On the Red-Green-Blue Model

We experimentally study the red-green-blue model, which is a sytem of loops obtained by superimposing three dimer coverings on offset hexagonal lattices. We find that when the boundary conditions are ``flat'', the red-green-blue loops are closely related to SLE_4 and double-dimer loops, which are the loops formed by superimposing two dimer coverings of the cartesian lattice. But we also find that the red-green-blue loops are more tightly nested than the double-dimer loops. We also investigate the 2D minimum spanning tree, and find that it is not conformally invariant.Comment: 4 pages, 7 figure

Tetratic Order in the Phase Behavior of a Hard-Rectangle System

Previous Monte Carlo investigations by Wojciechowski \emph{et al.} have found two unusual phases in two-dimensional systems of anisotropic hard particles: a tetratic phase of four-fold symmetry for hard squares [Comp. Methods in Science and Tech., 10: 235-255, 2004], and a nonperiodic degenerate solid phase for hard-disk dimers [Phys. Rev. Lett., 66: 3168-3171, 1991]. In this work, we study a system of hard rectangles of aspect ratio two, i.e., hard-square dimers (or dominos), and demonstrate that it exhibits a solid phase with both of these unusual properties. The solid shows tetratic, but not nematic, order, and it is nonperiodic having the structure of a random tiling of the square lattice with dominos. We obtain similar results with both a classical Monte Carlo method using true rectangles and a novel molecular dynamics algorithm employing rectangles with rounded corners. It is remarkable that such simple convex two-dimensional shapes can produce such rich phase behavior. Although we have not performed exact free-energy calculations, we expect that the random domino tiling is thermodynamically stabilized by its degeneracy entropy, well-known to be $1.79k_{B}$ per particle from previous studies of the dimer problem on the square lattice. Our observations are consistent with a KTHNY two-stage phase transition scenario with two continuous phase transitions, the first from isotropic to tetratic liquid, and the second from tetratic liquid to solid.Comment: Submitted for publicatio

Dimers on two-dimensional lattices

We consider close-packed dimers, or perfect matchings, on two-dimensional regular lattices. We review known results and derive new expressions for the free energy, entropy, and the molecular freedom of dimers for a number of lattices including the simple-quartic (4^4), honeycomb (6^3), triangular (3^6), kagome (3.6.3.6), 3-12 (3.12^2) and its dual [3.12^2], and 4-8 (4.8^2) and its dual Union Jack [4.8^2] Archimedean tilings. The occurrence and nature of phase transitions are also analyzed and discussed.Comment: Typos corrections in Eqs. (28), (32) and (43

Random on-board pixel sampling (ROPS) X-ray Camera

Recent advances in compressed sensing theory and algorithms offer new possibilities for high-speed X-ray camera design. In many CMOS cameras, each pixel has an independent on-board circuit that includes an amplifier, noise rejection, signal shaper, an analog-to-digital converter (ADC), and optional in-pixel storage. When X-ray images are sparse, i.e., when one of the following cases is true: (a.) The number of pixels with true X-ray hits is much smaller than the total number of pixels; (b.) The X-ray information is redundant; or (c.) Some prior knowledge about the X-ray images exists, sparse sampling may be allowed. Here we first illustrate the feasibility of random on-board pixel sampling (ROPS) using an existing set of X-ray images, followed by a discussion about signal to noise as a function of pixel size. Next, we describe a possible circuit architecture to achieve random pixel access and in-pixel storage. The combination of a multilayer architecture, sparse on-chip sampling, and computational image techniques, is expected to facilitate the development and applications of high-speed X-ray camera technology.Comment: 9 pages, 6 figures, Presented in 19th iWoRI

Electrospray synthesis of PLGA TIPS microspheres

We successfully demonstrate the synthesis of polymer microspheres using a single electrospray source, and show their physical characterisation. Electrospray has proven to be a versatile method to manufacture particles, giving tight control over size with quasi-monodisperse size distributions. It is a liquid atomisation technique that generates a monodisperse population of highly charged liquid droplets over a broad size range (nanometres to tens of microns). The droplets contain liquid precursors for the in-flight synthesis of particles, and control over the trajectory of these droplets can be precisely manipulated with the use of electric fields to drive them to a grounded substrate. This study reports a method to synthesize poly(lactic-co-glycolic) acid (PLGA) microspheres using the electrospray and thermally induced phase separation (TIPS) techniques, followed by subsequent freeze-drying, for particle production. These microspheres are of interest as vehicles for controlled drug release systems

A shortcut to identifying small molecule signals that regulate behavior and development in Caenorhabditis elegans

Small molecule metabolites play important roles in Caenorhabditis elegans biology, but effective approaches for identifying their chemical structures are lacking. Recent studies revealed that a family of glycosides, the ascarosides, differentially regulate C. elegans development and behavior. Low concentrations of ascarosides attract males and thus appear to be part of the C. elegans sex pheromone, whereas higher concentrations induce developmental arrest at the dauer stage, an alternative, nonaging larval stage. The ascarosides act synergistically, which presented challenges for their identification via traditional activity-guided fractionation. As a result the chemical characterization of the dauer and male attracting pheromones remained incomplete. Here, we describe the identification of several additional pheromone components by using a recently developed NMR-spectroscopic approach, differential analysis by 2D NMR spectroscopy (DANS), which simplifies linking small molecule metabolites with their biological function. DANS-based comparison of wild-type C. elegans and a signaling-deficient mutant, daf-22, enabled identification of 3 known and 4 previously undescribed ascarosides, including a compound that features a p-aminobenzoic acid subunit. Biological testing of synthetic samples of these compounds revealed additional evidence for synergy and provided insights into structure–activity relationships. Using a combination of the three most active ascarosides allowed full reconstitution of the male-attracting activity of wild-type pheromone extract. Our results highlight the efficacy of DANS as a method for identifying small-molecule metabolites and placing them within a specific genetic context. This study further supports the hypothesis that ascarosides represent a structurally diverse set of nematode signaling molecules regulating major life history traits

Vacancy localization in the square dimer model

We study the classical dimer model on a square lattice with a single vacancy by developing a graph-theoretic classification of the set of all configurations which extends the spanning tree formulation of close-packed dimers. With this formalism, we can address the question of the possible motion of the vacancy induced by dimer slidings. We find a probability 57/4-10Sqrt[2] for the vacancy to be strictly jammed in an infinite system. More generally, the size distribution of the domain accessible to the vacancy is characterized by a power law decay with exponent 9/8. On a finite system, the probability that a vacancy in the bulk can reach the boundary falls off as a power law of the system size with exponent 1/4. The resultant weak localization of vacancies still allows for unbounded diffusion, characterized by a diffusion exponent that we relate to that of diffusion on spanning trees. We also implement numerical simulations of the model with both free and periodic boundary conditions.Comment: 35 pages, 24 figures. Improved version with one added figure (figure 9), a shift s->s+1 in the definition of the tree size, and minor correction

A Bayesian approach to the analysis of time symmetry in light curves: Reconsidering Scorpius X-1 occultations

We present a new approach to the analysis of time symmetry in light curves, such as those in the x-ray at the center of the Scorpius X-1 occultation debate. Our method uses a new parameterization for such events (the bilogistic event profile) and provides a clear, physically relevant characterization of each event's key features. We also demonstrate a Markov Chain Monte Carlo algorithm to carry out this analysis, including a novel independence chain configuration for the estimation of each event's location in the light curve. These tools are applied to the Scorpius X-1 light curves presented in Chang et al. (2007), providing additional evidence based on the time series that the events detected thus far are most likely not occultations by TNOs.Comment: 24 pages, 18 figures. Preprint typeset using LaTeX style emulateapj v. 04/20/0