Characterization of cavity flow fields using pressure data obtained in the Langley 0.3-Meter Transonic Cryogenic Tunnel

Static and fluctuating pressure distributions were obtained along the floor of a rectangular-box cavity in an experiment performed in the LaRC 0.3-Meter Transonic Cryogenic Tunnel. The cavity studied was 11.25 in. long and 2.50 in. wide with a variable height to obtain length-to-height ratios of 4.4, 6.7, 12.67, and 20.0. The data presented herein were obtained for yaw angles of 0 deg and 15 deg over a Mach number range from 0.2 to 0.9 at a Reynolds number of 30 x 10(exp 6) per ft with a boundary-layer thickness of approximately 0.5 in. The results indicated that open and transitional-open cavity flow supports tone generation at subsonic and transonic speeds at Mach numbers of 0.6 and above. Further, pressure fluctuations associated with acoustic tone generation can be sustained when static pressure distributions indicate that transitional-closed and closed flow fields exist in the cavity. Cavities that support tone generation at 0 deg yaw also supported tone generation at 15 deg yaw when the flow became transitional-closed. For the latter cases, a reduction in tone amplitude was observed. Both static and fluctuating pressure data must be considered when defining cavity flow fields, and the flow models need to be refined to accommodate steady and unsteady flows

Measurements of fluctuating pressure in a rectangular cavity in transonic flow at high Reynolds numbers

An experiment was performed in the Langley 0.3 meter Transonic Cryogenic Tunnel to study the internal acoustic field generated by rectangular cavities in transonic and subsonic flows and to determine the effect of Reynolds number and angle of yaw on the field. The cavity was 11.25 in. long and 2.50 in. wide. The cavity depth was varied to obtain length-to-height (l/h) ratios of 4.40, 6.70, 12.67, and 20.00. Data were obtained for a free stream Mach number range from 0.20 to 0.90, a Reynolds number range from 2 x 10(exp 6) to 100 x 10(exp 6) per foot with a nearly constant boundary layer thickness, and for two angles of yaw of 0 and 15 degs. Results show that Reynolds number has little effect on the acoustic field in rectangular cavities at angle of yaw of 0 deg. Cavities with l/h = 4.40 and 6.70 generated tones at transonic speeds, whereas those with l/h = 20.00 did not. This trend agrees with data obtained previously at supersonic speeds. As Mach number decreased, the amplitude, and bandwidth of the tones changed. No tones appeared for Mach number = 0.20. For a cavity with l/h = 12.67, tones appeared at Mach number = 0.60, indicating a possible change in flow field type. Changes in acoustic spectra with angle of yaw varied with Reynolds number, Mach number, l/h ratios, and acoustic mode number

Formulas for ASEP with Two-Sided Bernoulli Initial Condition

For the asymmetric simple exclusion process on the integer lattice with two-sided Bernoulli initial condition, we derive exact formulas for the following quantities: (1) the probability that site x is occupied at time t; (2) a correlation function, the probability that site 0 is occupied at time 0 and site x is occupied at time t; (3) the distribution function for the total flux across 0 at time t and its exponential generating function.Comment: 18 page

Generalization of the Poisson kernel to the superconducting random-matrix ensembles

We calculate the distribution of the scattering matrix at the Fermi level for chaotic normal-superconducting systems for the case of arbitrary coupling of the scattering region to the scattering channels. The derivation is based on the assumption of uniformly distributed scattering matrices at ideal coupling, which holds in the absence of a gap in the quasiparticle excitation spectrum. The resulting distribution generalizes the Poisson kernel to the nonstandard symmetry classes introduced by Altland and Zirnbauer. We show that unlike the Poisson kernel, our result cannot be obtained by combining the maximum entropy principle with the analyticity-ergodicity constraint. As a simple application, we calculate the distribution of the conductance for a single-channel chaotic Andreev quantum dot in a magnetic field.Comment: 7 pages, 2 figure

The Dynamics of the One-Dimensional Delta-Function Bose Gas

We give a method to solve the time-dependent Schroedinger equation for a system of one-dimensional bosons interacting via a repulsive delta function potential. The method uses the ideas of Bethe Ansatz but does not use the spectral theory of the associated Hamiltonian

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

Interpolation between Airy and Poisson statistics for unitary chiral non-Hermitian random matrix ensembles

We consider a family of chiral non-Hermitian Gaussian random matrices in the unitarily invariant symmetry class. The eigenvalue distribution in this model is expressed in terms of Laguerre polynomials in the complex plane. These are orthogonal with respect to a non-Gaussian weight including a modified Bessel function of the second kind, and we give an elementary proof for this. In the large n limit, the eigenvalue statistics at the spectral edge close to the real axis are described by the same family of kernels interpolating between Airy and Poisson that was recently found by one of the authors for the elliptic Ginibre ensemble. We conclude that this scaling limit is universal, appearing for two different non-Hermitian random matrix ensembles with unitary symmetry. As a second result we give an equivalent form for the interpolating Airy kernel in terms of a single real integral, similar to representations for the asymptotic kernel in the bulk and at the hard edge of the spectrum. This makes its structure as a one-parameter deformation of the Airy kernel more transparent

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

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