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INFINITE ELEMENT METHOD FOR THE EXTERIOR PROBLEMS OF THE HELMHOLTZ EQUATIONS

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Journal of Computational Mathematics 2000年第6期18卷 657-672页

作者： Lung-an Ying (School of Mathematical sciences, peking university,{2.,{3.) 北京大学北京 100871

There are two cases of the exterior problems of the Helmholtz equation. If λ ≥ 0 the bilinear form is coercive, and if λ < 0 it is the scattering problem. We give a new approach of the infinite element method, which enables us to solve these exterior problems as well as corner problems. A numerical example of the scattering problem is given. [ABSTRACT FROM AUTHOR]

关键词： Helmholtz equation exterior problem infinite element method

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. 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.

BRILL-NOETHER MATRIX FOR RANK TWO VECTOR BUNDLES

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Chinese Annals of Mathematics,Series B 2002年第4期23卷 531-538页

作者： TAN XIAOJIANGSchool of Mathematical sciences, peking university,{2.,{3. School of Mathematical sciences Peking University Beijing 100871 China

Let X be an arbitrary smooth irreducible complex projective curve, E (?)X a rank two vector bundle generated by its sections. The author first represents ?as a triple {D1,D2.f}, where D1 , D2.are two effective divisors with d = deg(D1) + deg(D2., and f ∈ H?X, [D1] |D2. is a. collection of polynomials. E is the extension of [D2. by [D1] which is determined by f. By using / and the Brill-Noether matrix of D1+D2. the author constructs a 2. × d matrix WE whose zero space gives Im{H0(X,[D1]) (?) H0(X, [D1] |D1)}(?) Im{H?X, E) (?) H0(X,[D2.) (?) H0(X, [D2.|D2.} From this and H0(X,E) = H0(X,[D1]) (?)Im{H0(X,E) (?) H0(X, [D2.)}, it is got in particular that dimH0(X, E) = deg(E) - rank(WE) + 2.

关键词： Brill-Noether matrix Vector bundle Effective divisor

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. 1. Nansen-Zhu International Research Center Institute of Atmospheric Physics Chinese Academy of Sciences Beijing 100029 China 2. Department of atmospheric Science Yunnan University Kunming 650091 China 3. Graduate university of the Chinese Academy of {2. Beijing 100049 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.

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, beijing 100871,{2.) 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

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. {3. of Geosciences, beijing 100083.{2. 3. Department of Geology, peking university, beijing 100871,{2. 1. Laboratory of Material in the Earth’s Interior Institute of Geochemistry Chinese Academy of Sciences 550002 Guiyang China 2. Department of Geology China University of Geosciences 100083 Beijing China 3. Department of Geology Peking University 100871 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.

Milestone of the meridian science──970th anniversary of the Chinese Bronze Statue of Meridian

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Chinese Science Bulletin 1998年第5期43卷 353-362页

作者： ZHANG Renji College of Life sciences, peking university,{2.,{3. College of Life sciences Peking University Beijing 100871 China

For more than a thousand years, Chinese people were aware of the transmitted sensations by the application of needles on the body surface. This practice is called acupuncture. Acupuncture had been recorded and transcribed in writings and in drawings, until finally the acupoints were inscribed onto a bronze statue. The bronze statue was called the Meridian Figure. Deeply embodied in the bronze statue is a tripartite confrontation-prism representation of the humans body. This concept was a great scientific achievement in ancient china. The author traces the history of Meridian science described in traditional Chinese medical terms. Then he explores a clear analogy of the meridian pathway (MP) phenomenon. In a model system, by using a simple segmental in vertebrate, certain parallels can be demonstrated with the meridian concept. For example, the author demonstrated a clear correlation rule among the central mechano-sensory channels, and characteristics of positional discrimination in individual nerve cells from different receptive field inputs. The evidence suggests that the MP phenomenon is an objective neurobiological response. To clarify the research objective in this paper, the author suggests that the MP is a bi-directional pathway along which a positional message signal is transmitted. This phenomenon is evoked by physical stimulation, transmitted linearly across the human body segments, and is perceived by the brain. The MP consists of low resistance paths, is connected by the liquid media contained in the apposite membranous structure. At the cellular level, the regulation functions of MP must pass through along this low resistance path. Two aspects of the modern Meridian research are the functional regulation and the mechanism of intercellular liquid modulation at the nanometer level.

关键词： meridian pathway tripartite confrontation-prism coordinate position discriminative recognition apposite membranous structure.

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, peking university,{2.,{3.) 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.

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. Department of Civil and Structural Engineering, Hong Kong Polytechnic {3., Hung Hom, Hong Kong, china 3. Department of atmospheric {2., peking university, beijing 100871, china 1. Chinese Academy of Meteorological sciences 100081 Beijing China 2. Department of Civil and Structural Engineering Hong Kong Polytechnic University Hung Hom Hong Kong China 3. Department of atmospheric {2. Peking University 100871 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.