Morphology of Laplacian growth processes and statistics of equivalent many-body systems
The authors proposes a theory for the nonlinear evolution of two dimensional interfaces in Laplacian fields. The growing region is conformally mapped onto the unit disk, generating an equivalent many-body system whose dynamics and statistics are studied. The process is shown to be Hamiltonian, with the Hamiltonian being the imaginary part of the complex electrostatic potential. Surface effects are introduced through the Hamiltonian as an external field. An extension to a continuous density of particles is presented. The results are used to study the morphology of the interface using statistical mechanics for the many-body system. The distribution of the curvature and the moments of the growth probability along the interface are calculated exactly from the distribution of the particles. In the dilute limit, the distribution of the curvature is shown to develop algebraic tails, which may, for the first time, explain the origin of fractality in diffusion controlled processes.
- Research Organization:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Organization:
- USDOE, Washington, DC (United States)
- DOE Contract Number:
- W-7405-ENG-36
- OSTI ID:
- 10193766
- Report Number(s):
- LA-UR-94-3528; CONF-9409241-2; ON: DE95002734; TRN: 94:023907
- Resource Relation:
- Conference: NEEDS `94,Los Alamos, NM (United States),12-16 Sep 1994; Other Information: PBD: [1994]
- Country of Publication:
- United States
- Language:
- English
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