4,219 research outputs found
Kinetic Voronoi Diagrams and Delaunay Triangulations under Polygonal Distance Functions
Let be a set of points and a convex -gon in .
We analyze in detail the topological (or discrete) changes in the structure of
the Voronoi diagram and the Delaunay triangulation of , under the convex
distance function defined by , as the points of move along prespecified
continuous trajectories. Assuming that each point of moves along an
algebraic trajectory of bounded degree, we establish an upper bound of
on the number of topological changes experienced by the
diagrams throughout the motion; here is the maximum length of an
-Davenport-Schinzel sequence, and is a constant depending on the
algebraic degree of the motion of the points. Finally, we describe an algorithm
for efficiently maintaining the above structures, using the kinetic data
structure (KDS) framework
Measuring kinetic coefficients by molecular dynamics simulation of zone melting
Molecular dynamics simulations are performed to measure the kinetic
coefficient at the solid-liquid interface in pure gold. Results are obtained
for the (111), (100) and (110) orientations. Both Au(100) and Au(110) are in
reasonable agreement with the law proposed for collision-limited growth. For
Au(111), stacking fault domains form, as first reported by Burke, Broughton and
Gilmer [J. Chem. Phys. {\bf 89}, 1030 (1988)]. The consequence on the kinetics
of this interface is dramatic: the measured kinetic coefficient is three times
smaller than that predicted by collision-limited growth. Finally,
crystallization and melting are found to be always asymmetrical but here again
the effect is much more pronounced for the (111) orientation.Comment: 8 pages, 9 figures (for fig. 8 : [email protected]). Accepted for
publication in Phys. Rev.
A parallel algorithm for Delaunay triangulation of moving points on the plane
Delaunay Triangulation(DT) is one of the important geometric problems that is
used in various branches of knowledge such as computer vision, terrain
modeling, spatial clustering and networking. Kinetic data structures have
become very important in computational geometry for dealing with moving
objects. However, when dealing with moving points, maintaining a dynamically
changing Delaunay triangulation can be challenging. So, In this case, we have
to update triangulation repeatedly. If points move so far, it is better to
rebuild the triangulation. One approach to handle moving points is to use an
incremental algorithm. For the case that points move slowly, we can give a
faster algorithm than rebuilding it. Furthermore, sequential algorithms can be
computationally expensive for large datasets. So, one way to compute as fast as
possible is parallelism. In this paper, we propose a parallel algorithm for
moving points. we propose an algorithm that divides datasets into equal
partitions and give every partition to one block. Each block satisfay the
Delaunay constraints after each time step and uses delete and insert algorithms
to do this. We show this algorithm works faster than serial algorithms
Topological defect motifs in two-dimensional Coulomb clusters
The most energetically favourable arrangement of low-density electrons in an
infinite two-dimensional plane is the ordered triangular Wigner lattice.
However, in most instances of contemporary interest one deals instead with
finite clusters of strongly interacting particles localized in potential traps,
for example, in complex plasmas. In the current contribution we study
distribution of topological defects in two-dimensional Coulomb clusters with
parabolic lateral confinement. The minima hopping algorithm based on molecular
dynamics is used to efficiently locate the ground- and low-energy metastable
states, and their structure is analyzed by means of the Delaunay triangulation.
The size, structure and distribution of geometry-induced lattice imperfections
strongly depends on the system size and the energetic state. Besides isolated
disclinations and dislocations, classification of defect motifs includes defect
compounds --- grain boundaries, rosette defects, vacancies and interstitial
particles. Proliferation of defects in metastable configurations destroys the
orientational order of the Wigner lattice.Comment: 14 pages, 8 figures. This is an author-created, un-copyedited version
of an article accepted for publication in J. Phys.: Condens. Matter. IOP
Publishing Ltd is not responsible for any errors or omissions in this version
of the manuscript or any version derived from it. The definitive
publisher-authenticated version is available online at
10.1088/0953-8984/23/38/38530
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