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How Properties that Distinguish Solids from Fluids and Constraints of Spherical geometry.Suppress Lower Mantle Convection

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Journal of Earth Science 2018年第1期29卷 1-20页

作者： Anne M. Hofmeister Everett M. Criss Department of Earth and Planetary Sciences Washington University St. Louis MO 63130 USA Panasonic Avionics Corporation Lake Forest CA 92630 USA

The large magnitude of the dimensionless Rayleigh number （Ra-10^8） for Earth＇s -3 000 km thick mantle is considered evidence of whole mantle convection. However, the current formulation assumes behavior characteristic of gases and liquids and also assumes Cartesian geometry. Issues arising from neglecting physical properties unique to solids and ignoring the spherical shapes for planets include：（1） Planet radius must be incorporated into Ra, in addition to layer thickness, to conserve mass during radial displacements. （2） The vastly different rates for heat and mass diffusion in solids, which result from their decoupled transport mechanisms, promote stability. （3） Unlike liquids, sub- stantial stress is needed to deform solids, which independently promotes stability. （4） High interior compression stabilizes the mantle in additional minor ways. Therefore, representing conditions for convection in solid, self-gravitating spheroids, requires modifying formulae developed for bottom- heated fluids near ambient conditions under an invariant gravitational field. To derive stability criteria appropriate to solid spheres, we use dimensional analysis, and consider the effects of geometry. force competition, and microscopic behavior. We show that internal heating has been improperly ac- counted for in the Ra. We conclude that the lower mantle is stable for two independent reasons： heat diffusion far outpaces mass diffusion （creep） and yield strength of solids at high pressure exceeds the effective deviatoric stress. We discuss the role of partial melt in lubricating plate motion, and explain why the Ra is not applicable to the multi-component upper mantle. When conduction is insufficient to transport heat in the Earth, melt production and ascent are expected, not convection of solid rock.

关键词： plasticity diffusion mantle convection stability criteria dimensional analysis geometry.

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Morphometrics:History,development methods and prospects

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Zoological Systematics 2017年第1期42卷 4-33页

作者： Norman MacLeod The Natural History Museum Cromwell RoadLondon SW7 5BDUK

Morphometrics has been pursued by graphical and computational means since the European Renaissance, drawing on core geometric principles first discovered in China and Classical Greece. Through the late 1800s, two distinct approaches to such analyses were pursued： a deformationist approach, epitomized by D＇Arcy Thompson＇s graphical trans-formation grids and the statistical approach popularized by Francis Galton, Karl Pearson, and Julian Huxley in which Cartesian spaces were employed to summarize patterns of variation in size and/or shape variables. Unification of these approaches was an off-stated goal throughout the 20th century, but proved elusive until the mid-1980s when David Kendall, Fred Bookstein, and Colin Goodall proposed a radically new way of understanding form -- as the locations of configurations of landmarks on the surfaces of a nested series of hyperdimensional manifolds. Once this new mathematics of form was understood development of basic concepts, procedures, graphical tools, and statistical tests followed quickly such that the core of the long-hoped for synthesis took less than a decade to achieve. The result-- geometric morphometrics -- continues to develop into an ever-more extensive toolkit that can be used by researchers to describe and understand a wide range of problems involving the characterization of morphological similarities and differences in all of their many and varied contexts. In particular, the new approaches involving the direct analysis of image pixels and new tools such as machine learning and artificial intelligence are set to reinvigorate （and possibly to revolutionize） the field once again.

关键词： Morphometrics form size shape biology geometry.

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A Kind of Electrode Enhanced the Electrochemiluminescence

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Chinese Chemical Letters 2004年第1期15卷 101-104页

作者： GuiHongYAN DaXING ShiCiTAN InstituteofLaserLifeScience SouthChinaNormalUniversityGuangzhou510631

Three kinds of platinum electrodes with different geometry.were designed. The relation of the electrochemiluminescence (ECL) intensity with the geometry.of these electrodes has been investigated. The optical character of these electrodes was directly studied by observation of ECL image and measurement of the ECL intensity. The results showed that the ECL not only concentrated on the edge of the electrode but also concentrated on the edge of holes, which contain in the electrode. The ECL intensity from Ru(bpy)3Cl2·6H2O on round electrode was about half of that on four-hole round disk electrode for a same concentration of Ru(bpy)3Cl2·6H2O, so the detection limit was improved to 10-18 mol/L Ru(bpy)3Cl2·6H2O on four-hole round disk electrode, three times higher than that on round disk electrode.

关键词： Electrochemiluminescence electrode geometry.

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Numerical study of point spread function of a fast neutron radiography system based on scintillating-fiber array

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Science China(Physics,Mechanics & Astronomy) 2007年第6期50卷 698-706页

作者： ZHANG FaQiang1,LI ZhengHong1,YANG JianLun1,YE Fan1,2,WANG Zhen1,2,XIA GuangXin1,YING ChunTong2 & LIU GuangJun2 1 Institute of Nuclear Physics and Chemistry,Mianyang 621900,China 2 Department of Engineering Physics,Tsinghua University,Beijing 100084,China Institute of Nuclear Physics and Chemistry Mianyang China Department of Engineering Physics Tsinghua University Beijing China

For a scintillating-fiber array fast-neutron radiography system,a point-spread-function computing model was introduced,and the simulation code was developed. The results of calculation show that fast-neutron radiographs vary with the size of fast neutron sources,the size of fiber cross-section and the imaging geometry. The results suggest that the following qualifications are helpful for a good point spread function: The cross-section of scintillating fibers not greater than 200 μm×200 μm,the size of neutron source as small as a few millimeters,the distance between the source and the scintillating fiber array greater than 1 m,and inspected samples placed as close as possible to the array. The results give suggestions not only to experiment considerations but also to the estimation of spatial resolution for a specific system.

关键词： fast neutron radiography, scintillating-fiber array, point spread function, Monte Carlo simulation For a scintillating-fiber array fast-neutron radiography system, a point-spread- function computing model was introduced, and the simulation code was developed. The results of calculation show that fast-neutron radiographs vary with the size of fast neutron sources, the size of fiber cross-section and the imaging geometry. The results suggest that the following qualifications are helpful for a good point spread function: The cross-section of scintillating fibers not greater than 200μm×200μm, the size of neutron source as small as a few millimeters, the distance between the source and the scintillating fiber array greater than 1 m, and inspected samples placed as close as possible to the array. The results give suggestions not only to experiment considerations but also to the estimation of spatial resolution for a specific system.……

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A unified curvature theory in kinematic geometry.of mechanism

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Science China(Technological Sciences) 1998年第2期41卷 196-202页

作者：王德伦刘健肖大准 Department of Mechanical Engineering Dalian University of Technology Dalian China

Based on the differential geometry. the expressions of centrodes and axodes as well as their invariants are derived. And then, the kinematic meanings of them are revealed. Meanwhile, the properties of a point trajectory in planar, spherical and spatial motion or a line trajectory in spatial motion are discussed. A main clue for the unified curvature theory in kinematic geometry.of mechanism is set up in the form and content from plane to space motion.

关键词： curvature theory kinematic geometry of mechanism differential geometry.

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Explicit classification for torsion cyclic subgroups of rational points with even orders of elliptic curves

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Chinese Science Bulletin 1999年第21期44卷 1951-1953页

作者： Derong Qiu Xianke Zhang Tsing Hua Univ Dept Math Beijing 100084 Peoples R China

For elliptic curves E over the rationals Q, the classification according to their torsion subgroups Etors(Q) of rational points has been studied. When Etors(Q) are cyclic groups with even orders, the classification is given with explicit critria, and the generators of the torsion groups are also explicitly presented in each case. These results, together with the recent re-

关键词： elliptic curve rational point torsion group arithmetic algebraic geometry.

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Experimental study on NMR spectra of fluids in the pores of rock

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Science China Mathematics 1995年第11期38卷 1333-1343页

作者：肖立志杜有如叶朝辉 Laboratory of Magnetic Resonance and Atomic & Molecular Physics Wuhan Institute of Physics Chinese Academy of Sciences Wuhan 430071 China

Line broadening is an important property of the NMR for fluids in porous media. The main factors that induce line broadening include: (i) effect of solid-liquid interface; (ii) magnetic impurities on the surface of pores; (iii) susceptibility difference between solid matrix and pore fluids; (iv) pore geometry. An understanding of the broadening mechanisms is necessary for the NMR applications in porous media. NMR line broadening due to pore geometry.is studied and different pore models are analyzed. NMR spectra of different fluids absorbed in two kinds of molecular sieve (NaY and NaZSM-5), silica gel (SiO2) and natural sandstone are tested. It is pointed out that there is abundant pore geometry.information in NMR lines of fluids in porous solids, and very low speed magic angle spinning can effectively narrow the lines.

关键词： rock sample fluids NMR spectrum pore geometry.

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geometry.and its applications

Geometry and its applications

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1999年

作者： Meyer Walter J.

来源：畅想之星图书光盘版（南... 评论

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A Bound for the Number of Some Special AlgebraicLimit Cycles

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Chinese Science Bulletin 1994年第1期39卷 5-8页

作者：江其保 Department of Mathematics and Mechanics Southeast University Nanjing 210018 PRC

For planar polynomial systems, a limit cycle is called an algebraic limit cycle(ALC, for abbreviation) if it is a real closed component of an algebraic solution. Inthis note we initiate the study on the number of ALCs... 详细信息

关键词： qualitative theory in the complex domain algebraic limit cycles algebraic geometry.

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1D and 2D ~1H NMR studies on bisantrene complexes with short DNA oligomers

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Science China Chemistry 1995年第12期38卷 1462-1472页

作者：姚世杰 WILSON.W.David Department of Chemistry and Laboratory for Chemical and Biological Sciences Georgia State UniversityAtlantaGA30303USA

The binding of bisantrene to four DNA tetramers,d（CGCG）2,d（GCGC）2,d（CATG）2,and d（GTAC）2,was investigated by 1D and 2D NMR spectroscopy.Bisantrene is.a well knownanticancer drug and has been used clinically for years.DNA is believed to be one of its cellular targets.Re-suits from both ID and 2D 1H NMR are in agreement with an intercalation binding mode of bisantrene withthe four DNA tetramers in this study.The results further indicate that a threading intercalation birdingmode,in which one bisantrene side chain is in the minor groove and the other in the major groove of DNA,is preferred.The NMR results also suggest that bisantrene prefers binding at pyrimidine-（3’,5’）-purineintercalation sequences rather than at purine-（3’,5’）-pyrimidine sequences.The intramolecular andintermolecular NOE contacts of bisantrene-DNA tetramer complexes indicate that a C2’-endo uniform sugarpucker,rather than a mixed sugar conformation,is preferred by the intercalation site of both the 5’-（TA）-3’and the 5’-（CG）-3’ binding steps.

关键词： NOESY DNA bisantrene intercalation threading intercalation uniform intercalation geometry.

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