Математическое разрешение парадокса Гиббса
Mathematical notes. 2011. Т. 89. № 2. С. 272-284.
In this paper, we construct a new distribution corresponding to a real noble gas as well as the equation of state for it.
New critical points for the liquid phase and the construction of thermodynamics depending on the interaction potential
, Mathematical notes 2010 Vol. 88 No. 5 P. 723-731
The author constructs a one-particle distribution generalizing the Maxwell-Boltzmann and Bose-Einstein distributions for classical particles, without incurring the Gibbs paradox, and, simultaneously, constructs the thermodynamics of fluids and phase transitions on the basis of the concept of creation of dimes and clusters and obtains well-known laws. ...
Added: April 13, 2012
, Russian Journal of Mathematical Physics 2011 Vol. 18 No. 2 P. 163-175
For a gas mixture, the new concept of number-theoretic internal energy is introduced. This energy does not depend on the masses of the miscible gases. ...
Added: April 12, 2012
On the Introduction of the Temperature Standard in the Nondistinguishing Parastatistics of Objectively Distinguishable
, 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
, 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
, 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
, 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 ...
Added: October 26, 2014
, 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
, , World Futures: Journal of General Evolution 2009 Vol. 65 No. 7 P. 477-506
Added: March 7, 2013
, Mathematical notes 2016 Vol. 100 No. 1 P. 154-185
The author constructs a new conception of thermodynamics which is based on new results in number theory. We consider a maximally wide range of gases, liquids, and fluids to which, in principle, the Carathéodory approach can be applied. The Carathéodory principle is studied using the Lennard-Jones potential as an example. On the basis of this ...
Added: October 10, 2016
, 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
, 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
, Russian Journal of Mathematical Physics 2012 Vol. 19 No. 4 P. 485-499
It is shown that the Boltzmann-Maxwell distribution is not applicable to the generalized notion of ideal gas and corresponds to this ideal gas at low density only. The behavior of an ideal gas and its transition to liquid is studied as a result of a kind of generalization of the problem of “partitio numerorum”. The ...
Added: January 17, 2013
, 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
Роль кластеров и кластерной политики в развитии российских регионов: постановка проблемы и возможный подход к оценке
, , , Известия Русского географического общества 2018 Т. 150 № 3 С. 1-11
Исследование роли кластеров в российской экономике сталкивается с проблемами их идентификации. Сложностью для исследователей также является отсутствие полной базы данных кластеров России. Поэтому, прежде всего, нами была собрана и систематизирована информация о 191 кластере, на основании чего была построена карта регионов России с обозначенными на ней местами расположения кластеров. Далее в статье выделена группа регионов, ...
Added: November 18, 2018
, , Журнал экспериментальной и теоретической физики 2008 Т. 134 № 4 С. 772-778
Построена микроскопическая теория сверхпроводимости намагниченного электронного газа на цилиндрической поверхности. Вычислен термодинамический потенциал сверхпроводящей системы. Получено уравнение для энергетической щели, определяющее зависимость критической температуры от геометрических размеров квантового цилиндра и параметра Ааронова-Бома. Показано, что ширина энергетической щели наряду с осцилляциями Ааронова-Бома испытывает также осцилляции при изменении кривизны цилиндрической поверхности. ...
Added: January 4, 2013
, , , 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
, 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
Berlin: Springer, 2014
The volume is dedicated to Boris Mirkin on the occasion of his 70th birthday. In addition to his startling PhD results in abstract automata theory, Mirkin’s ground breaking contributions in various fields of decision making and data analysis have marked the fourth quarter of the 20th century and beyond. Mirkin has done pioneering work in ...
Added: October 7, 2013
Liquid but Durable: Molecular Dynamics Simulations Explain the Unique Properties of Archaeal-Like Membranes
, , et al., Scientific Reports 2014 Vol. 4 No. 7462 P. 1-8
Archaeal plasma membranes appear to be extremely durable and almost impermeable to water and ions, in contrast to the membranes of Bacteria and Eucaryota. Additionally, they remain liquid within a temperature range of 0–100° С. These are the properties that have most likely determined the evolutionary fate of Archaea, and it may be possible for bionanotechnology ...
Added: July 21, 2015
, , , Scientific Reports 2016 Vol. 6
We propose a modification of the Crow-Kimura and Eigen models of biological molecular evolution to include a mutator gene that causes both an increase in the mutation rate and a change in the fitness landscape. This mutator effect relates to a wide range of biomedical problems. There are three possible phases: mutator phase, mixed phase ...
Added: September 16, 2016
, , Stochastics-An International Journal of Probability and Stochastic Processes 2019 Vol. 91 No. 5 P. 754-772
In this paper, we consider limit laws for the model, which is a generalisation of the random energy model (REM) to the case when the energy levels have the mixture distribution. More precisely, the distribution of the energy levels is assumed to be a mixture of two normal distributions, one of which is standard normal, ...
Added: November 19, 2018
Bounds of the Repeated Limit for the Bose–Einstein Distribution and the Construction of Partition Theory of Integers*
, Mathematical notes 2017 Vol. 102 No. 4 P. 583-586
Added: November 17, 2018
Large Negative Numbers in Number Theory, Thermodynamics, Information Theory, and Human Thermodynamics
, Russian Journal of Mathematical Physics 2016 Vol. 23 No. 4 P. 509-524
We show how the abstract analytic number theory of Maier, Postnikov, and others can be extended to include negative numbers and apply this to thermodynamics, information theory, and human thermodynamics. In particular, we introduce a certain large number N_0 on the "zero level" with a high multiplicity number qi ≫ 1 related to the physical ...
Added: February 25, 2017
, , et al., World Order Transformation and Sociopolitical Destabilization / 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