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Nanodot deposition on a side surface of a rectangular sample and digital image correlation are used to quantify the in-plane strain fields associated with the propagation of a shear band in a PdNiP bulk metallic glass,induced by rolling.…
In this paper, we propose a method for tracking structures (e.g., ventricles and myocardium) in cardiac images (e.g., magnetic resonance) by propagating forward in time a previous estimate of the structures via a new deformation estimation…
Since the Voronoi diagram appears in many applications, the topic of improving its computational efficiency remains attractive. We propose a novel yet efficient method to compute Voronoi diagrams bounded by a given domain, i.e., the clipped…
In this paper, the Discontinuous Cell Method (DCM) is formulated with the objective of simulating cohesive fracture propagation and fragmentation in homogeneous solids without issues relevant to excessive mesh deformation typical of…
The transition from ordered to disordered structures in Voronoi tessellation is obtained by perturbing the seeds that were originally identified with two types of lattice in 2D and one type in 3D. The area in 2D and the volume in 3D are…
Mesoscopic particle based fluid models, such as dissipative particle dynamics, are usually assumed to be coarse-grained representations of an underlying microscopic fluid. A fundamental question is whether there exists a map from…
We map the kinematics of stars in simulated galaxy disks with spiral arms using the velocity ellipsoid vertex deviation (l$_v$). We use test particle simulations, and for the first time, fully self-consistent high resolution N-body models.…
A method for quantitative analysis of local pattern strength and defects in surface self-assembly imaging is presented and applied to images of stripe and hexagonal ordered domains. The presented method uses "shapelet" functions which were…
Functional properties of neurons are strongly coupled with their morphology. Changes in neuronal activity alter morphological characteristics of dendritic spines. First step towards understanding the structure-function relationship is to…
Voronoi Tessellations form an attractive and versatile geometrical asymptotic model for the foamlike cosmic distribution of matter and galaxies. In the Voronoi model the vertices are identified with clusters of galaxies. For a substantial…
We present an edge labeling of order-$k$ Voronoi diagrams, $V_k(S)$, of point sets $S$ in the plane, and study properties of the regions defined by them. Among them, we show that $V_k(S)$ has a small orientable cycle and path double cover,…
In this thesis we study sets of points in the plane and their Voronoi diagrams, in particular when the points coincide. We bring together two ways of studying point sets that have received a lot of attention in recent years: Voronoi…
In this paper, we investigate the optimization of Centroidal Voronoi Tessellations (CVT) under geometric constraints. For this purpose, we minimize a linear combination of the standard CVT energy functional with terms involving geometric…
We present a paralell approach to discrete geometry: the first one introduces Voronoi cell complexes from statistical tessellations in order to know the mean scalar curvature in term of the mean number of edges of a cell. The second one…
Dislocation patterning and self-organization during plastic deformation are associated with work hardening, but the exact mechanisms remain elusive. This is partly because studies of the structure and local strain during the initial stages…
Polycrystal microstructures, with their distinct physical, chemical, structural and topological entities, play an important role in determining the effective properties of materials. Particularly for computational studies, the well-known…
This paper presents a new approach for precisely estimating the renal vascular dominant region using a Voronoi diagram. To provide computer-assisted diagnostics for the pre-surgical simulation of partial nephrectomy surgery, we must obtain…
The goal of this paper is to quantitatively describe some statistical properties of higher-dimensional determinantal point processes with a primary focus on the nearest-neighbor distribution functions. Toward this end, we express these…
We describe a new algorithm for computing the Voronoi diagram of a set of $n$ points in constant-dimensional Euclidean space. The running time of our algorithm is $O(f \log n \log \Delta)$ where $f$ is the output complexity of the Voronoi…
The time-dependent radiation transport equation is discretized using the meshless-local Petrov-Galerkin method with reproducing kernels. The integration is performed using a Voronoi tessellation, which creates a partition of unity that only…