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COMPUTING HARMONIC MAPS AND CONFORMAL MAPS ON POINT CLOUDS

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Journal of Computational Mathematics 2023年第5期41卷 879-908页

作者： Tianqi Wu Shing-Tung Yau Center of Mathematical Sciences and Applications Harvard UniversityCambridgeMA 02138USA Department of Mathematics Harvard UniversityCambridgeMA 02138USA

We use a narrow-band approach to compute harmonic maps and conformal maps for surfaces embedded in the Euclidean 3-space,using point cloud data *** a surface,or a point cloud approximation,we simply use the standard cubic lattice to approximate itsϵ-*** the harmonic map of the surface can be approximated by discrete harmonic maps on *** conformal map,or the surface uniformization,is achieved by minimizing the Dirichlet energy of the harmonic map while deforming the target surface of constant *** propose algorithms and numerical examples for closed surfaces and topological *** the best of the authors’knowledge,our approach provides the first meshless method for computing harmonic maps and uniformizations of higher genus surfaces.

关键词： harmonic maps conformal maps point clouds

Stress waves propagation in solids under high-speed liquid impact

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Science China(Physics,Mechanics & Astronomy) 2004年第6期47卷 752-766页

作者： J.E.Field Cavendish Laboratory Cambridge UniversityMadingly RoadCambridge CB3 0HEUK

An experiment of impact between 450 m/s water jets and polymethylme- thacrylate (PMMA) materials with complex surface geometry was conducted. The testing surfaces were a corner, step change, surface-breaking notch, inclined surface, etc. Stress waves propagation in the solid such as reflection, interference and diffraction was observed using polarized optics and an Imacon high speed camera (operating at both of 106 and 5×105 framing rates per second, fps). A damage test by the impact of the side jetting of an 850 m/s water jet was also carried out. It was found that stress waves propagation in solids depends not only on the surface geometry but also on the contact situation between liquid and solid. It was shown that the side jetting has sufficient damage potential although its head may consist of finer droplets. The results of this paper are useful to further analyze the dynamic stress state of solids under high-speed liquid impact.

关键词： high-speed liquid/solid impact, stress waves, mechanical property of solid, high-speed photography.

Neuromodulator interactions and spinal cord injury in lamprey

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Neural Regeneration Research 2018年第4期13卷 643-644页

作者： David Parker Thomas J.McClelland Department of Physiology Neuroscience and DevelopmentUniversity of Cambridge

Neuromodulation is mediated by neurotransmitters that typically act on G-protein-coupled *** can confer behavioural flexibility by modifying the functional properties of anatomically hard-wired neural *** neuromodulators generally have divergent cellular and synaptic effects（Harris-Warrick and Johnson,2010）,and different modulators,

关键词： Figure Neuromodulator interactions and spinal cord injury in lamprey

A Multi-physics Methodology for Four States of Matter

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Communications on Applied Mathematics and Computation 2020年第3期2卷 487-514页

作者： Louisa Michael Stephen T.Millmore Nikolaos Nikiforakis Laboratory for Scientifc Computing Cavendish LaboratoryDepartment of PhysicsUniversity of CambridgeCambridgeUK

We propose a numerical methodology for the simultaneous numerical simulation of four states of matter:gas,liquid,elastoplastic solids,and *** distinct,interacting physical processes are described by a combination of compressible,inert,and reactive forms of the Euler equations,multi-phase equations,elastoplastic equations,and resistive MHD *** of systems of equations are usually solved by coupling finite element for solid modelling and CFD models for fluid modelling or including material effects through boundary conditions rather than full material *** simultaneous solution methodology lies on the recasting of all the equations in the same,hyperbolic form allowing their solution on the same grid with the same finite volume numerical *** use a combination of sharp-and diffuse-interface methods to track or capture material interfaces,depending on the *** communication between the distinct systems of equations(i.e.,materials separated by sharp interfaces)is facilitated by means of mixed-material Riemann solvers at the boundaries of the systems,which represent physical material *** this end,we derive approximate mixed-material Riemann solvers for each pair of the above models based on characteristic *** demonstrate the applicability of the new methodology,we consider a case study,where we investigate the possibility of ignition of a combustible gas that lies over a liquid in a metal container that is struck by a plasma arc akin to a lightning *** study the effect of the metal container material and its conductivity on the ignition of the combustible gas,as well as the effects of an additional dielectric coating,the sensitivity of the gas,and differences between scenarios with sealed and pre-damaged metal surfaces.

关键词： Plasma modelling Four states of matter Lightning Ignition Combustible gas Elastoplastic solids

High-yield fabrication of perpendicularly magnetised synthetic antiferromagnetic nanodiscs

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Nano Research 2021年第11期14卷 3873-3878页

作者： Emma N.Welbourne Tarun Vemulkar Russell P.Cowburn Department of Physics Cavendish LaboratoryUniversity of CambridgeJ.J.Thomson AvenueCambridgeCB30HEUK

Synthetic antiferromagnetic (SAF) particles with perpendicular anisotropy display a number of desirable characteristics for applications in biological and other fluid environments. We present an efficient and effective method for the patterning of ultrathin Ruderman-Kittel-Kasuya-Yoshida coupled, perpendicularly magnetised SAFs using a combination of nanosphere lithography and ion milling. A Ge sacrificial layer is utilised, which provides a clean and simple lift-off process, as well as maintaining the key magnetic properties that are beneficial to target applications. We demonstrate that the method is capable of producing a particularly high yield of well-defined, thin film based nanoparticles.

关键词： nanodiscs synthetic antiferromagnets perpendicular anisotropy sacrificial layers nanofabrication

Recent Advance in the Electrochemical Detection of Sulphide and Sulphhydryl Species

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Chemical Research in Chinese Universities 2002年第2期18卷 161-168页

作者： Nathan S. Lawrence 1, Timothy G. J. Jones 2, Richard G. Compton 1 and Li Jiang 2 1. Physical and Theoretical Chemistry Laboratory, university of Oxford, Oxford, OX1 3QZ, UK 2. Schlumberger cambridge Research, High Cross, Madingley Road, cambridge, Physical and Theoretical Chemistry Laboratory University of Oxford 英国 Oxford Schlumberger cambridge Research High Cross Madingley Road 英国 Cambridge

This article aims at providing a critical review of some most recent developments in the electrochemical detection and measurement of hydrogen sulphide and the related species, which are of great significance to a variety of industries and in environmental moitoring. The molecular recognition processes are initiated by using either an organic precursor or a catalytic complex, leading to extensive ranges of detection. A series of advanced chemical and simulation techniques are used to probe the mechanistic details of the analytical chemistry involved.

关键词： Advance, Electrochemical detection, Sulphide Sulphhydryl

Comprehensive Transcriptome Analysis of Auxin Responses in Arabidopsis

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Molecular Plant 2008年第2期1卷 321-337页

作者： Ivan A. Paponov Martina Paponovt William Teale Margit Menges Sohini Chakrabortee James A.H. Murray Klaus Palme Faculty of Biology University of Freiburg Schanzlestrasse 1 79104 Freiburg Germany Institute of Biotechnology University of Cambridge Cambridge CB2 1QT United Kingdom

In plants, the hormone auxin shapes gene expression to regulate growth and development. Despite the detailed characterization of auxin-inducible genes, a comprehensive overview of the temporal and spatial dynamics of auxinregulated gene expression is lacking. Here, we analyze transcriptome data from many publicly available Arabidopsis profiling experiments and assess tissue-specific gene expression both in response to auxin concentration and exposure time and in relation to other plant growth regulators. Our analysis shows that the primary response to auxin over a wide range of auxin application conditions and in specific tissues comprises almost exclusively the up-regulation of genes and iden- tifies the most robust auxin marker genes. Tissue-specific auxin responses correlate with differential expression of Aux/ IAA genes and the subsequent regulation of context- and sequence-specific patterns of gene expression. Changes in transcript levels were consistent with a distinct sequence of conjugation, increased transport capacity and down-regulation of biosynthesis in the temperance of high cellular auxin concentrations. Our data show that auxin regulates genes associated with the biosynthesis, catabolism and signaling pathways of other phytohormones. We present a transcriptional overview of the auxin response. Specific interactions between auxin and other phytohormones are highlighted, particularly the regulation of their metabolism. Our analysis provides a roadmap for auxin-dependent processes that underpins the concept of an ＇auxin code＇-a tissue-specific fingerprint of gene expression that initiates specific developmental processes.

关键词： Comprehensive Transcriptome Analysis Auxin Responses Arabidopsis

Cuscuta, the Merchant of Proteins

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Molecular Plant 2020年第4期13卷 533-535页

作者： Andrea Paterlini Yka Helariutta Sainsbury Laboratory University of CambridgeCambridgeUK Institute of Biotechnology HiLIFEUniversity of HelsinkiHelsinkiFinland

"If thou wilt lend this money,lend it not As to thy friends,[...]But lend it rather to thine enemy,Who,if he break,thou mayst with better face Exact the penalty"The merchant Antonio speaking to the moneylender Shylock... 详细信息

关键词： money chant Shy

Iwasawa Theory of Quadratic Twists of X0（49）

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Acta Mathematica Sinica,English Series 2018年第1期34卷 19-28页

作者： Junhwa CHOI John COATES Department of Mathematics POSTECH Emmanuel College Cambridge University

The field K ---- Q（x/-AT） is the only imaginary quadratic field with class number 1, in which the prime 2 splits, and we fix one of the primes p of K lying above 2. The modular elliptic curve X0 （49） has complex multiplication by the maximal order O of K, and we let E be the twist of Xo （49） by the quadratic extension K（v/M）/K, where M is any square free element of O with M -- i mod 4 and （M, 7） = 1. In the present note, we use surprisingly simple algebraic arguments to prove a sharp estimate for the rank of the MordeII-Weil group modulo torsion of E over the field F∞=k（Ep∞ ）, where Epic denotes the group of p∞-division points on E. Moreover, writing B for the twist of X0（49） by K（C/ET）/K, our Iwasawa-theoretic arguments also show that the weak form of the conjecture of Birch and Swinnerton-Dyer implies the non-vanishing at s =1 of the complex L-series of B over every finite layer of the unique Z2-extension of K unramified outside p. We hope to give a proof of this last non-vanishing assertion in a subsequent paper.

关键词： Birch-Swinnerton-Dyer conjecture elliptic curves Iwasawa theory