Bulletin of the American Physical Society
2006 APS March Meeting
Monday–Friday, March 13–17, 2006; Baltimore, MD
Session A8: Pattern Formation and Nonlinear Dynamics |
Hide Abstracts |
Sponsoring Units: DFD GSNP Chair: P. Palffy-Muhoray, Kent State University Room: Baltimore Convention Center 314 |
Monday, March 13, 2006 8:00AM - 8:12AM |
A8.00001: The effects of initial seed size and transients on dendritic crystal growth Andrew Dougherty, Thomas Nunnally The transient behavior of growing dendritic crystals can be quite complex, as a growing tip interacts with a sidebranch structure set up under an earlier set of conditions. In this work, we report on two observations of transient growth of NH$_4$Cl dendrites in aqueous solution. First, we study growth from initial nearly-spherical seeds. We have developed a technique to initiate growth from a well-characterized initial seed. We find that the approach to steady state is similar for both large and small seeds, in contrast to the simulation findings of Steinbach, Diepers, and Beckermann[1]. Second, we study the growth of a dendrite subject to rapid changes in temperature. We vary the dimensionless supersaturation $\Delta$ and monitor the tip speed $v$ and curvature $\rho$. During the transient, the tip shape is noticeably distorted from the steady-state shape, and there is considerable uncertainty in the determination of the curvature of that distorted shape. Nevertheless, it appears that the ``selection parameter'' $\sigma^* = 2 d_0 D / v \rho^2$ remains approximately constant throughout the transient. [1] I. Steinbach, H.-J. Diepers, and C. Beckermann, \textit{J. Cryst. Growth}, \textbf{275}, 624-638 (2005). [Preview Abstract] |
Monday, March 13, 2006 8:12AM - 8:24AM |
A8.00002: Control of eutectic solidification microstructures through laser spot perturbations Silvere Akamatsu, Kyuyong Lee, Wolfgang Losert We report on a new experimental technique for controlling lamellar eutectic microstructures and testing their stability in directional solidification (solidification at fixed rate V in a uniaxial temperature gradient) in thin sample of a model transparent alloy. A eutectic binary alloy solidifies into a mixture of two crystal phases. In stationary regimes, periodic front patterns made of an alternate stacking of lamellae of the two solid phases are observed. We observe the solidification front in real time by optical microscopy. We use micromanipulation with laser spot arrays for perturbing the solidification front on a scale ranging from one to ten times the average value of the lamellar spacing (spatial period), i.e., typically 10 to 100 microns. These perturbations arise from local heating due to the absorption of the laser light by the liquid slightly ahead of the front. We use the laser spot perturbation technique as a tool for mapping out the large range of accessible lamellar spacings at given V and for creating desired patterns (smooth spatial modulation, tilt domains). [Preview Abstract] |
Monday, March 13, 2006 8:24AM - 8:36AM |
A8.00003: Pattern Formation in a NaCl Crystal undergoing Strain-enhanced Dissolution Zvi Karcz, Deniz Ertas, Richard Polizzotti, Einat Aharonov, Chris Scholz Observations of an initially circular contact ($\sim $300$\mu $m in diameter) between the [100] face of a single-crystal NaCl shaped as a truncated cone and a flat silicate plate immersed in saturated solution indicate that the crystal deforms in two sequential stages under constant normal load. The first is characterized by contact area reduction and slow convergence rates, and the second by fluctuations in contact area and fast and fluctuating convergence rates. Fluctuations are on a timescale of $\sim $14 hours. The transition between the stages occurs at the maximum contact stress, which shortly precedes the maximum convergence rate. Confocal images indicate that the crystal dissolves coaxially during the first stage, producing a decreasing static contact. During the second stage, the contact shape is highly irregular, with channels and ridges forming inside the contact. These observations reflect a system evolving towards a non-equilibrium steady state, controlled by the interaction between strain-energy driven undercutting dissolution and plastic flow. Undercutting dissolution reduces the area of the contact, and preferentially removes regions with high dislocation density, while plastic flow increases the contact area by mobilizing dislocations that strain harden the crystal. The feedback between these two mechanisms drives the system towards a dynamic steady state. [Preview Abstract] |
Monday, March 13, 2006 8:36AM - 8:48AM |
A8.00004: Controlled Irradiative Formation of Penitentes Vance Bergeron, Charles Berger, M. D. Betterton Spike-shaped structures are produced by light-driven ablation in very different contexts. Penitentes 1-4 m high are common on Andean glaciers, where their formation changes glacier dynamics and hydrology. Laser ablation can produce cones 10-100 $\mu$m high with a variety of proposed applications in materials science. We report the first laboratory generation of centimeter-scale snow and ice penitentes. Systematically varying conditions allows identification of the essential parameters controlling the formation of ablation structures. We demonstrate that penitente initiation and coarsening requires cold temperatures, so that ablation leads to sublimation rather than melting. Once penitentes have formed, further growth of height can occur by melting. The penitentes intially appear as small structures (3 mm high) and grow by coarsening to 1-5 cm high. Our results are an important step towards understanding and controlling ablation morphologies. [Preview Abstract] |
Monday, March 13, 2006 8:48AM - 9:00AM |
A8.00005: Transient growth and controlled side branching of xenon dendrites Marco Fell, J. H. Bilgram In our experiments we study the influence of transient growth conditions on the growth of xenon dendrites from undercooled melt. Here we report on the response of crystal growth on heating the melt. We start heating at a given temperature and steady-state growth. The dendrite tip reacts on this change by slowing down growth rate $v$ and increasing tip radius $R$. We observe that side branches emerge from an unstable surface. As we continue heating up to slightly above melting temperature, the tip radius continuously decreases to a new value. The reverse temperature change unveils a hysteretic behavior: As soon as we cool down the melt from a temperature tight above melting temperature, $v$ and $R$ both increase. The curvature of the tip becomes too small to be stable at the given undercooling and an instability leads to a new, thin tip growing out of the oversized sphere-like tip. The value $R^2v$ shows a sharp peak and then settles to a constant value in only about 20 seconds. The same instability also gives rise to side branches whose formation can be controlled by a repetitive application of the described mechanisms. Highly symmetric xenon crystals can be grown by this technique. [Preview Abstract] |
Monday, March 13, 2006 9:00AM - 9:12AM |
A8.00006: Late time growth dynamics in the Cahn-Hilliard equation Tmothy S. Sullivan, P. Palffy-Muhoray Numerical simulations were carried out in 2D of the scaled Cahn-Hilliard equation $\left[ {\partial \psi /\partial t=(1/2)\nabla ^2(-\psi +\psi ^3-\nabla ^2\psi )} \right]$ starting from Gaussian distributed, random initial conditions on a 540x540 square grid. Simulations were run for a dimensionless time of 200,000, a factor of ten beyond previously reported results. The simulations also covered a broad range of values of the mean composition, including several at values that had not previously been reported. For each composition and for time intervals of no longer than 5000 in dimensionless time, the structure factor was calculated for sixty separate runs and averaged. The pair correlation function was then calculated from the average structure factor and its first zero crossing,$R_G (t)$, taken as a measure of the average domain size, was determined. An equation of the form $R_G (t)=at^b+c$ was then fit to our data over the dimensionless time range from 5000 to 200,000. In contrast to previous work, we find that the scaling exponent $b$ varies with mean coomposition and does not appear to be consistent with the Lifshitz-Slyozov result $b$ = 1/3. The largest deviation occurs at a mean composition of 0.2, where $b=0.244\pm 0.003$. We discuss the possible effects of morphology on both the scaling law and the time it takes to reach the scaling regime. [Preview Abstract] |
Monday, March 13, 2006 9:12AM - 9:24AM |
A8.00007: Domain Growth in 2D Hexagonal Patterns with Diffuse Interfaces Daniel A. Vega, Leopoldo R. G\'omez, Ricardo J. Pignol The coarsening process in planar patterns has been extensively studied during the last two decades. Although progress has been made in this area, there are still many open questions concerning the basic mechanisms leading the system towards equilibrium. Some of these mechanisms (including curvature driven growth, grain rotation and defect annihilation) have mostly been addressed in systems displaying sharp interfaces. In this work we traced the dynamics of phase separation in hexagonal patterns with diffuse interfaces through the Cahn-Hilliard model. By studying orientational and translational order and densities of topological defects we were able to identify a mechanism of coarsening simultaneously involving curvature driven growth, front propagation and grain rotation. In this regime we found that different correlation lengths characterizing the hexagonal pattern increase logarithmically with time. [Preview Abstract] |
Monday, March 13, 2006 9:24AM - 9:36AM |
A8.00008: Oscillatory patterns near the instability threshold in extended systems with reflection symmetry Alexander Nepomnyashchy, Irina Smagin, Vladimir Volpert, Alexander Golovin It is well known that the envelope function of a modulated traveling wave spontaneously generated by a short-wave instability is governed by a complex Ginzburg-Landau equation (CGLE). Various modulation phenomena, which include the nonlinear development of a modulational instability of periodic waves in the supercritical region, as well as the formation of stable modulated waves in the subcritical region, have been extensively studied in the framework of CGLE. The nonlinear interaction between two waves moving in the opposite directions is described by a system of two non-locally coupled CGLEs that has not been studied in detail yet. We use this system for studying several phenomena related to modulations of standing waves: (i) nonlinear development of a modulational instability; (ii) propagation of defects in standing-wave patterns; (iii) subcritical modulated waves. The results are applied to problems of transverse instabilities of fronts in combustion and explosive crystallization. [Preview Abstract] |
Monday, March 13, 2006 9:36AM - 9:48AM |
A8.00009: Effects of the Deep of Quench on the Mechanisms of Pattern Formation of Sphere Forming Block Copolymers Leopoldo R. G\'omez, Daniel A. Vega, Enrique M. Vall\'es The disorder-order transition of a two dimensional sphere forming block copolymer is studied through the Cahn-Hilliard model at different deeps of quench. The process of microphase separation and kinetic of pattern formation are controlled by the spinodal and order-disorder temperatures. In the spinodal region the deep of quench strongly affect both, ordering times and density of topological defects. As the spinodal temperature is approached, the density of disclination becomes very small and grains show a perfect orientational and translational order. In a narrow region of temperatures the system relax towards equilibrium via the nucleation and growth mechanism. In this region the critical grain size is approximately one lattice constant in the neighborhood of the spinodal line and diverges as the order-disorder temperature is approached. [Preview Abstract] |
Monday, March 13, 2006 9:48AM - 10:00AM |
A8.00010: Feedback Control of Pattern Formation Liam Stanton, Alexander Golovin Global feedback control of spatially-regular patterns described by the Swift-Hohenberg (SH) equation is studied. Two cases are considered: (i) the effect of control on the competition between roll and hexagonal patterns; (ii) the suppression of sub-critical instability by feedback control. In case (i), it is shown that control can change the stability boundaries of hexagons and rolls. Particularly, for certain values of the control parameter, both hexagons and rolls are unstable, and one observes non-stationary patterns with defects. In case (ii), the feedback control suppresses the unbounded solutions of a sub-critical SH equation and leads to the formation of spatially-localized patterns. [Preview Abstract] |
Monday, March 13, 2006 10:00AM - 10:12AM |
A8.00011: Grain boundary stability in stripe configurations of non potential, pattern forming systems Jorge Vinals, Zhi-Feng Huang We describe numerical solutions of nonpotential models of pattern formation in non equilibrium systems to address the motion of grain boundaries separating large domains of stripe configurations. One of the models allows for mean flows. Wavenumber selection at the boundaries, boundary instability, and defect formation and motion at the boundary are described as a function of the distance to onset. [Preview Abstract] |
Monday, March 13, 2006 10:12AM - 10:24AM |
A8.00012: Mesoscale Theory of Grains and Cells: Crystal Plasticity and Coarsening Surachate Limkumnerd, James Sethna Line-like topological defects inside metals are called dislocations. At high temperatures, polycrystalline grains form from the melt and coarsen with time: these dislocations can both climb and glide. At low temperatures under shear the dislocations (which allow only glide) form into cell structures. While both the microscopic laws of dislocation motion and the macroscopic laws of coarsening and plastic deformation are well studied, we have had no simple, continuum explanation for the evolution of dislocations into sharp walls. We present here a mesoscale theory of dislocation motion which provides a quantitative description of deformation and rotation, grounded in a microscopic order parameter field exhibiting the topologically conserved quantities. The topological current of the Nye dislocation density tensor is derived from a microscopic theory of glide driven by Peach-Koehler forces between dislocations using a simple closure approximation. The evolution law leads to singularity formation in finite time, both with and without dislocation climb. Implementation of finite difference simulations using the upwind scheme and the results in one and higher dimensions will be discussed. [Preview Abstract] |
Monday, March 13, 2006 10:24AM - 10:36AM |
A8.00013: Numerical Studies of annular electroconvection in the weakly nonlinear regime Peichun Tsai, Zahir A. Daya, Stephen W. Morris We study 2D electrically-driven convection in an annular geometry by direct numerical simulation. The simulation models a real experiment which consists of a weakly conducting, submicron thick liquid crystal film suspended between two concentric electrodes. The film is driven to convect by imposing a sufficiently large voltage $V$ across it. The flow is driven by a surface charge density inversion which is unstable to the electrical force. This instability is closely analogous to the mass density inversion which is unstable to the buoyancy force in conventional thermally-driven Rayleigh-B{\'e}nard convection. The important dimensionless parameters are a Rayleigh-like number $R$, proportional to $V^2$, a Prandtl-like number $P$, equal to the ratio of the charge and viscous relaxation times, and the radius ratio $\alpha$, characterizing the annular geometry. The simulation uses a pseudo-spectral method with Chebyshev polynomials in the radial direction and Fourier modes in the azimuthal direction. We deduce the coefficient $g$ of the leading cubic nonlinearity in the Landau amplitude equation from the computed amplitude of convection. We investigate the dependence of $g$ on $\alpha$ and $P$ and compare the results to experimental data and to linear and nonlinear theory. [Preview Abstract] |
Monday, March 13, 2006 10:36AM - 10:48AM |
A8.00014: Demodulation of Electroconvective patterns in Nematic Liquid Crystals Gyanu Acharya, Joshua Ladd, J.T. Gleeson, Iuliana Oprea, Gerhard Dangelmayr We present the results of pattern formation in electroconvection of liquid crystal 4-ethyl-2-fluoro-4'-[2-(trans-4-pentylclohexyl)-ethyl]biphenyl(I52) with planar alignment. The pattern was a function of three control parameters: applied ac voltage, driving frequency and electrical conductivity. Over certain range of conductivity, the initial transition (supercritical Hopf bifurcation) leads to right and left traveling zig and zag rolls .For the demodulation of images, Fourier transform (FT) of a time series of images were taken with the sampling rate greater than the Hopf frequency. To demodulate zig/zag rolls, the region around \textbf{k}$_{n }$( the wave vector of a given mode) of interest at one quarter of the FT was taken setting all FTs zero. Taking the index of the maximum FT value at that region as the reference point, again this region was separated into four parts and redistributed at four corners. The absolute value of the inverse FT of the modified function gives the required envelope. [Preview Abstract] |
Monday, March 13, 2006 10:48AM - 11:00AM |
A8.00015: Pattern Formation and Dynamics in Electroconvection of Nematic Liquid Crystals: a Theoretical and Experimental Study of the Weak Electrolyte Model Iuliana Oprea, J.T. Gleeson, Gerhard Dangelmayr Ginzburg Landau formalism is used in the study of electrohydrodynamic convection in a planar layer of nematic liquid crystal based on the weak electrolyte model. Stable wave patterns predicted by weak electrolyte model near a Hopf bifurcation of the basic state are analyzed and bounds for the Eckhaus stability are obtained. The weak electrolyte model, that treats the conductivity as a dynamical variable, is tested by quantitative comparison of experimentally measured and theoretically calculations of specific parameters, such as the recombination rate and charge transport, for the nematic I52. The experimentally observed spatiotemporal chaos evolving at the onset is qualitatively compared with the spatiotemporal chaos obtained in the numerical simulations of the four globally coupled Ginzburg Landau equations describing the dynamics of the amplitudes of the bifurcated patterns. [Preview Abstract] |
Follow Us |
Engage
Become an APS Member |
My APS
Renew Membership |
Information for |
About APSThe American Physical Society (APS) is a non-profit membership organization working to advance the knowledge of physics. |
© 2024 American Physical Society
| All rights reserved | Terms of Use
| Contact Us
Headquarters
1 Physics Ellipse, College Park, MD 20740-3844
(301) 209-3200
Editorial Office
100 Motor Pkwy, Suite 110, Hauppauge, NY 11788
(631) 591-4000
Office of Public Affairs
529 14th St NW, Suite 1050, Washington, D.C. 20045-2001
(202) 662-8700