Structural Relationship between Negative Thermal Expansion and Quartic Anharmonicity of Cubic ScF_3

Cubic scandium trifluoride (ScF_3) has a large negative thermal expansion over a wide range of temperatures. Inelastic neutron scattering experiments were performed to study the temperature dependence of the lattice dynamics of ScF3 from 7 to 750 K. The measured phonon densities of states show a large anharmonic contribution with a thermal stiffening of modes around 25 meV. Phonon calculations with first-principles methods identified the individual modes in the densities of states, and frozen phonon calculations showed that some of the modes with motions of F atoms transverse to their bond direction behave as quantum quartic oscillators. The quartic potential originates from harmonic interatomic forces in the DO_9 structure of ScF_3, and accounts for phonon stiffening with the temperature and a significant part of the negative thermal expansion

Effect of spin-orbit coupling on the excitation spectrum of Andreev billiards

We consider the effect of spin-orbit coupling on the low energy excitation spectrum of an Andreev billiard (a quantum dot weakly coupled to a superconductor), using a dynamical numerical model (the spin Andreev map). Three effects of spin-orbit coupling are obtained in our simulations: In zero magnetic field: (1) the narrowing of the distribution of the excitation gap; (2) the appearance of oscillations in the average density of states. In strong magnetic field: (3) the appearance of a peak in the average density of states at zero energy. All three effects have been predicted by random-matrix theory.Comment: 5 pages, 4 figure

Eynard-Mehta theorem, Schur process, and their pfaffian analogs

We give simple linear algebraic proofs of Eynard-Mehta theorem, Okounkov-Reshetikhin formula for the correlation kernel of the Schur process, and Pfaffian analogs of these results. We also discuss certain general properties of the spaces of all determinantal and Pfaffian processes on a given finite set.Comment: AMSTeX, 21 pages, a new section adde

Airy processes and variational problems

We review the Airy processes; their formulation and how they are conjectured to govern the large time, large distance spatial fluctuations of one dimensional random growth models. We also describe formulas which express the probabilities that they lie below a given curve as Fredholm determinants of certain boundary value operators, and the several applications of these formulas to variational problems involving Airy processes that arise in physical problems, as well as to their local behaviour.Comment: Minor corrections. 41 pages, 4 figures. To appear as chapter in "PASI Proceedings: Topics in percolative and disordered systems

The Variable Stars and Blue Horizontal Branch of the Metal-Rich Globular Cluster NGC 6441

We present time-series VI photometry of the metal-rich ([Fe/H] = -0.53) globular cluster NGC 6441. Our color-magnitude diagram shows that the extended blue horizontal branch seen in Hubble Space Telescope data exists in the outermost reaches of the cluster. The red clump slopes nearly parallel to the reddening vector. A component of this slope is due to differential reddening, but part is intrinsic. The blue horizontal branch stars are more centrally concentrated than the red clump stars. We have discovered about 50 new variable stars near NGC 6441, among them eight or more RR Lyrae stars which are very probably cluster members. Comprehensive period searches over the range 0.2-1.0 days yielded unusually long periods (0.5-0.9 days) for the fundamental pulsators compared with field RR Lyrae of the same metallicity. Three similar long-period RR Lyrae are known in other metal-rich globulars. With over ten examples in hand, it seems that a distinct sub-class of RR Lyrae is emerging. The observed properties of the horizontal branch stars are in reasonable agreement with recent models which invoke deep mixing to enhance the atmospheric helium abundance, while they conflict with models which assume high initial helium abundance. The light curves of the c-type RR Lyrae seem to have unusually long rise times and sharp minima. Reproducing these light curves in stellar pulsation models may provide another means of constraining the physical variables responsible for the anomalous blue horizontal branch extension and sloped red clump observed in NGC 6441.Comment: 30 pages plus 6 EPS and 6 JPEG figures; uses AAS TeX. Accepted by the Astronomical Journal. Minor changes include computing He abundance, modifications to Figs 1 and 8, and expansion on idea that blue HB stars may be produced in binarie

Bee-Friendly Beef: Developing Biodiverse Pastures to Increase Ecosystem Services

The capacity of grasslands to provide ecosystem services, such as pollinator resources, is often limited by lack of plant biodiversity. This is true of grasslands in the eastern US that are dominated by tall fescue (Festuca arundinacea) a non-native, cool-season grass that is typically toxic to cattle. This paper summarizes a research project in Virginia, USA exploring the idea that ecosystem services provided by tall fescue-dominated grasslands can be improved by increasing the plant biodiversity available to beef cattle and bees. Within three 6.5 ha tall fescue grasslands, we established 0.8 ha plots with a 17 species mix of native warm-season grasses (NWSGs) and wildflowers. Beginning in 2018, we measured grass and wildflower establishment, attractiveness of wildflowers to bees, abundance and diversity of bee communities in biodiverse pastures and adjacent tall fescue pastures. Many of the 18 species sown established well expect for NWSGs. Competition from wildflowers likely suppressed native grasses and limited forage availability for beef cattle. Cattle largely ignored the wildflowers. This finding suggests that cattle and pollinators can share this biodiverse grassland as their primary foods are mutually exclusive. The total number of bees was almost double in wildflower-enhanced grasslands compared with more typical tall fescue grasslands. We observed most bee landings on purple coneflower (Echinacea purpurea) and anise hyssop (Agastache foeniculum). Several weedy species such as milkweed (Asclepias syriaca) and musk thistle (Carduus nutans) were also attractive to bees. Preliminary analyses identified at least 28 bee morphospecies and a distinct bee community present in wildflower pastures. While these results were promising, more research is needed on ways to establish biodiverse grasslands so that a more optimal balance of grasses and wildflowers can be sustained to benefit both cattle production and pollinators

Q-Dependent Susceptibilities in Ferromagnetic Quasiperiodic Z-Invariant Ising Models

We study the q-dependent susceptibility chi(q) of a series of quasiperiodic Ising models on the square lattice. Several different kinds of aperiodic sequences of couplings are studied, including the Fibonacci and silver-mean sequences. Some identities and theorems are generalized and simpler derivations are presented. We find that the q-dependent susceptibilities are periodic, with the commensurate peaks of chi(q) located at the same positions as for the regular Ising models. Hence, incommensurate everywhere-dense peaks can only occur in cases with mixed ferromagnetic-antiferromagnetic interactions or if the underlying lattice is aperiodic. For mixed-interaction models the positions of the peaks depend strongly on the aperiodic sequence chosen.Comment: LaTeX2e, 26 pages, 9 figures (27 eps files). v2: Misprints correcte

The Determinant Representation for a Correlation Function in Scaling Lee-Yang Model

We consider the scaling Lee-Yang model. It corresponds to the unique perturbation of the minimal CFT model M(2,5). This is not a unitary model. We used known expression for form factors in order to obtain a closed expression for a correlation function of a trace of energy-momentum tensor. This expression is a determinant of an integral operator. Similar determinant representation were proven to be useful not only for quantum correlation functions but also in matrix models.Comment: 14 pages, LaTeX, no figure