Fields Analysis Working Group

The Fields Analysis Working Group (FAWG) seminars are a working group seminar and brown bag lunch devoted to nonlinear dynamics and the calculus of variations meeting once a week.. Interested persons are welcome to attend and to propose talks to the organizers Larry Guth, Robert McCann and James Colliander.

Seminars will be held on Thursdays at 12 noon in Room 210 at the Fields Institute unless stated otherwise. 

Additional information and previous seminars can be found at the following link:

http://wiki.math.toronto.edu/TorontoMathWiki/index.php/FAWG_Seminar

Details

On the coarsening rates in demixing binary viscous liquids

by Christian Seis | University of Toronto
Time: 12:10  (Thursday, Nov. 03, 2011)
Location: FI210, Fields Institute, 222 College St.
Abstract:
We consider the demixing process of a binary mixture of two liquids after a temperature quench. In viscous liquids, demixing is mediated by diffusion and convection. The typical particle size grows as a function of time t, a phenomenon called coarsening. Simple scaling arguments based on the assumption of statistical self-similarity of the domain morphology suggest the coarsening rates: from ? t^{1/3} for diffusion-mediated to ? t for flow-mediated coarsening. In joint works with Y. Brenier, F. Otto, and D. Slepcev, we derive the crossover of both scaling regimes in the sense of lower bounds on the energy, which scales, heuristically at least, as an inverse length. The mathematical model is a Cahn-Hilliard equation with an additional convection term. The velocity of the convecting fluid is determined by a Stokes equation. Our analysis follows closely a method proposed by R. V. Kohn and F. Otto, which is based on the gradient flow structure of the evolution.

Dates in this series

· Thursday, Jan. 07, 2010: Traveling waves for the cubic Szegö equation on the real line (Oana Pocovnicu)
· Thursday, Jan. 14, 2010: Competing Symmetries and convergence of sequences of random symmetrizations  (Almut Burchard)
· Thursday, Jan. 21, 2010: Minimal Navier-Stokes Singularities (Ian Zwiers)
· Thursday, Jan. 28, 2010: New examples on spaces of negative sectional curvature satisfying Ma-Trudinger-Wang conditions (Jiayong Li)
· Thursday, Feb. 25, 2010: The multi-marginal optimal transportation problem (Brendan Pass)
· Thursday, Mar. 04, 2010: Rectifiability of optimal transportation plans (Brendan Pass)
· Thursday, Mar. 11, 2010: Almost Sure Local Well-posedness for the Stochastic KdV-Burgers Equation (Geordie Richards)
· Thursday, Apr. 01, 2010: On the speed of the propagation of the thin film interface (Marina Chugunova)
· Thursday, Apr. 08, 2010: Ricci flow and the determinant of the Laplacian on non-compact manifolds (Frederic Rochon)
· Thursday, Apr. 15, 2010: Ricci flow and the determinant of the Laplacian on non-compact manifolds, Part 2 (Frederic Rochon)
· Thursday, Apr. 29, 2010: The probabilistic method in geometry: Bourgain's Theorem (Dominic Dotterrer)
· Wednesday, Jul. 14, 2010: Regularity of optimal transportation maps on multiple products of spheres (Young-Heon Kim)
· Friday, Jul. 23, 2010: Asymptotics of fast diffusion via dynamical systems (Jochen Denzler)
· Thursday, Sep. 16, 2010: Existence and uniquness of equilibrium in a noisy model of the marriage market (Colin Decker)
· Thursday, Sep. 30, 2010: Invariant Gibbs measures for periodic nonlinear Schrodinger equations (Geordie Richards)
· Thursday, Oct. 07, 2010: Regularity of solutions for a variational problem related to the Rochet-Chone model (Shibing Chen)
· Thursday, Oct. 21, 2010: A Generalized Euler-Lagrange Equation for the Principal-Agent Problem (Quentin Merigot)
· Thursday, Oct. 28, 2010: Global regularity of the reflector problem (Jiakun Liu)
· Thursday, Feb. 17, 2011: Sharp new conformally invariant integral inequalities (Shibing Chen)
· Thursday, Mar. 24, 2011: Aharonov--Bohm Effect in Resonances of Magnetic Schrodinger Operators with Potentials with Supports at Large Separation (Ivana Alexandrova)
· Thursday, Mar. 31, 2011: Global well-posedness for KdV in L2 (Jordan Bell)
· Thursday, Apr. 07, 2011: Structural results on optimal transportation plans (Brendan Pass)
· Thursday, Sep. 22, 2011: Rayleigh--Benard convection. A new bound on the Nusselt number (Christian Seis)
· Thursday, Sep. 29, 2011: Density functional theory and optimal transportation with Coulomb cost (Codina Cotar)
· Thursday, Oct. 06, 2011: Gradient flow methods for thin-film and related higher order equations (Ehsan Kamalinejad)
· Thursday, Oct. 13, 2011: OPTIMAL TRANSPORTATION WITH CAPACITY CONSTRAINTS (Jonathan Korman)
· Thursday, Oct. 20, 2011: Conductivity imaging from one interior measurement in the presence of perfectly conducting and insulating inclusions (Amir Moradifam)
· Thursday, Oct. 27, 2011: Loss of compactness and bubbling for complete minimal surfaces in hyperbolic space (Spryos Alexakis)
· Thursday, Nov. 03, 2011: On the coarsening rates in demixing binary viscous liquids (Christian Seis)
· Thursday, Nov. 10, 2011: Optimal transportation with infinitely many marginals (Brendan Pass)
· Thursday, Nov. 17, 2011: On uniqueness of the waiting-time type solution of the thin film equation (Marina Chugunova)
· Thursday, Nov. 24, 2011: Higher-order time asymptotics of fast diffusion in Euclidean space: a dynamical systems approach (Robert McCann)
· Thursday, Jan. 05, 2012: The Gamma-limit of the Ohta-Kawasaki energy. Derivation of the renormalized energy (Dorian Goldman)
· Thursday, Mar. 01, 2012: Well-posedness and finite-time blowup for the Zakharov system on two-dimensional torus (Nobu Kishimoto)
· Thursday, Mar. 08, 2012: A Generalized Representation Formula for Covariant Tensor Wave Equations on Curved Spacetimes (Arick Shao)
· Thursday, Mar. 29, 2012: Big frequency cascades in the cubic nonlinear Schrödinger flow on the 2-torus (James Colliander)