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Science China mathematics 2024年第1期67卷 187-210页

作者： Xiao Li Zhonghua Qiao Cheng Wang department of applied mathematics The Hong Kong Polytechnic UniversityHong KongChina department of mathematics The University of MassachusettsNorth DartmouthMA 02747USA

In this paper,we study a second-order accurate and linear numerical scheme for the nonlocal CahnHilliard *** scheme is established by combining a modified Crank-Nicolson approximation and the Adams-Bashforth extrapolation for the temporal discretization,and by applying the Fourier spectral collocation to the spatial *** addition,two stabilization terms in different forms are added for the sake of the numerical *** conduct a complete convergence analysis by using the higher-order consistency estimate for the numerical scheme,combined with the rough error estimate and the refined *** regarding the numerical solution as a small perturbation of the exact solution,we are able to justify the discrete?^(∞)bound of the numerical solution,as a result of the rough error ***,the refined error estimate is derived to obtain the optimal rate of convergence,following the established?∞bound of the numerical ***,the energy stability is also rigorously proved with respect to a modified *** proposed scheme can be viewed as the generalization of the second-order scheme presented in an earlier work,and the energy stability estimate has greatly improved the corresponding result therein.

关键词： nonlocal Cahn-Hilliard equation second-order stabilized scheme higher-order consistency analysis rough and refined error estimate

Mixed convectional and chemical reactive flow of nanofluid with slanted MHD on moving permeable stretching/shrinking sheet through nonlinear radiation,energy omission

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Chinese Physics B 2024年第5期33卷 193-202页

作者： Saleem Nasir Sekson Sirisubtawee Pongpol Juntharee Taza Gul department of mathematics Faculty of Applied ScienceKing Mongkut's University of Technology North BangkokBangkok 10800Thailand department of mathematics City University of Science and Information TechnologyPeshawarPakistan

Hybrid nanofluids are remarkable functioning liquids that are intended to reduce the energy loss while maximizing the heat *** the involvement of suction and nonlinear thermal radiation effects,this study attempted to explore the energy transmission features of the inclined magnetohydrodynamic(MHD)stagnation flow of CNTs-hybrid nanofluid across the nonlinear permeable stretching or shrinking *** work also included some noteworthy features like chemical reactions,variable molecular diffusivity,quadratic convection,viscous dissipation,velocity slip and heat omission *** appropriate similarity components,the model equations were modified to ODEs and computed by using the HAM *** impact of various relevant flow characteristics on movement,heat and concentration profiles was investigated and plotted on a *** various model factors,the significance of drag friction,heat and mass transfer rate were also computed in tabular and graphical *** leads to the conclusion that such factors have a considerable impact on the dynamics of fluid as well as other engineering measurements of ***,viscous forces are dominated by increasing the values ofλ_(p),δ_(m)andδ_(q),and as a result,F(ξ)accelerates while the opposite trend is observed for M andφ.The drag friction is boosted by the augmentation M,λ_(p)andφ,but the rate of heat transfer *** to our findings,hybrid nanoliquid effects dominate that of ordinary nanofluid in terms of F(ξ),Θ(ξ)andφ(ξ)*** HAM and the numerical technique(shooting method)were found to be in good agreement.

关键词： hybrid nanofluid(SWCNT+MWCNT/H_(2)O) velocity slip conditions nonlinear thermal radiation exponential stretching/shrinking sheet inclined magnetohydrodynamic(MHD)stagnation flow

Deep bed filtration model for cake filtration and erosion

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applied mathematics and Mechanics(English Edition) 2024年第2期45卷 355-372页

作者： L.I.KUZMINA Y.V.OSIPOV A.R.PESTEREV department of applied mathematics HSE UniversityMoscow 101000Russia department of Computer Science and applied mathematics Moscow State University of Civil EngineeringMoscow 129337Russia

Many phenomena in nature and technology are associated with the filtration of suspensions and colloids in porous media. Two main types of particle deposition,namely, cake filtration at the inlet and deep bed filtration throughout the entire porous medium, are studied by different models. A unified approach for the transport and deposition of particles based on the deep bed filtration model is proposed. A variable suspension flow rate, proportional to the number of free pores at the inlet of the porous medium, is considered. To model cake filtration, this flow rate is introduced into the mass balance equation of deep bed filtration. For the cake filtration without deposit erosion,the suspension flow rate decreases to zero, and the suspension does not penetrate deep into the porous medium. In the case of the cake filtration with erosion, the suspension flow rate is nonzero, and the deposit is distributed throughout the entire porous medium. An exact solution is obtained for a constant filtration function. The method of characteristics is used to construct the asymptotics of the concentration front of suspended and retained particles for a filtration function in a general form. Explicit formulae are obtained for a linear filtration function. The properties of these solutions are studied in detail.

关键词： deep bed filtration cake filtration porous medium particle deposition and erosion analytical solution concentration front

Parametric“non-nested”discriminants for multiplicities of univariate polynomials

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Science China mathematics 2024年第8期67卷 1911-1932页

作者： Hoon Hong Jing Yang department of mathematics North Carolina State UniversityRaleighNC 27695USA SMS-HCIC-School of mathematics and Physics Center for Applied Mathematics of GuangxiGuangxi Minzu UniversityNanning 530006China

We consider the problem of complex root classification,i.e.,finding the conditions on the coefficients of a univariate polynomial for all possible multiplicity structures on its complex *** is well known that such conditions can be written as conjunctions of several polynomial equalities and one inequality in the *** polynomials in the coefficients are called discriminants for *** is also known that discriminants can be obtained using repeated parametric greatest common *** resulting discriminants are usually nested determinants,i.e.,determinants of matrices whose entries are determinants,and so *** this paper,we give a new type of discriminant that is not based on repeated greatest common *** new discriminants are simpler in the sense that they are non-nested determinants and have smaller maximum degrees.

关键词： parametric polynomial complex roots discriminant multiplicity resultant

Integrability and solutions of a nonsymmetric discrete Korteweg-de Vries equation

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Communications in Theoretical Physics 2024年第2期76卷 45-50页

作者： Maebel Mesfun Da-jun Zhang Song-lin Zhao department of mathematics Shanghai UniversityShanghai 200444China Newtouch Center for mathematics of Shanghai university Shanghai 200444China department of applied mathematics Zhejiang University of TechnologyHangzhou 310023China

In this paper,we present Lax pairs and solutions for a nonsymmetric lattice equation,which is a torqued version of the lattice potential Korteweg-de Vries *** nonsymmetric equation is special in the sense that it contains only one spacing parameter but consists of two consistent cubes with other integrable lattice *** such a multidimensionally consistent property we are able to derive its two Lax pairs and also construct solutions using B?cklund transformations.

关键词： discrete Korteweg-de Vries equation nonsymmetric multi-dimensional consistency Backlund transformation solution

Center of the Yangian double in type A

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Science China mathematics 2024年第9期67卷 1957-1988页

作者： Fan Yang Naihuan Jing department of mathematics Jiaying UniversityMeizhou 514000China department of mathematics North Carolina State UniversityRaleighNC 27695USA

We prove that the R-matrix and Drinfeld presentations of the Yangian double in type A are *** central elements of the completed Yangian double in type A at the critical level are *** images of these elements under a Harish-Chandra-type homomorphism are calculated by applying a version of the Poincaré-Birkhoff-Witt theorem for the R-matrix *** images coincide with the eigenvalues of the central elements in the Wakimoto modules.

关键词： Yangian double Harish-Chandra homomorphism Wakimoto module

Investigation of coupling effect on the evolution of Richtmyer-Meshkov instability at double heavy square bubbles

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Science China(Physics,Mechanics & Astronomy) 2024年第1期67卷 52-70页

作者： Satyvir Singh Dhouha Taib Jalleli applied and Computational mathematics RWTH Aachen UniversityAachen 52056Germany department of mathematics Graphic Era Deemed to be UniversityDehradun 244712India mathematics department University College in DarbJazan UniversityAbu As Sadad 89653Saudi Arabia

This study investigates numerically the coupling effect on the evolution of Richtmyer-Meshkov instability at double heavy square *** scenarios are considered,each with varying initial separations S/L(where L demotes the side length of the square)ranging from 0.125 to *** are filled with SF6gas,and are enclosed by *** simulations of shock-induced multispecies flow are performed by solving the two-dimensional compressible Euler equations with a higher-order explicit modal discontinuous Galerkin *** simulations demonstrate that the flow morphology resulting from the coupling effect is highly dependent on the separation between two *** the separation is large,the squares experience a weaker coupling effect and evolve ***,as the separation reduces,the coupling effect manifests earlier in the interaction and becomes more *** a result,this phenomenon greatly intensifies the motion of inner upstream/downstream vortex rings towards the symmetry axis,leading to the emergence of multiple jets such as the twisted downward,upward,and coupled jets.A thorough exploration of the coupling effect of double squares is conducted by analyzing the vorticity ***,a significant quantity of vorticity is produced along the squares interface for smaller ***,these coupling effects result in various interface features(upstream/downstream movement,and height/width evolution),and temporal variations of various spatially integrated ***,the analysis of the flow structure also considers the interaction between two more flow parameters,the Mach and Atwood numbers,in order to evaluate the coupling effects.

关键词： RM instability shock wave double square bubbles coupling effect

Global Spherically Symmetric Solutions for a Coupled Compressible Navier–Stokes/Allen–Cahn System

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Acta Mathematica Sinica,English Series 2024年第8期40卷 2037-2064页

作者： Chang Ming SONG Jian Lin ZHANG Yuan Yuan WANG department of applied mathematics School of Mathematics and Information ScienceZhongyuan University of TechnologyZhengzhou 450007P.R.China

In this paper,we consider the global spherically symmetric solutions for the initial boundary value problem of a coupled compressible Navier–Stokes/Allen–Cahn system which describes the motion of two-phase viscous compressible *** prove the existence and uniqueness of global classical solution,weak solution and strong solution under the assumption of spherically symmetry condition for initial dataρ0 without vacuum state.

关键词： Diffuse interface model global solutions Navier-Stokes equations Allen-Cahn equation spherically symmetry

Semi-analytical investigation of heat transfer in a porous convective radiative moving longitudinal fin exposed to magnetic field in the presence of a shape-dependent trihybrid nanofluid

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applied mathematics and Mechanics(English Edition) 2024年第1期45卷 197-216页

作者： C.G.PAVITHRA B.J.GIREESHA M.L.KEERTHI department of PG Studies and Research in mathematics Kuvempu UniversityShankaraghatta 577451India department of mathematics and Statistics M.S.Ramaiah University of Applied SciencesBengaluru 560058India

The thermal examination of a non-integer-ordered mobile fin with a magnetism in the presence of a trihybrid nanofluid(Fe_3O_4-Au-Zn-blood) is carried out. Three types of nanoparticles, each having a different shape, are considered. These shapes include spherical(Fe_3O_4), cylindrical(Au), and platelet(Zn) configurations. The combination approach is utilized to evaluate the physical and thermal characteristics of the trihybrid and hybrid nanofluids, excluding the thermal conductivity and dynamic viscosity. These two properties are inferred by means of the interpolation method based on the volume fraction of nanoparticles. The governing equation is transformed into a dimensionless form, and the Adomian decomposition Sumudu transform method(ADSTM) is adopted to solve the conundrum of a moving fin immersed in a trihybrid nanofluid. The obtained results agree well with those numerical simulation results, indicating that this research is reliable. The influence of diverse factors on the thermal overview for varying noninteger values of γ is analyzed and presented in graphical representations. Furthermore, the fluctuations in the heat transfer concerning the pertinent parameters are studied. The results show that the heat flux in the presence of the combination of spherical, cylindrical, and platelet nanoparticles is higher than that in the presence of the combination of only spherical and cylindrical nanoparticles. The temperature at the fin tip increases by 0.705 759% when the value of the Peclet number increases by 400%, while decreases by 11.825 13% when the value of the Hartman number increases by 400%.

关键词： convection radiation moving longitudinal fin Adomian decomposition Sumudu transform method(ADSTM) trihybrid nanofluid magnetic field

A SCALAR AUXILIARY VARIABLE (SAV) FINITE ELEMENT NUMERICAL SCHEME FOR THE CAHN-HILLIARD-HELE-SHAW SYSTEM WITH DYNAMIC BOUNDARY CONDITIONS

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Journal of Computational mathematics 2024年第2期42卷 544-569页

作者： Changhui Yao Fengdan Zhang Cheng Wang School of mathematics and Statistics Zhengzhou UniversityZhengzhou 450001China department of mathematics University of MassachusettsNorth DartmouthMA 02747USA

In this paper,we consider the Cahn-Hilliard-Hele-Shaw(CHHS)system with the dynamic boundary conditions,in which both the bulk and surface energy parts play important *** scalar auxiliary variable approach is introduced for the physical system;the mass conservation and energy dissipation is proved for the CHHS ***,a fully discrete SAV finite element scheme is proposed,with the mass conservation and energy dissipation laws established at a theoretical *** addition,the convergence analysis and error estimate is provided for the proposed SAV numerical scheme.

关键词： Cahn-Hilliard-Hele-Shaw system Dynamic boundary conditions Bulk energy and surface energy Scalar auxiliary variable formulation Energy stability Convergence analysis