Bulletin of the American Physical Society
2006 APS March Meeting
Monday–Friday, March 13–17, 2006; Baltimore, MD
Session G8: Patterns and Instabilities II |
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Sponsoring Units: DFD GSNP Room: Baltimore Convention Center 314 |
Tuesday, March 14, 2006 8:00AM - 8:12AM |
G8.00001: Dynamics of Swarms Nicholas Mecholsky, Edward Ott, Tom Antonsen The collective behavior of animal groups (swarms, herds, flocks, etc.) provides a fascinating instance of a self-organizing system. In this poster we consider continuum model descriptions of animal groups with particular emphasis on dynamics and relaxation of the collective behavior of such groups. Topics considered will include equilibrium swarms, waves on swarms, relaxation to equilibrium, excitation of waves by obstacles and predators, and stability. [Preview Abstract] |
Tuesday, March 14, 2006 8:12AM - 8:24AM |
G8.00002: Drying Mediated Pattern Formation in a Capillary-Held Polymer Solution Zhiqun Lin, Jun Xu, Suck Won Hong, Jianfeng Xia We demonstrated that concentric ring patterns of high regularity could form spontaneously, simply by allowing a droplet to evaporate in a consecutive ``stick-slip'' motion in a confined geometry. The process resembled neatly stacked rows of driftwood abandoned by receding tides. The use of solutions with different concentrations and different solvents effectively mediated the evaporative loss of the solvent and the deposition time of the solute, thereby affecting the center-to-center distance between adjacent rings and the height of the ring. A theoretical calculation based on the mass conservation of the solution has, for the first time, been performed to reveal the nature of the formation of gradient ring patterns in a confined geometry. The studies demonstrate that dynamic self-assembly in a confined geometry may offer a new approach to produce gradient features, as well as a simple, versatile, generalizable approach to produce yet more complex patterns. This natural, pattern-forming process could find use in the fields such as nanotechnology and optoelectronics. [Preview Abstract] |
Tuesday, March 14, 2006 8:24AM - 8:36AM |
G8.00003: A network model of channel competition in fracture dissolution Tony Ladd, Piotr Szymczak During dissolution in porous or fractured rock, a positive feedback between fluid transport and chemical reactions at the mineral surfaces may lead to the formation of pronounced, wormhole-like channels. As the dissolution proceeds the channels interact, competing for the available flow, and eventually the growth of the shorter ones ceases. Thus the number of channels decreases with time while the characteristic distance between them increases, which leads to a scale-invariant, power-law distribution of channel lengths. A simple resistor network model of the evolution of dissolving channels is constructed and its properties studied. The results are compared with pore-scale simulations of fracture dissolution using a microscopic, three-dimensional numerical model. Despite its simplicity, the resistor model is found to retain the essential features of the nonlinear interaction between the channels. [Preview Abstract] |
Tuesday, March 14, 2006 8:36AM - 8:48AM |
G8.00004: Fractal growth of liquid crystals as a hysteresis phenomenon Ho-Kei Chan, Ingo Dierking Fractal percolation growth of liquid crystal phases within a supercooled isotropic liquid medium has been observed in recent years. Notable examples include the B2 phase of `banana' mesogens [1] and the smectic C phase of a calamitic hydrogen-bonding liquid crystal [2]. Here we present a dynamical model that describes such fractal growth as well as the spherical growth conventionally observed for nematics and cholesterics. The essential idea is that the supercooled medium does not fully respond to the temperature quench immediately (hysteresis). Its fraction of space available for the phase transition only relaxes from 0 to 1 at some finite rate. Depending on the coupling between the relaxation and growth rates, the liquid crystal phase either grows as a percolation cluster of fractal dimension $D \quad \approx $ 1.89 or approaches a spherical shape of Euclidean dimension $D \to $ 2. The crossover behaviour from relatively slow to fast relaxation is thoroughly investigated. Possible causes of the hysteresis for fractal growth will be discussed. \newline \newline [1] I. Dierking, Liq. Cryst. Today \textbf{12(1)}, (2003), 1 \newline [2] I. Dierking, Chan H. K., Culfaz F., McQuire S., Phys. Rev. E \textbf{70}, (2004), 051701 [Preview Abstract] |
Tuesday, March 14, 2006 8:48AM - 9:00AM |
G8.00005: Patterns in type-I superconductors and their dynamics Rinke J. Wijngaarden, Mariela Menghini We report on patterns and their dynamics as observed in magneto- optical experiments on type-I superconductors. We observe: (1) A stripe-spot transition that is hysteretic, leading to two modes of stripe formation: slow continuous growth and avalanche growth. (2) A wiggling instability, similar to that in ferrimagnetic garnet films. (3) A zigzag instability when a pattern of parallel lines is rotated through a sample with low pinning. (4) Breaking and reconnection of stripes as such a pattern is rotated in a sample with strong pinning. (5) Random telegraph behavior close to the depinning of such pattern in the presence of a constant driving force. The observed patterns consist of superconducting and normal domains of macroscopic size in thin lamina of type-I superconductors and are observed by an advanced magneto-optical technique. The patterns are manipulated by changing the applied magnetic field vector or by applying an electrical transport current. [Preview Abstract] |
Tuesday, March 14, 2006 9:00AM - 9:12AM |
G8.00006: Scaling in activated escape of underdamped systems Ira Schwartz, Mark Dykman, Michael Shapiro Noise-induced escape from potentials is ubiquitous in many areas of physics. Here, noise-induced escape from a metastable state of a dynamical system is studied close to a saddle-node bifurcation point, but in a region where the system remains underdamped. We find the activation energy of escape scales as a power of the distance to the bifurcation point. Moreover, we find two types of scaling and the corresponding critical exponents. [Preview Abstract] |
Tuesday, March 14, 2006 9:12AM - 9:24AM |
G8.00007: The Analysis of Spatiotemporal Chaos in Very Large Data Sets Generated by Electroconvective Experiments with Nematic Liquid crystals Joshua Ladd, Gyanu Acharya, J.T. Gleeson Spatiotemporal chaos (STC) has been empirically observed in electrohydrodynamic convection in a planar layer of the nematic liquid crystal I52. The observed spatiotemporal dynamics is due to the interaction of two families of counter propagating waves that loose stability at onset. Thus it is possible to describe the patterns through a system of Ginzburg --Landau equations that governs the evolution of the envelopes of these waves (\textit{Denin et al, Science 1996)}. In this work we extract the envelopes from spatiotemporal data generated by electroconvective experiments done at Kent State University using a demodulation procedure. Once obtained it is possible to separate spatial and temporal components of the dynamics by employing the singular value decomposition. This is done in order to study the chaotic nature of the pattern. Comparison is made with numerical STC obtained from computer simulations of the Ginzburg-Landau system derived from the weak electrolyte model (\textit{Dangelmayr {\&} Oprea, 2002) }of electroconvection. [Preview Abstract] |
Tuesday, March 14, 2006 9:24AM - 9:36AM |
G8.00008: Pattern formation in liquids under unipolar space charge injection Francisco Vega Reyes, Francisco J. Garcia We study experimentally the hydrodynamic stability of thin liquid layers subjected to corona discharge in the air. We obtain clear direct images and movies of the observed hydrodynamic instabilities and patterns. After this we apply an image processing method that allows us to quantify the liquid interface deformation. We use a variety of liquids whose properties may differ in orders of magnitude. Particularly, we use series of liquids with different electric conductivity or viscosity while keeping constant the rest of the properties. In this way, we can track quantitatively the instabilities as a function of only one of these properties. This, together with our image processing method, allows us to study and classify the different instabilities. The peculiar properties of the electric field in the liquid interface when there is a space charge injection have not been studied until very recently. Results show clearly the influence (and relevancy) that the properties of this electric field have in the formation (or not) of the different patterns observed when the liquid properties are varied. [Preview Abstract] |
Tuesday, March 14, 2006 9:36AM - 9:48AM |
G8.00009: Path stability of a rising bubble Binze Yang, Andrea Prosperetti A millimeter-size gas bubble rises in a zigzag or spiral path in still water. A linear analysis of this process is presented assuming that the bubble has a fixed ellipsoidal shape of varying aspect ratio. The results exhibit a strong similarity to the stability features of the flow past a solid sphere. By focusing on the $m$ = 1 azimuthal mode, it is found that a double-threaded wake responsible for the deviation from the vertical path develops when the aspect ratio is sufficiently large. The stability analysis of ``frozen'' states before steady conditions are achieved shows that the amount of vorticity accumulated at the rear of the bubble plays an essential role for the instability. It is also shown that, in the common parameter ranges of interest, the instability is very sensitive to the deformation of the bubble, but relatively insensitive to the Reynolds number. [Preview Abstract] |
Tuesday, March 14, 2006 9:48AM - 10:00AM |
G8.00010: Flame Propagation with Hydrodynamic and Body-Force Instabilities Kuo-Long Pan The hydrodynamic (Darrieus-Landau) instability is an intrinsic mechanism that wrinkles the flame surface. In the nonlinear stage, propagation of flame wrinkles can evolve to a quasi-stable state characterized by a solitary wave or chaotic form with corrugated front. The underlying structures, i.e. incessant merging of near wrinkles and creation of new cells, have been studied numerically. It reveals the significance of asymmetric perturbation in breaking the symmetry. The effect of gravity was also investigated. It was found that, while wrinkled flames can be stabilized by negative gravity of moderate magnitude, the wrinkles at short wavelength, \textit{$\lambda $}, remains intact if the magnitude is small while those at long \textit{$\lambda $ }are suppressed. As such, compared to the zero-gravity state, diminishing multiplicity of cellular scales and subsequently decreasing interactions among the multi-scale wrinkles mollify the chaotic complication. When slight positive gravity is introduced, the unsteady evolution is suppressed. The somehow stabilizing effect, while in contrast to the destabilization at linear stage, is due to the coupling of D-L instability and Rayleigh-Taylor instability that prevents excitation of secondary D-L instability. If the magnitude is strong enough, however, the ordered pattern degenerates and highly irregular flame surface is formed without specific cell structure. This is a typical appearance of R-T instability caused by buoyancy. [Preview Abstract] |
Tuesday, March 14, 2006 10:00AM - 10:12AM |
G8.00011: Numerical Simulation of Conductivity Gradient-Induced Electrokinetic Flow Instabilities Stephen Bradford, Carl Meinhart This research is focused on the electrokinetic flow instabilities observed in long, thin microchannels with conductivity gradients orthogonal to the streamwise direction and applied potential. This situation often occurs in field amplified sample stacking (FASS) and isoelectric focusing, where control of the instabilities is imperative. Alternatively, the inherently chaotic flow patterns can be leveraged to fabricate an efficient micromixer under specific conditions. These instabilities arise from fluid body forces generated by the action of applied electric fields on electrolyte concentration-based conductivity gradients. A model is developed to describe the phenomena in general and applied specifically to thin microchannels with the conductivity gradient perpendicular to the applied field (both DC and AC). A higher-order, depth averaged correlation is proposed to account for the out of plane effects. Numerical simulations performed using COMSOL 3.2 are compared to 2-D and 3-D simulations as well as experimental data for multiple geometries with good agreement. [Preview Abstract] |
Tuesday, March 14, 2006 10:12AM - 10:24AM |
G8.00012: Particle production in non-dissipative shock-waves Alexander Abanov, Fabio Franchini We study non-dissipative shock-waves in the effective hydrodynamics of some correlated one-dimensional integrable systems. The semiclassical dynamics of these systems is governed by integrable non-linear classical equations such as the Benjamin-Ono and the KdV equations. The development of non- dissipative shock-waves from a large disturbance of the fluid is described by Gurevich-Pitaevsky theory. The theory describes how the instability of a large disturbance of the fluid is resolved by producing oscillations which develop into a train of solitons at large times. We establish the connection between this classical picture and the production of quasi-particles in the underlying quantum system. The semiclassical (background) configuration can then be thought of as an effective metric in which these excitations move. This approach is done in the spirit of the original proposal of Unruh, who suggested to model the Hawking radiation from black holes by an emission of thermal sound waves from the sonic horizon in transsonic fluid flow. [Preview Abstract] |
Tuesday, March 14, 2006 10:24AM - 10:36AM |
G8.00013: Torsional Motion of Rotating Particles with Graded Couplings H.W. Tsang, J.J. Xiao, K.W. Yu Localization of excitations occurs in many physical systems. There are two common types of localization. The first type is a consequence of interference of coherent vibrational waves due to diffusive scattering like Anderson localization in lattice vibration. The other type of localization is due to confinement by impurities like defect modes. Graded systems occur in a variety of physical system. It is of great interest to analyze the localization of excitations in graded system [1]. In this work, we consider a system of rotating particles with graded torsional couplings. The steady-state solutions are solved directly from the dynamic equations. Energy is localized in the region of stronger couplings at high frequencies. A dynamic stimulation based on forced rotors is performed both for the graded linear and graded non-linear coupling potential subjected to a sinusoidal driving torque. In the small amplitude region, the results of non-linear potential are similar to those of the linear ones. The major difference is that the rotational amplitude is larger for the non-linear potential. Energy transfer may thus be more effective in the non-linear case. In the large amplitude region, chaos may occur and contribute to the localization. \newline [1] J. J. Xiao, K. Yakubo, and K. W. Yu, Harmonic vibrational excitations in graded elastic networks: transition from phonons to gradons, unpublished. [Preview Abstract] |
Tuesday, March 14, 2006 10:36AM - 10:48AM |
G8.00014: Numerical simulations of inertial migration in a square duct: An investigation of multiple equilibrium positions Byoungjin Chun, Tony Ladd In Poiseuille flow, a neutrally-buoyant particle migrates to a position that is determined by the balance of forces generated by the gradient of the shear rate and interactions of the flow field with the container walls. In a cylindrical flow, uniformly distributed particles migrate to form a stable ring located at approximately 0.6 times the cylinder radius. However, recent experiments show two interesting new observations. First the suspended particles tend to align near the walls to make linear chains of more or less equally-spaced particles, and second, at high Reynolds numbers (Re ~ 1000), an additional inner ring of particles is formed. The inner ring is only formed when the particle are large, of the order of 1:10 the cylinder diameter. We have used numerical simulations based on the lattice-Boltzmann method to investigate inertial migration of neutrally buoyant particles in a square duct over a range of Reynolds numbers from 100 to 1000. Our results show trains of particles being formed along the axis of the flow, near the planar equilibrium positions of single particles. At Reynolds number greater than 750, particles appear near the center of the duct as well. We will present a new mechanism to interpret and understand these results, which was discovered by examining the migration of single particles and rigid dumbbells. [Preview Abstract] |
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