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Preliminary results in Local Discontinuous Galerkin Methods for Two Classes of 2D Nonlinear Wave Equations

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Preliminary results in Local Discontinuous Galerkin Methods ...

A HIGH ORDER ENO CONSERVATIVE LAGRANGIAN SCHEME FOR EULER EQUATIONS

The Sixth World Congress on Computational Mechanics in Conjunction with the Second Asian-Pacific Congress on Computational MechanicsⅠ

作者： Yan Xu , Chi-Wang Shu Department of mathematics, university of Science and Technology of China, Hefei, Anhui 230026, China ~2 division of applied mathematics, brown university, providence, ri 02912, usa

In this presentation, we describe our preliminary work concerning the development of the local discontinuous Galerkin method to solve two classes of two-dimensional nonlinear wave equations formulated by the Kadomtsev-Petviashvili equation and the Zakharov-Kuznetsov equation. Our proposed scheme for the Kadomtsev-Petviashvili equation is by the use of a new class of piecewise polynomial basis functions, which satisfies the constraint from the PDE containing a non-local operator and at the same time has the local property of the discontinuous Galerkin methods. The scheme is also easy for implementation and details related to implementation process are also shown. The scheme for the Zakharov-Kuznetsov equation extends the previous work on local discontinuous Galerkin method solving one-dimensional nonlinear wave equations [3, 4] to the two-dimensional setting. The methods for these two nonlinear equations can be easily designed for non-periodic boundary conditions and such non-periodic boundary conditions are used in the numerical experiments. We prove the nonlinear L stability of the schemes for both of these two nonlinear equations. We use the explicit exponential time differencing method for time discretization, which can achieve high accuracy and maintaining good stability while avoiding the severe explicit stability limit of the traditional Runge-Kutta discontinuous Galerkin methods which use explicit and nonlinearly stable high order Runge-Kutta time discretization due to the presence of the high order derivative terms. Numerical examples will be shown to illustrate the accuracy and capability of the methods.

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A HIGH ORDER ENO CONSERVATIVE LAGRANGIAN SCHEME FOR EULER EQ...

THE LIMITING CASE OF THIELE'S INTERPOLATING CONTINUED FRACTION EXPANSION

庆祝中国力学学会成立50周年暨中国力学学会学术大会’2007

作者： CHENG Juan~(*,2)) SHU Chiwang~(**,3)) *(Institute of applied Physics and Computational mathematics,Beijing 100088,China) **(division of applied mathematics,brown university,providence,ri 02912)

We develop a class of Lagrangian schemes for solving the Euler equations of compressible gas dynamics both in the Cartesian coordinates and in the cylindrical coordinates。The schemes are based on high order essential... 详细信息

关键词： Lagrangian scheme high order accuracy conservative scheme ENO reconstruction ALE method

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Journal of Computational mathematics 2001年第4期19卷 433-444页

作者： Jie-qing Tan (Institute of applied mathematics, College of Science and CAD/CG division College of Computer & Information Hefei, university of Technology, Hefei 230009, China) 中国科学技术大学安徽合肥 230009

By means of the determinantal formulae for inverse and reciprocal differences with coincident data points, the limiting case of Thiele's interpolating continued fraction expansion is studied in this paper and given numerical example shows that the limiting Thiele's continued fraction expansion can be determined once for all instead of carrying out computations for each step to obtain each convergent as done in [3].

关键词： Continued fraction Inverse difference Reciprocal difference Expansion.

ON NONLINEAR WATER WAVES

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数学物理学报(英文版) 1983年第4期3卷 377-386页

作者：谢定裕 division of applied mathematics brown university providence Rhode Island 02912 U. S. A

Evolution equations for the amplitudes and phases of a dominant mode of the water wave are derived by using the variational method. A. fully nonlinear dispersion relation, which is valid for finite amplitudes, is obtained when the wave is representable by a dominant sinusoidal mode. The stability criterion of the sinusoidal wave state is established and it is shown that for small amplitudes the sinusoidal wave state is stable.

关键词： mode ON NONLINEAR WATER WAVES

DEVELOPMENT AND APPLICATIONS OF WENO SCHEMES IN CONTINUUM PHYSICS

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Transactions of Nanjing university of Aeronautics and Astronautics 2001年第Z1期18卷 16-20页

作者： Chiwang Shu(division of applied mathematics, Brovidence, Rhode Island 02912,usa) division of applied mathematics Brovidence Rhode Island 02912USA

This paper briefly presents the general ideas of high order accurate weighted essentially non oscillatory (WENO) schemes, and describes the similarities and differences of the two classes of WENO schemes: finite vo lume schemes and finite difference schemes. We also briefly mention a recent development of WENO schemes, namely an adaptive approach within the finite difference framework using smooth time dependent curvilinear coordinates.

关键词： weighted essentially non-oscillatory finite difference method finite volume method adaptive method

TEMPORAL AND SPATIAL VAriATION OF EMISSIONFACTORS IN CHINA

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Journal of Geographical Sciences 1996年第1期6卷 48-60页

作者： Bi Jun(Institute of Geography, CAS, Beijing 100101People’s Republic of China)CC.Yu Peter Rogers(division of applied Sciences, Harvard university, Cambridge 02138, usa) Inst of Geography CAS Beijing 100101 China

Emission factor is a measure of pollution intensities caused by economic activities, which can be used to assess potential for pollution reduection. With the emission factors derived based on relatively few datu points or based on data collected from a specfic region, one can predict the total environmental pollution levels for the drire economy or for another region once the total leve of economic actvities of the concemed economy or region is known or prescribed. Moreover,research on emission factors can not only guide the decision-making process in choosing the best environmental protection strategy, but also be used as indicators. for the assessment and comparison of the environmentally sound development. In this paper, emission factors based on output and employment in different periods,provinces and industries are calculated, based on which temporal and spatial analyses of emission factors are carried out. Obvious declining trends of emission factors both by provinces and industries are declared, and the regional differentiation by provinces and industries is also verified.

关键词： emission factor temporal and spatial variation

ON NON-ISOTROPIC JACOBI PSEUDOSPECTRAL METHOD

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Journal of Computational mathematics 2008年第4期26卷 511-535页

作者： Benyu Guo Keji Zhang Department of mathematics,Shanghai Normal university,Shanghai 200234,China Scientific Computing Key Laboratory of Shanghai Universities division of Computational Science of E-Institute of Shanghai Universities Department of mathematics Shanghai Normal University Shanghai 200234

In this paper, a non-isotropic Jacobi pseudospectral method is proposed and its appli- cations are considered. Some results on the multi-dimensional Jacobi-Gauss type interpolation and the related Bernstein-Jackson type inequalities are established, which play an important role in pseudospectral method. The pseudospectral method is applied to a twodimensional singular problem and a problem on axisymmetric domain. The convergence of proposed schemes is established. Numerical results demonstrate the efficiency of the proposed method.

关键词： Jacobi pseudospectral method in multiple dimensions Jacobi-Gauss type inter-polation Bernstein-Jackson type inequalities Singular problem Problem on axisymmetricdomain.

ON THE MODULI NUMBER OF PLANE CURVE SINGULAriTIES WITHONE CHARACTEriSTIC PAIR

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Chinese Annals of mathematics,Series B 1999年第4期20卷 407-412页

作者： CHEN HAO(Department of mathematics, Zhongshan university, Guangzhou 510275, China) Department of mathematics Zhongshan University Guangzhou 510275 China

The author gives another linear-algebraic proof of the famous result of Zariski, Delorme,Briancon- Granger- Maisonobe about the moduli number of plane curve singularities with the same topological type as Xa + Yb = 0 (i.e.,with one characteristic pair). Since the original proof depends very much on the division theorem of Briancon, it cannot be generalized to higher dimensions. It is hopeful that the proof here will be applied to the higher dimensional cases.

关键词： Moduli number Plane curve Singularity Characteristic pair

Reversal of isoproterenol-induced downregulation of phospholamban and FKBP12.6 by CPU0213-mediated antagonism of endothelin receptors

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Acta Pharmacologica Sinica 2007年第11期28卷 1746-1754页

作者： Yu FENG,Xiao-yun TANG,De-zai DAI~2,Yin DAIResearch division of Pharmacology,China Pharmaceutical university,Nanjing 210009,China ResearchdivisionofPharmacology ChinaPharmaceuticalUniversityNanjing210009China

Aim:The downregutation of phospholamban (PLB) and FKBP12.6 as a result of β-receptor activation is involved in the pathway(s) of congestive heart *** that the endothelin (ET)-1 system may link to downregulated PLBand ***:Rats were subjected to ischemia/reperfusion (I/R) tocause heart failure (HF).1 mg/kg isoproterenol (ISO) was injected subcutane-ously (sc) for 10 d to worsen HF.30 mg/kg CPU0213 (sc),a dual ET receptor.(ETAR/ETBR) antagonist was given from d 6 to d *** d 11,cardiac function wasassessed together with the determination of mRNA levels of ryanodine receptor 2,calstabin-2 (FKBP12.6),PLB,and sarcoplasmic reticulum Ca2+-*** rat ventricular myocytes were incubated with ISO at 1×10-6mol/L to set up anin vitro model of *** (PRO),CPU0213,and darusentan (DAR,anETAR antagonist) were incubated with cardiomyocytes at 1×10-5mol/L or 1×10-6mol/L in the presence of ISO (1×10-6mol/L).Immunocytochemistry and Westernblotting were applied for measuring the protein levels of PLB and ***:The worsened hemodynamics produced by I/R were exacerbated by *** significant downregulation of the gene expression of PLB andFKBP12.6 and worsened cardiac function by ISO were reversed by *** ISO 1×10-6mol/L produced a sharp decline of PLB and FKBP12.6 proteinsrelative to the *** downregulation of the protein expression was signifi-cantly reversed by the ET receptor antagonist CPU0213 or DAR,comparable tothat achieved by ***:This study demonstrates a role of ET inmediating the downregulation of the cardiac Ca2+-handling protein by ISO.

关键词： heart failure endothelin receptor antagonists phospholamban FKBP12.6 propranolol CPU0213