14,093 research outputs found

    Surface Networks

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    We study data-driven representations for three-dimensional triangle meshes, which are one of the prevalent objects used to represent 3D geometry. Recent works have developed models that exploit the intrinsic geometry of manifolds and graphs, namely the Graph Neural Networks (GNNs) and its spectral variants, which learn from the local metric tensor via the Laplacian operator. Despite offering excellent sample complexity and built-in invariances, intrinsic geometry alone is invariant to isometric deformations, making it unsuitable for many applications. To overcome this limitation, we propose several upgrades to GNNs to leverage extrinsic differential geometry properties of three-dimensional surfaces, increasing its modeling power. In particular, we propose to exploit the Dirac operator, whose spectrum detects principal curvature directions --- this is in stark contrast with the classical Laplace operator, which directly measures mean curvature. We coin the resulting models \emph{Surface Networks (SN)}. We prove that these models define shape representations that are stable to deformation and to discretization, and we demonstrate the efficiency and versatility of SNs on two challenging tasks: temporal prediction of mesh deformations under non-linear dynamics and generative models using a variational autoencoder framework with encoders/decoders given by SNs

    Extensive Hartree-Fock + BCS calculation with Skyrme SIII force

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    We have performed deformed Hartree-Fock+BCS calculations with the Skyrme SIII force for the ground states of even-even nuclei with 2 <= Z <= 114 and N ranging from outside the proton drip line to beyond the experimental frontier in the neutron-rich side. We obtained spatially localized solutions for 1029 nuclei, together with the second minima for 758 nuclei. The single-particle wavefunctions are expressed in a three-dimensional Cartesian-mesh representation, which is suitable to describe nucleon skins, halos, and exotic shapes as well as properties of ordinary stable nuclei. After explaining some of the practical procedures of the calculations, we compare the resulting nuclear masses with experimental data and the predictions of other models. We also discuss the quadrupole (m=0, 2) and hexadecapole (m=0, 2, 4) deformations, the skin thicknesses, the halo radii, and the energy difference between the oblate and the prolate solutions. Our results can be obtained via computer network.Comment: 20 pages in Latex, 11 Postscript figures, uuencode-gzip-tar file, to appear in Nuclear Physics A. Data tables available at ftp://nt1.c.u-tokyo.ac.jp/hfs3

    Basic principles of hp Virtual Elements on quasiuniform meshes

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    In the present paper we initiate the study of hphp Virtual Elements. We focus on the case with uniform polynomial degree across the mesh and derive theoretical convergence estimates that are explicit both in the mesh size hh and in the polynomial degree pp in the case of finite Sobolev regularity. Exponential convergence is proved in the case of analytic solutions. The theoretical convergence results are validated in numerical experiments. Finally, an initial study on the possible choice of local basis functions is included

    Wire mesh design

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    We present a computational approach for designing wire meshes, i.e., freeform surfaces composed of woven wires arranged in a regular grid. To facilitate shape exploration, we map material properties of wire meshes to the geometric model of Chebyshev nets. This abstraction is exploited to build an efficient optimization scheme. While the theory of Chebyshev nets suggests a highly constrained design space, we show that allowing controlled deviations from the underlying surface provides a rich shape space for design exploration. Our algorithm balances globally coupled material constraints with aesthetic and geometric design objectives that can be specified by the user in an interactive design session. In addition to sculptural art, wire meshes represent an innovative medium for industrial applications including composite materials and architectural façades. We demonstrate the effectiveness of our approach using a variety of digital and physical prototypes with a level of shape complexity unobtainable using previous methods

    FERONOC : FLEXIBLE AND EXTENSIBLE ROUTER IMPLEMENTATION FOR DIAGONAL MESH TOPOLOGY

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    International audienceNetworks on Chip (NoCs) can improve a set of perfor- mances criteria, in complex SoCs, such as scalability, flexibility and adaptability. However, performances of a NoC are closely related to its topology. The diameter and average distance represent an important factor in term of performances and implementation. The proposed diagonal mesh topology is designed to offer a good tradeoff between hardware cost and theoretical quality of service (QoS). It can contain a large number of nodes without changing the maximum diameter which is equal to 2. In this paper, we present a new router architecture called FeRoNoC (Flexible, extensible Router NoC) and its Register Transfer Level (RTL) hardware implementation for the diagonal mesh topology. The architecture of our NoC is based on a flexible and extensible router which consists of a packet switching technique and deterministic routing algorithm. Effectiveness and performances of the proposed topology have been shown using a virtex5 FPGA implementation. A comparative performances study of the proposed NoC architecture with others topology is performed

    Normal stresses in semiflexible polymer hydrogels

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    Biopolymer gels such as fibrin and collagen networks are known to develop tensile axial stress when subject to torsion. This negative normal stress is opposite to the classical Poynting effect observed for most elastic solids including synthetic polymer gels, where torsion provokes a positive normal stress. As recently shown, this anomalous behavior in fibrin gels depends on the open, porous network structure of biopolymer gels, which facilitates interstitial fluid flow during shear and can be described by a phenomenological two-fluid model with viscous coupling between network and solvent. Here we extend this model and develop a microscopic model for the individual diagonal components of the stress tensor that determine the axial response of semi-flexible polymer hydrogels. This microscopic model predicts that the magnitude of these stress components depends inversely on the characteristic strain for the onset of nonlinear shear stress, which we confirm experimentally by shear rheometry on fibrin gels. Moreover, our model predicts a transient behavior of the normal stress, which is in excellent agreement with the full time-dependent normal stress we measure.Comment: 12 pages, 8 figure

    A nanophotonic laser on a graph

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    Conventional nano-photonic schemes minimise multiple scattering to realise a miniaturised version of beam-splitters, interferometers and optical cavities for light propagation and lasing. Here instead, we introduce a nanophotonic network built from multiple paths and interference, to control and enhance light-matter interaction via light localisation. The network is built from a mesh of subwavelength waveguides, and can sustain localised modes and mirror-less light trapping stemming from interference over hundreds of nodes. With optical gain, these modes can easily lase, reaching ∼\sim100 pm linewidths. We introduce a graph solution to the Maxwell's equation which describes light on the network, and predicts lasing action. In this framework, the network optical modes can be designed via the network connectivity and topology, and lasing can be tailored and enhanced by the network shape. Nanophotonic networks pave the way for new laser device architectures, which can be used for sensitive biosensing and on-chip optical information processing
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