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Entropy generation analysis from the time-dependent quadratic combined convective flow with multiple diffusions and nonlinear thermal radiation

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chinese Journal of chemical Engineering 2023年第1期53卷 46-55页

作者： P.M.Patil Bharath Goudar department of Mathematics Karnatak UniversityPavate NagarDharwad 580003India wrangler dr.d.c.pavate institute of mathematical sciences Karnatak UniversityDharwad 580003India

diffusions of multiple components have numerous applications such as underground water flow, pollutant movement, stratospheric warming, and food processing. Particularly, liquid hydrogen is used in the cooling process of the aeroplane. Further, liquid nitrogen can find applications in cooling equipment or electronic devices, i.e., high temperature superconducting(HTS) cables. So, herein, we have analysed the entropy generation(EG), nonlinear thermal radiation and unsteady(time-dependent) nature of the flow on quadratic combined convective flow over a permeable slender cylinder with diffusions of liquid hydrogen and nitrogen. The governing equations for flow and heat transfer characteristics are expressed in terms of nonlinear coupled partial differential equations. The solutions of these equations are attempted numerically by employing the quasilinearization technique with the implicit finite difference approximation. It is found that EG is minimum for double diffusion(liquid hydrogen and heat diffusion)than triple diffusion(diffusion of liquid hydrogen, nitrogen and heat). The enhancing values of the radiation parameter R_(d) and temperature ratio θ_(w) augment the fluid temperature for steady and unsteady cases as well as the local Nusselt number. Because, the fluid absorbs the heat energy released due to radiation, and in turn releases the heat energy from the cylinder to the surrounding surface.

关键词： Unsteady flow Entropy Radiation Quasilinearization technique Numerical analysis Quadratic combined convection

An oscillation-free Hermite WENO scheme for hyperbolic conservation laws

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Science china Mathematics 2024年第2期67卷 431-454页

作者： Zhuang Zhao Jianxian Qiu School of mathematical sciences and institute of Natural sciences Shanghai Jiao Tong UniversityShanghai 200240China School of mathematical sciences and Fujian Provincial Key Laboratory of mathematical Modeling and High-Performance Scientific computing Xiamen UniversityXiamen 361005China

In this paper, the sixth-order oscillation-free Hermite weighted essentially non-oscillatory (OFHWENO) scheme is proposed for hyperbolic conservation laws on structured meshes, where the zeroth- andfirst-order moments are the variables for the governing equations. The main difference from other HWENOschemes existing in the literature is that we add high-order numerical damping terms in the first-order momentequations to control spurious oscillations for the OF-HWENO scheme. The OF-HWENO scheme not only canachieve the designed optimal numerical order, but also can be easily implemented as we use only one set ofstencils in the reconstruction procedure and the same reconstructed polynomials are applied for the zeroth- andfirst-order moment equations. In order to obtain the adaptive order resolution when facing discontinuities, atransition polynomial is added in the reconstruction, where the associated linear weights can also be any positivenumbers as long as their summation equals one. In addition, the OF-HWENO scheme still keeps compactnessas only immediate neighbor values are needed in the space discretization. Some benchmark numerical tests areperformed to illustrate the high-order accuracy, high resolution and robustness of the proposed scheme.

关键词： Hermite WENO scheme hyperbolic conservation laws oscillation-free adaptive order discontinuous Galerkin method

Rational Solutions of First Order Algebraic Ordinary differential Equations

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Journal of Systems Science & complexity 2024年第2期37卷 567-580页

作者： FENG Shuang SHEN Liyong School of Physical and mathematical sciences Nanjing Tech UniversityNanjing 211816China School of mathematical sciences University of Chinese Academy of SciencesBeijing 100049China

Let f(t,y,y')=∑ _(i=0)^(n )a_(i)(t,y)y'^(i)=0 be an irreducible first order ordinary differential equation with polynomial *** in 1998 proved that there exists a constant c such that every rational solution of f(t,y,y')=0 is of degree not greater than *** show that this degree bound c depends not only on the degrees of f in t,y,y' but also on the coefficients of f viewed as the polynomial in t,y,y'.In this paper,the authors show that if f satisfies deg(f,y)deg(f,y')or n max i=0{deg(a_(i),y)−2(n−i)}>0,then the degree bound c only depends on the degrees of f in t,y,y',and furthermore we present an explicit expression for c in terms of the degrees of f in t,y,y'.

关键词： degree bound first order AOdE height rational solution

Global well-posedness for 2d inhomogeneous asymmetric fluids with large initial data

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Science china Mathematics 2024年第3期67卷 527-556页

作者： chenyin Qian Beibei He Ting Zhang School of mathematical sciences Zhejiang Normal UniversityJinhua 321004China School of mathematical sciences Zhejiang UniversityHangzhou 310058China

In this paper, by using time-weighted global estimates and the Lagrangian approach, we first investigate the global existence and uniqueness of the solution for the 2d inhomogeneous incompressible asymmetric fluids with the initial(angular) velocity being located in sub-critical Sobolev spaces H^(s)(R^(2))(0d the initial density being bounded from above and below by some positive constants. The global unique solvability of the 2d incompressible inhomogeneous asymmetric fluids with the initial data in the critical Besov space(u_(0), w_(0))∈˙B^(0)_(2,1)(R^(2))andρ^(−1)−1∈˙B^(ε)_(2/ε),1(R^(2))is established. In particular, the uniqueness of the solution is also obtained without any more regularity assumptions on the initial density which is an improvement on the recent result of Abidi and Gui(2021) for the 2d inhomogeneous incompressible NavierStokes system.

关键词： inhomogeneous asymmetric fluids Littlewood-Paley theory Besov spaces global well-posedness

Partial regularity and nonlinear potential estimates for Stokes systems with super-quadratic growth

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Science china Mathematics 2024年第7期67卷 1525-1554页

作者： Lingwei Ma Zhenqiu Zhang School of mathematical sciences Tianjin Normal UniversityTianjin300387China School of mathematical sciences and LPMc Nankai UniversityTianjin300071China

This paper builds a bridge between partial regularity theory and nonlinear potential theory for the following generalized stationary Stokes system with super-quadratic growth and continuous coefficients:-div A(x,du)+■π=f,div u=0,where du is the symmetric part of the gradient■*** first establish anε-regularity criterion involving both the excess functional of the symmetric gradient du and Wolff potentials of the nonhomogeneous term f to guarantee the local vanishing mean oscillation(VMO)-regularity of du in an open subset Ω_(u) of Ω with full *** anε-regularity criterion leads to a pointwise Wolff potential estimate of du,which immediately infers that du is partially c^(0)-regular under appropriate ***,we give a local continuous modulus estimate of du.

关键词： nonlinear Stokes system partial regularity Wolff potential estimates continuous modulus estimates

NeuroPrim:An attention-based model for solving NP-hard spanning tree problems

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Science china Mathematics 2024年第6期67卷 1359-1376页

作者： Yuchen Shi congying Han Tiande Guo School of mathematical sciences University of Chinese Academy of SciencesBeijing100049China

Spanning tree problems with specialized constraints can be difficult to solve in real-world scenarios,often requiring intricate algorithmic design and exponential ***,there has been growing interest in end-to-end deep neural networks for solving routing ***,such methods typically produce sequences of vertices,which make it difficult to apply them to general combinatorial optimization problems where the solution set consists of edges,as in various spanning tree *** this paper,we propose NeuroPrim,a novel framework for solving various spanning tree problems by defining a Markov decision process for general combinatorial optimization problems on *** approach reduces the action and state space using Prim's algorithm and trains the resulting model using *** apply our framework to three difficult problems on the Euclidean space:the degree-constrained minimum spanning tree problem,the minimum routing cost spanning tree problem and the Steiner tree problem in *** results on literature instances demonstrate that our model outperforms strong heuristics and achieves small optimality gaps of up to 250 ***,we find that our model has strong generalization ability with no significant degradation observed on problem instances as large as 1,*** results suggest that our framework can be effective for solving a wide range of combinatorial optimization problems beyond spanning tree problems.

关键词： degree-constrained minimum spanning tree problem minimum routing cost spanning tree problem Steiner tree problem in graphs Prim's algorithm reinforcement learning

Holder continuous weak solutions of the 2d Boussinesq equation with thermal diffusion

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Science china Mathematics 2024年第8期67卷 1777-1806页

作者： Tianwen Luo Tao Tao Liqun Zhang Yau mathematical sciences center Tsinghua UniversityBeijing 100084China School of Mathematics Shandong UniversityJinan 250100China institute of Mathematics Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of mathematical sciences University of Chinese Academy of SciencesBeijing 100049China

We show the existence of Holder continuous periodic weak solutions of the 2d Boussinesq equation with thermal diffusion which satisfy the prescribed kinetic *** precisely,for any smooth e(t):[0,1]→R+andε∈(0,110),there exist v∈c 110−ε([0,1]×T2)andθ∈c 1,120−εt 2 c 2,1 x 10−ε([0,1]×T2),which satisfy(1.1)in the sense of distribution and e(t)=ˆT2|v(t,x)|2 dx,∀t∈[0,1].

关键词： 2d Boussinesq equation with thermal diffusion Holder continuous periodic weak solutions prescribed kinetic energy

Threshold Selection and Resource Allocation for Quantized Identification

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Journal of Systems Science & complexity 2024年第1期37卷 204-229页

作者： WANG Ying LI Xin ZHAO Yanlong ZHANG Ji-Feng Key Laboratory of Systems and control Institute of Systems ScienceAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of mathematical sciences University of Chinese Academy of SciencesBeijing 100049China

This paper is concerned with the optimal threshold selection and resource allocation problems of quantized identification, whose aims are improving identification efficiency under limited resources. Firstly, the first-order asymptotically optimal quantized identification theory is extended to the weak persistent excitation condition. Secondly, the characteristics of time and space complexities are established based on the cramér-Rao lower bound of quantized systems. On these basis, the optimal selection methods of fixed thresholds and adaptive thresholds are established under aperiodic signals, which answer how to achieve the best efficiency of quantized identification under the same time and space complexity. In addition, based on the principle of maximizing the identification efficiency under a given resource, the optimal resource allocation methods of quantized identification are given for the cases of fixed thresholds and adaptive thresholds, respectively, which show how to balance time and space complexity to realize the best identification efficiency of quantized identification.

关键词： Quantized output resource allocation system identification threshold selection.

GLOBAL SOLUTIONS IN THE cRITIcAL SOBOLEV SPAcE FOR THE LANdAU EQUATION

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Acta Mathematica Scientia 2024年第4期44卷 1347-1372页

作者： Hao WANG department of mathematical sciences Tsinghua UniversityBeijing 100084China

The Landau equation is studied for hard potential with-2≤γ≤*** a perturbation setting,a unique global solution of the cauchy problem to the Landau equation is established in a critical Sobolev space H_(x)^(d)L_(v)^(2)(d>3/2),which extends the results of[11]in the torus domain to the whole space R_(x)^(3).Here we utilize the pseudo-differential calculus to derive our desired result.

关键词： Landau equation nonlinear energy method global existence pseudo-differential calculus