2 research outputs found
Biharmonic pattern selection
A new model to describe fractal growth is discussed which includes effects
due to long-range coupling between displacements . The model is based on the
biharmonic equation in two-dimensional isotropic defect-free
media as follows from the Kuramoto-Sivashinsky equation for pattern formation
-or, alternatively, from the theory of elasticity. As a difference with
Laplacian and Poisson growth models, in the new model the Laplacian of is
neither zero nor proportional to . Its discretization allows to reproduce a
transition from dense to multibranched growth at a point in which the growth
velocity exhibits a minimum similarly to what occurs within Poisson growth in
planar geometry. Furthermore, in circular geometry the transition point is
estimated for the simplest case from the relation
such that the trajectories become stable at the growing surfaces in a
continuous limit. Hence, within the biharmonic growth model, this transition
depends only on the system size and occurs approximately at a distance far from a central seed particle. The influence of biharmonic patterns on
the growth probability for each lattice site is also analysed.Comment: To appear in Phys. Rev. E. Copies upon request to
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