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ON THE CELL ENTROPY INEQUALITY FOR THE FULLY DISCRETE RELAXING SCHEMES

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Journal of Computational Mathematics 2001年第5期19卷 511-518页

作者： hua-zhong tang hua-mo Wu School of Mathematical Sciences Peking UniversityBeijing 100871China LSEC JCMSECAcademy of Mathematics and Systems SciencesChinese Academy of SciencesBeijing 100080China

Presents a study on the cell entropy inequality for two classes of fully discrete relaxing schemes approximating scalar conservation laws. Main advantage of the schemes; Review of the construction of the relaxing syst... 详细信息

关键词： the relaxing schemes entropy inequality conservation laws

HIGH RESOLUTION SCHEMES FOR CONSERVATION LAWS AND CONVECTION-DIFFUSION EQUATIONS WITH VARYING TIME AND SPACE GRIDS

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Journal of Computational Mathematics 2006年第2期24卷 121-140页

作者： hua-zhong tang Gerald Warnecke LMAM School of Mathematical Sciences Peking University Beijing 100871 China Institut fiir Analysis und Numerik Otto-von-Guericke Universitat Magdeburg 39106 Magdeburg Germany

This paper presents a class of high resolution local time step schemes for nonlinear hyperbolic conservation laws and the closely related convection-diffusion equations, by projecting the solution increments of the underlying partial differential equations （PDE） at each local time step. The main advantages are that they are of good consistency, and it is convenient to implement them. The schemes are L^∞ stable, satisfy a cell entropy inequality, and may be extended to the initial boundary value problem of general unsteady PDEs with higher-order spatial derivatives. The high resolution schemes are given by combining the reconstruction technique with a second order TVD Runge-Kutta scheme or a Lax-Wendroff type method, respectively. The schemes are used to solve a linear convection-diffusion equation, the nonlinear inviscid Burgers＇ equation, the one- and two-dimensional compressible Euler equations, and the two-dimensional incompressible Navier-Stokes equations. The numerical results show that the schemes are of higher-order accuracy, and efficient in saving computational cost, especially, for the case of combining the present schemes with the adaptive mesh method [15]. The correct locations of the slow moving or stronger discontinuities are also obtained, although the schemes are slightly nonconservative.

关键词： Hyperbolic conservation laws Degenerate diffusion High resolution scheme,Finite volume method Local time discretization.

A Moving Mesh Method for the Euler Flow Calculations Using a Directional Monitor Function

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Communications in Computational Physics 2006年第4期1卷 656-676页

作者： hua-zhong tang LMAM School of Mathematical SciencesPeking UniversityBeijing 100871P.R.China

This paper is concerned with the adaptive grid method for computations of the Euler equations in fluid *** new feature of the present moving mesh algorithm is the use of a dimensional-splitting type monitor function,which is to increase grid concentration in regions containing shock waves and contact discontinuities or their *** two–dimensional flow problems are computed to demonstrate the effectiveness of the present adaptive grid algorithm.

关键词： Euler equations adaptive grid method finite volume method monitor function

Clinicopathological significance of overexpression of interleukin-6 in colorectal cancer

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World Journal of Gastroenterology 2017年第10期23卷 1780-1786页

作者： Jun Zeng zhong-hua tang Shuang Liu Shan-Shan Guo College of Life Sciences Chongqing Normal UniversityChongqing 401331China

AIM To compare the expression levels of interleukin(IL)-6 in colorectal cancer(CRC) tissues and adjacent noncancerous tissues, and analyse the correlation of IL-6 expression with the clinicopathological parameters of CRC. METHODS Fifty CRC tissue specimens and 50 matched adjacent mucosa specimens were collected. The expression of IL-6 in these clinical samples was examined by immunohistochemical staining. The correlation between IL-6 expression and clinicopathological parameters was assessed by statistical *** IL-6 expression was significantly elevated in CRC tissues compared with noncancerous tissues(P < 0.001). IL-6 expression was positively correlated with tumour TNM stage(P < 0.001), but a negative correlation was detected between IL-6 expression and tumor histological differentiation in CRC(P < 0.05). Furthermore, IL-6 expression was associated with invasion depth and lymph node metastasis in CRC. CONCLUSION IL-6 might be a useful marker for predicting a poor prognosis in patients with CRC and might be used as a potential therapeutic target in CRC.

关键词： Colorectal cancer Interleukin-6 Invasion depth Lymph node metastases

ON A CELL ENTROPY INEQUALITY OF THE RELAXINGSCHEMES FOR SCALAR CONSERVATION LAWS

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Journal of Computational Mathematics 2000年第1期18卷 69-74页

作者： hua-zhong tang hua-mo Wu(State Key Labomtory of Scientific and Engineering Computing, Institute of ComputationalMathematics, Chinese Academy of Sciences, Beijing 100080, China) 中科院计算数学所科学与工程计算国家重点实验室北京 100080

Presents a study which examined a cell entropy inequality for a class of local relaxation approximation relaxing scheme for scalar conservation laws. Way to obtain the scheme; Use of numerical entropy condition for th... 详细信息

关键词： hyperbolic conservation laws the relaxing schemes cell entropy inequality

ON THE EXPLICIT COMPACT SCHEMES II: EXTENSION OF THE STCE/CE METHOD ON NONSTAGGERED GRIDS ON THE EXPLICIT COMPACT SCHEMES II: EXTENSION OF THE STCE/CE METHOD ON NONSTAGGERED GRIDS

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Journal of Computational Mathematics 2000年第5期18卷 467-480页

作者： hua-zhong tang , hua-mu Wu (State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics, Chinese Academy of Sciences, Beijing 100080, China) 中科院计算数学所科学与工程计算国家重点实验室北京 100080

This paper continues to construct and study the explicit compact (EC) schemes for conservation laws. First, we axtend STCE/SE method on non-staggered grid, which has same well resolution as one in [1], and just requires half of the computational works. Then, we consider some constructions of the EC schemes for two-dimensional conservation laws, and some 1D and 2D numerical experiments are also given.

关键词： Conservation laws Compact scheme Shock-Capturing method Euler equations.

ON THE CENTRAL RELAXING SCHEMES I:SINGLE CONSERVATION LAWS

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Journal of Computational Mathematics 2000年第3期18卷 313-324页

作者： hua-zhong tang (LSEC, Institute of Computational Mathematics and Scientific /Engineering Computing, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing, 100080, China) 中科院计算数学与科学工程计算所科学与工程计算国家重点实验室北京 100080

Presents a central relaxing scheme for scalar conservation laws. Details on the preliminary equations; Properties of the relaxed schemes; Conclusions.

关键词： hyperbolic conservation laws the relaxing scheme TVD cell entropy inequality

ON THE CENTRAL RELAXING SCHEME Ⅱ: SYSTEMS OF HYPERBOLIC CONSERVATION LAWS

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Journal of Computational Mathematics 2001年第6期19卷 571-582页

作者： hua-zhong tang (School of Mathematical Sciences, Peking University, Beijing 100871, China) (LSEC,ICMSEC Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing 100080, China) School of Mathematical Sciences Peking University Beijing 100871 China

This paper continues to study the central relaxing schemes for system of hyperbolic conservation laws, based on the local relaxation approximation. Two classes of relaxing systems with stiff source term are introduced to approximate system of conservation laws in curvilinear coordinates. Based on them, the semi-implicit relaxing schemes are con- structed as in [6, 12] without using any linear or nonlinear Riemann solvers. Numerical experiments for one-dimensional and two-dimensional problems are presented to demon- strate the performance and resolution of the current schemes.

关键词： Hyperbolic conservation laws The relaxing system The central relaxing schemes The Euler equations.

Nuclear charge radius predictions by kernel ridge regression with odd-even effects

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Nuclear Science and Techniques 2024年第2期35卷 94-102页

作者： Lu tang Zhen-hua Zhang Mathematics and Physics Department North China Electric Power UniversityBeijing 102206China Hebei Key Laboratory of Physics and Energy Technology North China Electric Power UniversityBaoding 071000China

The extended kernel ridge regression(EKRR)method with odd-even effects was adopted to improve the description of the nuclear charge radius using five commonly used nuclear *** are:(i)the isospin-dependent A^(1∕3) formula,(ii)relativistic continuum Hartree-Bogoliubov(RCHB)theory,(iii)Hartree-Fock-Bogoliubov(HFB)model HFB25,(iv)the Weizsacker-Skyrme(WS)model WS*,and(v)HFB25**** the last two models,the charge radii were calculated using a five-parameter formula with the nuclear shell corrections and deformations obtained from the WS and HFB25 models,*** each model,the resultant root-mean-square deviation for the 1014 nuclei with proton number Z≥8 can be significantly reduced to 0.009-0.013 fm after considering the modification with the EKRR *** best among them was the RCHB model,with a root-mean-square deviation of 0.0092 *** extrapolation abilities of the KRR and EKRR methods for the neutron-rich region were examined,and it was found that after considering the odd-even effects,the extrapolation power was improved compared with that of the original KRR *** strong odd-even staggering of nuclear charge radii of Ca and Cu isotopes and the abrupt kinks across the neutron N=126 and 82 shell closures were also calculated and could be reproduced quite well by calculations using the EKRR method.

关键词： Nuclear charge radius Machine learning Kernel ridge regression method