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Diffusion-Reorganized Aggregates: Attractors in Diffusion Processes?
A process based on particle evaporation, diffusion and redeposition is
applied iteratively to a two-dimensional object of arbitrary shape. The
evolution spontaneously transforms the object morphology, converging to
branched structures. Independently of initial geometry, the structures found
after long time present fractal geometry with a fractal dimension around 1.75.
The final morphology, which constantly evolves in time, can be considered as
the dynamic attractor of this evaporation-diffusion-redeposition operator. The
ensemble of these fractal shapes can be considered to be the {\em dynamical
equilibrium} geometry of a diffusion controlled self-transformation process.Comment: 4 pages, 5 figure
Holographic turbulence
We construct turbulent black holes in asymptotically AdS_4 spacetime by
numerically solving Einstein equations. Both the dual holographic fluid and
bulk geometry display signatures of an inverse cascade with the bulk geometry
being well approximated by the fluid/gravity gradient expansion. We argue that
statistically steady-state black holes dual to d dimensional turbulent flows
have horizons which are approximately fractal with fractal dimension D=d+4/3.Comment: 6 pages, 3 figure
Fractals at T=Tc due to instanton-like configurations
We investigate the geometry of the critical fluctuations for a general system
undergoing a thermal second order phase transition. Adopting a generalized
effective action for the local description of the fluctuations of the order
parameter at the critical point () we show that instanton-like
configurations, corresponding to the minima of the effective action functional,
build up clusters with fractal geometry characterizing locally the critical
fluctuations. The connection between the corresponding (local) fractal
dimension and the critical exponents is derived. Possible extension of the
local geometry of the system to a global picture is also discussed.Comment: To appear in Physical Review Letter
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