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SUMMARY:Deterministic Pattern Formation in Diffusion-Limited Systems - Gli
 cksman\, M (University of Florida)
DTSTART:20140626T110000Z
DTEND:20140626T113000Z
UID:TALK53183@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:An interface evolving under local equilibrium develops gradien
 ts in the Gibbs-Thomson-Herring interface temperature distribution that pr
 ovide tangential energy fluxes. The Leibniz-Reynolds transport theorem exp
 oses a 4th-order\, net-zero energy field (the 'Bias' field) that autonomou
 sly deposits and removes capillary-mediated thermal energy. Where energy i
 s released locally\, the freezing rate is persistently retarded\, and wher
 e energy is removed\, the rate is enhanced. These contravening dynamic fie
 ld responses balance at points (roots) where the surface Laplacian of the 
 chemical potential vanishes\, inducing an inflection\, or curling\, of the
  interface. Interfacial inflection couples to the main transport fields pr
 oducing pattern branching\, folding\, and complexity. \n\nPrecision noise-
 free numerical schemes\, including integral equation sharp-interface solve
 rs (J. Lowengrub\, S. Li) and\, recently\, three noise-free phase-field si
 mulations (A. Mullis\, M. Zaeem\, K. Reuther) independently confirm that p
 attern branching initiates at locations predicted using analytical methods
  for smooth\, noise-free starting shapes in 2-D. A limit cycle may develop
  as the interface and its energy field co-evolve\, synchronizing the infle
 ction points to produce classical dendritic structures. Noise and stochast
 ics play no direct role in the proposed deterministic mechanism of branchi
 ng and pattern morphogenesis induced by persistent 'perturbations'. \n
LOCATION:Seminar Room 1\, Newton Institute
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