1,062 research outputs found

    A Framework of Multi-Dimensional and Multi-Scale Modeling with Applications

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    In this dissertation, a framework for multi-dimensional and multi-scale modeling is proposed. The essential idea is based on oriented space curves, which can be represented as a 3D slender object or 1D step parameters. SMILES and Masks provide functionalities that extend slender objects into branched and other objects. We treat the conversion between 1D, 2D, 3D, and 4D representations as data unification. A mathematical analysis of different methods applied to helices (a special type of space curves) is also provided. Computational implementation utilizes Model-ViewController design principles to integrate data unification with graphical visualizations to create a dashboard. Applications of multi-dimensional and multi-scale modeling are provided to study ā€œMagic Snakeā€, ā€œNanocarā€ and ā€œGenome Dashboardā€

    Shadows of CPR black holes and tests of the Kerr metric

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    We study the shadow of the Cardoso-Pani-Rico (CPR) black hole for different values of the black hole spin aāˆ—a_*, the deformation parameters Ļµ3t\epsilon_3^t and Ļµ3r\epsilon_3^r, and the viewing angle ii. We find that the main impact of the deformation parameter Ļµ3t\epsilon_3^t is the change of the size of the shadow, while the deformation parameter Ļµ3r\epsilon_3^r affects the shape of its boundary. In general, it is impossible to test the Kerr metric, because the shadow of a Kerr black hole can be reproduced quite well by a black hole with non-vanishing Ļµ3t\epsilon_3^t or Ļµ3r\epsilon_3^r. Deviations from the Kerr geometry could be constrained in the presence of high quality data and in the favorable case of a black hole with high values of aāˆ—a_* and ii. However, the shadows of some black holes with non-vanishing Ļµ3r\epsilon_3^r present peculiar features and the possible detection of these shadows could unambiguously distinguish these objects from the standard Kerr black holes of general relativity.Comment: 10 pages, 7 figures. v2: refereed version with minor change
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