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Harmonic measure probing of DLA clusters

Harmonic measure probing of DLA clusters. Lev N. Shchur Landau Institute for Theoretical Physics Chernogolovka, Russia. Models : Diffusion limited aggregation - DLA Dielectric breakdown model - DBM Laplacian growth. 2D aggregate growth. Crystal growth Dielectric breakdown

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Harmonic measure probing of DLA clusters

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

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

  3. Off-lattice killing-free algorithm • Seed at origin (0,0) • Particle starts at radius of birthRbirth • Diffusion in space • If touch, it sticks • If particles goes ot ofradius of death Rdeath it is returned onRbirth with probability • New iteration – from step 2. 50 000 000particles A. Menshutin, L.S., PRE 73, 011407 (2006)

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

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

  6. Fractal dimension

  7. Dependence of fractal dimension D onthe number of particles N Harmonic measure average

  8. Fluctuation of fractal dimension A. Menshutin, L.S., PRE 73, 011407 (2006) “weak self-averaging” of D

  9. Laplacian growth DLA

  10. Harmonic measure estimation Probe particles of radius

  11. D - harmonic measure

  12. D - harmonic measure A. Menshutin, L.S., V. Vinokur, cond-mat/0611005

  13. Probability P(r) to stick at distance r

  14. Summary • Two-parameter analysis (N and Rprob) versus one-parameter • Drastical increase of accuracy • Averaging over 1000 clusters with 50 000 000givesD=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, 011407 (2006) A. Menshutin, L.S., V. Vinokur, cond-mat/0611005

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