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# Timetable (PFDW02)

## Developments in Experimental Pattern Formation

Monday 8th August 2005 to Friday 12th August 2005

 08:30 to 10:00 Registration 10:00 to 11:00 Some unresolved issues in pattern-forming non-equilibrium systems This talk will present experimental results about a number of phenomena in pattern-forming non-equilibrium systems that have not yet been elucidated fully from a theoretical viewpoint. The issues to be addressed include critical phenomena near the bifurcation to electro-convection in nematic liquid crystals, wave-number selection in Rayleigh-Benard convection (RBC), the appearance of square patterns near onset in rotating RBC, and the scaling of correlation lengths near onset in systems with supercritical bifurcations to spatio-temporal chaos. INI 1 11:00 to 11:30 Coffee 11:30 to 12:30 Pattern formation in dense granular flow on an inclined plane Experimental results are presented for the periodic patterns formed in flowing granular media on a rough planar surface that was steeply inclined at 41.3$^\circ$ with respect to horizontal. The surface height profile was measured using laser deflection and the velocity field was determined simultaneously using particle image velocimetry. We demonstrate that the structure of the local flow making up the stripes has height maxima for fast flowing regions, that the amplitude of the pattern evolves over downstream length scales that are 50-100 times the lateral wave length, and that the thickness at which the flow becomes unstable to the formation of lateral stripes is quite close to the thickness at which the flow does not have an average terminal velocity. INI 1 12:30 to 13:30 Lunch at Wolfson Court 14:00 to 15:00 Homological characterization of complex spatiotemporal patterns Many physical systems exhibit complex spatio-temporal behaviors that are difficult to characterize. We describe an approach that uses topological tools (specifically, computational homology) to connect experimentally observed structures to underlying dynamics. As a specific example, we will discuss homological characterizations of spiral defect chaos, a weakly turbulent state of Rayleigh-Benard convection. We observe asymmetries between hot and cold flows and show novel measures of boundary influence and indicators of system control parameters. We also find the evolution of the global structure of the flow to be primarily stochastic unlike the locally chaotic signatures reported previously. INI 1 15:00 to 15:30 Tea 15:30 to 16:30 Insights from large scale numerical simulations of Rayleigh-Benard convection Experiments on Rayleigh-Bénard Convection have played an important role in the development of our understanding of pattern formation and spatiotemporal chaos. In this talk I will review the work of the Caltech-Argonne-Duke-Virginia Tech collaboration using large scale numerical simulations of experimentally realistic geometries to complement past and ongoing experimental work, and to gain new insights into these phenomena. Topics covered will include pattern chaos in small systems, Lyapunov exponents, mean flow, and domain chaos. INI 1 16:30 to 17:30 Poster session 1 17:30 to 18:30 Wine and Beer reception 18:45 to 19:30 Dinner at Wolfson Court (Residents only)
 09:00 to 10:00 Onset of wave drag due to capillary-gravity surface waves Phase diagrams of the flow states in Couette-Taylor flow of dilute polymer solutions as a function of three controlled parameters, namely the Reynolds number, the elasticity parameter, and the reduced polymer contribution to viscosity, that is proportional to the polymer concentration, are studied in detail. Flow visualization reveals that the Couette flow becomes unstable simultaneously either to one, two or three flow patterns depending on the location in the control parameter space. We investigate the character of flow motion in different patterns and the mechanism and type of transitions between different patterns using laser Doppler velocimetry. INI 1 10:00 to 11:00 L Tuckerman ([LIMSI-CNRS])Turbulent-laminar bands in plane Couette flow Recent experiments by Prigent and Dauchot have shown that the remarkable spiral turbulence state of Taylor-Couette flow also occurs in plane Couette flow. In both cases, a pattern of alternating turbulent and laminar bands appears at a well-defined Reynolds number.The pattern is tilted with respect to the streamwise (or azimuthal) direction and its wavelength is much larger than the gap.The angle and wavelength depend systematically on Reynolds number. We have numerically simulated these turbulent-laminar patterns for plane Couette flow. In our computational approach, we replace the large lateral dimensions of the experiment by a narrow periodically repeating rectangle which is tilted with respect to the streamwise direction. In this way we determine which angles and lengths support turbulent bands. INI 1 11:00 to 11:30 Coffee 11:30 to 12:30 Snaking and its consequences Recent simulations^1 of binary fluid convection in low Prandtl number liquids reveal the presence of multiple numerically stable spatially localized steady states at supercritical Rayleigh numbers. The length of these states decreases as the Rayleigh number decreases; below a critical Rayleigh number the steady states are replaced by relaxation oscillations in which the steady state is gradually eroded until no rolls are present (the slow phase), whereupon a new steady state regrows from small amplitude (the fast phase) and the process repeats. The Swift-Hohenberg equation (both variational and nonvariational) provides much insight into this behavior. This equation contains several classes of localized steady states whose length grows in a characteristic 'snaking' fashion as they approach spatially periodic states, and the associated dynamics resemble the binary fluid simulations. The origin of the snaking and the stability properties of the associated states will be elucidated, and the results used to shed light on the remarkable complexity of these simple systems. This talk is based on joint work with Oriol Batiste and John Burke. ^1 O. Batiste and E. Knobloch, Phys Fluids 17,064102 (2005). INI 1 12:30 to 13:30 Lunch at Wolfson Court 14:00 to 15:00 Universal behaviour of self-organized patterns in gas-discharge The understanding of self-organized patterns in spatially extended nonlinear dissipative systems is one of the great challenges in modern natural sciences. Such systems can be investigated in an exemplary manner using planar dc and ac gas-discharge systems. Examples for observed patterns are fronts, stripes, hexagons, targets, spirals, dissipative solitons, fractals and other complex patterns. These patterns are also found in systems that microscopically differ in a fundamental way from plasma systems. It is believed that pattern formation in the above mentioned plasma systems can be described within the scope of the drift-diffusion approximation. In addition, there is strong evidence that in many cases the corresponding equations can be transformed to a set of reaction-diffusion equations. It turn out that plasma specific equations provide insight into the underlying microscopic properties of the plasma involved, whereas reaction-diffusion models offer a convenient background for the identification of relevant pattern forming mechanisms and for the discussion of the experimentally observed universal behaviour. INI 1 15:00 to 15:30 Tea 15:30 to 16:30 Plant patterns and plant phylloFaxis The tiling of plant surfaces into polygonal shapes (stripes, hexagons) and the arrangements of leaves and stickers (phylloFaxis) has intrigued material scientists since the time of Kepler. Drawing on recent ideas of Paul Green and colleagues and of Donady and Conder, Patrick Shipman and I have suggested (J. Theor Bio. 236, 154-197 (2005)) that most observed patterns can be understood as the energy minimizing buckling states of a compressed sheet (the plant's Funica) on an elastic foundation. INI 1 16:30 to 17:30 Solitary states in forced Rayleigh-Benard convection INI 1 18:45 to 19:30 Dinner at Wolfson Court (Residents only)
 09:00 to 10:00 W Firth ([Strathclyde])Spontaneous patterns in nonlinear optics Spontaneous patterns in optics usually involve diffraction, rather than diffusion, as the primary spatial coupling mechanism. The simplest and most successful system involves a nonlinear medium with a single feedback mirror. The basic theory and experimental status of that system will be reviewed, along with discussion of other systems such as semiconductor micro-resonators, and the closely related topic of dissipative solitons in such systems. INI 1 10:00 to 11:00 Patterns and optical structures in liquid-crystal light-valve experiments I will review the basic mechanisms of optical pattern formation, with particular reference to Liquid-Crystal-Light-Valve (LCLV) experiments, where patterns and quasi-patterns have been observed for different settings in the optical feedback loop. I will show dynamical competition between different patterns (hexagons-stripes) and bistability between different states, either homogeneous or spatially periodic. In the bistable regimes, stable localized structures can be excited, that have features of addressable single elements. When bistability is between patterns, a new class of localized structures appear, that are localized peaks of one pattern nucleating over the other pattern state. INI 1 11:00 to 11:30 Coffee 11:30 to 12:30 Measuring fluid stretching to understand chemical reaction patterns and polymer mixing Normally when we talk about pattern formation in fluid systems, we are considering the spatial structure of the velocity or temperature or composition field. However, many physical processes, especially mixing and chemical reaction, depend on the local stretching or deformation produced by the fluid. We first show how stretching fields can be computed from high-resolution time-dependent velocity fields. Their patterns can be quite different from the velocity field patterns. Yet, the statistical properties of the stretching probability distributions for various two dimensional flows are similar. Then, we consider chemical mixing, and show that the global progress of an acid base reaction that is limited by advection and diffusion can be expressed in terms of a single function that depends only on the mean Lyapunov exponent, not on the details of the structure of the stretching field. Finally, we show how in a non-Newtonian fluid, the process of fluid stretching and the resulting mixing behavior can be substantially modified. Work supported by NSF-DMR. Related Links http://www.haverford.edu/physics-astro/Gollub/lab.html - Nonlinear Physics Lab, Haverford College INI 1 12:30 to 13:30 Lunch at Wolfson Court 19:30 to 18:00 Conference Dinner at Emmanuel College (Old Library)
 09:00 to 10:00 Dictysotelium aggregation: A meeting point of cell biology and pattern-formation physics The aggregation of Dictysotelium amoebae is an exciting example of how biological systems can utilize pattern-formation mechanisms to accomplish needed tasks. This talk will focus on the specific issue of chemotactic motion by which is meant the biasing of cell motion by external gradients. Cells must actively sense external concentrations in space and time and use reaction-diffusion based processing schemes to make a decision about the direction of motion. How this works and what limits the achievable accuracy are important issues that can be addressed by combining analytical insights, new computational schemes and quantitative experiments. INI 1 10:00 to 11:00 Order and disorder in columnar joints Columnar joints are three-dimensional fracture networks that form in cooling basaltic lava flows. The network organizes the solid flow into ordered, mostly hexagonal columns. Famous examples include the Giant's Causeway in Northern Ireland and Fingal's cave in Scotland. The same pattern can be observed on a smaller scale in desiccating corn starch, and in some other materials. We have made the first three dimensional study of the evolution of the network in corn starch and relate these observations to the mature patterns observed in basalt. The starch patterns are statistically similar to those found in the Giant's Causeway, suggesting that mature columnar joint patterns contain inherent residual disorder. We find that the starch patterns can be made more similar to the basaltic ones using controlled drying rate conditions. Discontinuous transitions in pattern scale can be observed under constant external drying conditions, which may prompt a reinterpretation of similar transitions found in basalt. We also made some field observations of basalts in the Columbia river formation in Washington State, and observed a possible secondary instability of the mature columnar pattern. INI 1 11:00 to 11:30 Coffee 11:30 to 12:30 Foam failure This work explores connections between two large fields of current research: the instability of fluid/fluid interfaces known as Saffman-Taylor fingering, and the opening of voids in solid materials known as crack propagation. A liquid foam in a Hele-Shaw cell is a unique model system with characteristics of both cases: The dynamics of air injected into the foam can be described by effective-medium theory as finger propagation, yet the detailed information about position and shape of individual bubbles makes a description in terms of solid microstructural changes possible. The accessibility of the microstructure (at the single-bubble level) allows for direct observation of defect dynamics and neighbor changes. Transitions akin to brittle/ductile crack behavior are also observed. INI 1 12:30 to 13:30 Lunch at Wolfson Court 14:00 to 15:00 Grid states and nonlinear selection in parametrically excited surface waves The nonlinear interactions of parametrically driven surface waves have been shown to yield a rich family of nonlinear states, when the system is driven by two commensurate frequencies. These patterns result from a variety of 3-wave resonant interactions. They include simple square or hexagonal patterns, different superlattices, and spatio-temporal chaotic states [1, 2, 3]. By perturbing the system with an additional (3rd) frequency, we can selectively favor either a desired temporal symmetry of the system or a selected nonlinear wave interaction. We will demonstrate the following: 1. In the region of phase space in which quadratic (three-wave) interactions are dominant, the only stable patterns correspond to grid states. Grid states are nonlinear states in which of two co-rotated sets of critical wavevectors are spanned by a sublattice whose basis states are linearly stable modes [4, 5]. A number of such states are observed. 2. By varying the phases of the driving frequencies, a variety of different superlattice states are selected. The selection is consistent with recent theoretical predictions of generalized phases which govern the pattern selection [6]. 3. Open loop control of the spatio-temporally disordered state can be achieved, with the controlled (ordered) state selected by the temporal parity of the perturbing frequency [7]. 1. H. Arbell and J. Fineberg, Phys. Rev. E65, 036224 (2002) 2. A. Kudrolli, B. Pier and J. P. Gollub, Physica D123, 9 (1998) 3. E. S. Edwards and S. Fauve, Phys. Rev. E47, R788 (1993). 4. M. Silber and M. R. E. Proctor, Phys. Rev. Lett. 81, 2450 (1998). 5. A. Rucklidge and W. J. Rucklidge, Physica D178, 62 (2003). 6. J. Porter, C. Topaz, and M. Silber, Phys. Rev. Lett. 93, 034502 (2004). 7. T. Epstein and J. Fineberg, Phys. Rev. Lett. 92, 244502 (2004). INI 1 15:00 to 15:30 Tea 15:30 to 16:30 An association of particules and waves on a fluid interface We will-first show in which conditions liquid drops can be kept bouncing indefinitely on the surface of a bath of the same fluid if this bath is oscillated vertically. With a fluid of small viscosity, this bouncing generates capillary waves. We thus obtain objects formed of the close association of a particle (the drop) with the wave it emits. Usually the drop is a simple" bouncer", motionless on the fluid surface. However, close to the Faraday instability threshold, a bifurcation is observed where the drop becomes what we call a "walker" moving at a constant velocity on the interface. A model describing the drop interaction with its own wave accounts for this bifurcation. When several bouncers or several walkers are present on the same interface they have non-local interactions due to the superposition of their waves. We will show that these interactions leed to the self organization of bouncers into bound states and crystalline clusters. With walkers the formation of orbiting pairs will be described. INI 1 16:30 to 17:30 Poster session 2 18:45 to 19:30 Dinner at Wolfson Court (Residents only)
 09:00 to 10:00 J Vinals ([McGill])Grain boundary motion and orientation selection in lamellar phases Mesophases are intermediate between unstructured fluids and fully ordered crystalline solids. They often self-assemble at the mesoscale, albeit into defected microstructures, fact that limits their applicability. We describe research on those classes of defects present in one dimensional (lamellar) and two dimensional (columnar) mesophases, their motion and interaction, and their relevance to microstructure coarsening. We also discuss how external shears can be used to accelerate the emergence of macroscopic order in mesophases, and the processes responsible for orientation selection relative to the shear. INI 1 10:00 to 11:00 Patterned segregation The results of experimental investigations into particle segregation in a binary mixture which is subject to periodic horizontal forcing will be presented. The iniinitially mixed state undergoes a surprising self-organization process such that the two constituent components separate to form patterned structures. The pattern formation process shows critical dependence on the concentration ratio of the mixture. Detailed features of the observations appear to be in accord with notions from equilibrium phase transitions and the type of transition depends on particle shape. INI 1 11:00 to 11:30 Coffee 11:30 to 12:30 Effect of multiplicative noise on instabilities It has been known for a long time that random fluctuations of the control parameters of a dynamical system, or multiplicative noise, may generate surprising effects, such as stabilization by noise, noise induced transitions, etc. Multiplicative noise can also modify scaling laws in the vicinity of bifurcation thresholds. We present an experimental study of the effect of noise on surface waves generated by vertically vibrating a layer of fluid (the Faraday instability). We show that multiplicative noise can both enhance or inhibit the instability and emphasize the differences between amplitude, frequency and phase noise. In the later case, we show that a deterministic amplitude equation can be derived, with coefficients renormalized by noise. In the former cases, we discuss the phenomenon of on-off intermittency. Finally, we present some other instability problemsinvolving fluctuations in time or space acting like a multiplicative noise. INI 1 12:30 to 13:30 Lunch at Wolfson Court 14:00 to 15:00 Fractal growth of viscous fingers It has long been noted that similar highly ramified structures are formed by Diffusion Limited Aggregation (DLA) clusters, viscous fingering patterns, dielectric breakdown, flame fronts, and the growth of bacterial colonies, but it remains unknown whether these patterns are in the same or different universality classes. We address that question in a comparison of DLA with radial viscous fingering patterns in a Hele-Shaw cell. In our experiments a thin oil layer is contained between closely spaced (0.127 mm separation) circular plates (diameter 288 mm). When the oil is withdrawn from the edges and replaced by air supplied through a hole in the center of a plate, the air bubble evolves into an asymptotic multi-fingered structure with a fractal dimension 1.70+/-0.02 [1]. Similarly, the dimension of Diffusion Limited Aggregation (DLA) clusters is 1.713+/-0.003 [2]. The asymptotic behavior of the viscous fingering patterns is achieved for structures larger than about 400 times the layer thickness, a regime not studied in previous experiments. Further, preliminary results indicate that the harmonic measure for the viscous fingering structure has the same multifractal [f(alpha)] spectrum as DLA aggregates. Thus DLA and viscous fingering patterns are in the same universality class [3]. References: [1] O. Praud & H.L. Swinney, Phys. Rev. E, in press (2005). [2] B. Davidovitch, A. Levermann, & I. Procaccia, Phys. Rev. E 62, R5919 (2000). [3] Work in progress with I. Procaccia, J. Mathieson, L. Ristroph, M. Thrasher, & M.G. Moore. Related Links http://chaos.utexas.edu/manuscripts/1100563930.pdf - manuscript pdf INI 1 15:00 to 15:30 Tea 15:30 to 16:30 P Hohenberg ([NYU])Summary and discussion session INI 1 18:45 to 19:30 Dinner at Wolfson Court (Residents only)