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## Remarks on the model of quasi-homogeneous binary mixtures with the NASG equations of state

Applied Mathematics Letters. 2023. Vol. 146. Article 108801.

We deal with the so-called four-equation model for dynamics of the heterogeneous binary mixtures of the Noble-Abel stiffened-gases (NASGes). In relation to the quasi-homogeneous form of the model, we suggest a new insight on a quadratic equation for the pressure, give a simple formula for the squared speed of sound and present a new proof for a formula connecting it to the Wood speed of sound. A short derivation of the balance equation for the pressure is included as well.

Zlotnik A., Lomonosov T., Doklady Mathematics 2023 Vol. 108 No. 3 P. 443–449

We consider the so-called four-equation model for dynamics of the heterogeneous compressible binary mixtures with the Noble-Abel stiffened-gas equations of state. We exploit its quasi-homogeneous form that arises after excluding the volume concentrations from the sought functions and is based on a quadratic equation for the common pressure of the components. We present new properties ...

Added: March 1, 2024

Chetverushkin B. N., Zlotnik A.A., Russian Journal of Mathematical Physics 2017 Vol. 24 No. 3 P. 299–309

We study a multidimensional hyperbolic quasi-gasdynamic (HQGD) system of equations containing terms with a regularizing parameter $\tau>0$ and 2nd order space and time derivatives; the body force is taken into account. We transform it to the form close to the compressible Navier-Stokes system of equations. Then we derive the entropy balance equation and show that ...

Added: July 19, 2017

V.A. Gavrilin, A.A. Zlotnik, Computational Mathematics and Mathematical Physics 2015 Vol. 55 No. 2 P. 264–281

The one-dimensional quasi-gasdynamic system of equations in the form of mass, momentum, and total energy conservation laws with general gas equations of state is considered. A family of three-point symmetric spatial discretizations of this system is studied for which the internal energy equation has a suitable form (without imbalance terms). An entropy balance equation is ...

Added: February 21, 2015

Zlotnik A., Журнал вычислительной математики и математической физики 2012 Т. 52 № 7 С. 1304–1316

For the quasi-gasdynamic system of equations, there holds the law of nondecreasing entropy. Difference methods based on this system have been successfully used in numerous applications and test gasdynamic computations. In theoretical terms, however, for standard spatial discretizations of this system, the nondecreasing entropy law does not hold exactly even in the onedimensional case because ...

Added: June 30, 2012

Zlotnik A., Gavrilin undefined. V., Вестник Московского энергетического института 2016 № 1 С. 5–14

Изучается семейство трехточечных симметричных дискретизаций по пространству квазигидродинамической системы уравнений с общими уравнениями состояния газа. Выводится уравнение баланса энтропии. В нем вид сеточных дисбалансных слагаемых зависит от выбора усреднений плотности и внутренней энергии; для специальных усреднений недивергентные дисбалансные слагаемые равны 0. Выполняются расчеты известных тестов для системы уравнений Эйлера при различных уравнениях состояния. Их результаты ...

Added: October 9, 2015

А. А. Злотник, Т. А. Ломоносов, Доклады Российской академии наук. Математика, информатика, процессы управления (ранее - Доклады Академии Наук. Математика) 2023 Т. 514 № 1 С. 26–33

Рассматривается так называемая модель из четырех уравнений динамики гетерогенных сжимаемых бинарных смесей при уравнениях состояния “сжатого” газа Ноубла-Абеля. Используется ее квазигомогенная форма, возникающая после исключения объемных концентраций из искомых функций и основанная на квадратном уравнении для общего давления компонент. Приводятся новые свойства этого уравнения и простая формула для квадрата скорости звука, предлагается альтернативный вывод формулы, ...

Added: December 23, 2023

Zlotnik A.A., Computational Mathematics and Mathematical Physics 2012 Vol. 52 No. 7 P. 1060–1071

For the quasi-gasdynamic system of equations, there holds the law of nondecreasing entropy. Difference methods based on this system have been successfully used in numerous applications and test gasdynamic computations. In theoretical terms, however, for standard spatial discretizations of this system, the nondecreasing entropy law does not hold exactly even in the one-dimensional case because ...

Added: February 4, 2013

I. A. Kondratyev, S. G. Moiseenko, Lobachevskii Journal of Mathematics 2023 Vol. 44 No. 1 P. 44–56

In astrophysical fluid dynamics, some types of flows, like e.g., magnetorotational super- nova explosions, deal with a highly variable Mach number (from M ≪ 1 in the protoneutron star region to M ≫ 1 near the shock wave expelling from the stellar envelope) in presence of a strong diﬀerential rotation. The Courant–Friedrichs–Lewy (CFL) stability condition ...

Added: May 22, 2023

Elizarova T.G., Zlotnik A.A., Chetverushkin B. N., Доклады Академии наук 2014 Vol. 90 No. 3 P. 1–5

The quasigasdynamic (QGD) approach makes it possible to construct convenient and reliable difference schemes for the numerical solution of various gasdynamic problems. Its description can be found in several books. In particular, the Boltzmann kinetic equation for a mixture of monatomic gases is used to derive and test QGD equations for binary mixtures of nonreactive ...

Added: November 29, 2014

Zlotnik A.A., Доклады Академии наук 2012 Vol. 86 No. 1 P. 464–468

Added: February 4, 2013

Elena R. Loubenets, Khrennikov A., Journal of Physics A: Mathematical and Theoretical 2019 Vol. 52 No. 43 P. 435304-1–435304-14

For an even qudit dimension d≥2, we introduce a class of two-qudit states exhibiting perfect correlations/ anticorrelations and prove via the generalized Gell-Mann representation that, for each two-qudit state from this class, the maximal violation of the original Bell inequality is bounded from above by the value 3/2 -- the upper bound attained on some ...

Added: September 26, 2019

Budkov Y., Journal of Physics: Condensed Matter 2019 Vol. 31 P. 078002–078003

We reply to the comment on our paper by Budkov (2018 J. Phys.: Condens. Matter 30 344001). ...

Added: January 4, 2019

Васильев М. А., Zotov A., Reviews in Mathematical Physics 2019 Vol. 31 No. 06 P. 1–42

In this paper we study factorization formulae for the Lax matrices of the classical Ruijsenaars-Schneider and Calogero-Moser models. We review the already known results and discuss their possible origins. The first origin comes from the IRF-Vertex relations and the properties of the intertwining matrices. The second origin is based on the Schlesinger transformations generated by ...

Added: September 16, 2024

CRC Press, 2016

In addition to explaining and modeling unexplored phenomena in nature and society, chaos uses vital parts of nonlinear dynamical systems theory and established chaotic theory to open new frontiers and fields of study. Handbook of Applications of Chaos Theory covers the main parts of chaos theory along with various applications to diverse areas. Expert contributors ...

Added: October 26, 2021

Musaev E., Akhmedov E., Gahramanov I., JETP Letters 2011 Vol. 93 No. 9 P. 545–550

The Polchinski equations for the Wilsonian renormalization group in the D-dimensional matrix scalar field theory can be written at large N in a Hamiltonian form. The Hamiltonian defines evolution along one extra holographic dimension (energy scale) and can be found exactly for the subsector of Trϕ n (for all n) operators. We show that at ...

Added: October 20, 2014

Kurkina O. E., Kurkin A. A., Rouvinskaya E. et al., Письма в Журнал экспериментальной и теоретической физики 2012 Т. 95 № 2 С. 98–103

Nonlinear wave dynamics is discussed using the extended modified Korteweg–de Vries equation that includes the combination of the third- and fifth- order terms and is valid for waves in a three-layer fluid with so-called symmetric stratification. The derived equation has solutions in the form of solitary waves of various polarities. At small amplitudes, they are ...

Added: August 24, 2012

Aseeva N., Gromov E., Onosova I. V. et al., JETP Letters 2016 Vol. 103 No. 10 P. 653–657

Evolution of solitons is addressed in the framework of a third-order nonlinear Schrödinger equation (NLSE), including nonlinear dispersion, third-order dispersion and a pseudo-stimulated-Raman-scattering (pseudo-SRS) term, i.e., a spatial-domain counterpart of the SRS term, which is well known as a part of the temporal domain NLSE in optics. In this context, it is induced by the ...

Added: June 28, 2016

Pelinovsky E., Didenkulova I., Rybkin A., Journal of Fluid Mechanics 2014 Vol. 748 P. 416–432

We present an exact analytical solution of the nonlinear shallow water theory for wave run-up in inclined channels of arbitrary cross-section, which generalizes previous studies on wave run-up for a plane beach and channels of parabolic cross-section. The solution is found using a hodograph-type transform, which extends the well-known Carrier–Greenspan transform for wave run-up on ...

Added: November 19, 2014

Vostrikov A. V., Borisov N., Abrameshin A. E., Качество. Инновации. Образование 2013 № 8 (99) С. 61–65

In work research of numerical stability of earlier reduced scheme of numerical integration of system of the linear ordinary differential equations developed by authors is conducted. The received condition of numerical stability of the reducing scheme proves possibility of use of this scheme in practice. Operability of the reduced scheme was tested on a real ...

Added: September 9, 2013

49606783, Russian Journal of Mathematical Physics 2019 Vol. 26 No. 2 P. 168–173

The parameters of unstable short-living isotopes are studied from
the mathematical point of view. The values of the chemical potential
and activity parameters that determine the neutron halo arising when
the neutron separates from the nucleus of an unstable isotope are
calculated. The analogy between nuclear physics and economics is
considered from the point of view of such parameters as ...

Added: August 25, 2019

Elena R. Loubenets, / Cornell University. Series arXiv "quant-ph". 2012. No. 1210.3270.

Added: September 25, 2016

Marshakov A., Миронов А. Д., Морозов А. Ю., Journal of Geometry and Physics 2011 Vol. 61 P. 1203–1222

We present a summary of current knowledge about the AGT relations for conformal blocks with additional insertion of the simplest degenerate operator, and a special choice of the corresponding intermediate dimension, when the conformal blocks satisfy hypergeometric-type differential equations in position of the degenerate operator. A special attention is devoted to representation of conformal block ...

Added: February 28, 2013

Min Namkung, Younghun K., Scientific Reports 2018 Vol. 8 No. 1 P. 16915-1–16915-18

Sequential state discrimination is a strategy for quantum state discrimination of a sender’s quantum
states when N receivers are separately located. In this report, we propose optical designs that can
perform sequential state discrimination of two coherent states. For this purpose, we consider not
only binary phase-shifting-key (BPSK) signals but also general coherent states, with arbitrary prior
probabilities. Since ...

Added: November 16, 2020

Dmitriev A., Kornilov V., Dmitriev V. et al., Frontiers in Physics 2022 Vol. 10 No. 839383 Article 839383

The sandpile cellular automata, despite the simplicity of their basic rules, are adequate mathematical models of real-world systems, primarily open nonlinear systems capable to self-organize into the critical state. Such systems surround us everywhere. Starting from processes at microscopic distances in the human brain and ending with large-scale water flows in the oceans. The detection ...

Added: March 14, 2022