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31.
《偏微分方程通讯》2013,38(11-12):2513-2525
ABSTRACT The Hopf map from minimal surfaces in H 3 to holomorphic quadratic differentials on H 2 is considered. Whether or not a given quadratic differential is in the image of this map is determined by the global existence/non-existence of solutions to a certain quasi-linear PDE. It is shown that this map is not surjective. 相似文献
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In this paper, the extension of an upwind least‐square based meshless solver to high Reynolds number flow is explored, and the properties of the meshless solver are analyzed both theoretically and numerically. Existing works have verified the meshless solver mostly with inviscid flows and low Reynolds number flows, and in this work, we are interested in the behavior of the meshless solver for high Reynolds number flow, especially in the near‐wall region. With both theoretical and numerical analysis, the effects of two parameters on the meshless solver are identified. The first one is the misalignment effect caused by the significantly skewed supporting points, and it is found that the meshless solver still yields accurate prediction. It is a very interesting property and is opposite to the median‐dual control volume based vertex‐centered finite volume method, which is known to give degraded result with stretched triangular/tetrahedral cells in the near‐wall region. The second parameter is the curvature, and according to theoretical analysis, it is found in the region with both large aspect ratio and curvature, and the streamwise residual is less affected; however, the wall‐normal counterpart suffers from accuracy degradation. In this paper, an improved method that uses a meshless solver for the streamwise residual and finite difference for wall‐normal residual is developed. This method is proved to be less sensitive to the curvature and provides improved accuracy. This work presents an understanding of the meshless solver for high Reynolds number flow computation, and the analysis in this paper is verified with a series of numerical experiments. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
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In this paper, we study conharmonic curvature tensor in Kenmotsu manifolds with respect to semi-symmetric metric connection and also characterize conharmonically flat, conharmonically semi-symmetric and φ-conharmonically flat Kenmotsu manifolds with respect to semi-symmetric metric connection. 相似文献
34.
Cangyi Chen Ping Tang Feng Qiu 《Journal of polymer science. Part A, Polymer chemistry》2014,52(24):1583-1599
Binary polymer brushes, including mixed homopolymer brushes and diblock copolymer brushes, are an attractive class of environmentally responsive nanostructured materials. Owing to microphase separation of the two chemically distinct components in the brush, multifaceted nanomaterials with functionalized and patterned surfaces can be obtained. This review summarizes recent progress on the theory and simulations related to binary polymer brushes grafted to flat, spherical, and cylindrical substrates, with a focus on patterned morphologies of multifaceted hairy nanoparticles, an intriguing class of hybrid nanostructured particles (e.g., nanospheres and nanorods). In particular, powerful field theory and particle-based simulations suitable for revealing novel structures on these patterned surfaces, including self-consistent field theory and dissipative particle dynamics simulations, are emphasized. The unsolved yet critical issues in this research field, such as dynamic response of binary polymer brushes to environmental stimuli and the hierarchical self-assembly of binary hairy nanoparticles, are briefly discussed. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014 , 52, 1583–1599 相似文献
35.
Xin Feng Kelin Xia Zhan Chen Yiying Tong Guo‐Wei Wei 《Journal of computational chemistry》2013,34(24):2100-2120
Geometric modeling of biomolecules plays an essential role in the conceptualization of biolmolecular structure, function, dynamics, and transport. Qualitatively, geometric modeling offers a basis for molecular visualization, which is crucial for the understanding of molecular structure and interactions. Quantitatively, geometric modeling bridges the gap between molecular information, such as that from X‐ray, NMR, and cryo‐electron microscopy, and theoretical/mathematical models, such as molecular dynamics, the Poisson–Boltzmann equation, and the Nernst–Planck equation. In this work, we present a family of variational multiscale geometric models for macromolecular systems. Our models are able to combine multiresolution geometric modeling with multiscale electrostatic modeling in a unified variational framework. We discuss a suite of techniques for molecular surface generation, molecular surface meshing, molecular volumetric meshing, and the estimation of Hadwiger's functionals. Emphasis is given to the multiresolution representations of biomolecules and the associated multiscale electrostatic analyses as well as multiresolution curvature characterizations. The resulting fine resolution representations of a biomolecular system enable the detailed analysis of solvent–solute interaction, and ion channel dynamics, whereas our coarse resolution representations highlight the compatibility of protein‐ligand bindings and possibility of protein–protein interactions. © 2013 Wiley Periodicals, Inc. 相似文献
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It is known that every locally projectively flat Finsler metric is of scalar flag curvature. Conversely, it may not be true. In this paper, for a certain class of Finsler metrics, we prove that it is locally projectively flat if and only if it is of scalar flag curvature. Moreover, we establish a class of new non-trivial examples. 相似文献
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Mohammed Larbi Labbi 《Mathematische Nachrichten》2015,288(4):402-411
The Weitzenböck curvature operators are the curvature terms of order zero that appear in the well‐known classical Weitzenböck formula. In this paper, we use the formalism of double forms to prove a simple formula for these operators and to study their geometric properties. 相似文献