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Density-functional formula for strongly correlated systems

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Progress in Natural Science:Materials International 2005年第5期15卷 395-401页

作者： WANG Huaiyu1*, HAN Rushan2.and CHEN Nanxian1(1. department of physics, Tsinghua{2., beijing 100084. China 2. department of physics, peking university, beijing 100871, China) department of physics Tsinghua University Beijing 100084 China department of physics Peking University Beijing 100871 China

Density functional method is applied for strongly correlated systems. Based on the assumption that the systems are composed of electrons in singly-occupied orbitals and those in doubly-occupied orbitals, a set of self-consistent equations are obtained by standard variation procedure. The equations consist of two parts. One part is to solve the wave functions of the electrons in singly-occupied orbitals and the other is to solve the wave functions of the electrons in doubly-occupied orbitals. The physical meanings of the terms appearing in the equations are discussed.

关键词： density-functional theory strongly correlated systems doubly-occupied orbital two-particle wave function self-consistent equations.

THE PHYSICAL ENTROPY OF SINGLE CONSERVATION LAWS

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Journal of Computational Mathematics 1998年第5期16卷 437-444页

作者： (department of Mathematics, peking university,{2., China) beijing Univ Dept Math Beijing 100871 Peoples R China

By means of the comparisons with the formulas in statistical mechanics and thermodynamics, in this paper it is demonstrated that for the single conservation law partial derivative(t)u + partial derivative(x)f(u) = 0, if the flux function f(u) is convex (or concave), then, the physical entropy is S = -f(u); Furthermore, if we assume this result can be generalized to any f(u) with two order continuous derivative, from the thermodynamical principle that the local entropy production must be non-negative, one entropy inequality is derived, by which the O.A. Olejnik's famous E- condition can be explained successfully in physics.

关键词： conservation laws entropy entropy production

A general information theoretical proof for the second law of thermodynamics

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Science China(physics,Mechanics & Astronomy) 2008年第7期51卷 813-816页

作者： ZHANG QiRen department of Technical physics,{2., beijing 100871, China 1. department of Technical physics Peking University Beijing 100871 China

It is shown that the conservation and the non-additivity of the information, together with the additivity of the entropy, make the entropy increase in an isolated system. The collapse of the entangled quantum state offers an example of the information non-additivity. Nevertheless, the non-additivity of information is also true in other fields in which the interaction information is important. Examples are classical statistical mechanics, social statistics and financial processes. The second law of thermodynamics is thus proven in its most general form. It is exactly true not only in quantum and classical physics but also in other processes in which the information is conservative and non-additive.

关键词： information conservation non-additivity of information entropy increase

Estimating surface evapotranspiration using combined MODIS and CBERS-02.data

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Science China(Technological Sciences) 2005年第S2期48卷 145-160页

作者： XIN Xiaozhou1,2. LIU Qinhuo1, TANG Yong1,3, TIAN Guoliang1, GU Xingfa1, LI Xiaowen1,2. ZHENG Hongsheng4.& CHEN Jiayi4.1. State Key Laboratory of Remote Sensing Science, Institute of Remote Sensing Applications, Chinese Academy of Sciences, {2. 100101, China 2. Research Center for Remote Sensing and GIS, department of Geography, {2. Normal university, {2. 100875, China 3. Graduate university of Chinese Academy of Sciences, {2. 100039, China 4. department of atmospheric physics, peking university, beijing 100871, China 1. State Key Laboratory of Remote Sensing Science Institute of Remote Sensing Applications Chinese Academy of Sciences 100101 Beijing China2. Research Center for Remote Sensing and GIS Department of Geography Beijing Normal University 100875 Beijing China3. Graduate University of Chinese Academy of Sciences 100039 Beijing China4. Department of Atmospheric Physics Peking University 100871 Beijing China

Spatial scale error is one of the most serious problems in the estimates of land surface heat fluxes of sensible and latent from satellite-borne data such as MODIS 1km resolution reflectance and emissive data. One of the feasible and economic ways to decrease the spatial scale error is to use high resolution land use class data together with the MODIS data. CBERS-02.data were used to produce land use class of Baiyangdian area, Hebei Province, China in the autumn of 2.04. The area ratio of each class in MODIS pixel was calculated, and used to derive the heat fluxes of the mixed pixel. The results showed that the estimated heat fluxes of soil, sensible and latent have been changed remarkably after using the high resolution land class data. It could be concluded from the comparison between simulated and ground-measured fluxes as well as the theoretical analysis that high resolution land class data are useful to diminishing the scale error of heat fluxes estimated from low resolution satellite data.

关键词： surface evapotranspiration spatial scale error MODIS CBERS land class.

Calculation of traversal time in tunneling by double-wave theory

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Chinese Science Bulletin 1998年第9期43卷 723-727页

作者： HUANG Xiangyou department of physics,{2., beijing 100871, China department of Physis Peking University Beijing China

Becausethe information contained in a wave function is not enough to describe an individual particle, the suggestion to define the state of a particle by two-wave functions is used. In the double-wave description, a general formula telling the traversal time of a particle in tunneling is obtained. When the double-wave description over an initial parameter is averaged , it reduces to the usual description. Two new relations between the transmission and the reflected coefficients are founded in the new cescription.

关键词： tunneling double-wave theory ensemble.

|m| Partial wave treatment for two-dimensional Coulomb-scattering and Regge pole

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Science China(physics,Mechanics & Astronomy) 2004年第6期47卷 676-684页

作者： WANG Jing & ZENG Jinyan department of physics,Tsinghua{2.,beijing 100084.China School of physics,peking{2.,beijing 100871,China department of physics Tsinghua University Beijing 100084 China School of physics Peking University Beijing 100871 China

The symmetry and |m| partial-wave analysis for two-dimensional (2.) Coulomb-scattering is investigated. As a function of energyE, the |m| partial-wave scattering amplitudef |m|(θ) is analytically continuated to the, negativeE (complexk) plane, and it is found that the bound state energy eigenvalues (E<0) are just located at the poles off |m|(θ) on the positive imaginaryk axis as is expected. In addition, as a function of |m|,f |m|(θ) is analytically continuated to the complex |m| plane, the bound state energy eigenvalues are just located at the poles off |m|(θ) on the positive real |m| axis.

关键词： two-dimensional Coulomb scattering, |m| partial-wave, Regge pole.

Frontal genesis of moisture atmosphere during the early 2.08 persistent freezing-rain event in southern China

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Science China Earth Sciences 2010年第3期53卷 454-464页

作者： QIAN WeiHong1 & FU JiaoLan1,2.1 department of atmospheric Sciences, School of{2., peking university,{4., China 2.National Meteorological Center of CMA, beijing, 100081, China 1. department of atmospheric Sciences School of Physics Peking University Beijing 100871 China2. National Meteorological Center of CMA Beijing 100081 China

From January 10 to February 2. 2.08, a severe and persistent freezing-rain event occurred in southern and southwestern China. Here we use an observational analysis to compare the persistent freezing-rain event in the early 2.08 with the winter precipita- tion in the late 2.07 over south of the Yangtze River (Jiangnan). The persistent freezing-rain event was directly linked to the activity of quasi-stationary front. The gradient of equivalent temperature (ET) can well indicate the frontal genesis of moist atmosphere (moisture front) and its activity as well as its relationship with precipitation belt. The precipitation types (snow and freezing rains) are related to the vertical structure of moisture front. The inversion profile of ET vertical distribution is a typical synoptic condition that caused the freezing-rain event. The horizontal gradient of ET with a criterion of 10℃ / 100 km, which reflects the accumulation and release of atmospheric energy, can be applied to predict the precipitation 5-10 days in advance.

关键词： freezing-rain event frontal genesis extended-range weather forecast winter Jiangnan

Experimental measurement of growth patterns on fossil corals:Secular variation in ancient Earth-Sun distances

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Chinese Science Bulletin 2010年第35期55卷 4010-4017页

作者： ZHANG WeiJia1,3,4.LI ZhengBin2.3 & LEI Yang1 1 department of {2.,peking university,{4. 100871,China 2.department of Electrical Engineering and Computer Science,peking university,{4. 100871,China 3 State Key Laboratory of Advanced Optical Communication Systems & Networks,peking university,{4. 100871,China 4.Committee of Yuanpei Honors Program,peking university,{4. 100871,China department of physics Peking University Beijing 100871 China State Key Laboratory of Advanced Optical Communication Systems & Networks Peking University Beijing 100871 China Committee of Yuanpei Honors Program Peking University Beijing 100871 China department of Electrical Engineering and Computer Science Peking University Beijing 100871 China

In recent years,much attention has been given to the increase in the Earth-Sun distance,with the modern rate reported as 5-15 m/cy on the basis of astronomical ***,traditional methods cannot measure the ancient leaving rates,so a myriad of research attempting to provide explanations were met with unmatched *** this paper we consider that the growth patterns on fossils could reflect the ancient Earth-Sun *** mechanical analysis of both the Earth-Sun and Earth-Moon systems,these patterns confirmed an increase in the Earth-Sun *** a large number of well-preserved specimens and new technology available,both the modern and ancient leaving rates could be measured with high precision,and it was found that the Earth has been leaving the Sun over the past 0.53 billion *** Earth's semi-major axis was 14. million kilometers at the beginning of the Phanerozoic Eon,equating to 97.6% of its current *** modern leaving rates are 5-14.m/cy,whereas the ancient rates were much *** results indicate a special expansion with an average expansion coefficient of 0.57H0 and deceleration in the form of Hubble *** the basis of experimental results,the Earth's semi-major axis could be represented by a simple formula that matches fossil measurements.

关键词：地球太阳古代距离生长模式实验石珊瑚量化

Adjoint method for the optimum planning of industrial pollutant sources

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Science China Earth Sciences 2005年第8期48卷 1270-1279页

作者： LIU Feng1,2. HU Fei2.& ZHU Jiang2.1. College of Environmental Sciences, peking university, beijing 100871, China 2. LAPC, Institute of{2. physics, Chinese Academy of Sciences, {4. 10002., China 1. College of Environmental Sciences Peking University 100871 Beijing China 2. LAPC Institute of Atmospheric Physics Chinese Academy of Sciences 100029 Beijing China

The optimum planning of industrial pollutant sources, which optimizes the economic object without violating environmental constraints, is an important and hard task to be conquered. In this paper, an adjoint method is developed to solve the problem. The penalty function is in-troduced to deal with the environmental inequality constraints, and Lagrange function is con-structed to derive the adjoint equation and the gradient of the object function. In this means, the gradient of the object function can be calculated by solving the adjoint equation, and the infor-mation from the gradient is used to make the object function descend and approach to an optimal solution after some iterations. A two-dimensional, simplified model is used for numerical experi-ments. The theoretical derivations are verified by the results of the experiments. Furthermore, the adjoint method is shown to be of excellent convergence and efficiency, which is adaptive to the fast development of air quality numerical models and super computers.

关键词： optimum planning, industrial pollutant sources, adjoint equation, penalty function, gradient.