Feedback control of unstable cellular solidification fronts

We present a numerical and experimental study of feedback control of unstable cellular patterns in directional solidification (DS). The sample, a dilute binary alloy, solidifies in a 2D geometry under a control scheme which applies local heating close to the cell tips which protrude ahead of the other. For the experiments, we use a real-time image processing algorithm to track cell tips, coupled with a movable laser spot array device, to heat locally. We show, numerically and experimentally, that spacings well below the threshold for a period-doubling instability can be stabilized. As predicted by the numerical calculations, cellular arrays become stable, and the spacing becomes uniform through feedback control which is maintained with minimal heating.Comment: 4 pages, 4 figures, 1 tabl

Shear band dynamics from a mesoscopic modeling of plasticity

The ubiquitous appearance of regions of localized deformation (shear bands) in different kinds of disordered materials under shear is studied in the context of a mesoscopic model of plasticity. The model may or may not include relaxational (aging) effects. In the absence of relaxational effects the model displays a monotonously increasing dependence of stress on strain-rate, and stationary shear bands do not occur. However, in start up experiments transient (although long lived) shear bands occur, that widen without bound in time. I investigate this transient effect in detail, reproducing and explaining a t^1/2 law for the thickness increase of the shear band that has been obtained in atomistic numerical simulations. Relaxation produces a negative sloped region in the stress vs. strain-rate curve that stabilizes the formation of shear bands of a well defined width, which is a function of strain-rate. Simulations at very low strain-rates reveal a non-trivial stick-slip dynamics of very thin shear bands that has relevance in the study of seismic phenomena. In addition, other non-stationary processes, such as stop-and-go, or strain-rate inversion situations display a phenomenology that matches very well the results of recent experimental studies.Comment: 10 pages, 10 figure

Non-Gaussian velocity distributions in excited granular matter in the absence of clustering

The velocity distribution of spheres rolling on a slightly tilted rectangular two dimensional surface is obtained by high speed imaging. The particles are excited by periodic forcing of one of the side walls. Our data suggests that strongly non-Gaussian velocity distributions can occur in dilute granular materials even in the absence of significant density correlations or clustering. When the surface on which the particles roll is tilted further to introduce stronger gravitation, the collision frequency with the driving wall increases and the velocity component distributions approach Gaussian distributions of different widths.Comment: 4 pages, 5 figures. Additional information at http://physics.clarku.edu/~akudrolli/nls.htm

Breakdown of Energy Equipartition in a 2D Binary Vibrated Granular Gas

We report experiments on the equipartition of kinetic energy between grains made of two different materials in a mixture of grains vibrated in 2 dimensions. In general, the two types of grains do not attain the same granular temperature, Tg = 1/2m v^2. However, the ratio of the two temperatures is constant in the bulk of the system and independent of the vibration velocity. The ratio depends strongly on the ratio of mass densities of the grains, but is not sensitive to the inelasticity of grains. Also, this ratio is insensitive to compositional variables of the mixture such as the number fraction of each component and the total number density. We conclude that a single granular temperature, as traditionally defined, does not characterize a multi-component mixture.Comment: 4 pages, 5 figures, submitted to Physical Review Letters, updated reference

Nonequilibrium steady states in a vibrated-rod monolayer: tetratic, nematic and smectic correlations

We study experimentally the nonequilibrium phase behaviour of a horizontal monolayer of macroscopic rods. The motion of the rods in two dimensions is driven by vibrations in the vertical direction. Aside from the control variables of packing fraction and aspect ratio that are typically explored in molecular liquid crystalline systems, due to the macroscopic size of the particles we are also able to investigate the effect of the precise shape of the particle on the steady states of this driven system. We find that the shape plays an important role in determining the nature of the orientational ordering at high packing fraction. Cylindrical particles show substantial tetratic correlations over a range of aspect ratios where spherocylinders have previously been shown by Bates et al (JCP 112, 10034 (2000)) to undergo transitions between isotropic and nematic phases. Particles that are thinner at the ends (rolling pins or bails) show nematic ordering over the same range of aspect ratios, with a well-established nematic phase at large aspect ratio and a defect-ridden nematic state with large-scale swirling motion at small aspect ratios. Finally, long-grain, basmati rice, whose geometry is intermediate between the two shapes above, shows phases with strong indications of smectic order.Comment: 18 pages and 13 eps figures, references adde

Fluctuation-Dissipation relations in Driven Granular Gases

We study the dynamics of a 2d driven inelastic gas, by means of Direct Simulation Monte Carlo (DSMC) techniques, i.e. under the assumption of Molecular Chaos. Under the effect of a uniform stochastic driving in the form of a white noise plus a friction term, the gas is kept in a non-equilibrium Steady State characterized by fractal density correlations and non-Gaussian distributions of velocities; the mean squared velocity, that is the so-called {\em granular temperature}, is lower than the bath temperature. We observe that a modified form of the Kubo relation, which relates the autocorrelation and the linear response for the dynamics of a system {\em at equilibrium}, still holds for the off-equilibrium, though stationary, dynamics of the systems under investigation. Interestingly, the only needed modification to the equilibrium Kubo relation is the replacement of the equilibrium temperature with an effective temperature, which results equal to the global granular temperature. We present two independent numerical experiment, i.e. two different observables are studied: (a) the staggered density current, whose response to an impulsive shear is proportional to its autocorrelation in the unperturbed system and (b) the response of a tracer to a small constant force, switched on at time $t_w$, which is proportional to the mean-square displacement in the unperturbed system. Both measures confirm the validity of Kubo's formula, provided that the granular temperature is used as the proportionality factor between response and autocorrelation, at least for not too large inelasticities.Comment: 11 pages, 7 figures, submitted for publicatio

RefCell: multi-dimensional analysis of image-based high-throughput screens based on ‘typical cells’

Image-based high-throughput screening (HTS) reveals a high level of heterogeneity in single cells and multiple cellular states may be observed within a single population. Currently available high-dimensional analysis methods are successful in characterizing cellular heterogeneity, but suffer from the “curse of dimensionality” and non-standardized outputs. Here we introduce RefCell, a multi-dimensional analysis pipeline for image-based HTS that reproducibly captures cells with typical combinations of features in reference states and uses these “typical cells” as a reference for classification and weighting of metrics. RefCell quantitatively assesses heterogeneous deviations from typical behavior for each analyzed perturbation or sample. We apply RefCell to the analysis of data from a high-throughput imaging screen of a library of 320 ubiquitin-targeted siRNAs selected to gain insights into the mechanisms of premature aging (progeria). RefCell yields results comparable to a more complex clustering-based single-cell analysis method; both methods reveal more potential hits than a conventional analysis based on averages.https://doi.org/10.1186/s12859-018-2454-

Self-diffusion in dense granular shear flows

Diffusivity is a key quantity in describing velocity fluctuations in granular materials. These fluctuations are the basis of many thermodynamic and hydrodynamic models which aim to provide a statistical description of granular systems. We present experimental results on diffusivity in dense, granular shear in a 2D Couette geometry. We find that self-diffusivities are proportional to the local shear rate with diffusivities along the mean flow approximately twice as large as those in the perpendicular direction. The magnitude of the diffusivity is D \approx \dot\gamma a^2 where a is the particle radius. However, the gradient in shear rate, coupling to the mean flow, and drag at the moving boundary lead to particle displacements that can appear sub- or super-diffusive. In particular, diffusion appears superdiffusive along the mean flow direction due to Taylor dispersion effects and subdiffusive along the perpendicular direction due to the gradient in shear rate. The anisotropic force network leads to an additional anisotropy in the diffusivity that is a property of dense systems with no obvious analog in rapid flows. Specifically, the diffusivity is supressed along the direction of the strong force network. A simple random walk simulation reproduces the key features of the data, such as the apparent superdiffusive and subdiffusive behavior arising from the mean flow, confirming the underlying diffusive motion. The additional anisotropy is not observed in the simulation since the strong force network is not included. Examples of correlated motion, such as transient vortices, and Levy flights are also observed. Although correlated motion creates velocity fields qualitatively different from Brownian motion and can introduce non-diffusive effects, on average the system appears simply diffusive.Comment: 13 pages, 20 figures (accepted to Phys. Rev. E

Studies of Mass and Size Effects in Three-Dimensional Vibrofluidized Granular Mixtures

We examine the steady state properties of binary systems of driven inelastic hard spheres. The spheres, which move under the influence of gravity, are contained in a vertical cylinder with a vibrating base. We computed the trajectories of the spheres using an event-driven molecular dynamics algorithm. In the first part of the study, we chose simulation parameters that match those of experiments performed by Wildman and Parker. Various properties computed from the simulation including the density profile, granular temperature and circulation pattern are in good qualitative agreement with the experiments. We then studied the effect of varying the mass ratio and the size ratio independently while holding the other parameters constant. The mass and size ratio are shown to affect the distribution of the energy. The changes in the energy distributions affect the packing fraction and temperature of each component. The temperature of the heavier component has a non-linear dependence on the mass of the lighter component, while the temperature of the lighter component is approximately proportional to its mass. The temperature of both components is inversely dependent on the size of the smaller component.Comment: 14 Pages, 12 Figures, RevTeX