Энтропийно консервативная пространственная дискретизация многомерной квазигазодинамической системы уравнений

А. А. Злотник

Publications

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Энтропийно консервативная пространственная дискретизация многомерной квазигазодинамической системы уравнений

Журнал вычислительной математики и математической физики. 2017. Т. 57. № 4. С. 710–729.

Zlotnik A.

Priority areas: IT and mathematics

Language: Russian

Full text

Keywords: квазигазодинамическая система уравнений дискретизация по пространству spatial discretization quasi-gasdynamic system of equations The Navier-Stokes equations for viscous compressible heat-conducting gas conservativity the law of non-decreasing entropy уравнения Навье--Стокса вязкого сжимаемого теплопроводного газа консервативность закон неубывания энтропии

Консервативные энтропийно и энергетически корректные разностные методы для одномерных квазигазодинамических систем уравнений

Zlotnik A., Математические заметки 2026 Т. 120 № 6 С. 1005–1009

Численным методам решения систем газодинамических уравнений посвящена обширная литература. Ранее было разработано и успешно апробировано специальное семейство симметричных по пространству консервативных разностных методов, основанных на предварительной кинетической, точнее, квазигазодинамической (КГД), регуляризации этих уравнений. Актуальной задачей является построение численных методов, которые обладают не только свойством консервативности по массе, импульсу и полной энергии, но и удовлетворяют условиям энтропийной ...

Added: October 1, 2026

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

Timur Teregulov, Elena R. Loubenets, / 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

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

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

ML-based Fast Simulation of FARICH Responses

Shipilov F., Barnyakov A., Ivanov A. et al., / Series Physics "arxiv.org". 2026.

A fast simulation of the detector response is a vital task in high-energy physics (HEP). Traditional Monte-Carlo methods form the backbone of modern particle physics simulation software but are computationally expensive. We present a machine-learning-based approach to fast simulation of the Focusing Aerogel Ring Imaging Cherenkov (FARICH) detector response. Given a particle track and momentum, ...

Added: May 19, 2026

Natural hazard database from Internet publications: text mining with a large language model

Derkacheva A., Sakirkina M., Kraev G. et al., /. 2026.

Comprehensive data on natural hazards and their consequences are crucial for effective for risk assessment, adaptation planning, and emergency response. However, many countries face challenges with fragmented, inconsistent, and inaccessible data, particularly regarding local-scale events. To address this data gap in Russia, we developed an end-to-end processing pipeline that scrapes news from various online sources, ...

Added: April 28, 2026

Algorithmic overlaps as thermodynamic variables: from local to cluster Monte Carlo dynamics in critical phenomena

Pilé I., Deng Y., Shchur L., / Series arXiv "math". 2026. No. 2604.10254.

We investigate the spatial overlap of successive spin configurations in Markov chain Monte Carlo simulations using the local Metropolis algorithm and the Svendsen-Wang and Wolff cluster algorithms. We examine the dynamics of these algorithms for two models in different universality classes: the Ising model and the Potts model with three components. The overlap of two ...

Added: April 20, 2026

Using predefined vector systems to speed up neural network multimillion class classification

Gabdullin N., Androsov I., / Series Computer Science "arxiv.org". 2026.

Label prediction in neural networks (NNs) has O(n) complexity proportional to the number of classes. This holds true for classification using fully connected layers and cosine similarity with some set of class prototypes. In this paper we show that if NN latent space (LS) geometry is known and possesses specific properties, label prediction complexity can ...

Added: April 2, 2026

Iterative Ricci-Foster Curvature Flow with GMM-Based Edge Pruning: A Novel Approach to Community Detection

Sorokin K., Beketov M., Онучин А. et al., / arxiv.org. Серия cs.SI "Social and Information Networks ". 2025.

Community detection in complex networks is a fundamental problem, open to new approaches in various scientific settings. We introduce a novel community detection method, based on Ricci flow on graphs. Our technique iteratively updates edge weights (their metric lengths) according to their (combinatorial) Foster version of Ricci curvature computed from effective resistance distance between the ...

Added: January 15, 2026

Theoretical and Methodological Substantiation of Boundaries and Integrity in Landscape Cover and Its Components

A. N. Krenke, R. B. Sandlersky, A. S. Baybar et al., Известия РАН. Серия биологическая. 2023 Vol. 50 No. 1 P. S85–S99

Four main models of the appearance of boundaries (in a particular case, integrity), arising from the theory of nonlinear dynamic systems, are considered briefly. On the basis of Kotelnikov’s fundamental sampling theorem and, accordingly, general information theory, the character of a distinguished boundary as a function of the sampling frequency in a spatial series with a ...

Added: December 2, 2022

Условия диссипативности явной разностной схемы для линеаризованной многомерной квазигазодинамической системы уравнений

А. А. Злотник, Доклады Российской академии наук. Математика, информатика, процессы управления (ранее - Доклады Академии Наук. Математика) 2022 Т. 505 № 1 С. 30–36

Изучается явная двухслойная разностная схема для линеаризованной многомерной квазигазодинамической системы уравнений. Для начально-краевой задачи на неравномерной прямоугольной сетке впервые даются достаточные условия $L^2$-диссипативности типа Куранта энергетическим методом. Для задачи Коши на равномерной сетке усовершенствуются как необходимые, так и достаточные условия $L^2$-диссипативности в спектральном методе. Указывается новая форма задания параметра релаксации, гарантирующая равномерную ограниченность сверху и снизу числа ...

Added: June 20, 2022

Модельный риск и базовые подходы к его численному измерению на примере моделей оценки рыночного риска

Нэвэла А. Ю., Lapshin V. A., Финансовый журнал 2022 Т. 14 № 2 С. 91–112

Model risk is currently a topic of great interest both to the academic community and to the financial industry; however, there is not yet any generally accepted approach to measuring it as of now. We give a review of basic model risk definitions and different indicators and approaches to model risk estimation and calculation within ...

Added: April 25, 2022

Properties of an aggregated quasi-gasdynamic system of equations for a homogeneous gas mixture

Zlotnik A.A., Fedchenko A.S., Doklady Mathematics 2021 Vol. 104 No. 3 P. 340–346

For an aggregated quasi-gasdynamic system of equations for a homogeneous gas mixture, we give an entropy balance equation with a nonnegative entropy production in the presence of diffusion fluxes. We also derive the existence, uniqueness, and L^2 -dissipativity of weak solutions to an initial-boundary value problem for the system linearized at a constant solution. Additionally, the Petrovskii parabolicity ...

Added: February 17, 2022

Свойства агрегированной квазигазодинамической системы уравнений гомогенной газовой смеси

Злотник А.А., Федченко А.С., Доклады Российской академии наук. Математика, информатика, процессы управления (ранее - Доклады Академии Наук. Математика) 2021 Т. 501 № 1 С. 31–37

For an aggregated quasi-gasdynamic system of equations for a homogeneous gas mixture, we give the entropy balance equation with a nonnegative entropy production in the presence of diffusion fluxes. We also derive the existence, uniqueness and $L^2$-dissipativity of weak solutions to an initial-boundary value problem for a system linearized at a constant solution as well as ...

Added: September 28, 2021

О L^2-диссипативности линеаризованной явной разностной схемы с КГД-регуляризацией для системы уравнений баротропной газовой динамики

А. А. Злотник, Т. А. Ломоносов, Доклады Российской академии наук. Математика, информатика, процессы управления (ранее - Доклады Академии Наук. Математика) 2020 Т. 492 № 1 С. 31–37

We study an explicit two-level symmetric in space finite-difference scheme for the multi\-di\-men\-si\-onal barotropic gas dynamics system of equations with quasi-gasdynamic regulari\-za\-tion linearized at a constant solution (with arbitrary velocity). A criterion and both necessary and sufficient conditions for the $L^2$-dissipativity of the solutions to the Cauchy problem for the scheme are derived by the spectral ...

Added: March 4, 2020

Conditions for L^2-Dissipativity of Linearized Explicit Difference Schemes with Regularization for 1D Barotropic Gas Dynamics Equations

Zlotnik A.A., Lomonosov T.A., Computational Mathematics and Mathematical Physics 2019 Vol. 59 No. 3 P. 452–464

Explicit two-level in time and symmetric in space finite-difference schemes constructed by approximating the 1D barotropic quasi-gas-/quasi-hydrodynamic systems of equations are studied. The schemes are linearized about a constant solution with a nonzero velocity, and, for them, necessary and sufficient conditions for the L2-dissipativity of solutions to the Cauchy problem are derived depending on the Mach number. These conditions ...

Added: March 11, 2019

On conditions for L2-dissipativity of linearized explicit QGD finite-difference schemes for one-dimensional gas dynamics equations

Zlotnik A., Lomonosov T., Doklady Mathematics 2018 Vol. 98 No. 2 P. 458–463

An explicit two-time-level and spatially symmetric finite-difference scheme approximating the 1D quasi-gasdynamic system of equations is studied. The scheme is linearized about a constant solution, and new necessary and sufficient conditions for the L2 -dissipativity of solutions of the Cauchy problem are derived, including, for the first time, the case of a nonzero background velocity ...

Added: September 12, 2018

Слайдинг и вариабельность длины интронов для генов, обогащенных длинными интронами фазы 1

Поверенная И. В., Горев Д., Астахова Т. В. et al., Математическая биология и биоинформатика 2017 Т. 12 № 2 С. 302–316

Due to high mutagenesis of intron sequences, intron evolution is usually considered in terms of evolution of exon-intron structures (EIS). The shifting of intron over short distances (rare evolutionary event called intron sliding) could lead to the change of intron phase, i.e. the intron position relative to the open reading frame. Here we analyze the ...

Added: September 12, 2018

Об условиях $L^2$-диссипативности линеаризованных явных КГД-разностных схем для уравнений одномерной газовой динамики

Zlotnik A., Lomonosov T., Доклады Академии наук 2018 Т. 482 № 4 С. 375–380

Изучается явная двухслойная по времени и симметричная по пространству разностная схема, аппроксимирующая 1D квазигазодинамическую систему уравнений. Она линеаризуется на постоянном решении и для нее выводятся новые как необходимые, так и достаточные условия $L^2$-диссипативности решений задачи Коши, в том числе впервые при ненулевой фоновой скорости в зависимости от числа Маха. Показано, что можно обеспечить независимость условия на число ...

Added: May 21, 2018

On the energy dissipative spatial discretization of the barotropic quasi-gasdynamic and compressible Navier-Stokes systems of equations in polar coordinates

Zlotnik A., Russian Journal on Numerical Analysis and Mathematical Modelling 2018 Vol. 33 No. 3 P. 199–210

The barotropic quasi-gasdynamic system of equations in polar coordinates is treated. It can be considered a kinetically motivated parabolic regularization of the compressible Navier-Stokes system involving additional 2nd order terms with a regularizing parameter $\tau>0$. A potential body force is taken into account. The energy equality is proved ensuring that the total energy is non-increasing ...

Added: December 16, 2017

On some properties of multidimensional hyperbolic quasi-gasdynamic systems of equations

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

Entropy Balance for the One-Dimensional Hyperbolic Quasi-Gasdynamic System of Equations

Zlotnik A. A., Chetverushkin B. N., Doklady Mathematics 2017 Vol. 95 No. 3 P. 276–281

Entropy balance in the one-dimensional hyperbolic quasi-gasdynamic (HQGD) system of equations is analyzed. In regular flow regimes, it is shown that the behavior of entropy in the HQGD system is determined by terms involving the natural viscosity and thermal conductivity coefficients. The total entropy production differs from the Navier–Stokes equations for viscous compressible heat-conducting gases ...

Added: April 25, 2017