On conditions for weak conservativeness of regularized explicit finite-difference schemes for 1D barotropic gas dynamics equations

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On conditions for weak conservativeness of regularized explicit finite-difference schemes for 1D barotropic gas dynamics equations

2018.

We consider explicit two-level three-point in space finite-difference schemes for solving 1D barotropic gas dynamics equations. The schemes are based on special quasi-gasdynamic and quasi-hydrodynamic regularizations of the system. We linearize the schemes on a constant solution and derive the von Neumann type necessary condition and a CFL type criterion (necessary and sufficient condition) for weak conservativeness in L2 for the corresponding initial-value problem on the whole line. The criterion is essentially narrower than the necessary condition and wider than a sufficient one obtained recently in a particular case; moreover, it corresponds most well to numerical results for the original gas dynamics system.

Priority areas: IT and mathematics mathematics

Language: English

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A Three-Party W-State Quantum Secret Sharing Protocol with X-Gate Encoding and Forbidden-Outcome Detection

Teregulov T., Loubenets E. R., / Series Quantum Physics "arXiv". 2026. No. 2609.31472.

We develop a new three-party quantum secret-sharing (QSS) protocol based on a three-qubit W state. This protocol encodes the secret-sequence bits using X gates and employs randomly selected Hadamard operations and measurement bases to generate information and security-test rounds. We evaluate the efficiency of the proposed protocol and analyze its security against an internal adversary ...

Added: September 28, 2026

Pairings on the algebra of Laurent series over a ring

Levashev V., / Series arXiv "math". 2026. No. 2609.06010.

We prove that continuous A-bilinear pairings on the ring of Laurent series that are invariant under continuous automorphisms coincide, up to a constant, with the pairing given by the residue of a differential form over any commutative associative ring with identity. ...

Added: September 24, 2026

Iterative construction of the R-matrices in arbitrary dimensions

Pyatov P. N., Pivovarov P. A., / Series math "arxiv.org". 2026. No. 2609.06274.

We investigate a special ansats that allows for an iterative solution of the constant Yang-Baxter equation. Testing this ansatz, we construct four sequences of the constant R-matrices. In each sequence the R-matrices act on the tensor squares of vector spaces of linearly growing dimensions. Each R-matrix also depends on a single complex parameter. By analyzing the ...

Added: September 24, 2026

On static manifolds with boundary admitting a nowhere-vanishing static potential

Medvedev V., / Series arXiv "math". 2026.

We study complete static manifolds with boundary admitting a nowhere-vanishing static potential. Our main result shows that, under a natural lower bound relating the scalar curvature and the boundary mean curvature, a simple static manifold with boundary must in fact have positive scalar curvature, negative boundary mean curvature, and be compact; we also obtain explicit ...

Added: September 19, 2026

Vague stimulating ideas, images and metaphors in scientific thinking: researchers' work with horizons of unclear knowledge

Poddiakov A., / Series Social Science Research Network "Social Science Research Network". 2026. No. 7437658.

Clarity of knowledge and reasoning is necessary in many cases. Yet vagueness in scientific thinking related to surprise, curiosity, "ability to engage with not-knowing" (de Freitas) and abductive reasoning is also a crucially important source of scientific creativity which supplements combinatorial logic when dealing with the already known. Starting from studies by C. S. Peirce ...

Added: September 15, 2026

On phase-lock area parquet in a special slow-fast limit of model of Josephson junction.

Glutsyuk A., / Series arXiv "math". 2026.

B.Josephson (Nobel Prize, 1973) predicted a tunnelling effect for a system of two superconductors separated by a narrow dielectric (such a system is called Josephson junction): existence of a supercurrent through it and equations governing it. The overdamped Josephson junction is modeled by the family of differential equations on the 2-torus, dθdτ=1ω(cosθ+B+Acosτ), which is known as ...

Added: September 8, 2026

Infinitely many graph manifolds with unique geometrical piece that admit arbitrarily many Anosov flows

Pochinka O., Shmukler V., / Series math.RT "arXiv:1808.06395 [math.RT]". 2026.

Anosov flows have a long and rich history, firstly motivated by the study of geodesic flows in negative curvature surface by Anosov and Sinai. Not every closed manifold admits an Anosov flow for well-known reasons: the fundamental group of a 3-manifold M admitting an Anosov flow must have exponential growth, and M must be universally covered by R3. Nevertheless, there ...

Added: August 31, 2026

On calibration of remote sensing retrievals of ecosystem respiration (Reco) with tower measurements over,Russian forests and wetlands

Shabanov N., Kuricheva O., Kurbatova J. et al., / Series Working Papers SSRN "Department of Economics Ca’ Foscari University of Venice". 2026.

The carbon balance of an ecosystem is the difference between Gross Primary Productivity (GPP) and Ecosystem Respiration (Reco) as expressed by Net Ecosystem Exchange (NEE). While remote sensing retrievals of GPP have reached maturity, Reco estimation remains underexplored and ultimately cast bias on NEE. Here we present an end-to-end multi-scale analysis of the mechanism of ...

Added: August 21, 2026

Three Algorithms for Merging Hierarchical Navigable Small World Graphs

Ponomarenko A., / Series Computer Science "arxiv.org". 2025.

This paper addresses the challenge of merging hierarchical navigable small world (HNSW) graphs, a critical operation for distributed systems, incremental indexing, and database compaction. We propose three algorithms for this task: Naive Graph Merge (NGM), Intra Graph Traversal Merge (IGTM), and Cross Graph Traversal Merge (CGTM). These algorithms differ in their approach to vertex selection ...

Added: July 30, 2026

New bound on S1× S2-setting Bell locality of a nonseparable Werner state

Loubenets E. R., / Series arxiv.org "quant-ph". 2026. No. 2607.18050.

In many quantum applications it is important to know whether or not a Bell nonlocal two-qudit state exhibits its nonlocality under correlation scenarios with some given numbers S1,S2≥1 of generalized quantum measurements at two sites. In the present article, we find analytically a new general locality condition sufficient for a nonseparable Werner state with a ...

Added: July 21, 2026

On functional equations for Chow polylogarithms

Bolbachan V., / Series math "arxiv.org". 2024.

Chow polylogarithms are some special functions arising in explicit description of the Beilinson regulator map. The most interesting functional equation for this function reflects its vanishing on the boundary in the Bloch's cycle complex. We show that this functional equation formally follows from more simple ones, namely skew-symmetry, functoriality and multiplicativity. To prove this, we study ...

Added: July 16, 2026

On Goncharov’s conjecture in next to Milnor degree

Bolbachan V., / Series math "arxiv.org". 2024.

Let K be a field of characteristic zero. We prove that its motivic cohomology in degree m−1 and weight m is rationally isomorphic to the cohomology of the polylogarithmic complex. This gives a partial extension of A. Suslin theorem describing the indecomposable K3 of a field. ...

Added: July 16, 2026

Statistical inference based on band-limited kernels: Rational-infinitely divisible distributions and beyond

Panov V., Ryabchenko A., / Series arXiv "stat.ME". 2026. No. 2607.05048.

This paper investigates the problem of statistical inference for a mixture distribution consisting of a discrete and a continuous component, with a particular focus on the class of rational-infinitely divisible distributions. We consider non-parametric estimation of both components of the mixture as well as the quasi-L{é}vy measure, assuming that the mixture belongs to the class ...

Added: July 9, 2026

Growth in noncommutative algebras and entropy in derived categories

Piontkovski D., / Series arXiv "math". 2026.

A noncommutative projective variety is defined, following Artin and Zhang, by a graded coherent algebra 𝐴. The category of coherent sheaves is then the quotient qgr(𝐴) of the category of finitely presented graded modules by the subcategory of torsion modules. We consider the categorical and polynomial entropies of the Serre twist, that is, of the ...

Added: June 23, 2026

Multilinear nilalgebras and the Jacobian theorem

Piontkovski D., / Series arXiv "math". 2025.

If a symmetric multilinear algebra is weakly nil, then it is Engel. This result may be regarded as an infinite-dimensional analogue of the well-known Jacobian theorem, which states that if a polynomial mapping has a polynomial inverse, then its Jacobian matrix is invertible. This refines a theorem of Gerstenhaber and partially answers a question posed ...

Added: June 23, 2026

Strong Approximations for Markov Chains Weakly Converging to Diffusions

Konakov V., Kucher D., Mammen E., / Series arXiv "math". 2026. No. 2606.11142v1.

In this paper, we construct strong approximations for discrete-time Markov chains weakly converging to continuous diffusion processes, as well as for their perturbed counterparts. Under the assumption of bounded coefficients, we construct closely coupled versions of these processes on a shared probability space. In particular, for both non-degenerate and degenerate cases, we maximize the probability ...

Added: June 11, 2026

Regularized Equations for Dynamics of the Heterogeneous Binary Mixtures of the Noble-Abel Stiffened-Gases and Their Application

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

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

Zlotnik A., 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 ...

Added: August 4, 2023

A Semi-Implicit Numerical Method for Differentially Rotating Compressible Flows

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

Properties of regularized equations for barotropic gas mixtures

Fedchenko A., Journal of Mathematical Sciences 2023 Vol. 270 No. 6 P. 815–826

We consider regularizations of systems of equations for a multicomponent gas mixture dynamics in the barotropic multi-velocity and one-velocity cases. Energy balance equations are derived for them. For the system of equations in the one-velocity case, the system linearized on a constant solution is studied, and, for the weak solutions to the initial-boundary value problem with ...

Added: May 11, 2023

Stability Analysis of a Multi-server Model with Simultaneous Service and a Regenerative Input Flow

Afanaseva L., Bashtova E., Grishunina S., , in: Methodology and Computing in Applied ProbabilityVol. 22: Methodology and Computing in Applied Probability. Issue 4: Methodology and Computing in Applied Probability.: Netherlands: Springer, 2020. Ch. 3 P. 1439–1455.

We study the stability conditions of the multiserver system in which each customer requires a random number of servers simultaneously. The input flow is supposed to be a regenerative one and a random service time is identical at all occupied servers. The service time has an exponential or a phase-type distribution. We define an auxiliary ...

Added: February 2, 2021

Исследование масштабируемости FlowVision на кластере с интерконнектом Ангара

Акимов В. С., Силаев Д. П., Симонов А. С. et al., Вычислительные методы и программирование: новые вычислительные технологии 2017 Т. 18 С. 406–415

The scalability of computations in FlowVision CFD software on the Angara-C1 cluster equipped with Angara interconnect is studied. Several test problems with 260 thousand, 5.5 million and 26.8 million computational cells are considered. Computations in FlowVision are performed using a new solver of linear systems based on the algebraic multigrid (AMG) method. It is shown ...

Added: October 30, 2019

Analysis of the approximate solutions of HII region expansion problem

Krasnobaev K. V., Fedchenko A., Journal of Physics: Conference Series 2018 No. 1129 P. 012012

The properties of interstellar gas produce significant effect on dynamic phenomena which occur at large heliocentric distances. HII region is a vivid example of the objects with extremely high radiation, where atoms of hydrogen are heated and ionized by ultraviolet radiation. This article deals with the HII region expansion. To study this process researches need ...

Added: October 13, 2019

Условия L^2-диссипативности линеаризованных явных разностных схем с регуляризацией для уравнений 1D баротропной газовой динамики

Zlotnik A., Lomonosov T., Журнал вычислительной математики и математической физики 2019 Т. 59 № 3 С. 481–493

Изучаются явные двухслойные по времени и симметричные по пространству разностные схемы, построенные посредством аппроксимации 1D баротропных квазигазо/квазигидродинамических систем уравнений. Они линеаризуются на постоянном решении с ненулевой скоростью, и для них выводятся как необходимые, так и достаточные условия $L^2$-диссипативности решений задачи Коши в зависимости от числа Маха. Эти условия различаются между собой не более чем в 2 раза. Результаты ...

Added: September 26, 2018