Laplacian Growth of Parallel Needles: Their Mullins-Sekerka Instability

Abstract

We study analytically the kinetics of growth of parallel needles using a conformal transformation to set up the iterative nonlinear equations. This allows to build the discrete Fokker-Planck equation for the probability of finding at time t a given distribution of needle lengths. We consider here two specific cases: we find the exact Fokker-Planck equation for pairs of needles and its solutions and the linear behavior of a set of n needles with equal initial lengths. The corresponding Fokker-Planck equations show the short-wavelength Mullins-Sekerka instability of these parallel needles and the possible structure of the screening leading to the scale invariance of the model.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2000
Accession Number
ADP010914

Entities

People

  • J. F. Gouyet
  • M. O. Bernard

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Conformal Mapping
  • Differential Equations
  • Diffusion
  • Eigenvalues
  • Equations
  • Fokker Planck Equations
  • Instability
  • Materials
  • Partial Differential Equations
  • Particles
  • Personal Information Managers
  • Probability
  • Scaling Laws
  • Short Wavelengths
  • Technical Information Centers
  • Two Dimensional
  • Vector Spaces

Fields of Study

  • Mathematics

Readers

  • Cardiovascular Physiology
  • Computer Programming and Software Development.
  • Linear Algebra