Periodic orbit theory and spectral rigidity in pseudointegrable systems

We calculate numerically the periodic orbits of pseudointegrable systems of low genus numbers $g$ that arise from rectangular systems with one or two salient corners. From the periodic orbits, we calculate the spectral rigidity $\Delta_3(L)$ using semiclassical quantum mechanics with $L$ reaching up to quite large values. We find that the diagonal approximation is applicable when averaging over a suitable energy interval. Comparing systems of various shapes we find that our results agree well with $\Delta_3$ calculated directly from the eigenvalues by spectral statistics. Therefore, additional terms as e.g. diffraction terms seem to be small in the case of the systems investigated in this work. By reducing the size of the corners, the spectral statistics of our pseudointegrable systems approaches the one of an integrable system, whereas very large differences between integrable and pseudointegrable systems occur, when the salient corners are large. Both types of behavior can be well understood by the properties of the periodic orbits in the system

Unstructured-grid methods development for unsteady aerodynamic and aeroelastic analyses

The current status of unstructured grid methods development in the Unsteady Aerodynamics Branch at NASA-Langley is described. These methods are being developed for unsteady aerodynamic and aeroelastic analyses. The flow solvers are highlighted which were developed for the solution of the unsteady Euler equations and selected results are given which show various features of the capability. The results demonstrate 2-D and 3-D applications for both steady and unsteady flows. Comparisons are also made with solutions obtained using a structured grid code and with experimental data to determine the accuracy of the unstructured grid methodology. These comparisons show good agreement which thus verifies the accuracy

α_1L-adrenoceptors mediate contraction of human erectile tissue

α1-adrenoceptor antagonists can impact upon sexual function and have potential in the treatment of erectile dysfunction. Human erectile tissue contains predominantly α1A-adrenoceptors, and here we examined whether contractions of this tissue are mediated by the functional phenotype, the α1L-adrenoceptor. Functional experiments using subtype selective agonists and antagonists, along with radioligand ([3H]tamsulosin) binding assays, were used to determine the α1-adrenoceptor population. A61603, a α1A-adrenoceptor agonist, was a full agonist with a potency 21-fold greater than that of noradrenaline. The α1A- and α1D-adrenoceptor antagonist tamsulosin antagonized noradrenaline responses with high affinity (pKD = 9.7 ± 0.3), whilst BMY7378 (100 nM) (α1D-adrenoceptor antagonist) failed to antagonize responses. In contrast, relatively low affinity estimates were obtained for both prazosin (pKD = 8.2 ± 0.1) and RS17053 (pKD = 6.9 ± 0.2), antagonists which discriminate between the α1A- and α1L-adrenoceptors. [3H]Tamsulosin bound with high affinity to the receptors of human erectile tissue (pKD = 10.3 ± 0.1) with a receptor density of 28.1 ± 1.4 fmol mg−1 protein. Prazosin displacement of [3H]tamsulosin binding revealed a single homogenous population of binding sites with a relatively low affinity for prazosin (pKi = 8.9). Taken together these data confirm that the receptor mediating contraction in human erectile tissue has the pharmacological properties of the α1L-adrenoceptor. Keywords: Erectile tissue, α1-adrenoceptor subtypes, α1L-adrenoceptor, Tamsulosin, Prazosi

An Optical and Infrared Time-Domain Study of the Supergiant Fast X-ray Transient Candidate IC 10 X-2

We present an optical and infrared (IR) study of IC 10 X-2, a high-mass X-ray binary in the galaxy IC 10. Previous optical and X-ray studies suggest X-2 is a Supergiant Fast X-ray Transient: a large-amplitude (factor of $\sim$ 100), short-duration (hours to weeks) X-ray outburst on 2010 May 21. We analyze R- and g-band light curves of X-2 from the intermediate Palomar Transient Factory taken between 2013 July 15 and 2017 Feb 14 show high-amplitude ($\gtrsim$ 1 mag), short-duration ($\lesssim8$ d) flares and dips ($\gtrsim$ 0.5 mag). Near-IR spectroscopy of X-2 from Palomar/TripleSpec show He I, Paschen-$\gamma$, and Paschen-$\beta$ emission lines with similar shapes and amplitudes as those of luminous blue variables (LBVs) and LBV candidates (LBVc). Mid-IR colors and magnitudes from Spitzer/IRAC photometry of X-2 resemble those of known LBV/LBVcs. We suggest that the stellar companion in X-2 is an LBV/LBVc and discuss possible origins of the optical flares. Dips in the optical light curve are indicative of eclipses from optically thick clumps formed in the winds of the stellar counterpart. Given the constraints on the flare duration ($0.02 - 0.8$ d) and the time between flares ($15.1\pm7.8$ d), we estimate the clump volume filling factor in the stellar winds, $f_V$, to be $0.01 < f_V < 0.71$, which overlaps with values measured from massive star winds. In X-2, we interpret the origin of the optical flares as the accretion of clumps formed in the winds of an LBV/LBVc onto the compact object.Comment: 15 pages, 4 figures. Submitted to ApJ on Sep 26 201

Application of the Trace Formula in Pseudointegrable Systems

We apply periodic-orbit theory to calculate the integrated density of states $N(k)$ from the periodic orbits of pseudointegrable polygon and barrier billiards. We show that the results agree so well with the results obtained from direct diagonalization of the Schr\"odinger equation, that about the first 100 eigenvalues can be obtained directly from the periodic-orbit calculations in good accuracy.Comment: 5 Pages, 4 Figures, submitted to Phys. Rev.

Second Order Perturbations of Flat Dust FLRW Universes with a Cosmological Constant

We summarize recent results concerning the evolution of second order perturbations in flat dust irrotational FLRW models with $\Lambda\ne 0$. We show that asymptotically these perturbations tend to constants in time, in agreement with the cosmic no-hair conjecture. We solve numerically the second order scalar perturbation equation, and very briefly discuss its all time behaviour and some possible implications for the structure formation.Comment: 6 pages, 1 figure. to be published in "Proceedings of the 5th Alexander Friedmann Seminar on Gravitation and Cosmology", Int. Journ. Mod. Phys. A (2002). Macros: ws-ijmpa.cls, ws-p9-75x6-50.cl

Photometric variability of candidate white dwarf binary systems from Palomar Transient Factory archival data

We present a sample of 59 periodic variables from the Palomar Transient Factory, selected from published catalogues of white dwarf (WD) candidates. The variability can likely be attributed to ellipsoidal variation of the tidally distorted companion induced by the gravity of the primary (WD or hot subdwarf) or to the reflection of hot emission by a cooler companion. We searched 11311 spectroscopically or photometrically selected WD candidates from three hot star/WD catalogues, using the Lomb-Scargle periodogram to single out promising sources. We present period estimates for the candidates, 45 of which were not previously identified as periodic variables, and find that most have a period shorter than a few days. Additionally, we discuss the eclipsing systems in our sample and present spectroscopic data on selected sources

Level statistics and eigenfunctions of pseudointegrable systems: dependence on energy and genus number

We study the level statistics (second half moment $I_0$ and rigidity $\Delta_3$) and the eigenfunctions of pseudointegrable systems with rough boundaries of different genus numbers $g$. We find that the levels form energy intervals with a characteristic behavior of the level statistics and the eigenfunctions in each interval. At low enough energies, the boundary roughness is not resolved and accordingly, the eigenfunctions are quite regular functions and the level statistics shows Poisson-like behavior. At higher energies, the level statistics of most systems moves from Poisson-like towards Wigner-like behavior with increasing $g$. Investigating the wavefunctions, we find many chaotic functions that can be described as a random superposition of regular wavefunctions. The amplitude distribution $P(\psi)$ of these chaotic functions was found to be Gaussian with the typical value of the localization volume $V_{\rm{loc}}\approx 0.33$. For systems with periodic boundaries we find several additional energy regimes, where $I_0$ is relatively close to the Poisson-limit. In these regimes, the eigenfunctions are either regular or localized functions, where $P(\psi)$ is close to the distribution of a sine or cosine function in the first case and strongly peaked in the second case. Also an interesting intermediate case between chaotic and localized eigenfunctions appears