Bulletin of the American Physical Society
2007 APS March Meeting
Volume 52, Number 1
Monday–Friday, March 5–9, 2007; Denver, Colorado
Session W30: Pattern Formation and Nonlinear Dynamics |
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Sponsoring Units: DFD Chair: Carsten Beta, Max Planck Society for the Advancement of Science Room: Colorado Convention Center 304 |
Thursday, March 8, 2007 2:30PM - 2:42PM |
W30.00001: Optically-Induced Spatial Forcing in Rayleigh-Benard Convection Gabriel Seiden, Stephan Weiss, Eberhard Bodenschatz Spatial forcing of spatially extended pattern forming systems has received little attention over the past years. Here we report experimental results on optically forced Rayleigh-Benard (isotropic system) and inclined layer convection (anisotropic system). These include a mapping of the phase space as a function of forcing periodicity and forcing strength. A comparison of the observed patterns with the predictions from Ginzburg-Landau theories is made. [Preview Abstract] |
Thursday, March 8, 2007 2:42PM - 2:54PM |
W30.00002: Apparatus for Real-Time Acoustic Imaging of Rayleigh-B\`{e}nard Convection Kerry Kuehn, Jonathan Polfer, Joanna Furno Shadowgraph visualization of the Rayleigh-B\`{e}nard instability in optically transparent fluids has enabled comparison between theoretical and experimental work on a well defined nonlinear system. Rayleigh-B\`{e}nard convection in liquid metals, however, remains largely unexplored owing primarily to the difficulty of imaging flow patterns in opaque fluids. We have designed and built an apparatus for high-resolution real-time imaging of convective flow patterns in optically opaque fluids which takes advantage of recent advances in two-dimensional ultrasound transducer array technology. The experimental apparatus employs a modified version of a commercially available two-dimensional ultrasound camera, similar to those now employed in non-destructive testing of solids. Images of convection patterns are generated by observing the lateral variation of the temperature dependent speed of sound \textit{via} refraction of acoustic plane waves passing vertically through the fluid layer. The apparatus has been utilized to observe straight rolls in transparent 5 cSt. silicone oil. Thus far, we have not observed stable convection rolls in liquid mercury. [Preview Abstract] |
Thursday, March 8, 2007 2:54PM - 3:06PM |
W30.00003: Tension kills ... harmonic moments in viscous fingering Matthew Thrasher, Alexander Leshchiner, Harry L. Swinney, Mark B. Mineev-Weinstein We measure the displacement of oil by air between two horizontal, closely-spaced glass plates to track the evolution of harmonic moments, which are integrals of integer powers of $z = x+iy$ over the oil domain. Richardson's theory (1972) predicts that the harmonic moments should be \emph{time invariant in the absence of surface tension}. When we extend the theory to include surface tension, the harmonic moments are predicted to \emph{decay in time because of surface tension}. From measurements of the time decay of the harmonic moments, we obtain a value for the surface tension within 5\% of the accepted value. To obtain such precise agreement, the effect of silicone oil wetting the glass plates must be included. Our results implicitly validate Richardson's theory and directly demonstrate that a full description of interface dynamics in terms of harmonic moments is physically realizable and robust. In addition, a novel growth method using feedback produces nearly n-fold symmetric bubbles. [Preview Abstract] |
Thursday, March 8, 2007 3:06PM - 3:18PM |
W30.00004: The early stages of sidebranching in dendritic crystal growth. Andrew Dougherty, Thomas Nunnally We report an experimental study of the early stages of sidebranching in the dendritic crystal growth of NH$_4$Cl crystals in aqueous solution. In steady state, the growing dendrites are characterized by a smooth, nearly parabolic tip. A short distance behind the tip, sidebranches begin to emerge. We characterize the growth of the sidebranches by an envelope $A(z)$, where $z$ is the distance behind the tip. We consider two basic models. In one model, the smooth tip is unstable, and the sidebranches result from the selective amplification of microscopic noise. In this model, $A(z)$ depends on the amplitude of the noise $\bar{S}$ and on various materials parameters. In the second model, the dendrite tip grows in an oscillating mode, with sidebranches emerging like waves in its wake. We have observed no strong oscillations, but very small amplitude ones can not be ruled out. Given the finite experimental resolution, no measurement of the tip region can be completely free of contamination from early sidebranches. We will discuss this and other experimental challenges that need to be overcome before we can understand the origin of sidebranches. [Preview Abstract] |
Thursday, March 8, 2007 3:18PM - 3:30PM |
W30.00005: Pattern selection in columnar joints Lucas Goehring, Stephen Morris The pattern of columnar jointing is well known from geological formations such as the Giant's Causeway in N. Ireland, or the Devil's Postpile in California. It arises when a directionally propagating array of cracks arrange themselves into a roughly hexagonal network, which leaves behind a remarkably well ordered collection of prismatic columns. This ordering is efficient, and visually impressive, but not perfect. Experimental observations of columnar jointing in corn starch have shown that, as it matures, the pattern settles down into a well defined, statistically steady state with residual disorder. The same quantifiable amount of disorder can be shown to exist in the pattern of igneous columnar jointing. We report on the dynamics of the mature pattern of columnar jointing, and compare it to models of this phenomenon. In particular, we compare it to an evolution model based on voronoi tessellations, a phase-field model, and a model inspired by 2D foam coarsening. [Preview Abstract] |
Thursday, March 8, 2007 3:30PM - 3:42PM |
W30.00006: Flowers in the Fourth Dimension Rebecca Thompson-Flagg, Michael Marder Buckling membranes are seen often in nature from daffodils to torn plastic sheets. These patterns are produced by imposing certain types of metrics on thin sheets. This work looks specifically at patterns formed at the edge of trumpet shaped sheets which are forced to obey an exponentially decreasing metric. Using geometrical techniques a condition for cylindrical symmetry is found. Equations developed by Nash are used to evolve a trumpet from below the limit past the limit. These equations are used to demonstrate that trumpets past this limit cannot fully adopt the metric in three dimensions. A molecular dynamics code is used to create a sheet with points connected by Hookian springs. By changing the equilibrium distance between the springs a target metric can be imposed on the sheet. The energy of the sheet is minimized. The sheet is allowed to move into a fourth spacial dimension and the energy of the sheet in four dimensions, both below and above the symmetry limit, is compared to the minimum energy in three dimensions. [Preview Abstract] |
Thursday, March 8, 2007 3:42PM - 3:54PM |
W30.00007: Pattern formation in heterogeneous self-oscillating polymer gels. Victor Yashin, Anna Balazs The chemical reaction and deformations are inherently coupled in the chemo-responsive polymer gels that participate in the Belousov-Zhabotinsky reaction (BZ gels). Chemical oscillations due to the BZ reaction cause variations in the gel's size and shape because of the hydrating effect of the oxidized metal-ion catalyst linked to the polymer. Physical and chemical patterning of self-oscillating gels would facilitate creating active materials that exhibit desirable spatiotemporal behavior. The heterogeneous self-oscillating gels might be designed to respond to external stimuli by switching between pre-programmed dynamic patterns. We explore these potentialities through modeling 2D dynamics of the structurally heterogeneous BZ gels. We start by considering the effects of a spatially non-uniform crosslink density, volume fraction of polymer, and catalyst distribution on the domain of the oscillatory regime. Then, the propagation of the swelling-deswelling waves through the structurally patterned gels is simulated using the gel lattice-spring model approach. We demonstrate and discuss how the spatial organization of the heterogeneous gel affects the origination and propagation of waves. [Preview Abstract] |
Thursday, March 8, 2007 3:54PM - 4:06PM |
W30.00008: The effects of pattern morphology on late time scaling in the Cahn-Hilliard model Timothy Sullivan, Peter Palffy-Muhoray As previously reported, numerical simulations of the dimensionless Cahn-Hilliard equation, have been performed in 2D. The initial state consisted of Gaussian distributed random values on a 540 by 540 grid. The Cahn-Hilliard equation conserves the spatial average of the dimensionless concentration difference, $\left\langle \psi \right\rangle $, and initial conditions were chosen with $\left\langle \psi \right\rangle $ ranging from 0 to 0.9. As time progresses the system quickly separates into distinct regions where $\left\langle \psi \right\rangle \approx +1$ or $\left\langle \psi \right\rangle \approx -1$ and then slowly coarsens. Analysis of the late time scaling of a characteristic pattern size scale,$R_G (t)$, the first zero of the pair correlation function, showed that near $\left\langle \psi \right\rangle $ = 0.2 the time to reach the expected dynamical scaling regime grew very long. This, coupled with the change in the pattern from sinuous structures near $\left\langle \psi \right\rangle =0$ to a pattern of circular regions for larger values of $\left\langle \psi \right\rangle $, suggest a morphological phase transition. We explore this idea and will report on our attempts to create order parameters describing the pattern and will present results on the behavior of the candidate order parameters near $\left\langle \psi \right\rangle $ = 0.2. [Preview Abstract] |
Thursday, March 8, 2007 4:06PM - 4:18PM |
W30.00009: The onset of activations in the oscillatory Belousov-Zhabotinsky reaction Harold Hastings, Sabrina Sobel, Richard Field The unstirred, ferroin catalyzed Belousov-Zhabotinsky (BZ) is a prototype chemical system exhibiting traveling waves of oxidation in an oscillatory or excitable medium. A typical thin- layer BZ medium (approx. 2D) displays a red (reduced) induction phase lasting several minutes, followed by ``spontaneous'' formation of ``pacemaker'' centers that oscillate between red and blue states and generate target patterns of concentric, outward- moving waves of oxidation (blue) in the red medium. The origin of these pacemaker centers is not yet completely understood. This talk will describe a reduced stochastic model for the origin of pacemaker centers (extending the Oregonator of Field, Koros and Noyes) and recent work of the authors (J. Phys. Chem. A. (Letter); 2006; 110; 5-7), which reproduces experimentally observed oxidation states and nucleation rates. [Preview Abstract] |
Thursday, March 8, 2007 4:18PM - 4:30PM |
W30.00010: Classical 2d dynamics simulations of metallic spheres in highly viscous medium Peter Fleck, Alfred Hubler We study the classical dynamics computations of metallic spheres immersed in highly viscous, but weakly conducting medium while exposed to the electro-static field of external electrodes of varying geometries. We represent the system's charge dynamics by the spheres' multipole moments as induced by the electrodes. We theoretically derive the force contributions on an individual sphere including feedback effects, and compare these with results from finite-element computations. We find an individual sphere to oscillate between opposite electrodes only if sufficient charge is retained on the sphere on its path for given material parameters of the medium and distance between the electrodes. We discuss the system's parameter ranges necessary for line arrangements of multiple spheres to emerge. Finally, we compare our computations with an experiment of ballbearings in castor oil. [Preview Abstract] |
Thursday, March 8, 2007 4:30PM - 4:42PM |
W30.00011: Particle-based model of Min-protein oscillations in {\it Escherichia coli} Adam Berman, Kerwyn Huang, Ned Wingreen In {\it Escherichia coli} cells, the Min proteins, which are required for division site selection, oscillate from pole to pole via a Turing instability. During these oscillations, two of the Min proteins, MinD and MinE self-associate and co- associate on the bacterial inner membrane forming dynamic structures including a ring of MinE protein, compact polar zones of MinD, and zebra stripes in filamentous cells. Such rich behavior in a system with so few species has made the Min proteins a model system for applying computational methods to study intracellular dynamics in bacteria. Though mean-field computational models successfully reproduce the coarse-grained oscillatory dynamics in both rod-shaped and round {\it E. coli} cells and also predict that the Min-proteins actively detect cell shape, the mean-field models cannot address questions raised by the recent finding that MinD forms a small number of large polymers on the membrane. First, it is unclear how the intrinsic dynamics of polymer formation, namely polymer nucleation and growth, affect the pole-to-pole oscillations. Second, it is not understood how the oscillations influence the morphology of the MinD polymers. To study this coupling between MinD polymerization and pole-to-pole oscillation, we employ a particle-based computational model. In this talk, we will describe this model, which produces both large polymers and pole-to-pole oscillations. [Preview Abstract] |
Thursday, March 8, 2007 4:42PM - 4:54PM |
W30.00012: Highly nonlinear dynamics in 1D granular metamaterials: anomalous interaction of solitary waves with interfaces Chiara Daraio, Vitali F. Nesterenko, Eric B. Herbold One dimensional chains of uniform beads support the formation and propagation of a new type of highly nonlinear solitary waves with compact support. The interaction of these solitary waves with an interface between two strongly nonlinear discrete granular media results in novel dynamic phenomena. Here we present a detailed study of the behavior of the reflected and transmitted waves at the interface between two media composed of spherical beads with dramatically different elastic properties and the influence of the static precompression on their formation and propagation. The presence of static precompression can be effectively utilized to monitor the information flow through the interfaces. The formation of anomalous waves caused by the selective ability of the media to support compressive or rarefaction stationary pulses is presented for interfaces of various materials and investigated numerically and experimentally. [Preview Abstract] |
Thursday, March 8, 2007 4:54PM - 5:06PM |
W30.00013: Topology of the intermediate state in pinning-free type-I superconductors of different shapes Jacob R. Hoberg, Ruslan Prozorov Equilibrium patterns of the intermediate state were studied in pinning-free Pb samples of different shapes by using direct magneto-optical visualization as well as AC and DC susceptibility measurements. It is found that equilibrium topology of the intermediate state in spheres and hemispheres consists of flux tubes both on flux penetration and exit. Samples with geometric barrier (two flat surfaces perpendicular to an applied magnetic field) exhibit topological hysteresis (and corresponding magnetic hysteresis) -- tubes for flux penetration and Landau laminar structure on flux exit. Finally, obtuse-cone shaped samples show laminar structure both on penetration and exit. Based on the experimental results, general discussion of the equilibrium topology of the intermediate state is given. Video of real-time intermediate state evolution with an applied field for various samples is available at: http://www.cmpgroup.ameslab.gov/supermaglab/video/Pb.html [Preview Abstract] |
Thursday, March 8, 2007 5:06PM - 5:18PM |
W30.00014: Continuum Model for Chaotic Pattern Dynamics on Au Surfaces Sputtered by Focused Ion Beam Kevin Mitchell, Arvin Yazdi, Tom Tiedje Under bombardment by a rastered 30keV Ga$^+$ ion beam, a flat Au surface is found to exhibit the well known sputter ripple instability with a characteristic lateral length scale on the order of 100nm and an RMS saturation height on the order of 10nm. Using {\it in situ} SEM imaging, we are able observe the dynamics of these ripples as they form and evolve. Accurate topography data is also gathered using {\it ex situ} AFM. These experimental data are compared to 2D numerical solutions of the dimensionless partial differential equation $\partial_t{h}=-\nabla^2{h}-\nabla^4{h}-\alpha\left|\nabla{h}\right|^2+\beta\nabla^2\left|\nabla{h}\right|$, which capture the essential features of the sputter ripples. A semi-implicit spectral method is used to solve the equation on a $128\times128$ grid covering a $20(2\pi)\times20(2\pi)$ periodic domain. A length scale near $2\pi\sqrt{2}$, consistent with linearized stability is observed, as is a saturation height of order $1$ when the constraint $\alpha^2+\beta^2=1$ is enforced. Interestingly, the ratio $\alpha/\beta$ is found to control the timescale of the chaotic post-saturation dynamics in addition to fine tuning the length and height scales. [Preview Abstract] |
Thursday, March 8, 2007 5:18PM - 5:30PM |
W30.00015: Degenerate four-wave mixing with defocusing nonlinearity Jason Fleischer, Wenjie Wan, Shu Jia We experimentally demonstrate four-wave mixing (FWM) effects in a defocusing nonlinear photorefractive medium, in both one and two dimensions. By using a rectangular crystal, we observe the nonlinear generation of new (spatial) frequencies as a function of propagation distance. Both position-space and momentum-space images are taken, allowing a detailed study of dynamical energy transfer. For degenerate FWM, consisting of a cos(kx) profile superimposed on a k=0 background, there is a direct energy cascade to higher momenta (smaller spatial scales). For the asymmetric case, sum- and difference-frequency generation leads to complex patterns. In two dimensions, interactions also lead to a change in the spatial geometry. Numerical simulations show excellent agreement with the experimental results. [Preview Abstract] |
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