The Experts below are selected from a list of 1917 Experts worldwide ranked by ideXlab platform
Rukmini Dey - One of the best experts on this subject based on the ideXlab platform.
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A complete conformal metric of preassigned Negative Gaussian Curvature for a punctured hyperbolic Riemann surface
arXiv: Analysis of PDEs, 2004Co-Authors: Rukmini DeyAbstract:Let $h$ be a complete metric of Gaussian Curvature $K_0$ on a punctured Riemann surface of genus $g \geq 1$ (or the sphere with at least three punctures). Given a smooth Negative function $K$ with $K=K_0$ in neighbourhoods of the punctures we prove that there exists a metric conformal to $h$ which attains this function as its Gaussian Curvature for the punctured Riemann surface. We do so by minimizing an appropriate functional using elementary analysis.
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A complete conformal metric of preassigned Negative Gaussian Curvature for a punctured hyperbolic Riemann surface
Proceedings of the Indian Academy of Sciences - Mathematical Sciences, 2004Co-Authors: Rukmini DeyAbstract:Let h be a complete metric of Gaussian Curvature K_0 on a punctured Riemann surface of genus g ≥ 1 (or the sphere with at least three punctures). Given a smooth Negative function K with K = K _0 in neighbourhoods of the punctures we prove that there exists a metric conformal to h which attains this function as its Gaussian Curvature for the punctured Riemann surface. We do so by minimizing an appropriate functional using elementary analysis.
Carl D Modes - One of the best experts on this subject based on the ideXlab platform.
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Negative Gaussian Curvature from induced metric changes.
Physical Review E, 2015Co-Authors: Carl D Modes, Mark WarnerAbstract:We revisit the light or heat-induced changes in topography of initially flat sheets of a solid that elongate or contract along patterned in-plane director fields. For radial or azimuthal directors, Negative Gaussian Curvature is generated-so-called "anticones." We show that azimuthal material displacements are required for the distorted state to be stretch free and bend minimizing. The resultant shapes are smooth and asterlike and can become reentrant in the azimuthal coordinate for large deformations. We show that care is needed when considering elastomers rather than glasses, although the former offer huge deformations.
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hard disks on the hyperbolic plane
Physical Review Letters, 2007Co-Authors: Carl D Modes, Randall D. KamienAbstract:We examine a simple hard disk fluid with no long range interactions on the two-dimensional space of constant Negative Gaussian Curvature, the hyperbolic plane. This geometry provides a natural mechanism by which global crystalline order is frustrated, allowing us to construct a tractable model of disordered monodisperse hard disks. We extend free-area theory and the virial expansion to this regime, deriving the equation of state for the system, and compare its predictions with simulation near an isostatic packing in the curved space.
Randall D. Kamien - One of the best experts on this subject based on the ideXlab platform.
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hard disks on the hyperbolic plane
Physical Review Letters, 2007Co-Authors: Carl D Modes, Randall D. KamienAbstract:We examine a simple hard disk fluid with no long range interactions on the two-dimensional space of constant Negative Gaussian Curvature, the hyperbolic plane. This geometry provides a natural mechanism by which global crystalline order is frustrated, allowing us to construct a tractable model of disordered monodisperse hard disks. We extend free-area theory and the virial expansion to this regime, deriving the equation of state for the system, and compare its predictions with simulation near an isostatic packing in the curved space.
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Geometric theory of columnar phases on curved substrates
Physical Review Letters, 2007Co-Authors: Christian Santangelo, Randall D. Kamien, Vincenzo Vitelli, David R. NelsonAbstract:We study thin self-assembled columns constrained to lie on a curved, rigid substrate. The Curvature presents no local obstruction to equally spaced columns in contrast with curved crystals for which the crystalline bonds are frustrated. Instead, the vanishing compressional strain of the columns implies that their normals lie on geodesics which converge (diverge) in regions of positive (Negative) Gaussian Curvature, in analogy to the focusing of light rays by a lens. We show that the out of plane bending of the cylinders acts as an effective ordering field.
Sergo Kukudzhanov - One of the best experts on this subject based on the ideXlab platform.
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The stability of orthotropic shells of revolution, close to cylindrical ones, with an elastic filler, under the action of torsion, normal pressure and temperature
Transactions of A. Razmadze Mathematical Institute, 2018Co-Authors: Sergo KukudzhanovAbstract:Abstract The paper investigates the stability of orthotropic shells of revolution which are by their form close to cylindrical ones, with an elastic filler, under the action of torques, external pressure and temperature. The shell is assumed to be thin and elastic. Temperature is uniformly distributed in the shell body. The filler is simulated by an elastic base. The shells of positive and Negative Gaussian Curvature are considered. Formulas for finding critical loadings and corresponding forms of stability loss are derived.
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The stability of orthotropic shells of revolution, close to cylindrical ones, with an elastic filler, under the action of torsion, normal pressure and temperature
Elsevier, 2018Co-Authors: Sergo KukudzhanovAbstract:The paper investigates the stability of orthotropic shells of revolution which are by their form close to cylindrical ones, with an elastic filler, under the action of torques, external pressure and temperature. The shell is assumed to be thin and elastic. Temperature is uniformly distributed in the shell body. The filler is simulated by an elastic base. The shells of positive and Negative Gaussian Curvature are considered. Formulas for finding critical loadings and corresponding forms of stability loss are derived. Keywords: Stability, Shells, Filler, Critical load, Curvature, Temperatur
Shingtung Yau - One of the best experts on this subject based on the ideXlab platform.
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adiabatic isometric mapping algorithm for embedding 2 surfaces in euclidean 3 space
Classical and Quantum Gravity, 2015Co-Authors: Shannon Ray, Warner A Miller, Paul M Alsing, Shingtung YauAbstract:Alexandrov proved that any simplicial complex homeomorphic to a sphere with strictly non-Negative Gaussian Curvature at each vertex can be isometrically embedded uniquely in as a convex polyhedron. Due to the nonconstructive nature of his proof, there have yet to be any algorithms, that we know of, that realizes the Alexandrov embedding in polynomial time. Following his proof, we developed the adiabatic isometric mapping (AIM) algorithm. AIM uses a guided adiabatic pull-back procedure on a given polyhedral metric to produce an embedding that approximates the unique Alexandrov polyhedron. Tests of AIM applied to two different polyhedral metrics suggests that its run time is sub cubic with respect to the number of vertices. Although Alexandrov's theorem specifically addresses the embedding of convex polyhedral metrics, we tested AIM on a broader class of polyhedral metrics that included regions of Negative Gaussian Curvature. One test was on a surface just outside the ergosphere of a Kerr black hole.
