Exact Solution of a Jamming Transition: Closed Equations for a Bootstrap Percolation Problem

Jamming, or dynamical arrest, is a transition at which many particles stop moving in a collective manner. In nature it is brought about by, for example, increasing the packing density, changing the interactions between particles, or otherwise restricting the local motion of the elements of the system. The onset of collectivity occurs because, when one particle is blocked, it may lead to the blocking of a neighbor. That particle may then block one of its neighbors, these effects propagating across some typical domain of size named the dynamical correlation length. When this length diverges, the system becomes immobile. Even where it is finite but large the dynamics is dramatically slowed. Such phenomena lead to glasses, gels, and other very long-lived nonequilibrium solids. The bootstrap percolation models are the simplest examples describing these spatio-temporal correlations. We have been able to solve one such model in two dimensions exactly, exhibiting the precise evolution of the jamming correlations on approach to arrest. We believe that the nature of these correlations and the method we devise to solve the problem are quite general. Both should be of considerable help in further developing this field.Comment: 17 pages, 4 figure

Cooperative heterogeneous facilitation: multiple glassy states and glass-glass transition

The formal structure of glass singularities in the mode-coupling theory (MCT) of supercooled liquids dynamics is closely related to that appearing in the analysis of heterogeneous bootstrap percolation on Bethe lattices, random graphs and complex networks. Starting from this observation one can build up microscopic on lattice realizations of schematic MCT based on cooperative facilitated spin mixtures. I discuss a microscopic implementation of the F13 schematic model including multiple glassy states and the glass-glass transition. Results suggest that our approach is flexible enough to bridge alternative theoretical descriptions of glassy matter based on the notions of quenched disorder and dynamic facilitation.Comment: 4 pages, 2 figure

Near-IR imaging of T Cha: evidence for scattered-light disk structures at solar system scales

T Chamaeleontis is a young star surrounded by a transitional disk, and a plausible candidate for ongoing planet formation. Recently, a substellar companion candidate was reported within the disk gap of this star. However, its existence remains controversial, with the counter-hypothesis that light from a high inclination disk may also be consistent with the observed data. The aim of this work is to investigate the origin of the observed closure phase signal to determine if it is best explained by a compact companion. We observed T Cha in the L and K s filters with sparse aperture masking, with 7 datasets covering a period of 3 years. A consistent closure phase signal is recovered in all L and K s datasets. Data were fit with a companion model and an inclined circumstellar disk model based on known disk parameters: both were shown to provide an adequate fit. However, the absence of expected relative motion for an orbiting body over the 3-year time baseline spanned by the observations rules out the companion model. Applying image reconstruction techniques to each dataset reveals a stationary structure consistent with forward scattering from the near edge of an inclined disk.Comment: 6 pages, 3 figures, accepted for publication in MNRAS Letter

Assessment of experimental optical techniques for characterizing heat transfer using numerical simulations

This manuscript addresses the application of numerical simulations for assessing the error in the measurement of the bulk temperature along the laser beam of a 3D flow using a 2D Moiré deflectometry analysis. To analyze the effect of different flow parameters on the error, a 3D computational model of an experimental system was developed. The simulated domain represents the well-known solution of the backward facing step in a rectangular channel but includes a hot-plate at the bottom of the step to enhance the heat transfer effects. The geometry resembles that found in a general heat exchanger. The difference between the computed bulk temperature of the flow and the average temperature obtained via the 2D Moiré is analytically evaluated for various assumed general temperature profiles; the numerically computed profiles of temperature indicates that the error decreases with the channel aspect ratio. The use of CFD enables the determination of the flow topology and thus an evaluation of the 3D flow behavior that will cause the measurement error. A parametric study was performed for different flow conditions, namely, the aspect ratio of the channel, the inflow conditions (flow velocity or Reynolds number), and the temperature of the hot wall. The results indicate that the Moiré technique is suitable for evaluating the bulk temperature in typical heat exchange devices and flow conditions