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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.,{3.) 北京大学数学系北京

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.,{3., china department of technical Physics Peking University Beijing 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

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 university, {2. 100084,{3. 2. department of Physics, peking university, beijing 100871,{3.) Dept. of Phys. Tsinghua Univ. Beijing 100084 China Dept. of Phys. Peking Univ. 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.

Dehydration melting of solid amphibolite at 2.0 GPa: Effects of time and temperature

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Science china Earth Sciences 2005年第8期48卷 1120-1133页

作者： ZHOU Wenge1, XIE Hongsen1, LIU Yonggang1, ZHENG Xiaogang1, ZHAO Zhidan2.& ZHOU Hui3.1. Laboratory of Material in the Earth’s Interior, Institute of Geochemistry, Chinese Academy of Sciences, Guiyang 550002. china 2. {2. of Geology, china {3. of Geosciences, beijing 100083. china 3. {2. of Geology, peking university, beijing 100871, china Laboratory of Material in the Earth’s Interior Institute of Geochemistry Chinese Academy of Sciences Guiyang China department of Geology China University of Geosciences Beijing China department of Geology Peking University Beijing China

Two sets of dehydration-melting with a natural solid amphibolite, collected from North Himalayan structure zone, Tibet, have been carried out in multi-anvil apparatus at 2.0 GPa and 800―1000℃, for 12.2.0 h. One is keeping the pressure at 2.0 GPa and the annealing time of 12.h, changing the temperature (800―1000℃). The other is keeping the pressure at 2.0 GPa and temperature at 850℃, varying the annealing time (12.2.0 h). The products are inspected with microscope and electron probe. The results indicate that at 2.0 GPa, annealing time of 12.h, garnets, melts and clinopyroxenes occur in amphibolite gradually with increasing temperature and the chemical compositions of melt vary from tonalite to granodiorite, and then to tonalite. However, at 2.0 GPa and 850℃, with the annealing time increasing, the garnets, melts and cli-nopyroxenes also occur in amphibolite gradually and the chemical compositions of melt vary from tonalite to granodiorite. In both cases, melts interconnect with each other when the contents of melt are over the 5 vol.%. the viscosities of the melt produced in amphibolite at temperature higher than 850℃ are on a level with 104 Pa·s. The interconnected melt with such a viscosity may segregate from the source rock and form the magma over reasonable geological time. Therefore, it is believed that at the lower part of the overthickened crust, the tonlitic and grano-dioritic magma may be generated through the dehydration melting of amphibolite.

关键词： solid amphibolite, high pressure, high temperature, time, partial melting.

Petrogenesis of Songshugou dunite body in the Qinling orogenic belt, Central china: Constraints from geochemistry and melt inclusions

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Science china Earth Sciences 2005年第8期48卷 1146-1157页

作者： SU Li1,2. SONG Shuguang3.& ZHOU Dingwu1 1. Key Laboratory of Continental Dynamics of the Ministry of Education, department of Geology, Northwestern {2., Xi’an 710069, china 2. The Geological Lab Center, china {2. of Geosciences (beijing), beijing 100083. china 3. Key Laboratory of Orogenic Belts of the Ministry of Education, department of Geology,{12., beijing 100871, china Key Laboratory of Continental Dynamics of the Ministry of Education Department of Geology Northwestern University Xi’an China The Geological Lab Center China University of Geosciences (Beijing)Beijing China Key Laboratory of Orogenic Belts of the Ministry of Education Department of Geology Peking University Beijing China

The Songshugou dunite body, which occupies an area of about 2. km2. is the largest ultramafic massif in the eastern Qinling orogenic belt, Central china. The major compo-nent of this body is dunitic rocks including mylonitic dunite and coarse-grained dunite; they oc-cupy about 95 vol% of the total body. Petrography, mineral composition, major and trace ele-ments and primitive melt inclusions have been investigated in this paper; all revealed that this dunite body is the product of melt-rock interaction by porous percolation flow. In comparison with dunite sills or veins in harzburgite from the basal part of Oman ophiolite, this dunite body is characterized by lower contents of Al2.3. CaO and HREE but higher content of highly incom-patible elements and Zr and Hf. The LREE enriched patterns and primitive mantle normalized spidergrams of trace elements are also different from the Oman dunite. Combining with melt in-clusions observed in olivines, we conclude that this dunite body is the product of large- scale porous percolation flow of high-MgO melts within depleted mantle peridotites. The high-MgO magma, in essence, was most probably produced at the hot head of an upwelling mantle plume. The occurrence of the Songshugou dunite body is closely associated with the activity of mantle super-plume in Neo-Proterozoic era in the Yangtze Craton.

关键词： Songshugou dunite body, geochemistry, melt inclusion, mantle plume, Qinling orogenic belt.

THE FUNCTION d_k(n) AT CONSECUTIVE INTEGERS

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Chinese Annals of Mathematics,Series B 1999年第4期20卷 473-478页

作者： MENG ZAIZHAO(department of Mathematics, peking university,{2.,{3.) department of Mathematics Peking University Beijing 100871 China

Let dk(n) denote the k-fold iterated divisor function (k ≥ 2.. It is proved that for sufficiently large x) dk(n) = dk(n + 1) holds for >> x(log log x)-3.integers n ≤x.

关键词： Divisor function Multiplicative function Congruence

Neuroimaging studies of self-reflection

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Progress in Natural Science:Materials International 2004年第4期14卷 10-16页

作者： ZHU Ying(department of Psychology, peking university,{2.,{3.) Dept. of Psychology Peking Univ. Beijing 100871 China

This paper reviews some basic findings and methodological issues in neuroimaging studies of self-referential processing. As a general rule, making judgments about one’s self, inclusive of personality trait adjectives or current mental states (person’ s preferences, norms, aesthetic values and feeling) uniformly generates medial prefrontal activations, regardless of stimulus materials (words or pictures) and modality (visual or auditory). Cingulate activations are also observed in association with most self-referential processing. Methodological issues include treating self-referential processing as either representing one’s own personality traits or representing one’s own current mental states. Finally, self-referential processing could be considered as implement of "I think therefore I am" approach to neuroimaging the self.

关键词： self self-referential processing medial prefrontal cortex cingulate brain image.

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 {2. of Physics,peking university,{3. 100871,china 2.{2. of Electrical Engineering and Computer Science,peking university,{3. 100871,china 3.State Key Laboratory of Advanced Optical Communication Systems & Networks,peking university,{3. 100871,china 4 Committee of Yuanpei Honors Program,peking university,{3. 100871,china department of Physics Peking University Beijing China State Key Laboratory of Advanced Optical Communication Systems & Networks Peking University Beijing China Committee of Yuanpei Honors Program Peking University Beijing China department of Electrical Engineering and Computer Science Peking University Beijing 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 146 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

Oblique Derivative Problems for Second OrderNonlinear Equations of Mixed Type inMultiply Connected Domains

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Communications in Nonlinear Science and Numerical Simulation 1999年第4期4卷 281-284页

作者： Guochun WEN(department of Mathematics, peking university,{2.,{3.) department of Mathematics Peking University Beijing 100871 China

1FormulationoftheProblemLetDbeNconnectedboundeddomaininthecomplexplaneCwiththeboundaryNZNOD=WUL,wherer=ZrjEn（00},L=ULi’andrhastheendj=1j=1poiatsal=02.LiaredeadedasLI={x=;)05x51}L:={x=--y+hi,hi... 详细信息

关键词： oblique derivative problems quasinonlinear equations of mixed type mul-tiply connected domains.