Bulletin of the American Physical Society
APS March Meeting 2014
Volume 59, Number 1
Monday–Friday, March 3–7, 2014; Denver, Colorado
Session Q15: Pattern Formation & Nonlinear Dynamics 
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Sponsoring Units: DFD Chair: Sandra Troian, California Institute of Technology Room: 304 
Wednesday, March 5, 2014 2:30PM  2:42PM 
Q15.00001: Coherent structures for front propagation in fluids Kevin Mitchell, John Mahoney Our goal is to characterize the nature of reacting flows by identifying important ``coherent'' structures. We follow the recent work by Haller, BeronVera, and Farazmand which formalized the notion of lagrangian coherent structures (LCSs) in fluid flows. In this theory, LCSs were derived from the CauchyGreen strain tensor. We adapt this perspective to analogously define coherent structures in \emph{reacting} flows. By this we mean a fluid flow with a reaction front propagating through it such that the propagation does not affect the underlying flow. A reaction front might be chemical (BelousovZhabotinsky, flame front, etc.) or some other type of front (electromagnetic, acoustic, etc.). While the recently developed theory of burning invariant manifolds (BIMs) describes barriers to front propagation in timeperiodic flows, this current work provides an important complement by extending to the aperiodic setting. [Preview Abstract] 
Wednesday, March 5, 2014 2:42PM  2:54PM 
Q15.00002: Exact coherent structures: from fluid turbulence to cardiac arrhythmias Roman Grigoriev, Christopher Marcotte, Gregory Byrne Ventricular fibrillation, a life threatening cardiac arrhythmia, is an example of spatiotemporally chaotic state dominated by multiple interacting spiral waves. Recent studies of weak fluid turbulence suggest that spatiotemporal chaos in general can be understood as a walk among exact unstable regular solutions (exact coherent states, ECS) of nonlinear evolution equations. Several classes of ECS are believed to play a dominant role; most typically these are equilibria and periodic orbits or relative equilibria and relative periodic orbits for systems with global continuous symmetries. Numerical methods originally developed in the context of fluid turbulence can also be applied to models of cardiac dynamics which possess translational and rotational symmetries and, indeed, allowed us to identify relative equilibria and periodic orbits describing isolated spirals with, respectively, fixed and drifting cores. In order to find regular solutions featuring multiple interacting spirals a new approach is required that takes into consideration the dynamics of slowly drifting cores associated with local, rather than global, symmetries. We describe how local symmetries can be reduced and more general types of ECS computed that dominate spiral wave chaos in models of cardiac tissue. [Preview Abstract] 
Wednesday, March 5, 2014 2:54PM  3:06PM 
Q15.00003: Untying the Knot: Topological Vortex Dynamics Dustin Kleckner, Martin Scheeler, Davide Proment, William T.M. Irvine Knots and links are thought to be associated with topologically conserved quantities in many physical fields, including quantum and classical fluids, plasmas and electromagnetic fields. Observing topological dynamics in experiment, however, has proven difficult. Recent advances have made it possible to generate and measure vortex knots in classical fluids, revealing that they spontaneously untie themselves through a series of topologychanging reconnections. Similar behavior is found for simulations of superfluid knots. We will discuss these dynamics as well as their implications for the role of knots in fluids and other areas of physics. [Preview Abstract] 
Wednesday, March 5, 2014 3:06PM  3:18PM 
Q15.00004: Lie Group Reduction Analysis of the Moving Boundary Problem Governing BenardLike Fluctuations in Nanofilms Zachary Nicolaou, Sandra Troian The underlying mechanism responsible for the spontaneous formation of nanopillar arrays in thin viscous films whose free surface is subject to a large transverse thermal gradient continues to be debated. Recent experimental measurements by our group strongly suggest that thermocapillary forces play a central role in the formation and growth of these 3D periodic structures, in a process somewhat akin to the conventional Benard problem. Here we present both analytic and numerical results of the governing thin film equation in the long wavelength approximation for films of constant viscosity subject to capillary and thermocapillary forces. We focus on exact reductions of the highly nonlinear, fourth order equation of motion which reveal steady state solutions, similarity solutions, and other reductions obtained through Lie group analysis. In particular, we predict the possibility of solutions describing isolated droplet formation well beyond the linearized regime. A linear stability analysis of these solutions has been carried out numerically and relevant bounds on droplet stability obtained within restricted parameter regimes. Experimental realization of such isolated droplet formations may find use in scientific and industrial applications such as nanolenses or other optical components. [Preview Abstract] 
Wednesday, March 5, 2014 3:18PM  3:30PM 
Q15.00005: Reanalysis of Incipient Wavelength Measurements in Free Surface Nanofilms Undergoing Benard Instability Kevin Fiedler, Sandra Troian Ultrathin liquid films whose free surface is subject to large thermal gradients are known to develop spontaneous periodic arrays of nanopillars. Theoretical predictions based on linear stability theory in the long wavelength approximation suggest that these formations arise either from fluctuations in the electrostatic forces between the fluid and opposing substrate, acoustic phonon radiation pressure within the film, or Benard instability due to surface thermocapillary forces. Experimental confirmation of the mechanism responsible for such emergent structures requires measurements of the pattern formation process at very early times, a difficult task given that incipient film distortions are of the order of a few nanometers. We reported last year that while our measurements of the dominant wavelength seem to rule out electrostatic effects and acoustic radiation pressure at the source of instability, there remained significant discrepancy between the predictions of the thermocapillary model and measurements of the dominant wavelength obtained from image Fourier analysis. We describe how earlier time analysis and more accurate modeling of the temperature field derived from substrate resistive heating leads to much closer agreement with predictions of the thermocapillary model than previously reported. [Preview Abstract] 
Wednesday, March 5, 2014 3:30PM  3:42PM 
Q15.00006: The Origin and Evolution of Icicle Ripples Antony SzuHan Chen, Stephen W. Morris Natural icicles often exhibit ripples about their circumference which are due to a morphological instability. We present an experimental study that explores the origin of the instability, using laboratorygrown icicles. Contrary to theoretical expectations, icicles grown from pure water do not exhibit growing ripples. The addition of a nonionic surfactant, which reduces the surface tension, does not produce ripples. Instead, ripples emerge on icicles grown from water with dissolved ionic impurities. We find that even very small levels of impurity are sufficient to trigger ripples, and that the growth speed of the ripples increases only approximately logarithmically with impurity concentration. With impurities present, the ripple wavelength remains constant under all other variations of the growth conditions. Ripples are observed to travel during their growth. For low impurity concentrations, they travel upward at speeds of mm/hr. For higher impurity concentrations, some ripples moved nonlinearly and different ripples on the same icicle sometimes traveled in opposite directions. Existing theories of ripple formation do not account for the effect of impurities and cannot be easily generalized to include them. [Preview Abstract] 
Wednesday, March 5, 2014 3:42PM  3:54PM 
Q15.00007: Sidebranch development in free dendritic crystal growth Andrew Dougherty We report measurements of the free dendritic crystal growth of NH$_4$Cl from supersaturated aqueous solution at small supersaturations, with a goal of understanding the origin and development of the sidebranching structure. The origin of sidebranches is not fully understood. The functional form and scaling of the sidebranches seem reasonably consistent with a noisedriven model, but the amplitude of the branches in this system appears larger than would be expected from simple thermal noise. An underlying dynamic oscillation can not be ruled out. We do sometimes observe short regions with highly regular branches, but such regularity is usually quite shortlived. In the context of directional solidification, Pocheau, Bodea, and Georgelin [Phys. Rev. E 80, 031601 (2009)] found randomlydistributed bursts of sidebranches that had strong coherence within each burst, but that were not wellcorrelated between bursts. In this talk, I will explore applying that idea to free dendritic growth. [Preview Abstract] 

Q15.00008: ABSTRACT WITHDRAWN 
Wednesday, March 5, 2014 4:06PM  4:18PM 
Q15.00009: Characterizing Branched Flow Byron Drury, Anna Klales, Eric Heller Branched flow appears in a variety of physical systems spanning length scales from microns to thousands of kilometers. For instance, it plays an important role in both electron transport in two dimensional electron gases and the propagation of tsunamis in the ocean. Branches have typically been identified with caustics in the theoretical literature, but concentrations of flux recognizable as branches can arise from other mechanisms. We propose a generalized definition of branching based on a local measure of the stability of trajectories. We analytically and numerically study the characteristics of Hamiltonian flow in phase space and characterize the relationship between branch formation and trajectory stability. [Preview Abstract] 

Q15.00010: ABSTRACT WITHDRAWN 
Wednesday, March 5, 2014 4:30PM  4:42PM 
Q15.00011: Collisions of localized convection structures in binary fluid mixtures Manfred Luecke, Alexander Taraut, Boris Smorodin Collisions of a localized traveling wave structure with a localized stationary structure are investigated. In ethanolwater mixtures with appropriately chosen negative separation ratios both exist bistably in the unstable quiescent surrounding for a range of supercritical heating rates. Depending on the Rayleigh number we observe different evolution scenarios of the onvection structures that appear as a result of the collision. The incident localized traveling wave can be absorbed by the stationary structure and then the latter expands: either both of its fronts get unpinned and propagate into the quiescent fluid or only the one that is hit propagates while the opposing one remains pinned. For smaller Rayleigh numbers the stationary structure is destroyed while the incident localized traveling wave survives and a second one is created that moves ahead of the incoming one, both being coupled together. The mechanisms involved in these scenarios are analyzed and elucidated with the help of finite difference numerical simulations that are carried out subject to realistic boundary conditions. [Preview Abstract] 
Wednesday, March 5, 2014 4:42PM  4:54PM 
Q15.00012: Excitability dependent pattern formation Kaumudi Prabhakara, Azam Gholami, Eberhard Bodenschatz On starvation, the amoebae Dictyostelium discoideum emit the chemoattractant cyclic adenosine monophosphate (cAMP) at specific frequencies. The neighboring amoebae sense cAMP through membrane receptors and produce their own cAMP. Soon the cells synchronize and move via chemotaxis along the gradient of cAMP. The response of the amoebae to the emission of cAMP is seen as spiral waves or target patterns under a dark field microscope. The causal reasons for the selection of one or the other patterns are still unclear. Here we present a possible explanation based on excitability. The excitability of the amoebae depends on the starvation time because the gene expression changes with starvation. Cells starved for longer times are more excitable. In this work, we mix cells of different excitabilities to study the dependence of the emergent patterns on the excitability. Preliminary results show a transition from spirals to target patterns for specific excitabilities. A phase map of the patterns for different combinations of excitability and number densities is obtained. We compare our findings with numerical simulations of existing theoretical models. [Preview Abstract] 
Wednesday, March 5, 2014 4:54PM  5:06PM 
Q15.00013: Noiseinduced nucleation in a bistable tunnel diode circuit R.A. McGeehan, S.J. Jones, Yu. Bomze, S.W. Teitsworth We report the measurement of firstpassage time distributions associated with electrical current switching in a bistable tunnel diode circuit driven by a noise generator with adjustable noise intensity $D$. In such a system, it is particularly interesting to study the behavior of the mean switching time $\tau $ near the boundary of the bistable regime where the metastable state approaches and collides with a saddle point in the underlying noisefree dynamical system. In the tunnel diode circuit and for sufficiently large noise intensity, we find a \textit{linear} scaling relationship $\ln \tau \propto \left {VV_{th} } \right/D$ valid over several decades of time, where $V$ denotes the applied voltage and $V_{th}$ denotes the value corresponding to the end of the bistable regime. At smaller noise intensities, we typically find that the mean switching time versus $VV_{th}$ possesses multiple scaling regimes. These experimental results are interpreted in light of theoretical work that shows how lateral charge transport dynamics can strongly affect the noiseinduced nucleation events that lead to current switching [1]. [1] O. A. Tretiakov and K. A. Matveev, Phys. Rev. B \textbf{71}, 165326 (2005). [Preview Abstract] 
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