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A centroidal Voronoi tessellation is a Voronoi tessellation whose generating points are the centroids (centers of mass) of the corresponding Voronoi regions. We give some applications of such tessellations to problems in image compression, quadrature, finite difference methods, distribution of resources, cellular biology, statistics, and the territorial(More)
In this paper, we prove the energy diminishing of a normalized gradient flow which provides a mathematical justification of the imaginary time method used in physical literatures to compute the ground state solution of Bose-Einstein condensates (BEC). We also investigate the energy diminishing property for the discretization of the normalized gradient flow.(More)
In this paper, we introduce a novel definition of the anisotropic centroidal Voronoi tessellation (ACVT) corresponding to a given Riemann metric tensor. A directional distance function is used in the definition to simplify the computation. We provide algorithms to approximate the ACVT using the Lloyd iteration and the construction of anisotropic Delaunay(More)
Abstract. Centroidal Voronoi tessellations are useful for subdividing a region in Euclidean space into Voronoi regions whose generators are also the centers of mass, with respect to a prescribed density function, of the regions. Their extensions to general spaces and sets are also available; for example, tessellations of surfaces in a Euclidean space may be(More)
The centroidal Voronoi tessellation based Delaunay triangulation (CVDT) provides an optimal distribution of generating points with respect to a given density function and accordingly generates a high-quality mesh. In this paper, we discuss algorithms for the construction of the constrained CVDT from an initial Delaunay tetrahedral mesh of a(More)
For a Bose-Einstein condensate placed in a rotating trap and strongly confined along the z axis, we set a framework of study for the Gross-Pitaevskii energy in the Thomas-Fermi regime for an effective twodimensional ~2D! situation in the x-y plane. We investigate an asymptotic expansion of the energy, the critical angular velocities of nucleation of(More)
Centroidal Voronoi tessellations (CVTs) are Voronoi tessellations of a bounded geometric domain such that the generating points of the tessellations are also the centroids (mass centers) of the corresponding Voronoi regions with respect to a given density function. Centroidal Voronoi tessellations may also be defined in more abstract and more general(More)
In this paper, we study the three-dimensional deformation of a vesicle membrane under the elastic bending energy, with prescribed bulk volume and surface area. Both static and dynamic deformations are considered. A newly developed energetic variational formulation is employed to give an effective Eulerian description. Efficient time and spatial(More)
Centroidal Voronoi tessellations (CVTs) are Voronoi tessellations of a region such that the generating points of the tessellations are also the centroids of the corresponding Voronoi regions. Such tessellations are of use in very diverse applications, including data compression, clustering analysis, cell biology, territorial behavior of animals, and optimal(More)
In this paper, we study the dynamics of rotating Bose–Einstein condensates (BEC) based on the Gross–Pitaevskii equation (GPE) with an angular momentum rotation term and present an efficient and accurate algorithm for numerical simulations. We examine the conservation of the angular momentum expectation and the condensate width and analyze the dynamics of a(More)