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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

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.{2. 2. department of Geology,{2. University of Geosciences, beijing 100083.{2. 3. department of Geology, peking University,{12.,{2. 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.

Abrupt climate change and collapse of ancient civilizations at 2.00BC-2.00BC

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Progress in Natural Science:Materials International 2005年第10期15卷 46-52页

作者： WANG Shaowu (department of atmospheric Science, School of Physics, {2. University,{3., china) department of atmospheric Science School of Physics Peking University Beijing 100871 China

Plentiful evidence of historical, archaeological and palaeoclimatic studies proved that an abrupt change from wetter to drier climate occurred over the Nile Valley,the Mesopotamia, the Indus Valley and Huanghe River Valley at 2.00BC-2.00BC. The abrupt change was developed based on the general lowering of temperature in the middle latitudes, and was a strong cold event since the beginning of the Megathermal (8.5-3.0 kaBP). Collapse of Nile civilization appeared at the First Intermediate Period (2.81BC-2.40BC). Civilization of Mesopotamia began collapse following the disintegration of Akkadian Empire. This process lasted to the foundation of Babylon Kingdom from 2.00BC to 1900BC. Indus civilization abruptly fell off at 1800BC. A widespread alternation of archaeological cultures happened in china at ca. 2.00BC except only in its central part. Longsheng culture was replaced by the Erlitou culture, which is now acknowledged in china as Xia Culture. Foundation of Xia Dynasty at 2.70BC opened a new chapter in the development of Chinese civilization. Studies indicated that abrupt climate change may be caused by the weakening of the Thermohaline Circulation (THC).

关键词： 2.00BC-2.00BC abrupt climate change collapse of ancient civilization.

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, beijing 100084,{2. 2. department of Physics, peking University, beijing 100871,{2.) 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.

Characteristics of vertical ozone distribution in the lower troposphere in the Yangtze River Delta at Lin'an in the spring of 2.01

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Science china Earth sciences 2005年第9期48卷 1519-1528页

作者： ZHENG Xiangdong1, CHAN Chuenyu2. CUI Hong2. QIN Yu3. CHAN Loyan2. ZHENG Yongguang3.& LEE Yusiang2.1. Chinese Academy of Meteorological {2., beijing 100081, china 2. {3. of Civil and Structural Engineering, Hong Kong Polytechnic University, Hung Hom, Hong Kong, china 3. department of atmospheric sciences, peking University, beijing 100871, china Chinese Academy of Meteorological sciences Beijing China department of Civil and Structural Engineering Hong Kong Polytechnic University Hung Hom Hong Kong China department of atmospheric {2. Peking University Beijing China

We analyzed vertical distributions of ozone (O3. in the lower troposphere (< 5 km above ground) at Lin’an (119.75°E, 3..3.°N), Zhejiang Province using electrochemical concen- tration cell (ECC) ozonesonde data obta... 详细信息

We analyzed vertical distributions of ozone (O3. in the lower troposphere (3..3.°N), Zhejiang Province using electrochemical concen- tration cell (ECC) ozonesonde data obtained from February 2. to April 13. 2.01. The results showed that the vertical O3.distributions are controlled by metrological conditions and the char- acteristics of O3.profiles are related to those of wet bulb potential temperature and wind field. O3.below 2.km showed that the strongest variability and enhanced O3.mixing ratios were associated with easterly winds that blow pollutants from the upwind source region of the Yangtze River Delta (YRD) region. Vertical O3.profiles below 5 km can be grouped into 5 categories: (1) peak mixing ratio type, (2. well-mixed type, (3. layered-structure type, (4) episodic pollution type and (5) alti- tudinal increasing type. Vertical distributions of O3.affected by regional transport of polluted air masses were investigated. Transport of polluted air from high latitudes of northern china, ac- companying subsiding motion of air and stagnant {12. conditions are important factors that lead to high mixing ratios of O3.at Lin’an. The stagnant {12. conditions associated with a continental high pressure system and pollution plume transported from the YRD and cen- tral-eastern china also lead to regional accumulation of O3.and high O3.mixing ratio at Lin’an. Long-range transport of O3.and pollutants from the Pearl River Delta in South china and in-situ O3.formation also resulted in elevated O3.mixing ratios at around 1 km altitudes and layered O3.distribution in the lower troposphere.

关键词： vertical ozone distribution, lower troposphere, Yangtze River Delta, Lin'an.

Interannual variability of Antarctic Oscillation and its influence on East Asian climate during boreal winter and spring

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Science china Earth sciences 2006年第5期49卷 554-560页

作者： FAN Ke1,2.3.& WANG Huijun2.1. Nansen-Zhu International Research Center, Institute of atmospheric Physics, Chinese Academy of {2., beijing 10002.,{3. 2. department of atmospheric Science, Yunnan University, Kunming 650091,{3. 3. Graduate University of the Chinese Academy of {2., beijing 100049,{3. Nansen-Zhu International Research Center Institute of Atmospheric Physics Chinese Academy of Sciences Beijing China department of atmospheric Science Yunnan University Kunming China Graduate University of the Chinese Academy of sciences Beijing China

The interannual variability of Antarctic Oscillation (AAO) and its influence on East Asian climate during both boreal winter and spring are addressed. The results show that the positive AAO anomaly decreases the cold activity over East Asia during both boreal winter and spring. AAO-related barotropic meridional teleconnection from Antarctic to Arctic is found through analysis of mean me- ridional circulations. This meridional teleconnection is remarkable over Eurasia during boreal winter and over the Pacific Ocean during boreal spring. The results also show that zonal mean zonal wind at high latitudes in Southern Hemisphere has well positive correlation with that of Eurasia during boreal winter and has negative correlation with Pacific North American teleconnection (PNA) during boreal spring, which again display the meridional teleconnection. Thus, local meridional teleconnection is a possible linkage for interaction of circulations at mid-high latitudes between both hemispheres.

关键词： Antarctic Oscillation, Eurasian west wind, meridional teleconnection, mean meridional circulation.

Debating about the climate warming

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Progress in Natural Science:Materials International 2006年第1期16卷 1-6页

作者： WANG Shaowu1, LUO Yong2. ZHAO Zongci2. DONG Wenje2.and YANG Bao3.(1.department of {2. sciences, School of Physics, {3. University, beijing 100871, china 2. Laboratory for Climate Studies, china Meteorological Administration, beijing 100081, china 3. Institute of Cold and Arid Regions Environmental and Engineering, Chinese Academy of sciences, Lanzhou 73.000, china) department of atmospheric {2. School of Physics Peking University Beijing 100871 China Laboratory for Climate Studies China Meteorological Administration Beijing 100081 China Institute of Cold and Arid Regions Environmental and Engineering Chinese Academy of Sciences Lanzhou 730000 China

Debating about the climate warming is reviewed. Discussions have focused on the validity of the temperature reconstruction for the last millennium made by Mann et al. Arguments against and for the reconstruction are introduced. Temperature reconstructions by other authors are examined, including the one carried out by Wang et al. in 1996. It is concluded that: (1) Ability of reproducing temperature variability of time scale less than 10 a is limited, so no sufficient evidence proves that the 1990s was the warmest decade, and 1998 was the warmest year over the last millennium. (2. All of the temperature reconstructions by different authors demonstrate the occurrence of the MWP (Medieval Warm Period) and LIA (Little Ice Age) in low frequency band of temperature variations, though the peak in the MWP and trough in LIA varies from one reconstruction to the others. Therefore, terms of MWP and LIA can be used in studies of climate change. (3. The warming from 1975 to 2.00 was significant, but we do not know if it was the strongest for the last millennium, which needs to be proved by more evidence.

关键词： climate warming MWP LIA the 2.th century.

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,{2.,{3. 2. LAPC, Institute of atmospheric Physics, Chinese Academy of sciences, beijing 10002.,{3. College of Environmental sciences Peking University Beijing China LAPC Institute of Atmospheric Physics Chinese Academy of Sciences 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.

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 University, Xi’an 710069,{2. 2. The Geological Lab Center,{2. University of Geo{3. (beijing), beijing 100083.{2. 3. Key Laboratory of Orogenic Belts of the Ministry of Education, department of Geology, peking University,{12.,{2. 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.