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UID:678@math.technion.ac.il

DTSTART;TZID=Asia/Jerusalem:20260816T143000

DTEND;TZID=Asia/Jerusalem:20260816T153000

DTSTAMP:20260804T081818Z

URL:https://math.technion.ac.il/events/a-coupled-surface-diffusion-and-mea
 n-curvature-flow-problem-steady-states-and-stability/

SUMMARY: A Coupled Surface Diffusion and Mean Curvature Flow Problem — 
 Steady States and Stability   
DESCRIPTION:Lecturer: Daniel Goldberg (Technion)\n Location:Conference Room
 \, Eighth Floor\, Amado Mathematics Building\n Patterned thin gold lines w
 hen undergoing solid-state dewetting break up into linear grain sections i
 nterspersed with occasionally larger ”abacus” particles. We model this
  system using coupled geometric flows\, where the exterior surfaces of the
  grains evolve via Surface Diffusion\, V = −∆Γ(t)H\, and the internal
  grain boundaries evolve via Mean Curvature Flow\, V = AH. In this talk we
  first motivate the problem based on these experimental observations. Next
 \, we describe the steady states for this mixed-order system. By assuming 
 axi-symmetry\, we can systematically construct composite equilibria by pie
 cing together Delaunay surfaces—specifically\, combining unduloidal\, cy
 lindrical and spherical exterior surfaces which are partitioned by planar 
 or catenoidal internal grain boundaries. We then undertake a stability ana
 lysis by first linearising the coupled (nonlinear) problem about these com
 posite steady states\, deriving a Jacobi operator whose strict positivity 
 implies asymptotic stability of the linearised\nproblem. Using this approa
 ch and building upon classical Rayleigh stability criteria\, we obtain sta
 bility/instability predictions for steady-state configurations consisting 
 of near-cylindrical and near-spherical grains which join together along a 
 planar grain boundary.\n 
CATEGORIES:Nonlinear Analysis and Optimization Seminar,Seminars
LOCATION:Conference Room\, Eighth Floor\, Amado Mathematics Building

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DTSTART:20260327T030000

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