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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, beijing 100871,{3.) 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

Probability parametric imaging with DCE-MRI data to identify prostate cancer in the peripheral zone

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Progress in Natural Science:Materials International 2006年第9期16卷 948-953页

作者： HUANG Xinrui, WANG Qiang, XU Yufeng, WANG Xiaoying and BAO Shanglian ( The Key Laboratory of Medical Physics and Engineering, peking university, beijing 100871, china The Medical School of peking university, beijing 100083. china 3. The First Hospital of peking university, beijing 10003., china) [a]The key Laboratory of Medical Physics and Engineering Peking University Beijing China [b]The Medical School of peking university Beijing China [c]The First Hospital of peking university Beijing China

To quantitatively analyze prostate dynamic contrast-enhanced magnetic resonance images (DCE-MRI), a retrospective study was carried out to construct a mathematical model to predict whether a lesion is cancerous or not. With known diagnosis of 52 re-gions-of-interest (10 malignant, 26 benign and 16 normal) in peripheral zone (PZ) of prostate from 18 patients undergoing needle biopsy and 8 normal volunteers, we combined feature parameters (k1, k2 and tp) from the linear-slope model with logistic regression to determine the statistical probability model. Prostate cancerous probability maps were derived using the model on each subject to examine the correlation between the model-based prediction and the known diagnosis. Compared the model prediction results of 52 regions-of-interest with the histopathologic results, the total agreement rate was 90.4 % ; the agreement rate was 60 % for the malignant and 97. 6 % for the nonmalignant. The diagnostic results only referencing the probability maps by two radiologists showed a high agreement in tissue characteristics and lesion location with the combining results from other diagnostic techniques such as PSA (prostate specific antigen) level and MRS (magnetic resonance spectroscopy) .

关键词： time-intensity curve prostate DCE-MRI logistic regression probability parametric image.

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. department of Geology, china {3. of Geosciences, beijing 100083. china 3. department of Geology, peking university, beijing 100871, china 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―200 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―200 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 university, Xi’an 710069, china 2. The Geological Lab Center, china university of Geosciences (beijing), beijing 100083. china 3. Key Laboratory of Orogenic Belts of the Ministry of Education, department of Geology, peking university, beijing 100871, china 1. Key Laboratory of Continental Dynamics of the Ministry of Education Department of Geology Northwestern University 710069 Xi’an China 2. The Geological Lab Center China University of Geosciences 100083 (Beijing)Beijing China 3. Key Laboratory of Orogenic Belts of the Ministry of Education Department of Geology Peking University 100871 Beijing China

The Songshugou dunite body, which occupies an area of about 20 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 Al2O3. 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, beijing 100871,{3.) peking Univ Dept Math Beijing 100871 Peoples R 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

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 Physics,peking university,{3. 100871,china 2 department 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 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 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

Study on the two and three-parameter working stability regions of 3.-TZP suspension

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Science china(Technological Sciences) 2006年第5期49卷 547-568页

作者： CHEN Youqiang1, 2, ZHANG Xinni3. CHEN Sha’ou3.& QI Ping3.1. department of Chemistry, Qingdao university, Qingdao 266071, china 2. department of Chemistry, Tsinghua university, beijing 100084, china 3. department of Physics, Qingdao university, Qingdao 266071, china 1. department of Chemistry Qingdao University Qingdao 266071 China 2. department of Chemistry Tsinghua University Beijing 100084 China 3. department of Physics Qingdao University Qingdao 266071 China

We determined the variation tendency of viscosity (η) at various solids load- ing (α) for 3.-TZP suspension as a function of dispersant concentration (Cw) using vis- cosity measurement, measured the diameter of particles as a function of Cw in very dilute suspension using light scattering method, and obtained the surface features of the sedi- ment of suspension with different Cw using SEM. We also discussed the influence of the microstructure of adsorbed polymer layers on particles and their interactions in the dis- persing medium on the stability of suspension. Then two different stable states and two different unstable states for 3.-TZP suspension were given. Accordingly, the (Cw, η), (Cw, α), and (α, η) two-parameter, and (Cw, α, η) three-parameter stability maps were con- structed. Based on the DLVO theory calculations, the dispersant concentration, particle distance (r), and interparticle potential energy (VT) maps with various solids loading for 3.-TZP aqueous suspension were also constructed. In (Cw, r) two-parameter coordinate system, the stable motion region map for particles was established. The Cw, α, and VT,max (the highest potential energy) surface of the potential barrier map was obtained through calculation and simulation on the basis of the surfaces of Cw, r, VT maps introduced above. The (Cw, α) two-parameter stability map was then obtained from the Cw, α, VT,max map. The results showed that this theoretical map can qualitatively prove the experimentally obtained results—the existence of different dispersed states of particles in suspension system and the variation tendency of suspension stability with changing each parame- ter—were reasonable.

关键词： 3.-TZP, suspension, stability, DLVO theory, interparticle potential energy.

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, beijing 100871,{3.) peking Univ Dept Psychol Beijing 100871 Peoples R 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.

Kinetic characteristics of continuous flow polymerase chain reaction chip: A numerical investigation

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Science china(Technological Sciences) 2010年第7期53卷 1967-1972页

作者： WANG ShiYing1 & WANG Wei2,3.1 School of Physics, peking university, beijing 100871, china 2 Institute of Microelectronics, peking university, beijing 100871, china 3.National Key Laboratory of Science and Technology on Micro/Nano Fabrication, beijing 100871, china 1. School of Physics Peking University Beijing 100871 China2. Institute of Microelectronics Peking University Beijing 100871 China3. National Key Laboratory of Science and Technology on Micro/Nano Fabrication Beijing 100871 China

Continuous flow PCR (polymerase chain reaction) chip holds impressive advantages compared to micro chamber PCR chip. In order to have better understanding of kinetic characteristics of continuous flow PCR chip, a comprehensive mathematical model is presented in this paper, including melting, annealing and extension phases of a typical PCR process which has the essence of a convection-diffusion-reaction system. Using this model, we can simulate the PCR process in series of reaction cycles. Numerical results show that the average sample velocity plays a significant role in affecting the amplification efficiency. Also, appropriate combination of the PCR mixture is important for high-quality DNA amplification. Giving a large initial DNA concentration range, the continuous flow PCR scheme holds excellent real-time detection ability theoretically. The present numerical model bridges the temperature distribution to the real DNA amplification, and thereby is able to successfully predict continuous flow PCR properties which are important for the chip design.

关键词： continuous flow PCR chip numerical simulation convection-diffusion-reaction system