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

Tangent Graeffe Iteration

Graeffe iteration was the choice algorithm for solving univariate polynomials in the XIX-th and early XX-th century. In this paper, a new variation of Graeffe iteration is given, suitable to IEEE floating-point arithmetics of modern digital computers. We prove that under a certain generic assumption the proposed algorithm converges. We also estimate the error after N iterations and the running cost. The main ideas from which this algorithm is built are: classical Graeffe iteration and Newton Diagrams, changes of scale (renormalization), and replacement of a difference technique by a differentiation one. The algorithm was implemented successfully and a number of numerical experiments are displayed

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

Characterization of two new alleles at the goat CSN1S2 locus.

Two novel alleles at the goat CSN1S2 locus have been identified: CSN1S2(F) and CSN1S2(D). Sequence analyses revealed that the CSN1S2(F) allele is characterized by a G --> A transition at the 13th nucleotide in exon 3 changing the seventh amino acid of the mature protein from Val to Ile. The CSN1S2(D) allele, apparently associated with a decreased synthesis of alpha s2-casein, is characterized by a 106-bp deletion, involving the last 11 bp of the exon 11 and the first 95 bp of the following intron. Methods (PCR-RFLP and PCR) for identification of carriers of these alleles have been developed

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

Use of EcoTILLING to Find Genes Related to Salt Tolerance in Rice. W622

Salinity is considered one of important physical factors influencing rice (Oryza sativa L.) production. Roots are the first parts of the plant to experience any soil-based salt stress and it is at the roots that the entry of Na+ and Cl? is determined. Rice as other plants, have several strategies to cope with salinity including minimizing the entry of toxic ions through roots, and/or maintaining low Na+/K+ ratios at shoot level, etc...A tremendous variation for salt tolerance within genotypes provides opportunities to improve rice salt-stress tolerance through genetic means. Aiming to find alleles associated with salinity tolerance we used the EcoTILLING technique to explore the natural variability existing in 390 rice germplasm accessions at key genes related to salt stress. This working collection is representative of the large morphological, physiological, and ecological variation available in domesticated rice. All targets genes, namely OsNHX1, OsHKT1;5, SalT, OsRMC and OsCPK17, have been previously described and characterized as related to salt-tolerance enhancement in rice, through different mechanisms such as Na+/K+ equilibrium, signaling cascade and stress protection. Sequence results showed hundreds of SNPs (Single Nucleotides Polymorphisms) and small INDELs, resulting in a total of 40 allelic variants, thus coding 31 different proteins. After phenotypic characterization of the allelic variants at CDS level, we found significant statistical associations between some particular gene haplotypes and phenotypic parameters under salt stress. We will discuss the utility of EcoTILLING and SNP discovery in breeding efforts for salt tolerance, with particular emphasis to the mechanisms related to root genomics. (Texte integral