Birational Mappings and Matrix Sub-algebra from the Chiral Potts Model

We study birational transformations of the projective space originating from lattice statistical mechanics, specifically from various chiral Potts models. Associating these models to \emph{stable patterns} and \emph{signed-patterns}, we give general results which allow us to find \emph{all} chiral $q$-state spin-edge Potts models when the number of states $q$ is a prime or the square of a prime, as well as several $q$-dependent family of models. We also prove the absence of monocolor stable signed-pattern with more than four states. This demonstrates a conjecture about cyclic Hadamard matrices in a particular case. The birational transformations associated to these lattice spin-edge models show complexity reduction. In particular we recover a one-parameter family of integrable transformations, for which we give a matrix representationComment: 22 pages 0 figure The paper has been reorganized, splitting the results into two sections : results pertaining to Physics and results pertaining to Mathematic

Metastability of a granular surface in a spinning bucket

The surface shape of a spinning bucket of granular material is studied using a continuum model of surface flow developed by Bouchaud et al. and Mehta et al. An experimentally observed central subcritical region is reproduced by the model. The subcritical region occurs when a metastable surface becomes unstable via a nonlinear instability mechanism. The nonlinear instability mechanism destabilizes the surface in large systems while a linear instability mechanism is relevant for smaller systems. The range of angles in which the granular surface is metastable vanishes with increasing system size.Comment: 8 pages with postscript figures, RevTex, to appear in Phys. Rev.

Droplet and cluster formation in freely falling granular streams

Particle beams are important tools for probing atomic and molecular interactions. Here we demonstrate that particle beams also offer a unique opportunity to investigate interactions in macroscopic systems, such as granular media. Motivated by recent experiments on streams of grains that exhibit liquid-like breakup into droplets, we use molecular dynamics simulations to investigate the evolution of a dense stream of macroscopic spheres accelerating out of an opening at the bottom of a reservoir. We show how nanoscale details associated with energy dissipation during collisions modify the stream's macroscopic behavior. We find that inelastic collisions collimate the stream, while the presence of short-range attractive interactions drives structure formation. Parameterizing the collision dynamics by the coefficient of restitution (i.e., the ratio of relative velocities before and after impact) and the strength of the cohesive interaction, we map out a spectrum of behaviors that ranges from gas-like jets in which all grains drift apart to liquid-like streams that break into large droplets containing hundreds of grains. We also find a new, intermediate regime in which small aggregates form by capture from the gas phase, similar to what can be observed in molecular beams. Our results show that nearly all aspects of stream behavior are closely related to the velocity gradient associated with vertical free fall. Led by this observation, we propose a simple energy balance model to explain the droplet formation process. The qualitative as well as many quantitative features of the simulations and the model compare well with available experimental data and provide a first quantitative measure of the role of attractions in freely cooling granular streams

Effectiveness of Heat Detection Patches for Determining Cyclicity Status in Peripubertal Heifers

Response to most estrous synchronization programs is improved in cycling females, compared to pre-pubertal heifers or anestrus cows. Cycling status is often monitored for research purposes by measuring progesterone concentrations in serum. Producers may want to use information on cyclicity status when determining which estrous synchronization program to use or as a component of their heifer selection. Heat detection patches are routinely used to aid or reduce time needed for heat detection. The most data on their use is for a 3 to 5-day period after estrous synchronization. Little information is available on retention of patches for longer time periods or how they may compare with serum progesterone for determining cyclicity status. Therefore, the objective of the current study was to compare Standing Heat and Estrotect heat detection patches with serum concentrations of progesterone for identifying cycling (pubertal) heifers before the start of the breeding season

Comparing Standing Heat and Estrotect Heat Detection Patches

A recent survey showed that 66% of producers surveyed used some amount of heat detection in their artificial insemination program, and 74% of producers that used heat detection aids had tried Estrotect (Rockway, Inc.; Spring Valley, WS) heat detection patches. The peel-and-stick application made Estrotect more popular than types that required adhesive application. The patches are designed so that when the animal is mounted the top surface layer is removed, much like scratching a lottery ticket. After several mounts the entire layer is removed, leaving a bright-colored surface behind. A new type of patch, Standing Heat (Standing Heat, LLC; Dannebrog, NE), was recently released and has a surface layer designed to rub off with the goal of reducing false positive readings due to inadvertent scratches such as from branches or tail switching. The objective of the current study was to compare the efficacy of two different heat detection patches