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Differential complexes and numerical stability

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Differential complexes and numerical stability

MIXED FInITE ELEMEnTS FOR ELASTICITY

CCAST“保结构算法2003”研讨会

作者： Douglas n.arnold Institute for Mathematics and its Applications University of Minnesota 400 Church St.S.E. Minneapolis MN 55455 USA.

＜正＞ Differential complexes such as the de Rham complex have recently come to play an important role in the design and analysis of numerical methods for partial differential equations. The design of stable discretizations of systems of partial differential equations often hinges on capturing subtle aspects of the structure of the system in the discretization. In many cases the differential geometric structure captured by a differential complex has proven to be a key element, and a discrete differential complex which is appropriately related to the original complex is essential. This new geometric viewpoint has provided a unifying understanding of a variety of innovative numerical methods developed over recent decades and pointed the way to stable discretizations of problems for which none were previously known, and it appears likely to play an important role in attacking some currently intractable problems in numerical *** complexes such as the de Rham complex have recently come to play an important role in the design and analysis of numerical methods for partial differential equations. The design of stable discretizations of systems of partial differential equations often hinges on capturing subtle aspects of the structure of the system in the discretization. In many cases the differential geometric structure captured by a differential complex has proven to be a key element, and a discrete differential complex which is appropriately related to the original complex is essential. This new geometric viewpoint has provided a unifying understanding of a variety of innovative numerical methods developed over recent decades and pointed the way to stable discretizations of problems for which none were previously known, and it appears likely to play an important role in attacking some currently intractable problems in numerical PDE.

关键词： finite element numerical stability differential complex

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MIXED FINITE ELEMENTS FOR ELASTICITY

Specific interaction of hepatitis C virus glycoproteins with mannan binding lectin inhibits virus entry

CCAST“保结构算法2003”研讨会

作者： DOUGLAS n.arnold RAGnAR WInTHER

＜正＞ There have been many efforts, dating back four decades, to develop stable mixed finite elements for the stress-displacement formulation of the plane elasticity system. This requires the development of a compatible pair of finite element spaces, one to discretize the space of symmetric tensors in which the stress field is sought, and one to discretize the space of vector fields in which the displacement is sought. Although there are number of well-known mixed finite element pairs known for the analogous problem involving vector fields and scalar fields, the symmetry of the stress field is a substantial additional difficulty, and the elements presented here are the first ones using polynomial shape functions which are known to be stable. We present a family of such pairs of finite element spaces, one for each polynomial degree, beginning with degree two for the stress and degree one for the displacement, and show stability and optimal order approximation. We also analyze some obstructions to the construction of such finite element spaces, which account for the paucity of elements *** have been many efforts, dating back four decades, to develop stable mixed finite elements for the stress-displacement formulation of the plane elasticity system. This requires the development of a compatible pair of finite element spaces, one to discretize the space of symmetric tensors in which the stress field is sought, and one to discretize the space of vector fields in which the displacement is sought. Although there are number of well-known mixed finite element pairs known for the analogous problem involving vector fields and scalar fields, the symmetry of the stress field is a substantial additional difficulty, and the elements presented here are the first ones using polynomial shape functions which are known to be stable. We present a family of such pairs of finite element spaces, one for each polynomial degree, beginning with degree two for the stress and degree o

关键词： mixed method finite element elasticity.

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Protein & Cell 2010年第7期1卷 664-674页

作者： Kristelle S.Brown Michael J.Keogh Ania M.Owsianka Richard Adair Arvind H.Patel James n.arnold Jonathan K.Ball Robert B.Sim Alexander W.Tarr Timothy P.Hickling Institute of Infection Immunity and InflammationSchool of Molecular Medical SciencesThe University of NottinghamQueen’s Medical CentreNottinghamNG72UHUK The Medical Research Council-University of Glasgow Centre for Virus Research University of GlasgowChurch StreetGlasgowG115JRUK MRC Immunochemistry Unit Department of BiochemistryUniversity of OxfordOX13QUUK Present address:Vitrology Biotech 5 South AvenueClydebank Business ParkGlasgowG812LGUK Present address:Pfizer Technologies Ltd. Ramsgate RoadSandwichKentCT139NJUK

Mannan-binding lectin(MBL)is a soluble innate immune protein that binds to glycosylated *** acts as an opsonin and activates complement,contributing to the destruction and clearance of infecting *** C virus(HCV)encodes two envelope glycoproteins E1 and E2,expressed as non-covalent E1/E2 heterodimers in the viral envelope.E1 and E2 are potential ligands for *** we describe an analysis of the interaction between HCV and MBL using recombinant soluble E2 ectodomain fragment,the full-length E1/E2 heterodimer,expressed in vitro,and assess the effect of this interaction on virus entry.A binding assay using antibody capture of full length E1/E2 heterodimers was used to demonstrate calcium dependent,saturating binding of MBL to HCV *** with various saccharides further confirmed that the interaction was via the lectin domain of *** binds to E1/E2 representing a broad range of virus *** was shown to neutralize the entry into Huh-7 cells of HCV pseudoparticles(HCVpp)bearing E1/E2 from a wide range of *** were neutralized to varying *** was also shown to neutralize an authentic cell culture infectious virus,strain JFH-1(HCVcc).Furthermore,binding of MBL to E1/E2 was able to activate the complement system via MBL-associated serine protease *** conclusion,MBL interacts directly with HCV glycoproteins,which are present on the surface of the virion,resulting in neutralization of HCV particles.

关键词： hepatitis C virus neutralization mannose binding lectin chronic viral infection

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灰色烤烟上的棕色斑点与铁的关系

核农学通报 1988年第6期 285-286页

作者： n.arnold 朱岩

灰包烟草,是一种营养失调的烤烟,外表呈青铜色和胡椒状。当全部叶片接近成熟时,逐渐出现灰色。这种低质烟草,在世界各地均有发现。切成烟丝后带有霉味,销量不好。烟草的营养失调往往与过量的金属离子,特别是铁有关。过量铁被植物吸收后... 详细信息

灰包烟草,是一种营养失调的烤烟,外表呈青铜色和胡椒状。当全部叶片接近成熟时,逐渐出现灰色。这种低质烟草,在世界各地均有发现。切成烟丝后带有霉味,销量不好。烟草的营养失调往往与过量的金属离子,特别是铁有关。过量铁被植物吸收后,沉积在输导组织中。灰烟草的分支叶脉系统

关键词：分支叶脉叶基部叶尖营养液液体培养基烟草叶烟叶

noninvasive Low-Intensity Focused Ultrasound Mediates Tissue Protection following Ischemic Stroke

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Biomedical Engineering Frontiers 2022年第1期3卷 356-366页

作者： Alexandra M.Kaloss Lauren n.arnold Eman Soliman Maya Langman nathalie Groot Eli Vlaisavljevich Michelle H.Theus Department of Biomedical Sciences and Pathobiology Virginia TechBlacksburgVA 24061USA Department of Biomedical Engineering and Mechanics Virginia TechBlacksburg VA 24061USA Center for Engineered Health Virginia TechBlacksburg Virginia 24061USA

Objective and Impact *** study examined the efficacy and safety of pulsed,low-intensity focused ultrasound(LIFU)and determined its ability to provide neuroprotection in a murine permanent middle cerebral artery occlusion(pMCAO)*** ultrasound(FUS)has emerged as a new therapeutic strategy for the treatment of ischemic stroke;however,its nonthrombolytic properties remain ***,we examined how LIFU influenced neuroprotection and vascular changes following *** to the critical role of leptomeningeal anastomoses or pial collateral vessels,in cerebral blood flow restoration and tissue protection following ischemic stroke,we also investigated their growth and *** were exposed to transcranial LIFU(fundamental frequency:1.1 MHz,sonication duration:300 ms,interstimulus interval:3 s,pulse repetition frequency:1 kHz,duty cycle per pulse:50%,and peak negative pressure:-2.0 MPa)for 30 minutes following induction of pMCAO and then evaluated for infarct volume,blood-brain barrier(BBB)disruption,and pial collateral remodeling at 24 hrs *** found significant neuroprotection in mice exposed to LIFU compared to mock *** findings correlated with a reduced area of IgG deposition in the cerebral cortex,suggesting attenuation of BBB breakdown under LIFU *** also observed increased diameter of CD31-postive microvessels in the ischemic *** observed no significant difference in pial collateral vessel size between FUS and mock treatment at 24 hrs *** data suggests that therapeutic use of LIFU may induce protection through microvascular remodeling that is not related to its thrombolytic activity.

关键词： Focus repetition treatment

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CYBER205上的向量优化

计算机工程与科学 1984年第2期 45-57页

作者： CLIFFORD n.arnold ARDEn HILLS 何玉兰明尼苏达软件研究控制数据公司明尼苏达软件研究控制数据公司

向量优化是指在一台给定机■上,对一个已知的向量计算生成最好的结果代码。本文为在控制政据 CYBER 205上运行的标量和向量源代码提出了性能分析模型。这些模型的精度对于标量代码一般是在30%以内,对于向量代码一般是在10%以内。对于一... 详细信息

向量优化是指在一台给定机■上,对一个已知的向量计算生成最好的结果代码。本文为在控制政据 CYBER 205上运行的标量和向量源代码提出了性能分析模型。这些模型的精度对于标量代码一般是在30%以内,对于向量代码一般是在10%以内。对于一个已知的并行计算,如果编译程序可以产生一个以上的代码程序,则可以利用来自这些模型的性能估计,以便选择应当执行哪一个代码程序。把含有两个或更多个源代码版本的16个FORTRAn 核作为测试这个方法的标准检查程序。13个核正确地进行了“向量优化”。没有进行常规优化的3个核有17%的平均性能损失。用一批核作为标准检查程序表明向量优化把它的性能改进了四倍多,所有已经正确优化了的核,有98%的在程序上也可改进。

关键词：向量优化标量检查程序 CYBER205 代码

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肿瘤学中的分子遗传学和细胞遗传学技术

德国医学 2000年第3期17卷 143-144页

作者： D.niederacher M.Kiechle n.arnold 冯玲 Molekulargenetisches Labor der Frauenklinik Moorenstr. 5 D-40225 Düsseldorf Germany 同济医科大学附属同济医院

随着致癌机制模型的建立,从正常上皮细胞演变为癌组织,随基因改变,最终导致表型的改变。目前已知的两种基因改变形式:原癌基因的激活和肿瘤抑制基因的失活,基因的激活是原癌基因的改变或者功能失控而引起的基因扩增、过表达和突变的结... 详细信息

随着致癌机制模型的建立,从正常上皮细胞演变为癌组织,随基因改变,最终导致表型的改变。目前已知的两种基因改变形式:原癌基因的激活和肿瘤抑制基因的失活,基因的激活是原癌基因的改变或者功能失控而引起的基因扩增、过表达和突变的结果。采用分子遗传学分析技术,在家族性肿瘤疾病中通过已知缺失基因而预测疾病风险。

关键词：肿瘤分子遗传学细胞遗传学

Transfer learning framework for multi-scale crack type classification with sparse microseismic networks

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International Journal of Mining Science and Technology 2024年第2期34卷 167-178页

作者： arnold Yuxuan Xie Bing QLi Department of Civil and Environmental Engineering Western UniversityLondon N6A 3K7Canada

Rock fracture mechanisms can be inferred from moment tensors(MT)inverted from microseismic ***,MT can only be inverted for events whose waveforms are acquired across a network of *** is limiting for underground mines where the microseismic stations often lack azimuthal ***,there is a need for a method to invert fracture mechanisms using waveforms acquired by a sparse microseismic ***,we present a novel,multi-scale framework to classify whether a rock crack contracts or dilates based on a single *** framework consists of a deep learning model that is initially trained on 2400000+manually labelled field-scale seismic and microseismic waveforms acquired across 692 *** learning is then applied to fine-tune the model on 300000+MT-labelled labscale acoustic emission waveforms from 39 individual experiments instrumented with different sensor layouts,loading,and rock types in *** optimal model achieves over 86%F-score on unseen waveforms at both the lab-and *** model outperforms existing empirical methods in classification of rock fracture mechanisms monitored by a sparse microseismic *** facilitates rapid assessment of,and early warning against,various rock engineering hazard such as induced earthquakes and rock bursts.

关键词： Multi-scale Fracture processes Microseismic Acoustic emission Source mechanism Deep learning

Chebyshev polynomial-based Ritz method for thermal buckling and free vibration behaviors of metal foam beams

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Applied Mathematics and Mechanics(English Edition) 2024年第5期45卷 891-910页

作者： n.D.nGUYEn T.n.nGUYEn Faculty of Civil Engineering Ho Chi Minh City University of Technology and EducationHo Chi Minh City 71309Viet Nam Faculty of Engineering and Technology Kien Giang UniversityChau Thanh 92000Viet Nam

This study presents the Chebyshev polynomials-based Ritz method to examine the thermal buckling and free vibration characteristics of metal foam *** analyses include three models for porosity distribution and two scenarios for thermal *** material properties are assessed under two conditions,i.e.,temperature dependence and temperature *** theoretical framework for the beams is based on the higher-order shear deformation theory,which incorporates shear deformations with higher-order *** governing equations are established from the Lagrange equations,and the beam displacement fields are approximated by the Chebyshev *** simulations are performed to evaluate the effects of thermal load,slenderness,boundary condition(BC),and porosity distribution on the buckling and vibration behaviors of metal foam *** findings highlight the significant influence of temperature-dependent(TD)material properties on metal foam beams'buckling and vibration responses.

关键词： Ritz method Chebyshev function buckling vibration metal foam beam higher-order beam theory(HOBT)