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  1. Abstract

    Differential operators are widely used in geometry processing for problem domains like spectral shape analysis, data interpolation, parametrization and mapping, and meshing. In addition to the ubiquitous cotangent Laplacian, anisotropic second‐order operators, as well as higher‐order operators such as the Bilaplacian, have been discretized for specialized applications. In this paper, we study a class of operators that generalizes the fourth‐order Bilaplacian to support anisotropic behavior. The anisotropy is parametrized by asymmetric frame field, first studied in connection with quadrilateral and hexahedral meshing, which allows for fine‐grained control of local directions of variation. We discretize these operators using a mixed finite element scheme, verify convergence of the discretization, study the behavior of the operator under pullback, and present potential applications.

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  3. Abstract ATHENA has been designed as a general purpose detector capable of delivering the full scientific scope of the Electron-Ion Collider. Careful technology choices provide fine tracking and momentum resolution, high performance electromagnetic and hadronic calorimetry, hadron identification over a wide kinematic range, and near-complete hermeticity.This article describes the detector design and its expected performance in the most relevant physics channels. It includes an evaluation of detector technology choices, the technical challenges to realizing the detector and the R&D required to meet those challenges. 
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