6,853 research outputs found
Strategies for Optimize Off-Lattice Aggregate Simulations
We review some computer algorithms for the simulation of off-lattice clusters
grown from a seed, with emphasis on the diffusion-limited aggregation,
ballistic aggregation and Eden models. Only those methods which can be
immediately extended to distinct off-lattice aggregation processes are
discussed. The computer efficiencies of the distinct algorithms are compared.Comment: 6 pages, 7 figures and 3 tables; published at Brazilian Journal of
Physics 38, march, 2008 (http://www.sbfisica.org.br/bjp/files/v38_81.pdf
Dynamic Scaling of Non-Euclidean Interfaces
The dynamic scaling of curved interfaces presents features that are
strikingly different from those of the planar ones. Spherical surfaces above
one dimension are flat because the noise is irrelevant in such cases. Kinetic
roughening is thus a one-dimensional phenomenon characterized by a marginal
logarithmic amplitude of the fluctuations. Models characterized by a planar
dynamical exponent , which include the most common stochastic growth
equations, suffer a loss of correlation along the interface, and their dynamics
reduce to that of the radial random deposition model in the long time limit.
The consequences in several applications are discussed, and we conclude that it
is necessary to reexamine some experimental results in which standard scaling
analysis was applied
Curves orthogonal to a vector field in Euclidean spaces
A curve is rectifying if it lies on a moving hyperplane orthogonal to its
curvature vector. In this work, we extend the main result of [B.-Y. Chen,
Tamkang J. Math. \textbf{48} (2017) 209--214] to any space dimension: we prove
that rectifying curves are geodesics on the hypersurface of higher dimensional
cones. We later use this association to characterize rectifying curves that are
also slant helices in three-dimensional space as geodesics of circular cones.
In addition, we consider curves that lie on a moving hyperplane normal to (i)
one of the normal vector fields of the Frenet frame and to (ii) a rotation
minimizing vector field along the curve. The former class is characterized in
terms of the constancy of a certain vector field normal to the curve, while the
latter contains spherical and plane curves. Finally, we establish a formal
mapping between rectifying and spherical curves in any dimension.Comment: 12 pages; keywords: Rectifying curve, geodesic, cone, spherical
curve, plane curve, slant heli
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