Harmonic measure probing of DLA clusters Lev N. Shchur Landau Institute for Theoretical Physics Chernogolovka, Russia.

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Harmonic measure probing of DLA clusters Lev N. Shchur Landau Institute for Theoretical Physics Chernogolovka, Russia

2D aggregate growth Models: Diffusion limited aggregation - DLA Dielectric breakdown model - DBM Laplacian growth Crystal growth Dielectric breakdown Liquid spot between two plates

Off-lattice killing-free algorithm 1.Seed at origin (0,0) 2.Particle starts at radius of birth Rbirth 3.Diffusion in space 4.If touch, it sticks 5.If particles goes ot of radius of death Rdeath it is returned on Rbirth with probability 6.New iteration – from step particles A. Menshutin, L.S., PRE 73, (2006)

Fractal dimension Deposition radius Mean-square radius Radius of gyration Seed-to-center-of-mass distance Penetration depth …

Fractal dimension Deposition radius Mean-square radius Effective radius Maximal radius Penetration depth … (harmonic measure)

Fractal dimension

Dependence of fractal dimension D on the number of particles N Harmonic measure average

Fluctuation of fractal dimension “weak self-averaging” of D A. Menshutin, L.S., PRE 73, (2006)

Laplacian growth DLA

Harmonic measure estimation Probe particles of radius

D - harmonic measure

A. Menshutin, L.S., V. Vinokur, cond-mat/

Probability P(r) to stick at distance r

Summary Two-parameter analysis (N and R prob) versus one-parameter Drastical increase of accuracy Averaging over 1000 clusters with gives D=1.7100(3) For comparison – accuracy of the one-parameter method (DLA – 1.715(4) TOLMAN-Meakin’1989 and Ossadnik’1991, conformal mapping 1.713(5) – Davidovich et al, 2000) and our estimate over the 1000 clusters are May be usefull to look on the lacunarity and other surface and screening properties A. Menshutin, L.S., PRE 73, (2006) A. Menshutin, L.S., V. Vinokur, cond-mat/