temperature and pressure ...

Added: December 23, 2013

Physical Review B: Condensed Matter and Materials Physics 2016 Vol. 94 No. 19 P. 195302-1-195302-8

Time evolution of long-range spatial coherence in a freely decaying cavity-polariton condensate excited resonantly in a high-Q GaAs microcavity is found to be qualitatively different from that in nonresonantly excited condensates. The first-order spatial correlation function g(1)(r1,r2) in response to resonant 1.5 ps pump pulses at normal incidence leaving the exciton reservoir empty is found to be nearly ...

Added: February 15, 2018

Mathematical notes 2014 Vol. 95 No. 6 P. 881-885

After the work of Irving Fisher, who formulated the main law of economics as an analog of the Claiperon--Clausius--Mendeleev relation corresponding to the Boltzmann--Maxwell ideal gas, the authors have developed this approach on the basis of the general principles of UD-statistics by assigning to the nominal interest rate the role of the chemical potential mu ...

Added: December 21, 2014

Mathematical notes 2015 Vol. 98 No. 1-2 P. 138-157

The notion of ideal liquid for the number of degrees of freedom less than 2, i.e., γ < 0, is introduced. The values of the pressure P and of the compressibility factor Z on the spinodal in the negative pressure region for the van der Waals equation determine the value of γ, γ(T) < 0, ...

Added: October 7, 2015

NY: Nova Science Publishers, 2014

We single out the main features of the mathematical theory of noble gases. It is proved that the points of degeneracy of the Bose gas fractal dimension in momentum space coincide with the critical points of noble gases, while the jumps of the critical indices and the Maxwell rule are related to tunnel quantization in ...

Added: November 18, 2013

Mathematical notes 2014 Vol. 96 No. 3 P. 403-415

In this paper, we refine some of the original notions, such as the number of degrees of freedom, for an arbitrary temperature
and an ideal Boltzmann--Maxwell gas. Using the van der Waals model, we illustrate the notion of Frenkel temperature,
which separates soft and rigid liquid. ...

Added: December 21, 2014

Physics Letters A 2020 Vol. 384 No. 36 P. 126942-1-126942-6

Formation of exciton-polariton condensate due to incoherent pumping of an excitonic reservoir is considered. The condensate dynamics is governed by a system of stochastic integro-differential equations of Langevin's type corresponding to the model developed by Elistratov and Lozovik [12]. Attention is concentrated on non-Markovian interaction of the condensate with the excitonic and photonic reservoirs. It ...

Added: October 30, 2020

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

, in: Advances in Chemistry Research. Vol. 21.: NY: Nova Science Publishers, 2014.. Ch. 6. P. 197-219.

We single out the main features of the mathematical theory of noble gases. It is proved that the points of degeneracy of the Bose gas fractal dimension in momentum space coincide with the critical points of noble gases, while the jumps of the critical indices and the Maxwell rule are related to tunnel quantization in ...

Added: February 24, 2014

Mathematical notes 2014 Vol. 96 No. 1 P. 50-67

This paper presents UD-statistics almost coinciding with Gentile statistics for negative chemical potentials, but having another extension in the case of positive chemical potentials. The physical meaning of the metamorphosis of the phase transition of the third kind to the phase transition of the first kind is explained. The coincidence of isochores and isotherms in the supercritical ...

Added: December 21, 2014

AIP Conference Proceedings 2020 Vol. 2272 No. 1 P. 070055-1-070055-5

We present a new quantum accurate Spectral Neighbor Analysis Potential (SNAP) machine-learning potential for simulating carbon under extreme conditions of dynamic compression (pressures up to 1 TPa and temperatures up to 10,000 K). The development of SNAP potential involves (1) the generation of the training database comprised of the consistent and meaningful set of first-principles ...

Added: January 21, 2021

Physical Review B: Condensed Matter and Materials Physics 2018 Vol. 98 No. 20 P. 205424-1-205424-6

The dynamics of a pure low polariton (LP) system created by resonant broadband excitation in a wide range of wave vectors was investigated in a high-Q GaAs-based microcavity. The LP system is shown to inherit the high spatial coherence from the laser pulse and does not lose it during decay. As a result, its dynamics ...

Added: January 9, 2019

Computer Physics Communications 2011 Vol. 182 P. 1819-1823

Two-dimensional structures grown with Witten and Sander algorithm are investigated. We analyze clusters grown off-lattice and clusters grown with antenna method with Nfp=3,4,5,6,7 and 8 allowed growth directions. With the help of variable probe particles technique we measure fractal dimension of such clusters D(N) as a function of their size N . We propose that in the thermodynamic limit of ...

Added: March 25, 2014

Selecta Mathematica, New Series 2018 Vol. 24 No. 1 P. 21-62

We study plane partitions satisfying condition a_{n+1,m+1}=0 (this condition is called “pit”) and asymptotic conditions along three coordinate axes. We find the formulas for generating function of such plane partitions. Such plane partitions label the basis vectors in certain representations of quantum toroidal gl1 algebra, therefore our formulas can be interpreted as the characters of ...

Added: October 24, 2018

Functional Analysis and Its Applications 2006 Vol. 40 No. 2 P. 81-90

It is well known that every module M over the algebra ℒ(X) of operators on a finite-dimensional space X can be represented as the tensor product of X by some vector space E, M ≅ = E ⊗ X. We generalize this assertion to the case of topological modules by proving that if X is a stereotype space with the stereotype approximation property, then for each stereotype module M over the ...

Added: September 23, 2016

М.: МЦНМО, 2013

Предлагаемая книга—первый том двухтомной монографии, посвящённой аналитической теории дифференциальных уравнений.
В первой части этого тома излагается формальная и аналитическая теория нормальных форм и теорема о разрешении особенностей для векторных полей на плоскости.
Вторая часть посвящена алгебраически разрешимым локальным задачам теории аналитических дифференциальных уравнений , квадратичным векторным полям и проблеме локальной классификации ростков векторных полей в комплексной области ...

Added: February 5, 2014

Известия РАН. Серия математическая 2016 Т. 80 № 6 С. 173-216

Полимодальная логика доказуемости
GLP была введена Г. К. Джапаридзе в 1986 г. Она является логикой доказуемости для ряда цепочек предикатов доказуемости возрастающей силы. Всякой полимодальной логике соответствует многообразие полимодальных алгебр. Л. Д. Беклемишевым и А. Виссером был поставлен вопрос о разрешимости элементарной теории свободной GLP-алгебры, порожденной константами 0, 1 [1]. В этой статье для любого натурального n решается аналогичный вопрос для логик GLPn, являющихся ...

Added: December 4, 2017

Physica A: Statistical Mechanics and its Applications 2014 Vol. 413 No. 1 P. 59-70

A general approach to measure statistical uncertainty of different filtration techniques for market network analysis is proposed. Two measures of statistical uncertainty are introduced and discussed. One is based on conditional risk for multiple decision statistical procedures and another one is based on average fraction of errors. It is shown that for some important cases ...

Added: July 19, 2014

Теоретическая и математическая физика 2019 Т. 201 № 1 С. 65-83

We study the process of a nucleon separating from an atomic nucleus from the mathematical standpoint
using experimental values of the binding energy for the nucleus of the given substance. A nucleon becomes
a boson at the instant of separating from a fermionic nucleus. We study the further transformations of
boson and fermion states of separation in a ...

Added: November 1, 2019