Bulletin of the American Physical Society
2006 APS March Meeting
Monday–Friday, March 13–17, 2006; Baltimore, MD
Session K33: Novel Moving Boundary Problems |
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Sponsoring Units: GSNP Chair: Wim Saarloos, Leiden University Room: Baltimore Convention Center 336 |
Tuesday, March 14, 2006 2:30PM - 3:06PM |
K33.00001: Nonlinear shape evolution of electromigration-driven single-layer islands Invited Speaker: Electromigration is the transport of matter induced by an electric current in the bulk or at the surface of a conducting material. Electromigration along interfaces and grain boundaries is a central factor limiting the reliability of integrated circuits. This has motivated numerous theoretical studies of the shape evolution of voids in metallic thin films caused by electromigration along the void boundary [1]. In this case the coupling of the void shape to the current distribution in the film leads to a nonlocal moving boundary problem driven by a mass current \textit{tangential} to the boundary. Here we are concerned with the \textit{local} version of the problem, which applies to the electromigration of single-layer islands on metallic surfaces [2]. We show that the introduction of crystal anisotropy in the mobility of atoms along the island boundary induces a rich variety of dynamical behaviors, ranging from spontaneous symmetry breaking to periodic and chaotic modes of island migration [3]. Under suitable physical conditions these phenomena can be reproduced in kinetic Monte Carlo simulations of a realistic microscopic model of the Cu(100) surface. Finally, we discuss recent results on the electromigration of vacancy islands in the kinetic regime dominated by exchange with the adatom diffusion field \textit{inside} the island. The talk is based on joint work with P. Kuhn, F. Hausser, A. Voigt and M. Rusanen. [1] M. Schimschak, J. Krug, J. Appl. Phys. \textbf{87}, 685 (2000). [2] O. Pierre-Louis, T.L. Einstein, Phys. Rev. B \textbf{62}, 13697 (2000). [3] P. Kuhn, J. Krug, F. Hausser, A. Voigt, Phys. Rev. Lett. \textbf{94}, 166105 (2005). [Preview Abstract] |
Tuesday, March 14, 2006 3:06PM - 3:42PM |
K33.00002: Fluctuation-regularized front propagation dynamics in reaction-diffusion systems Invited Speaker: We introduce and study a new class of fronts in finite particle number reaction-diffusion systems, corresponding to propagating up a reaction rate gradient. We show that these systems have no traditional mean-field limit, as the nature of the long-time front solution in the stochastic process differs essentially from that obtained by solving the mean-field deterministic reaction-diffusion equations. Instead, one can incorporate some aspects of the fluctuations via introducing a density cutoff. Using this method, we derive analytic expressions for the front velocity dependence on bulk particle density and show self-consistently why this cutoff approach can get the correct leading-order physics. [Preview Abstract] |
Tuesday, March 14, 2006 3:42PM - 4:18PM |
K33.00003: Spark formation as a moving boundary process Invited Speaker: The growth process of spark channels recently becomes accessible through complementary methods. First, I will review experiments with nanosecond photographic resolution and with fast and well defined power supplies that appropriately resolve the dynamics of electric breakdown [1]. Second, I will discuss the elementary physical processes as well as present computations of spark growth and branching with adaptive grid refinement [2]. These computations resolve three well separated scales of the process that emerge dynamically. Third, this scale separation motivates a hierarchy of models on different length scales. In particular, I will discuss a moving boundary approximation for the ionization fronts that generate the conducting channel. The resulting moving boundary problem shows strong similarities with classical viscous fingering. For viscous fingering, it is known that the simplest model forms unphysical cusps within finite time that are suppressed by a regularizing condition on the moving boundary. For ionization fronts, we derive a new condition on the moving boundary of mixed Dirichlet-Neumann type ($\phi=\epsilon\partial_n\phi$) that indeed regularizes all structures investigated so far. In particular, we present compact analytical solutions with regularization, both for uniformly translating shapes and for their linear perturbations [3]. These solutions are so simple that they may acquire a paradigmatic role in the future. Within linear perturbation theory, they explicitly show the convective stabilization of a curved front while planar fronts are linearly unstable against perturbations of arbitrary wave length. \newline [1] T.M.P. Briels, E.M. van Veldhuizen, U. Ebert, TU Eindhoven. \newline [2] C. Montijn, J. Wackers, W. Hundsdorfer, U. Ebert, CWI Amsterdam. \newline [3] B. Meulenbroek, U. Ebert, L. Sch\"afer, Phys. Rev. Lett. {\bf 95}, 195004 (2005). [Preview Abstract] |
Tuesday, March 14, 2006 4:18PM - 4:54PM |
K33.00004: Stalactite Growth as a Free-Boundary Problem Invited Speaker: As far back in recorded history as the writings of the Elder Pliny in the first century A.D. are found references to the fascinating structures found in limestone caves, particularly stalactites. Although the subject of continuing inquiry since that time, the chemical mechanisms responsible for their growth have only been well-established since the 19th century, and there has been no quantitative understanding of the morphological evolution of these strange and beautiful forms. In this talk I will describe a synthesis of calcium carbonate chemistry, diffusion, thin-film fluid dynamics, and nonlinear dynamics which shows that stalactites evolve according to a novel geometric growth law which exhibits extreme amplification at the tip. Studies of this model show that a broad class of initial conditions is attracted to an ideal parameter-free shape, not previously known in science, which is strikingly close to a statistical average of natural stalactites. Similar hydrodynamic and geometric considerations lead to a quantitative theory for the shapes of icicles, and an understanding of why stalactites and icicles look so similar, despite the vastly different physics underlying their growth. [Preview Abstract] |
Tuesday, March 14, 2006 4:54PM - 5:30PM |
K33.00005: Unsteady Crack motion and branching Invited Speaker: |
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