Bulletin of the American Physical Society
APS March Meeting 2013
Volume 58, Number 1
Monday–Friday, March 18–22, 2013; Baltimore, Maryland
Session R39: Pattern Formation and Nonlinear Dynamics |
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Sponsoring Units: DFD Chair: Gregory Eyink, Johns Hopkins University Room: 348 |
Wednesday, March 20, 2013 2:30PM - 2:42PM |
R39.00001: The Peierls Transport Equation --- Revised Yi-Kang Shi, Gregory Eyink In 1929 Peierls derived an equation for the joint probability distribution of all wave amplitudes in classical and quantum anharmonic systems, still widely used in quantum transport theory, plasma physics and weak wave turbulence. For uncorrelated amplitudes, it implies the kinetic equation for the wave spectrum/occupation numbers. This equation was rederived by Brout \& Prigogine (1956), Zaslavskii \& Sagdeev (1967), and recently by Choi et al. (2005) in wave turbulence. We show that these derivations are non-systematic, retaining terms smaller than those neglected. We obtain an equation simpler than Peierls', which still implies the kinetic equation and also a generalized kinetic equation for the distribution of single-mode amplitudes, previously obtained by Choi et al. We show by an H-theorem that the single-mode distributions approach Gaussian, if this equation is valid for all amplitudes. Non-Gaussian statistics can arise if the equation breaks down for large amplitudes/strong nonlinearity. This may explain intermittency observed in laboratory experiments of weak turbulence. Moreover, we show the most general solutions of our revised Peierls equations are statistical ensembles of chaotic solutions of kinetic equations, or ``super-turbulence'', another source of intermittency. [Preview Abstract] |
Wednesday, March 20, 2013 2:42PM - 2:54PM |
R39.00002: Controlling the position of traveling fronts Jakob L\"{o}ber, Harald Engel, Eckehard Sch\"{o}ll We present a method to control the position as a function of time of a one-dimensional traveling front solution of a one-component reaction-diffusion system according to a specified protocol of movement. Given this protocol, the control function is found as the solution of a perturbatively derived integral equation. Two cases are considered. First, we derive an analytical expression for the space $(x)$ and time $(t)$ dependent control function $f\left(x,t\right)$ valid for arbitrary protocols and arbitrary bistable reaction kinetics. These results for the control agree well with results of an optimal control algorithm. Second, for stationary control the integral equation reduces to a Fredholm integral equation of the first kind. For the Schl\"{o}gl model, we present an analytical solution of the problem to stop a front at a specified position. All analytical results are in good agreement with numerical simulations of the underlying reaction-diffusion equations. Extensions to two spatial dimensions and other equations supporting traveling wave solutions are considered. [Preview Abstract] |
Wednesday, March 20, 2013 2:54PM - 3:06PM |
R39.00003: Experimental studies of stationary reaction fronts in a chain of vortices with imposed wind Tom Solomon, Carleen Boyer We present experiments that study the behavior of the excitable Belousov-Zhabotinsky (BZ) reaction in a chain of alternating vortices with an imposed uniform wind. Previous experiments\footnote{M.E. Schwartz and T.H. Solomon, Phys. Rev. Lett. {\bf 100}, 028302 (2008).} have shown that fronts in this system are pinned for a wide range of imposed wind speeds, propagating neither forward against the wind nor in the downwind direction. We explain this behavior with a recent theory\footnote{J. Mahoney, D. Bargteil, M. Kingsbury, K. Mitchell and T. Solomon, Europhys. Lett. {\bf 98}, 44005 (2012).} that proposes the existence of {\em burning invariant manifolds} (BIMs) that act as local barriers to front propagation. Fronts are pinned when a BIM or a combination of BIMs spans the width of the vortex chain, blocking the reaction front. We show experimental measurements of the shape of the pinned front for a range of different wind speeds, and compare these shapes to the BIMs calculated theoretically. We also consider the dependence of the front shape on the location of the initial trigger for the front. [Preview Abstract] |
Wednesday, March 20, 2013 3:06PM - 3:18PM |
R39.00004: Pinning of reaction fronts by burning invariant manifolds in spatially-disordered fluid flows Maya Najarian, Tom Solomon We present experiments on the pinning of reaction fronts in spatially-disordered fluid flows with an imposesd wind. The disordered flow is driven by a magnetohydrodynamic forcing technique, and there is a uniform wind imposed on the flow with the use of a translation stage. Reaction fronts are produced using the excitable Belousov-Zhabotinsky chemical reaction. For a wide range of wind speeds, a complicated stationary front forms, pinned to the underlying vortex flow, neither propagating forward against the wind nor being blown backwards. The shape of the front depends significantly on the magnitude of the imposed wind. We propose that the shape of the stationary front is determined by a collection of overlapping BIMs that act as barriers against forward movement of the reaction front. The location of the BIMs can be predicted by integrating a three-dimensional set of ordinary differential equations\footnote{J. Mahoney, D. Bargteil, M. Kingsbury, K. Mitchell and T. Solomon, Europhys. Lett. {\bf 98}, 44005 (2012).} that describes the dynamics of an element of an evolving reaction front in the fluid flow. [Preview Abstract] |
Wednesday, March 20, 2013 3:18PM - 3:30PM |
R39.00005: Laboratory Scale Simulating of Strange Spiral Plumes in Fluid with Hight Ptandtl Number Albert Sharifulin, Anatoly Poludnitsin We experimentally investigated the appearance of a plumes from local hot spot and study its interaction with cellular flow in closed cavity filled by silicon oil with Prandtl number $\Pr \approx 2\cdot 10^{3}$. Convective plume generated by a local heat source, located on the top of the small rubber cylinder, which is located in the center of the bottom of the rectangular cell. To simulate the hot-spot green laser has been used. Roll-type large-scale convective flow was generated by heating of the one vertical sides of cavity. Influence of power of hot point on the shape of plume has been investigated. It is shown that the presence of cellular convective motion may lead to the formation of a strange spiral convective plume. This plume looks like Archimedes spiral replaced on vertical plane. Physical mechanism of the formation of strange spiral plume and application of obtained results for mantle convection problems are discussed. [Preview Abstract] |
Wednesday, March 20, 2013 3:30PM - 3:42PM |
R39.00006: Double-diffusive layers adjacent to cold chimney flows during transient mushy-layer growth Jin-Qiang Zhong, Qiwei Xue, John Wettlaufer We examine the cooling effect of chimney flows in the liquid region during transient upward growth of a mushy layer in solidifying aqueous ammonium chloride. Through drainage channels in a mushy layer, cold, relatively fresh fluid is carried into the warm, salt-stratified liquid region. Double-diffusive cells form due to the cooling effect of the chimney flows and evolve into a series of downwelling horizontal layers. Using shadowgraph methods and dyed fluids we demonstrate the vigorous flow circulations and compositional mixing within each layer. Vertical concentration and temperature profiles reveal the double-diffusive staircase structure across the layers. The downward velocity of the layers decreases as they approach to the mush-liquid interface, which is interpreted by a filling-box model representing the momentum and compositional transport of turbulent continuous plumes in a confined region. The present experiment provides insight to evaluate the solute fluxes from growing mushy layers. [Preview Abstract] |
Wednesday, March 20, 2013 3:42PM - 3:54PM |
R39.00007: Connectivity-disorder effect on collective synchronization Jaegon Um, Hyunsuk Hong, Hyunggyu Park We investigate a system of random frequency oscillators coupled through sparse random networks and explore connectivity-disorder effects on collective synchronization. In particular, we pay attention to how the random quenched disorder in connectivity affects the nature of synchronization transitions. The oscillator frequencies are assigned independently from an unimodal, bimodal, or uniform distribution. Extensive numerical simulations as well as the mean-field analysis have been performed on Erd{\"o}s-R{\'e}nyi random networks. We find that the quenched connectivity disorder invalidates the mean-field prediction of distinctive transition natures depending on frequency distributions in random networks. In fact, the same continuous synchronization transition is found for all types of frequency distributions. The physical origin of this unexpected result is discussed. [Preview Abstract] |
Wednesday, March 20, 2013 3:54PM - 4:06PM |
R39.00008: Geometry of branching stream networks Hansjorg Seybold, Robert Yi, Alex Petroff, Olivier Devauchelle, Daniel Rothman River networks have been a source of fascination for centuries. Yet, how these networks form and create these geometries remains elusive. Recently we have shown that streams branching in a diffusive field bifurcate at a characteristic angle of $\alpha=2\pi/5=72^\circ$. This result is obtained from Lowner dynamics by combining classical results of groundwater hydrology with the hypothesis that streams grow in the direction of maximal water flux into the channel's tip. Our theoretical results are umambigously consistent with field measurements we conducted in a 100 km$^2$ channel network on the Florida Panhandle. Here we extend our theory to include slope effects and apply our analysis to large drainage basins. We hypothesize that the extension of the network at the tip is driven by a diffusive process leading to a (slope corrected) $2\pi/5$ branching at the leaves of the network. [Preview Abstract] |
Wednesday, March 20, 2013 4:06PM - 4:18PM |
R39.00009: Absence of power-law scaling in the dendritic crystal growth of ammonium chloride Andrew Dougherty We report measurements of the dendritic crystal growth of NH$_4$Cl from supersaturated aqueous solution at small supersaturations, with a goal of understanding the origin of the sidebranching structure. The early detection of sidebranches requires measurements of small deviations from the smooth steady state shape, but that underlying shape is not precisely known at the intermediate distances relevant for sidebranch measurements. We find that no simple power law describes the average crystal shape, the average sidebranch amplitude, or the average sidebranch envelope. Instead, the effective power law exponents appear to increase steadily as a function of distance from the dendritic tip. Comparisons of the amplitude of sidebranches with that predicted by models of noise-driven sidebranching require careful measurements of materials parameters such as the capillary length. Previous published estimates for this material varied by over a factor of 20. We report new measurements of the capillary length and find $d_0 = 0.224 \pm 0.005\;$nm. Based on those new measurements, we find that the amplitude of the sidebranches in this system is larger than expected from numerical models. [Preview Abstract] |
Wednesday, March 20, 2013 4:18PM - 4:30PM |
R39.00010: ABSTRACT WITHDRAWN |
Wednesday, March 20, 2013 4:30PM - 4:42PM |
R39.00011: Multistable dynamics in electroconvecting liquid crystals Zrinka Greguric Ferencek, John Cressman Nonlinear driven system can exhibit a diverse range of dynamics, from highly ordered to chaotic. These systems are ubiquitous, from atmospheric phenomena to brain function. Here we study such dynamics in electroconvecting liquid crystals. There applied electric fields create structured roll-like patterns that support the creation, evolution, and annihilation of defects in the rolls. By using a time scale separation algorithm based on diffusion map delay coordinates we have been able to identify a small number of multistable dynamics in this system. We utilize perturbations to control or steer the system between these different dynamics. We will discuss how this method of identification and interaction can be utilized to better interact with a wide range of dynamic systems. [Preview Abstract] |
Wednesday, March 20, 2013 4:42PM - 4:54PM |
R39.00012: Coherent Pattern Prediction in Swarms of Delay-Coupled Agents Luis Mier-y-Teran-Romero, Eric Forgoston, Ira Scwartz We consider a general swarm model of self-propelling particles interacting through a pairwise potential in the presence of a fixed communication time delay. Previous work has shown that swarms with communication time delays and noise may display pattern transitions that depend on the size of the coupling amplitude. We extend these results by completely unfolding the bifurcation structure of the mean field approximation. Our analysis reveals a direct correspondence between the different dynamical behaviors found in different regions of the coupling-time delay plane with the different classes of simulated coherent swarm patterns. We derive the spatio-temporal scales of the swarm structures, and also demonstrate how the complicated interplay of coupling strength, time delay, noise intensity, and choice of initial conditions can affect the swarm. In addition, when adding noise to the system, we find that for sufficiently large values of the coupling strength and/or the time delay, there is a noise intensity threshold that forces a transition of the swarm from a misaligned state into an aligned state. We show that this alignment transition exhibits hysteresis when the noise intensity is taken to be time dependent. [Preview Abstract] |
Wednesday, March 20, 2013 4:54PM - 5:06PM |
R39.00013: Structure-Property Relationships for Branched Worm-Like Micelles Gregory Beaucage, Durgesh Rai Micellar solutions can display a wide range of phase structure as a function of counter ion content, surfactant concentration, and the presence of ternary components. Under some conditions, common to consumer products, extended cylindrical structures that display persistence and other chain features of polymers are produced. These worm-like micelles (WLMs) can form branched structures that dynamically change under shear and even in quiescent conditions. The rheology of these branched WLMs is strongly dependent on migration of the branch points, and the dynamics of branch formation and removal. Persistence and other polymer-based descriptions are also of importance. We have recently developed a scattering model for branched polyolefins and other topologically complex materials that can quantify the branching density, branch length, branch functionality and the hyperbranch (branch-on-branch) content of polymers. This work is being extended to study branching in WLMs in work coupled with Ron Larson at UMich to predict rheological properties. [Preview Abstract] |
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