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ДВУХФЛЮИДНАЯ КАРТИНА НАДКРИТИЧЕСКИХ ЯВЛЕНИЙ
Теоретическая и математическая физика. 2014. Т. 180. № 3. С. 394-432.
We consider a parastatistics that does not distinguish objectively different objects but describes clusters in the supercritical state and determines the relation between the mesoscopic physics of clusters and the macroscopic thermodynamics of supercritical isotherms. We construct the supercritical picture of isochores and isotherms under the condition that the Boyle temperature, the Boyle density, and the critical point are known, and we justify the two-fluid model of supercritical thermodynamics mathematically. For the “cluster sponge,” this leads to new relations different from the relations of the known Gentile statistics. We calculate the Frenkel temperature of the transition from rigid liquid to soft liquid.
Research target:
Mathematics
Language:
Russian
49606783, Russian Journal of Mathematical Physics 2014 Vol. 21 No. 1 P. 99-111
In the article, the relationship between the mesoscopic picture and the microscopic and macroscopic pictures is considered in the light of the work of V. E. Panin and his school. The coincidence of isochores and isotherms obtained by applying the undistinguishing statistics of objectively distinguishable objects with those of the Van-der-Waals model allows us to ...
Added: June 5, 2014
49606783, Mathematical notes 2014 Vol. 95 No. 5 P. 3-18
In this paper, a new approach to the two-body problem is considered in greater detail than in previous papers of the author.
The semiclassical transition from quantum statistics to classical statistics is studied and an analog of superfluidity
in classical thermodynamics for supercritical states is obtained. ...
Added: December 21, 2014
49606783, Mathematical notes 2014 Vol. 95 No. 1 P. 91-97
We consider various normalizations enabling us to change the scale of the graphs of isotherms and isochores. The relationship between parastatisticsal value of the maximal number of particles, corresponding to a given energy, and temperature allows us to pass in the domain of positive chemical potentials from the parastatisticsal number K (K = ∞ corresponds ...
Added: June 5, 2014
49606783, 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
49606783, Mathematical notes 2014 Vol. 95 No. 3 P. 399-406
Undistinguishing parastatistics of objectively distinguishable objects is considered. It describes clusters in the supercritical state. The relationship between the mesoscopic physics of clusters and the macroscopic thermodynamics of supercritical isotherms is established. We construct the supercritical pattern of isochores and isotherms under the assumption that the following three points: the Boyle temperature, the Boyle density, and the critical ...
Added: December 20, 2014
49606783, 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
49606783, Russian Journal of Mathematical Physics 2014 Vol. 21 No. 2 P. 256-284
We consider the main ideas that led the author to the construction of the new
thermodynamics; this construction explains the Gibbs paradox and the new experimental effects of supercritical thermodynamics, as well as the law of preference of cluster formation before passage of gases to the liquid state. The law of invariance of the fractional number ...
Added: November 30, 2014
Maslov V., 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
Maslov V., Mathematical notes 2013 Vol. 94 No. 4 P. 532-546
It is well known that the supercritical state of a gas has great dissolving capacity. In this paper, the mathematical reason for this phenomenon is studied in great detail. ...
Added: November 18, 2013
49606783, Mathematical notes 2014 Vol. 96 No. 5 P. 732-738
For UD-statistics, we present formulas that are in agreement with the value of the second virial coefficient as $\rho\to 0$
at the initial point of the activity a\to 0 and with the temperature on the critical isochore rho=\rho_c at the final point.
This leads to two invariants: (1) the number of collective degrees of freedom and 2) ...
Added: December 24, 2014
Талипова Т. Г., Kurkina O. E., Giniyatullin A. et al., Экологические системы и приборы 2013 № 12 С. 17-25
The surface-active substances everywhere are presented on the water surface, they are exposed to waves and currents, and are involved in the processes of ocean-atmosphere exchange. They play a prominent role in the formation of small-scale part of the spectrum of wind waves and affect the manifestations of internal waves on the sea surface. In ...
Added: November 18, 2013
Maslov V., Теоретическая и математическая физика 2015 Т. 182 № 2 С. 365-367
In contrast to the supercritical region where the isotherms ideally coincide with the isotherms of the van
der Waals model, we introduce an additional condition for the Hartley entropy to attain maximum on the
spinodal in the subcritical region. To determine the parameters of the distribution and isotherms, we use
spinodal equation. ...
Added: March 8, 2017
49606783, 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
D. V. Gribanov, D.S. Malyshev, P. M. Pardalos et al., Journal of Combinatorial Optimization 2018 Vol. 35 No. 4 P. 1128-1146
In this paper, we present fixed-parameter tractable algorithms for special cases of the shortest lattice vector, integer linear programming, and simplex width computation problems, when matrices included in the problems’ formulations are near square. The parameter is the maximum absolute value of the rank minors in the corresponding matrices. Additionally, we present fixed-parameter tractable algorithms ...
Added: February 19, 2018
Malyshev D., Вестник Нижегородского университета им. Н.И. Лобачевского 2008 № 6 С. 141-146
Рассматривается понятие граничного класса, которое является полезным инструментом для анализа вычислительной сложности задач на графах. Исследуются два конкретных класса графов, и приводятся задачи, для которых эти классы являются граничными. ...
Added: August 31, 2012
Belomestny D., Iosipoi L., Mathematics and Computers in Simulation 2021 No. 181 P. 351-363
Markov Chain Monte Carlo methods become increasingly popular in applied mathematics as a tool for numerical integration with respect to complex and high-dimensional distributions. However, application of MCMC methods to heavy-tailed distributions and distributions with analytically intractable densities turns out to be rather problematic. In this paper, we propose a novel approach towards the use ...
Added: October 31, 2020
МГУ, 2014
Тезисы докладов научной конференции «Ломоносовские чтения» 2013 ...
Added: December 11, 2016
Beklemishev L. D., Оноприенко А. А., Математический сборник 2015 Т. 206 № 9 С. 3-20
We formulate some term rewriting systems in which the number of computation steps is finite for each output, but this number cannot be bounded by a provably total computable function in Peano arithmetic PA. Thus, the termination of such systems is unprovable in PA. These systems are derived from an independent combinatorial result known as the Worm ...
Added: March 13, 2016
Yasnitsky L., Пермь : Пермский государственный национальный исследовательский университет. – Электронные данные. , 2020
The collection contains materials from the international conference "Intelligent systems in science and technology" and the Sixth all-Russian scientific and practical conference "Artificial intelligence in solving urgent social and economic problems of the XXI century", which was held on October 12-18, 2020 in Perm as part of the Perm natural science forum "Mathematics and global ...
Added: December 4, 2020
Revenko A., Kuznetsov S., Fundamenta Informaticae 2012 Vol. 4 No. 115 P. 377-394
An approach for studying relations between properties of functions on sets is proposed. The approach is based on Attribute Exploration. 16 properties of functions are considered, among them monotonicity, idempotency, path independence, exchange properties, convexity, etc. Example functions are partially computer generated on the powersets of sets with 2, 3 and 4 elements. Attribute Exploration ...
Added: December 31, 2012
Feigin B. L., Finkelberg M. V., Rybnikov L. G. et al., Selecta Mathematica, New Series 2011 Vol. 17 No. 3 P. 573-607
Laumon moduli spaces are certain smooth closures of the moduli spaces of maps from the projective line to the flag variety of GLn. We construct the action of the Yangian of sln in the cohomology of Laumon spaces by certain natural correspondences. We construct the action of the affine Yangian (two-parametric deformation of the universal ...
Added: October 9, 2012
Barcelona : IEEE, 2017
International Conference on Control, Decision and Information Technologies. ...
Added: January 17, 2018
Vyalyi M., Дискретная математика 1991 Т. 3 № 3 С. 35-45
Added: October 17, 2014
Lanham : University Press of America, 2012
The history of logic and analytic philosophy in Central and Eastern Europe is still known to very few people. As an exception to the rule, only two scientific schools became internationally popular: the Vienna Circle and the Lvov-Warsaw School. Nevertheless, the countries included in this region have not only joint history, but also joint cultural ...
Added: February 13, 2013