Stochastic approximations to curve-shortening flows via particle systems

Gérard B. Arous, Allen Tannenbaum, Ofer Zeitoum

Research output: Contribution to journalArticle

Abstract

Curvature-driven flows have been extensively considered from a deterministic point of view. Besides their mathematical interest, they have been shown to be useful for a number of applications including crystal growth, flame propagation, and computer vision. In this paper, we describe a random particle system, evolving on the discretized unit circle, whose profile converges toward the Gauss-Minkowsky transformation of solutions of curve-shortening flows initiated by convex curves. Our approach may be considered as a type of stochastic crystalline algorithm. Our proofs are based on certain techniques from the theory of hydrodynamical limits.

Original languageEnglish (US)
Pages (from-to)119-142
Number of pages24
JournalJournal of Differential Equations
Volume195
Issue number1
DOIs
StatePublished - Nov 20 2003

Fingerprint

Stochastic Approximation
Particle System
Crystal growth
Computer vision
Crystalline materials
Convex Curve
Random Systems
Curve
Crystal Growth
Flame
Unit circle
Computer Vision
Gauss
Curvature
Propagation
Converge
Profile

Keywords

  • Curvature-driven flows
  • Curve shortening
  • Hydrodynamical limits
  • Interacting particle systems
  • Stochastic approximations

ASJC Scopus subject areas

  • Analysis

Cite this

Stochastic approximations to curve-shortening flows via particle systems. / Arous, Gérard B.; Tannenbaum, Allen; Zeitoum, Ofer.

In: Journal of Differential Equations, Vol. 195, No. 1, 20.11.2003, p. 119-142.

Research output: Contribution to journalArticle

Arous, Gérard B. ; Tannenbaum, Allen ; Zeitoum, Ofer. / Stochastic approximations to curve-shortening flows via particle systems. In: Journal of Differential Equations. 2003 ; Vol. 195, No. 1. pp. 119-142.
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