Local Statistics of Realizable Vertex Models

We study planar "vertex" models, which are probability measures on edge subsets of a planar graph, satisfying certain constraints at each vertex, examples including dimer model, and 1-2 model, which we will define. We express the local statistics of a large class of vertex models on a finite hexagonal lattice as a linear combination of the local statistics of dimers on the corresponding Fisher graph, with the help of a generalized holographic algorithm. Using an $n\times n$ torus to approximate the periodic infinite graph, we give an explicit integral formula for the free energy and local statistics for configurations of the vertex model on an infinite bi-periodic graph. As an example, we simulate the 1-2 model by the technique of Glauber dynamics

Pattern densities in fluid dimer models

In this paper, we introduce a family of observables for the dimer model on a bi-periodic bipartite planar graph, called pattern density fields. We study the scaling limit of these objects for liquid and gaseous Gibbs measures of the dimer model, and prove that they converge to a linear combination of a derivative of the Gaussian massless free field and an independent white noise.Comment: 38 pages, 3 figure

A high-throughput mass spectrometric assay for discovery of human lipoxygenase inhibitors and allosteric effectors.

Lipoxygenases (LOXs) regulate inflammation through the production of a variety of molecules whose specific downstream effects are not entirely understood due to the complexity of the inflammation pathway. The generation of these biomolecules can potentially be inhibited and/or allosterically regulated by small synthetic molecules. The current work describes the first mass spectrometric high-throughput method for identifying small molecule LOX inhibitors and LOX allosteric effectors that change the substrate preference of human lipoxygenase enzymes. Using a volatile buffer and an acid-labile detergent, enzymatic products can be directly detected using high-performance liquid chromatography-mass spectrometry (HPLC-MS) without the need for organic extraction. The method also reduces the required enzyme concentration compared with traditional ultraviolet (UV) absorbance methods by approximately 30-fold, allowing accurate binding affinity measurements for inhibitors with nanomolar affinity. The procedure was validated using known LOX inhibitors and the allosteric effector 13(S)-hydroxy-9Z,11E-octadecadienoic acid (13-HODE)

Low Mass Stars and Brown Dwarfs around Sigma Orionis

We present optical spectroscopy of 71 photometric candidate low-mass members of the cluster associated with Sigma Orionis. Thirty-five of these are found to pass the lithium test and hence are confirmed as true cluster members, covering a mass range of <0.055-0.3M_{sun}, assuming a mean cluster age of <5 Myr. We find evidence for an age spread on the (I, I-J) colour magnitude diagram, members appearing to lie in the range 1-7 Myr. There are, however, a significant fraction of candidates that are non-members, including some previously identified as members based on photometry alone. We see some evidence that the ratio of spectroscopically confirmed members to photometric candidates decreases with brightness and mass. This highlights the importance of spectroscopy in determining the true initial mass-function.Comment: To appear in the 12th Cambridge Workshop on Cool Stars Stellar Systems and the Su

Discrete complex analysis on planar quad-graphs

We develop a linear theory of discrete complex analysis on general quad-graphs, continuing and extending previous work of Duffin, Mercat, Kenyon, Chelkak and Smirnov on discrete complex analysis on rhombic quad-graphs. Our approach based on the medial graph yields more instructive proofs of discrete analogs of several classical theorems and even new results. We provide discrete counterparts of fundamental concepts in complex analysis such as holomorphic functions, derivatives, the Laplacian, and exterior calculus. Also, we discuss discrete versions of important basic theorems such as Green's identities and Cauchy's integral formulae. For the first time, we discretize Green's first identity and Cauchy's integral formula for the derivative of a holomorphic function. In this paper, we focus on planar quad-graphs, but we would like to mention that many notions and theorems can be adapted to discrete Riemann surfaces in a straightforward way. In the case of planar parallelogram-graphs with bounded interior angles and bounded ratio of side lengths, we construct a discrete Green's function and discrete Cauchy's kernels with asymptotics comparable to the smooth case. Further restricting to the integer lattice of a two-dimensional skew coordinate system yields appropriate discrete Cauchy's integral formulae for higher order derivatives.Comment: 49 pages, 8 figure

Vorticity-transport and unstructured RANS investigation of rotor-fuselage interactions

The prediction capabilities of unstructured primitive-variable and vorticity-transport-based Navier-Stokes solvers have been compared for rotorcraft-fuselage interaction. Their accuracies have been assessed using the NASA Langley ROBIN series of experiments. Correlation of steady pressure on the isolated fuselage delineates the differences between the viscous and inviscid solvers. The influence of the individual blade passage, model supports, and viscous effects on the unsteady pressure loading has been studied. Smoke visualization from the ROBIN experiment has been used to determine the ability of the codes to predict the wake geometry. The two computational methods are observed to provide similar results within the context of their physical assumptions and simplifications in the test configuration

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

The Nature of Hypervelocity Stars and the Time between Their Formation and Ejection

We obtain Keck HIRES spectroscopy of HVS5, one of the fastest unbound stars in the Milky Way halo. We show that HVS5 is a 3.62 ± 0.11 M_☉ main-sequence B star at a distance of 50 ± 5 kpc. The difference between its age and its flight time from the Galactic center is 105 ± 18 (stat) ±30 (sys) Myr; flight times from locations elsewhere in the Galactic disk are similar. This 10^8 yr "arrival time" between formation and ejection is difficult to reconcile with any ejection scenario involving massive stars that live for only 10^7 yr. For comparison, we derive arrival times of 10^7 yr for two unbound runaway B stars, consistent with their disk origin where ejection results from a supernova in a binary system or dynamical interactions between massive stars in a dense star cluster. For HVS5, ejection during the first 10^7 yr of its lifetime is ruled out at the 3σ level. Together with the 10^8 yr arrival times inferred for three other well-studied hypervelocity stars (HVSs), these results are consistent with a Galactic center origin for the HVSs. If the HVSs were indeed ejected by the central black hole, then the Galactic center was forming stars ≃200 Myr ago, and the progenitors of the HVSs took ≃100 Myr to enter the black hole's loss cone