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Method for passivation of propellant residues in orbital stage tank of launch vehicle

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Chinese Journal of Aeronautics 2024年第1期37卷 64-76页

作者： Valeriy TRUSHLYAKOV Ivan LESNYAK Alexey PANICHKIN Department of Aviation and Rocket Building Omsk State Technical UniversityOmsk 644050Russia sobolev institute of mathematics of the Siberian Branch of Russian Academy of Sciences Novosibirsk 630090Russia

The problem of removing unused liquid propellant residues from the tanks of spent spacecraft and orbital stages of Launch Vehicles(LV)leads to their explosion and the formation of space debris in *** provide a solution to this problem,a method for removing liquid propellant residues from the LV tanks after the mission completion is *** method is based on the gasification of liquid propellant residues in the tanks under acoustic-vacuum exposure and the discharge of the gasification products into the surrounding outer *** investigations were carried out on a Ground-based Experimental Installation(GEI)to determine the coefficient of heat transfer from the surface of an acoustic radiator to a *** obtained coefficient was then used to calculate the energy costs for the gasification of *** estimates are given on the example of the tank with kerosene residues from a spent second stage of the LV“Soyuz-2.1 v”.The optimal discharge rate at which kerosene does not freeze is 0.14 m^(3)/***,the acoustic exposure leads to an increase in the mass of evaporated kerosene over a given time by96.1%,and the energy costs are 1756.7 kJ(approximately 50% of the remaining electrical energy).

关键词： Propellant Weightlessness Liquid evaporation Heat and mass transfer Acoustics Vacuum Vapor bubbles

On Differential Equations of Integrable Billiard Tables

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Acta Mathematica Sinica,English Series 2024年第1期40卷 417-424页

作者： Vladimir DRAGOVIC Andrey E.MIRONOV Department of Mathematical Sciences The University of Texas at DallasRichardson TXUSA Mathematical institute SANU BelgradeSerbia Novosibirsk State University NovosibirskRussia sobolev institute of mathematics of the Siberian Branch of the Russian Academy of Sciences NovosibirskRussia

We introduce a method to find differential equations for functions which define tables,such that associated billiard systems admit a local first *** illustrate this method in three situations:the case of(locally)integrable wire billiards,for finding surfaces in R^(3)with a first integral of degree one in velocities,and for finding a piece-wise smooth surface in R^(3)homeomorphic to a torus,being a table of a billiard admitting two additional first integrals.

关键词： Polynomial first integrals wire billiards piece-wise smooth surfaces

Centroid Hom-associative Algebras and Centroid Hom-Lie Algebras

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Acta Mathematica Sinica,English Series 2024年第4期40卷 935-961页

作者： Yu Xiu BAI Leonid A.BOKUT Yu Qun CHEN Ze Rui ZHANG Department of mathematics Teaching Guangzhou Civil Aviation CollegeGuangzhou 510403P.R.China sobolev institute of mathematics Novosibirsk 630090Russia Novosibirsk State University Novosibirsk 630090Russia School of Mathematical Sciences South China Normal UniversityGuangzhou 510631P.R.China

In this article,we construct free centroid hom-associative algebras and free centroid hom-Lie *** also construct some other relatively free centroid hom-associative algebras by applying the Gr?bner-Shirshov basis theory for(unital)centroid hom-associative ***,we prove that the"Poincaré-Birkhoff-Witt theorem"holds for certain type of centroid hom-Lie algebras over a field of characteristic 0,namely,every centroid hom-Lie algebra such that the eigenvectors of the mapβlinearly generates the whole algebra can be embedded into its universal enveloping centroid hom-associative algebra,and the linear basis of the universal enveloping algebra does not depend on the multiplication table of the centroid hom-Lie algebra under consideration.

关键词： Centroid hom-Lie algebra centroid hom-associative algebra Gr?bner-Shirshov basis

Biderivations of Hom-Lie Algebras and Superalgebras

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Acta Mathematica Sinica,English Series 2024年第10期40卷 2337-2358页

作者： La Mei YUAN Jia Xin LI School of mathematics Harbin Institute of Technology

On Hom-Lie algebras and superalgebras, we introduce the notions of biderivations and linear commuting maps, and compute them for some typical Hom-Lie algebras and superalgebras,including the q-deformed W(2, 2) algebra... 详细信息

关键词： 17A30 17A60 17B05 17B60 17B70 biderivations Hom-Lie algebras linear commuting maps q-deformed W(2 2) algebra q-deformed Witt algebra q-deformed Witt superalgebra

On equivalence of state-based potential games

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Science China(Information Sciences) 2024年第6期67卷 313-327页

作者： Han WU Jinhuan WANG institute of mathematics School of ScienceHebei University of Technology

In this paper, we explore state-based potential games using the semi-tensor product of ***, applying the potential equation, we derive both a necessary and sufficient condition as well as a sufficient condition to verify whether a state-based game qualifies as a potential game. Next, we present two static equivalence conditions of state-based potential games. We then delve into dynamic equivalence. We propose a criterion that allows us to identify state-based games that are dynamically equivalent to state-based potential games and share similar dynamic properties. Ultimately, we introduce the concept of state-based networked evolutionary games. We provide a necessary and sufficient condition to ensure that a state-based networked evolutionary game can be classified as a state-based potential game.

关键词： semi-tensor product of matrices state-based potential game verification equivalence state-based networked evolutionary game

Exploration of microscopic physical processes of Z-pinch by a modified electrostatic direct implicit particle-in-cell algorithm

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Chinese Physics B 2024年第9期33卷 433-442页

作者： Kaixuan Li Cheng Ning Ye Dong Chuang Xue institute of Applied Physics and Computational mathematics Beijing 100088China

For investigating efficiently the stagnation kinetic-process of Z-pinch,we develop a novel modified electrostatic implicit particle-in-cell algorithm in radial one-dimension for Z-pinch simulation in which a small-angle cumulative binary collision algorithm is *** our algorithm,the electric field in z-direction is solved by a parallel electrode-plate model,the azimuthal magnetic field is obtained by Ampere’s law,and the term for charged particle gyromotion is approximated by the cross product of the averaged velocity and magnetic *** simulation results of 2 MA deuterium plasma shell Zpinch,the mass-center implosion trajectory agrees generally with that obtained by one-dimensional MHD simulation,and the plasma current also closely aligns with the external *** phase space diagrams and radial-velocity probability distributions of ions and electrons are *** main kinetic characteristic of electron motion is thermal equilibrium and oscillation,which should be oscillated around the ions,while that of ion motion is implosion *** the region of stagnation radius,the radial-velocity probability distribution of ions transits from the non-equilibrium to equilibrium state with the current increasing,while of electrons is basically the equilibrium *** the initial ion density and current peak are not high enough,the ions may not reach their thermal equilibrium state through collisions even in its stagnation phase.

关键词： Z-pinch particle-in-cell ion heating charged particle collisions

Influence of variable viscosity and double diffusion on the convective stability of a nanofluid flow in an inclined porous channel

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Applied mathematics and Mechanics(English Edition) 2024年第3期45卷 563-580页

作者： N.HUMNEKAR D.SRINIVASACHARYA Department of mathematics National Institute of TechnologyWarangal 506004TelanganaIndia

The influence of variable viscosity and double diffusion on the convective stability of a nanofluid flow in an inclined porous channel is *** DarcyBrinkman model is used to characterize the fluid flow dynamics in porous *** analytical solutions are obtained for the unidirectional and completely developed *** on a normal mode analysis,the generalized eigenvalue problem under a perturbed state is *** eigenvalue problem is then solved by the spectral ***,the critical Rayleigh number with the corresponding wavenumber is evaluated at the assigned values of the other flow-governing *** results show that increasing the Darcy number,the Lewis number,the Dufour parameter,or the Soret parameter increases the stability of the system,whereas increasing the inclination angle of the channel destabilizes the ***,the flow is the most unstable when the channel is vertically oriented.

关键词： nanofluid inclined channel variable viscosity linear stability double dif-fusion porous medium

Stability of the Phase Separation State for Compressible Navier-Stokes/Allen-Cahn System

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Acta Mathematicae Applicatae Sinica 2024年第1期40卷 45-74页

作者： Ya-zhou Chen Hakho Hong Xiao-ding Shi Department of mathematics College of Mathematics and PhysicsBeijing University of Chemical TechnologyBeijing100029China institute of mathematics State Academy of SciencesPyongyangKorea

This paper is concerned with the large time behavior of the Cauchy problem for Navier-Stokes/AllenCahn system describing the interface motion of immiscible two-phase flow in 3-D. The existence and uniqueness of global solutions and the stability of the phase separation state are proved under the small initial perturbations. Moreover, the optimal time decay rates are obtained for higher-order spatial derivatives of density,velocity and phase. Our results imply that if the immiscible two-phase flow is initially located near the phase separation state, then under small perturbation conditions, the solution exists globally and decays algebraically to the complete separation state of the two-phase flow, that is, there will be no interface fracture, vacuum, shock wave, mass concentration at any time, and the interface thickness tends to zero as the time t → +∞.

关键词： Navier-Stokes/Allen-Cahn system existence uniqueness large time behavior decay rate

AN EXPLANATION ON FOUR NEW DEFINITIONS OF FRACTIONAL OPERATORS

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Acta Mathematica Scientia 2024年第4期44卷 1271-1279页

作者： Jiangen LIU Fazhan GENG School of mathematics and Statistics Changshu Institute of TechnologyChangshu 215500China Qin institute of mathematics Shanghai Hanjing Centre for Science and TechnologyShanghai 201609China

Fractional calculus has drawn more attentions of mathematicians and engineers in recent years.A lot of new fractional operators were used to handle various practical *** this article,we mainly study four new fractional operators,namely the CaputoFabrizio operator,the Atangana-Baleanu operator,the Sun-Hao-Zhang-Baleanu operator and the generalized Caputo type operator under the frame of the k-Prabhakar fractional integral ***,the theory of the k-Prabhakar fractional integral is regarded as a much broader than classical fractional ***,we firstly give a series expansion of the k-Prabhakar fractional integral by means of the k-Riemann-Liouville ***,a connection between the k-Prabhakar fractional integral and the four new fractional operators of the above mentioned was shown,*** terms of the above analysis,we can obtain this a basic fact that it only needs to consider the k-Prabhakar fractional integral to cover these results from the four new fractional operators.

关键词： k-Prabhakar fractional operator Caputo-Fabrizio operator Atangana-Baleanu operator Sun-Hao-Zhang-Baleanu operator generalized Caputo type operator