Bulletin of the American Physical Society
2008 APS March Meeting
Volume 53, Number 2
Monday–Friday, March 10–14, 2008; New Orleans, Louisiana
Session B9: Pattern Formation and Nonlinear Dynamics |
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Sponsoring Units: GSNP Chair: Vladimir Privman, Clarkson University Room: Morial Convention Center RO7 |
Monday, March 10, 2008 11:15AM - 11:27AM |
B9.00001: Intermediate State in Type-I Superconducting Strip with Current Jacob Hoberg, Ruslan Prozorov The dynamic structure of the intermediate state was studied in pinning-free Pb strips using real-time magneto-optical visualization. It is found that topological hysteresis can be lifted by applying sufficiently large current. Namely, laminar structure that appears on flux exit in a static case is turned into tubular when the current is present. Temperature, magnetic field and current phase diagram is discussed. [Preview Abstract] |
Monday, March 10, 2008 11:27AM - 11:39AM |
B9.00002: Generation of dynamic self-propelled structures by symmetry breaking mechanism in driven magnetic layers on the surface of liquid Alexey Snezhko, Maxim Belkin, Igor Aranson Magnetic particles suspended over the surface of a liquid and energized by a vertical alternating magnetic field give rise to remarkable dynamic multi-segment magnetic structures (``snakes''). These structures (dynamic by nature) are directly related to surface waves in the liquid generated by the collective response of magnetic microparticles to the alternating magnetic field. The self-assembly process and existence of the magnetic snakes is accompanied by a generation of strong surface flows in the liquid. Properties of the snake and corresponding surface flows could be tuned by the parameters of the external magnetic driving. We demonstrate that above some critical frequency threshold magnetic snakes lose their stability and start to swim in the container. The effect is attributed to the development of symmetry breaking instability of the structure with respect to self-generated surface flows in the liquid. Parameters of the driving magnetic field are effectively used to control rich behavior of the dynamic magnetic swimmers. [Preview Abstract] |
Monday, March 10, 2008 11:39AM - 11:51AM |
B9.00003: Collective dynamics and pattern formation in 2D regular arrays of spherical particles in Stokes flow between two parallel walls Jerzy Blawzdziewicz, Eligiusz Wajnryb, Matthew Baron, Nidhi Khurana We present results of our numerical and theoretical investigations of collective dynamics of linear trains and regular square arrays of spherical particles suspended in a fluid bounded by two parallel walls. The simulations reveal propagation of particle-displacement waves, deformation and rearrangements of a particle lattice, propagation of dislocation-like defects in ordered arrays, and transitions between ordered and disordered regions that can coexist for a long time. We argue that ordered motion of the arrays is associated with the dipolar form of the quasi-2D asymptotic far-field flow produced by the particles. We also show that the overall deformation of the arrays can be described using a macroscopic theory where the array is treated as a 2D effective medium. The theory predicts a fingering instability near the array corners, and this instability is confirmed by our microscopic simulations. [Preview Abstract] |
Monday, March 10, 2008 11:51AM - 12:03PM |
B9.00004: Theory of slope-dependent disjoining pressure with application to Lennard-Jones liquid films Taeil Yi, Harris Wong A liquid film of thickness h $<$ 100 nm is subject to additional intermolecular forces, which are collectively called disjoining pressure P. Since dominates at small film thicknesses, it determines the stability and wettability of thin films. Current theory derived for uniform films gives P=P(h). This solution has been applied recently to non-uniform films and becomes unbounded near a contact line as h-$>$0. Consequently, many different effects have been considered to eliminate or circumvent this singularity. We present a mean-field theory of that depends on the slope as well as the height h of the film.[1] When this theory is implemented for Lennard-Jones liquid films, the new P=P(h,hx) is bounded near a contact line as h-$>$0. Thus, the singularity in P(h) is artificial because it results from extending a theory beyond its range of validity. We also show that the new can capture all three regimes of drop behavior (complete wetting, partial wetting, and pseudo partial wetting) without altering the signs of the long and short-range interactions. We find that a drop with an unbounded precursor film is linearly stable.1] Wu {\&} Wong, J. Fluid Mech. \underline {506}, 157 (2004)2] Yi {\&} Wong, J. Colloid Inter. Sci. \underline {313}, 579 (2007) [Preview Abstract] |
Monday, March 10, 2008 12:03PM - 12:15PM |
B9.00005: The effects of chaotic mixing on patterns and fronts in an advection-reaction-diffusion system Tom Solomon, Jeffrey Boehmer We present experimental studies of the effects of fluid flows on reaction fronts and spatial patterns in the excitable Belousov- Zhabotinsky reaction. The flow is a square array of vortices, generated using magnetohydrodynamic techniques. Time-dependent forcing of the flow is achieved by displacing the fluid periodically in a circular manner relative to the vortex flow. Mixing of passive impurities in this flow is chaotic, with long- range transport that is typically diffusive (enhanced), although superdiffusion with L\'evy flights is also possible. Reaction fronts in this flow show small-scale patterns that reflect the stable and unstable manifolds that characterize chaotic mixing in this flow. Even on a larger scale, front structure reflects the underlying anisotropy of the vortex lattice. In many cases, the front mode-locks to the external forcing, lining up with the vortex array in a self-correcting manner. Self-generating trigger waves are also found in this system, producing both spiral and target patterns similar to those found in reaction- diffusion systems. [Preview Abstract] |
Monday, March 10, 2008 12:15PM - 12:27PM |
B9.00006: Spatial Forcing in Thermal Convection Gabriel Seiden, Stephan Weiss, Eberhard Bodenschatz An intrinsic characteristic of thermal convection is the preference of a particular wavenumber at onset. This fact renders experimental investigations of different important aspects, such as the exploration of phase space, difficult. The main tool employed to overcome this difficulty is spatial forcing, whereby, using external means, one forces a desired pattern and observes the evolution of the system thereafter. We present results on topologically and optically induced modulations of large aspect ratio isotropic (horizontal) and anisotropic (inclined layer) Rayleigh-B\'{e}nard convection. These include detailed bifurcation curves and phase diagrams for different forcing scenarios. [Preview Abstract] |
Monday, March 10, 2008 12:27PM - 12:39PM |
B9.00007: Renormalization group method for predicting frequency clusters in a chain of nearest-neighbor Kuramoto oscillators. Oleg Kogan, Gil Refael, Michael Cross, Jeffrey Rogers We develop a renormalization group (RG) method to predict frequency clusters and their statistical properties in a 1-dimensional chain of nearest-neighbor coupled Kuramoto oscillators. The intrinsic frequencies and couplings are random numbers chosen from a distribution. The method is designed to work in the regime of strong randomness, where the distribution of intrinsic frequencies and couplings has long tails. Two types of decimation steps are possible: elimination of oscillators with exceptionally large frequency and renormalization of two oscillators bonded by a very large coupling into a single one. Based on these steps, we perform a numerical RG calculation. The oscillators in the renormalized chain correspond to frequency clusters. We compare the RG results with those obtained directly from the numerical solution of the chain's equations of motion. [Preview Abstract] |
Monday, March 10, 2008 12:39PM - 12:51PM |
B9.00008: Pattern morphology and dynamical scaling in the Cahn Hilliard model Timothy Sullivan, Pushkar Dahal, Peter Palffy-Muhoray Numerical simulations were carried out in two-dimensions of the dimensionless Cahn-Hilliard equation. Simulations were run for a factor of ten in time beyond previously reported results. The simulations also covered a broad range of values of the mean composition,$\left\langle \psi \right\rangle _0 $. To determine the dynamical scaling exponent, $b,$ an equation of the form $R_G (t)=at^b+c$ was fit to a measure of average domain size. In contrast to previous results, we found that $b$ varied substantially with$\left\langle \psi \right\rangle _0 $. The largest deviation from the Lifshitz-Slyozov value of 1/3 occurred at $\left\langle \psi \right\rangle _0 =0.15$, where $b=0.221\pm 0.04$. We used a measure of the non-circularity of minority domains to show that for $\left\langle \psi \right\rangle _0 \mathbin{\lower.3ex\hbox{$\buildrel<\over {\smash{\scriptstyle\sim}\vphantom{_x}}$}} 0.20$ the domain shapes are not scale invariant for times exceeding our simulation times. We also point out the possible existence of a phase boundary $\left\langle \psi \right\rangle _{0,c} $that separates a phase with circular domains of minority component from a phase with non-circular minority component domains. [Preview Abstract] |
Monday, March 10, 2008 12:51PM - 1:03PM |
B9.00009: Experimental Evidence for Mixed Reality States Vadas Gintautas, Alfred Hubler We present experimental data on the limiting behavior of an inter-reality system: a virtual pendulum with a bi-directional instantaneous coupling to its real-world counterpart [Gintautas \& Hubler, Phys.Rev.E 75, 057201 (2007)]. The data show that if the physical parameters of the simplified virtual system are close to the parameters of the real system, there is a phase transition from an uncorrelated dual reality state to a mixed reality state in which the motion of the two pendulums is highly correlated. As virtual systems better approximate real ones, even weak couplings in inter-reality systems may induce sudden transitions to mixed reality states. This phenomenon may be typical for systems with instantaneous coupling and was recently featured on the tip sheet of the American Physical Society [http://www.aps.org/about/tipsheets/tip68.cfm ]. We show that mixed reality states in physical systems are related to out-of- body experiences of humans in 3D-video feedback systems [H. H. Ehrsson, The Experimental Induction of Out-of-Body Experiences. Science 317, 1048 (2007)]. [Preview Abstract] |
Monday, March 10, 2008 1:03PM - 1:15PM |
B9.00010: Classical dynamics simulations on pattern formation by metallic spheres with induced electrostatic interactions Peter Fleck, Alfred Hubler We study classical dynamics simulations of metallic spheres immersed in a highly viscous, but weakly conducting medium while exposed to the electrostatic field of external electrodes of various geometries. We represent the system's charge dynamics by the spheres' multipole moments as induced by the electrodes. We simulate the sphere dynamics for various particle numbers retaining force contributions up to dipole-dipole order. Besides the electrodes' location and the spheres' initial positions, we find the system's dynamics to be governed by the ratio of a spheres motion time scale and a charge dynamics time scale alone. We find the spheres to form line arrangements between opposing electrodes for an important region of parameter space. We determine the phase boundaries of this line formation behavior in the sphere dynamics simulations. We find the phase diagram to be in good agreement with analytical predictions. [Preview Abstract] |
Monday, March 10, 2008 1:15PM - 1:27PM |
B9.00011: Hopping Conduction and Bacteria: Transport Properties of Disordered Reaction-Diffusion Systems Andrew Missel, Karin Dahmen Reaction-diffusion (RD) systems are used to model everything from the formation of animal coat patterns to the spread of genes in a population to the seasonal variation of plankton density in the ocean. In all of these problems, disorder plays a large role, but determining its effects on transport properties in RD systems has been a challenge. We present here both analytical and numerical studies of a particular disordered RD system consisting of particles which are allowed to diffuse and compete for resources ($2A\to A$) with spatially homogeneous rates, reproduce ($A\to2A$) in certain areas (``oases''), and die ($A\to0$) everywhere else (the ``desert''). In the low oasis density regime, transport is mediated through rare ``hopping events'' in which a small number of particles diffuse through the desert from one oasis to another; the situation is mathematically analogous to hopping conduction in doped semiconductors, and this analogy, along with some ideas from first passage percolation theory, allows us to make some quantitative predictions about the transport properties of the system on a large scale. [Preview Abstract] |
Monday, March 10, 2008 1:27PM - 1:39PM |
B9.00012: Efficient Desalination with Fractal Absorbers Martin Singleton, Gregor Heiss, Alfred Hubler A class of Ramified graphs (RG) is introduced as Iterated Function Systems (IFS) to optimally design networks for efficient reverse osmosis desalination in deep seawater. Different forms of the IFS are presented, along with a corresponding contractivity factor $s_c,$ in order to identify the attractors of the systems and their fractal dimension. Using the analogy to electrostatics, the diffusion equation is solved for the desalination systems under three different boundary conditions, i) all nodes having the same pressure difference across the absorbers, ii) all nodes producing permeate at identical rates, and iii) each node having the same salt node strength. Optimal branching angles and branch length ratios are found by phase-space and discrete simulated annealing search techniques for each boundary condition, which either maximize production of permeate or minimize expenditure of energy for different fixed numbers of absorbers. Dependence of desalination recovery ratios on the geometry and fractal dimension of the RG is also explored. [Preview Abstract] |
Monday, March 10, 2008 1:39PM - 1:51PM |
B9.00013: Static and Dynamical Properties of Polar Fluids Girija S. Dubey Molecular dynamics simulations are reported for a system whose pair potential can be separated as the sum of a Lennard-Jones term and a dipole-dipole interaction. The simulations were done for a chosen value of electric dipole moment and for a set of temperatures. Chain formation is observed when the potential is dipolar as well as when both terms are included. However. our simulation shows some differences in the pattern formation of the chains. [Preview Abstract] |
Monday, March 10, 2008 1:51PM - 2:03PM |
B9.00014: Statistical Light in Nonlinear Media as Photonic Plasma Dmitry Dylov, Jason Fleischer We consider the nonlinear propagation of partially-spatially-incoherent light as a photonic plasma. Using wave-kinetic theory and Wigner formalism, we interpret the speckles of statistical light as quasi-particles which can interact via the nonlinearity. We analytically derive a Bohm-Gross dispersion relation for these speckles and their Langmuir-type interaction waves, and identify an effective plasma frequency, effective Debye length, etc. Experimentally, we demonstrate this mapping by studying the nonlinear propagation of diffused light in a self-focusing photorefractive crystal. Observed phenomena include modulation instability, two-stream and bump-on-tail instabilities, wave collapse and optical turbulence. By recording a hologram of the internal dynamics, we observe speckle-wave and wave-wave interactions, in both position (x) space and momentum (k) space. The results generalize ideas from plasma physics, lead to new wave dynamics in nonlinear statistical optics, and allow the experimental study of phenomena that are difficult, if not impossible, to observe in material plasma. [Preview Abstract] |
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