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

Removal of the center of mass in nuclei and its effects on 4He

Abstract The singular value decomposition of rectangular matrices is shown to provide the recipe for removing the center of mass spurious admixtures from the multiphonon basis generated by an equation of motion method for solving the nuclear eigenvalue problem. It works for any single particle basis without any energy restriction on the selection of the configurations. Its effects on 4He are illustrated

Growth by insertion: The family of bacterial DDxP proteins

We have identified a variety of proteins in species of the Legionella, Aeromonas, Pseudomonas, Vibrio, Nitrosomonas, Nitrosospira, Variovorax, Halomonas, and Rhizobia genera, which feature repetitive modules of different length and composition, invariably ending at the COOH side with Asp–Asp–x–Pro (DDxP) motifs. DDxP proteins range in size from 900 to 6200 aa (amino acids), and contain 1 to 5 different module types, present in one or multiple copies. We hypothesize that DDxP proteins were modeled by the action of specific endonucleases inserting DNA segments into genes encoding DDxP motifs. Target site duplications (TSDs) formed upon repair of staggered ends generated by endonuclease cleavage would explain the DDxP motifs at repeat ends. TSDs acted eventually as targets for the insertion of more modules of the same or different types. Repeat clusters plausibly resulted from amplification of both repeat and flanking TSDs. The proposed growth shown by the insertion model is supported by the identification of homologous proteins lacking repeats in Pseudomonas and Rhizobium. The 85 DDxP repeats identified in this work vary in length, and can be sorted into short (136–215 aa) and long (243–304 aa) types. Conserved Asp–Gly–Asp–Gly–Asp motifs are located 11–19 aa from the terminal DDxP motifs in all repeats, and far upstream in most long repeats

High resolution observations of the outer disk around T Cha: the view from ALMA

T Cha is a young star surrounded by a transitional disk with signatures of planet formation. We have obtained high-resolution and high-sensitivity ALMA observations of T Cha in the ${\rm CO}(3$--$2)$, ${\rm ^{13}CO}(3$--$2)$, and ${\rm CS}(7$--$6)$ emission lines to reveal the spatial distribution of the gaseous disk around the star. In order to study the dust within the disk we have also obtained continuum images at 850$\mu$m from the line-free channels. We have spatially resolved the outer disk around T Cha. Using the CO(3-2) emission we derive a radius of $\sim$230 AU. We also report the detection of the $^{13}$CO(3-2) and the CS(7-8) molecular emissions, which show smaller radii than the CO(3-2) detection. The continuum observations at 850$\mu$m allow the spatial resolution of the dusty disk, which shows two emission bumps separated by $\sim$40AU, consistent with the presence of a dust gap in the inner regions of the disk, and an outer radius of $\sim$80AU. Therefore, T Cha is surrounded by a compact dusty disk and a larger and more diffuse gaseous disk, as previously observed in other young stars. The continuum intensity profiles are different at both sides of the disk suggesting possible dust asymmetries. We derive an inclination of i(deg)=67$\pm$5, and a position angle of PA (deg)= 113$\pm$6, for both the gas and dust disks. The comparison of the ALMA data with radiative transfer models shows that the gas and dust components can only be simultaneously reproduced when we include a tapered edge prescription for the surface density profile. The best model suggests that most of the disk mass is placed within a radius of $R<$ 50AU. Finally, we derive a dynamical mass for the central object of $M_{*}$=1.5$\pm$0.2M$_{\odot}$, comparable to the one estimated with evolutionary models for an age of $\sim$10Myr.Comment: 5 pages, 5 figures, accepted for publication in A&A Letter

Submillimetre dust polarisation and opacity in the HD163296 protoplanetary ring system

We present ALMA images of the sub-mm continuum polarisation and spectral index of the protoplanetary ringed disk HD163296. The polarisation fraction at 870{\mu}m is measured to be ~0.9% in the central core and generally increases with radius along the disk major axis. It peaks in the gaps between the dust rings, and the largest value (~4%) is found between rings 1 and 2. The polarisation vectors are aligned with the disk minor axis in the central core, but become more azimuthal in the gaps, twisting by up to +/-9degrees in the gap between rings 1 and 2. These general characteristics are consistent with a model of self-scattered radiation in the ringed structure, without requiring an additional dust alignment mechanism. The 870/1300{\mu}m dust spectral index exhibits minima in the centre and the inner rings, suggesting these regions have high optical depths. However, further refinement of the dust or the disk model at higher resolution is needed to reproduce simultaneously the observed degree of polarisation and the low spectral index.Comment: 5 pages +2 pages supplemental data. v2 - revised figures and final values; conclusions unchange

On Singularity Formation of a Nonlinear Nonlocal System

We investigate the singularity formation of a nonlinear nonlocal system. This nonlocal system is a simplified one-dimensional system of the 3D model that was recently proposed by Hou and Lei in [13] for axisymmetric 3D incompressible Navier-Stokes equations with swirl. The main difference between the 3D model of Hou and Lei and the reformulated 3D Navier-Stokes equations is that the convection term is neglected in the 3D model. In the nonlocal system we consider in this paper, we replace the Riesz operator in the 3D model by the Hilbert transform. One of the main results of this paper is that we prove rigorously the finite time singularity formation of the nonlocal system for a large class of smooth initial data with finite energy. We also prove the global regularity for a class of smooth initial data. Numerical results will be presented to demonstrate the asymptotically self-similar blow-up of the solution. The blowup rate of the self-similar singularity of the nonlocal system is similar to that of the 3D model.Comment: 28 pages, 9 figure

Harmonic damped oscillators with feedback. A Langevin study

We consider a system in direct contact with a thermal reservoir and which, if left unperturbed, is well described by a memory-less equilibrium Langevin equation of the second order in the time coordinate. In such conditions, the strength of the noise fluctuations is set by the damping factor, in accordance with the Fluctuation and Dissipation theorem. We study the system when it is subject to a feedback mechanism, by modifying the Langevin equation accordingly. Memory terms now arise in the time evolution, which we study in a non-equilibrium steady state. Two types of feedback schemes are considered, one focusing on time shifts and one on phase shifts, and for both cases we evaluate the power spectrum of the system's fluctuations. Our analysis finds application in feedback cooled oscillators, such as the Gravitational Wave detector AURIGA.Comment: 17 page