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Level Set interface treatment and its application in Euler method

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science china(Physics,Mechanics & Astronomy) 2010年第2期53卷 227-236页

作者： WU KaiTeng1,2.HAO Li3,WANG Cheng4 & ZHANG Li1,2.1 Numerical Simulation Sichuan Higher School Key Laboratory,neijiang normal university,neijiang 64.112.china 2.College of {2. and information science,neijiang normal university,neijiang 64.112.china 3 College of science,Beijing university of Civil Engineering and Architecture,Beijing 100044,china 4 State Key Laboratory of Explosion science and Technology,Beijing Institute of Technology,Beijing 100081,china 1. Numerical Simulation Sichuan Higher School Key Laboratory Neijiang Normal University Neijiang 641112 China2. College of Mathematics and Information Science Neijiang Normal University Neijiang 641112 China3. College of Science Beijing University of Civil Engineering and Architecture Beijing 100044 China4. State Key Laboratory of Explosion Science and Technology Beijing Institute of Technology Beijing 100081 China

Level Set interface treatment method is introduced into Euler method,which is employed for interface treatment method for multi-materials. Combined with the ghost fluid method,the moving interface is tracked. Fifth-order WENO spatial discretization and third-order TVD Runge-Kutta time discretization methods are used. Shock-wave action on bubble,implosion and velocity field Shock effect bubbles; implosion and velocity field are simulated by means of LS-MMIC3D programmed by C++. Nu-merical results show that the Level Set interface treatment method is effective and feasible for multi-material interface treatment in comparison with the WENO method.

关键词： Euler method Level Set method shock-wave action on bubble implosion numerical simulation

Weighted composition operators between μ-Bloch spaces on the unit ball

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science china {2. 2005年第10期48卷 1349-1368页

作者： ZHANG Xuejun~1 & XIAO Jianbin~2.1. College of mathematics and Computer science,Hunan {2. university,Changsha 410006,china(email:xuejunttt@2.3. net) 2. The School of science,Hangzhou Dianzi university,Hangzhou 310037,china 1. College of mathematics and Computer science Hunan Normal University 410006 Changsha China 2. The School of science Hangzhou Dianzi University 310037 Hangzhou China

In this paper,necessary and sufficient conditions are given for the weighted composition operator T_(ψ,ψ) to be bounded or compact from the space β_μ to β_ν (or β_(μ,0) to β_(ν,0) ) on the unit ball of C^***... 详细信息

关键词： μ-Bloch space, weighted composition operator, boundedness, compactness.

An equality on Hochschild homology groups

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Chinese science Bulletin 1997年第8期42卷 624-627页

作者： ZHANG Pu and LIU Shaoxue1. Department of mathematics, university of {2. and Technology of china, Hefei 2.002., china 2. Department of mathematics, Beijing normal university, Beijing 100875, china Department of mathematics University of Science and Technology of China Hefei China Department of mathematics Beijing Normal University Beijing China

LET A be finite-dimensional algebra over field k,and Ae the enveloping algebra of A,i.e.Ae=A kAop,where Aop is the opposite algebra of *** A-bimodule has a natural left Ae-module structure as follows:

关键词： finite-dimensional algebra Hochschild homology groups dimensions.

K-uniformly rotund spaces and k-uniformly smooth spaces

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Chinese science Bulletin 1998年第2期43卷 92-95页

作者： Suyalatu 1 and WU Congxin 2.1. Department of mathematics,Inner Mongolia normal {2., Huhhot 01002., china 2. Department of mathematics, Harbin Institute of Technology, Harbin 150006, china Department of mathematics Inner Mongolia Normal University Huhhot China Department of mathematics Harbin Institute of Technology Harbin China

The conception of k_uniform smoothness (KUS) is introduced. It is the extension of the conception of uniform smoothness. It is proved that the k_uniform smoothness and Sullivan’s K_uniform rotundity (KUR) are the daul notions. X+* is a KUR space if and only if X is a KUS space, X+* is a KUS space if and only if X is a KUR space. If X is a KUS space, then X is a (K+1)US space. It is also proved that the KUS space includes the Nan’s k_strongly smooth space.

关键词： K_uniform smoothness K_uniform convexity.

Existence of the solutions and the attractors for the large-scale atmospheric equations

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science china Earth sciences 2006年第6期49卷 650-660页

作者： HUANG Haiyang1 & GUO Boling2.1. Department of mathematics, Beijing normal {2., Beijing 100875, china 2. Institute of Applied Physics and Computational mathematics, Beijing 100080, china 1. Department of mathematics Beijing Normal University Beijing 100875 China 2. Institute of Applied Physics and Computational mathematics Beijing 100080 China

In this paper, firstly, the proper function space is chosen, and the proper expression of the operators is introduced such that the complex large-scale atmospheric motion equations can be described by a simple and abstract equation, by which the definition of the weak solution of the atmospheric equations is made. Secondly, the existence of the weak solution for the atmospheric equations and the steady state equations is proved by using the Galerkin method. The existence of the non-empty global attractors for the atmospheric equations in the sense of the Chepyzhov-Vishik’s definition is obtained by constructing a trajectory attractor set of the atmospheric motion equations. The result obtained here is the foundation for studying the topological structure and the dynamical behavior of the atmosphere attractors. Moreover, the methods used here are also valid for studying the other atmospheric motion models.

关键词： atmosphere equations, weak solution, trajectory attractor, global attractor, equilibrium.

Minimal systems of generators for central division algebra and semi-simple algebra

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Chinese science Bulletin 1998年第21期43卷 1777-1780页

作者： QIU Qizhang 1 and SUN Ling 2.1. Department of mathematics, Wuhan university, Wuhan 430072. {2. 2. Department of information science, Wuhan university, Wuhan 430072. {2.. Department of mathematics Wuhan University Wuhan China Department of information science Wuhan University Wuhan China

Suppose that F is a field of characteristic zero and (ⅰ) D is a finite-dimensional central division algabra over F; (ⅱ) A is a finite-dimensional semi-simple algabra over F. It is proved that as F-algebras, D and A ... 详细信息

关键词： central division algebra semi-simple algebra generator minimal system of generators.

Joint density of hitting time and point to an ellipse for Brownian motion

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Chinese science Bulletin 1997年第24期42卷 2054-2058页

作者： YIN Chuancun ZHAO Xuelei Department of mathematics, Qufu normal {2., Qufu 2.3165, china 2. Institute of mathematics, Shantou {2., Shantou 515063, china Department of mathematics Qufu Normal University Qufu 273165 China

IT is well known that the distribution of hitting time, hitting point, last exiting time, and lastexiting point for Brownian motion to balls has been extensively studied. A similar investi-gation of rectangles or cubes has also been well done. However, analogous questions for Brow-nian motion to ellipsoid are rarely concerned. Bai and Cai obtained the distribution of

关键词： Brownian motion hitting time hitting point ellipse.

Transitional function of DG to CA3 in the hippocampus

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Progress in Natural science:Materials International 2007年第12期17卷 1436-1444页

作者： Yan Chuankui1 and Liu Shenquan2.1. Department of mathematics, Hangzhou normal {2., Hangzhou 310036, china 2. Department of Applied mathematics, School of Mathematical sciences, South china {2. of Technology, Guangzhou 510640, china) Department of mathematics Hangzhou Normal University Hangzhou 310036 China Department of Applied mathematics School of Mathematical Sciences South China University of Technology Guangzhou 510640 China

Using single cell channel model, the transmission features of CA3-DG network in the hippocampus are investigated. The influence of the stimulation on discharge pattern of pyramidal neurons is analyzed, which shows that it starts with period spiking discharges, followed by period-doubling bifurcation to chaos, and period 3 discharge evolving into chaos, and ultimately a period of bursting discharges. By the synaptic model, the CA3-DG network model is constructed, which analyzes the summation of postsynaptic currents in the network, the influence of postsynaptic current on discharge rhythm as well as the mechanism of bursting discharges. The strong capacity of spatiotemporal encoding in the network indicates the features of CA3 network during the information transmission process in the hippocampus. The modeling result with time delay of the synaptic transmission is in accordance with the experimental phenomena of action potential in the hippocampus.

关键词： hippocampus CA3-DG period-doubling bifurcation chaos.

Cartesian closedness of categories of completely distributive lattices

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Chinese science Bulletin 1998年第24期43卷 2059-2063页

作者： ZHANG Dexue 1 and YANG Zhongqiang 2.1. Department of mathematics, Sichuan university, Chengdu 610064, {2. 2. Department of mathematics, Shaanxi normal university, Xi’an 710062. {2. Department of mathematics Sichuan University Chengdu China Department of mathematics Shaanxi Normal University Xi’an China

The category of completely distributive lattices with Scott continuous functions is cartesian closed. Neither the category of completely distributive lattices with arbitrary union preserving mappings nor the category ... 详细信息

关键词： completely distributive lattice continuous lattice cartesian closedness.