Statistical mechanics of glass transition in lattice molecule models

Lattice molecule models are proposed in order to study statistical mechanics of glass transition in finite dimensions. Molecules in the models are represented by hard Wang tiles and their density is controlled by a chemical potential. An infinite series of irregular ground states are constructed theoretically. By defining a glass order parameter as a collection of the overlap with each ground state, a thermodynamic transition to a glass phase is found in a stratified Wang tiles model on a cubic lattice.Comment: 18 pages, 8 figure

First Order Phase Transition of a Long Polymer Chain

We consider a model consisting of a self-avoiding polygon occupying a variable density of the sites of a square lattice. A fixed energy is associated with each $90^\circ$-bend of the polygon. We use a grand canonical ensemble, introducing parameters $\mu$ and $\beta$ to control average density and average (total) energy of the polygon, and show by Monte Carlo simulation that the model has a first order, nematic phase transition across a curve in the $\beta$-$\mu$ plane.Comment: 11 pages, 7 figure

Phase transition in a static granular system

We find that a column of glass beads exhibits a well-defined transition between two phases that differ in their resistance to shear. Pulses of fluidization are used to prepare static states with well-defined particle volume fractions $\phi$ in the range 0.57-0.63. The resistance to shear is determined by slowly inserting a rod into the column of beads. The transition occurs at $\phi=0.60$ for a range of speeds of the rod.Comment: 4 pages, 4 figures. The paper is significantly extended, including new dat

Dilatancy transition in a granular model

We introduce a model of granular matter and use a stress ensemble to analyze shearing. Monte Carlo simulation shows the model to exhibit a second order phase transition, associated with the onset of dilatancy.Comment: Future versions can be obtained from: http://www.ma.utexas.edu/users/radin/papers/shear2.pd

An ultrametric state space with a dense discrete overlap distribution: Paperfolding sequences

We compute the Parisi overlap distribution for paperfolding sequences. It turns out to be discrete, and to live on the dyadic rationals. Hence it is a pure point measure whose support is the full interval [-1; +1]. The space of paperfolding sequences has an ultrametric structure. Our example provides an illustration of some properties which were suggested to occur for pure states in spin glass models

Genetic factors in antiphospholipid syndrome: Preliminary experience with whole exome sequencing

As in many autoimmune diseases, the pathogenesis of the antiphospholipid syndrome (APS) is the result of a complex interplay between predisposing genes and triggering environmental factors, leading to a loss of self-tolerance and immune-mediated tissue damage. While the first genetic studies in APS focused primarily on the human leukocytes antigen system (HLA) region, more recent data highlighted the role of other genes in APS susceptibility, including those involved in the immune response and in the hemostatic process. In order to join this intriguing debate, we analyzed the single-nucleotide polymorphisms (SNPs) derived from the whole exome sequencing (WES) of two siblings affected by APS and compared our findings with the available literature. We identified genes encoding proteins involved in the hemostatic process, the immune response, and the phospholipid metabolism (PLA2G6, HSPG2, BCL3, ZFAT, ATP2B2, CRTC3, and ADCY3) of potential interest when debating the pathogenesis of the syndrome. The study of the selected SNPs in a larger cohort of APS patients and the integration of WES results with the network-based approaches will help decipher the genetic risk factors involved in the diverse clinical features of APS