Acoustics of tachyon Fermi gas

We consider a Fermi gas of free tachyons as a continuous medium and find whether it satisfies the causality condition. There is no stable tachyon matter with the particle density below critical value $n_T$ and the Fermi momentum $k_F<\sqrt{\frac 32}m$ that depends on the tachyon mass $m$. The pressure $P$ and energy density $E$ cannot be arbitrary small, but the situation $P>E$ is not forbidden. Existence of shock waves in tachyon gas is also discussed. At low density $n_T<n<3.45n_T$ the tachyon matter remains stable but no shock wave do survive.Comment: 14 pages, 2 figures (color

The effect of tip shields on a horizontal tail surface

A series of experiments made in the wind tunnel of the Daniel Guggenheim School of Aeronautics, New York University, on the effect of tip shields on a horizontal tail surface are described and discussed. It was found that some aerodynamic gain can be obtained by the use of tip shields though it is considered doubtful whether their use would be practical

Reduced-order Description of Transient Instabilities and Computation of Finite-Time Lyapunov Exponents

High-dimensional chaotic dynamical systems can exhibit strongly transient features. These are often associated with instabilities that have finite-time duration. Because of the finite-time character of these transient events, their detection through infinite-time methods, e.g. long term averages, Lyapunov exponents or information about the statistical steady-state, is not possible. Here we utilize a recently developed framework, the Optimally Time-Dependent (OTD) modes, to extract a time-dependent subspace that spans the modes associated with transient features associated with finite-time instabilities. As the main result, we prove that the OTD modes, under appropriate conditions, converge exponentially fast to the eigendirections of the Cauchy--Green tensor associated with the most intense finite-time instabilities. Based on this observation, we develop a reduced-order method for the computation of finite-time Lyapunov exponents (FTLE) and vectors. In high-dimensional systems, the computational cost of the reduced-order method is orders of magnitude lower than the full FTLE computation. We demonstrate the validity of the theoretical findings on two numerical examples

Large spin behavior of anomalous dimensions and short-long strings duality

We are considering the semi-classical string soliton solution of Gubser, Klebanov and Polyakov which represents highly excited states on the leading Regge trajectory, with large spin in $AdS_5$. A prescription relates this soliton solution with the corresponding field theory operators with many covariant derivatives, whose anomalous scaling dimension grows logarithmically with the space-time spin. We explicitly derive the dependence of anomalous dimension on spin for all leading and next-to-leading orders at strong coupling. We develop an iteration procedure which, in principle, allows to derive all terms in the large spin expansion of the anomalous scaling dimension of twist two operators. Our string theory results are consistent with the conjectured "reciprocity" relation, which has been verified to hold in perturbation theory up to five loops in N=4 SYM. We also derive a duality relation between long and short strings.Comment: 15 pages, 1 figure, comments and references adde

A New Star-Formation Rate Calibration from Polycyclic Aromatic Hydrocarbon Emission Features and Application to High Redshift Galaxies

We calibrate the integrated luminosity from the polycyclic aromatic hydrocarbon (PAH) features at 6.2\micron, 7.7\micron\ and 11.3\micron\ in galaxies as a measure of the star-formation rate (SFR). These features are strong (containing as much as 5-10\% of the total infrared luminosity) and suffer minimal extinction. Our calibration uses \spitzer\ Infrared Spectrograph (IRS) measurements of 105 galaxies at $0 < z < 0.4$, infrared (IR) luminosities of 10^9 - 10^{12} \lsol, combined with other well-calibrated SFR indicators. The PAH luminosity correlates linearly with the SFR as measured by the extinction-corrected \ha\ luminosity over the range of luminosities in our calibration sample. The scatter is 0.14 dex comparable to that between SFRs derived from the \paa\ and extinction-corrected \ha\ emission lines, implying the PAH features may be as accurate a SFR indicator as hydrogen recombination lines. The PAH SFR relation depends on gas-phase metallicity, for which we supply an empirical correction for galaxies with 0.2 < \mathrm{Z} \lsim 0.7~\zsol. We present a case study in advance of the \textit{James Webb Space Telescope} (\jwst), which will be capable of measuring SFRs from PAHs in distant galaxies at the peak of the SFR density in the universe ($z\sim2$) with SFRs as low as $\sim$~10~\sfrunits. We use \spitzer/IRS observations of the PAH features and \paa\ emission plus \ha\ measurements in lensed star-forming galaxies at $1 < z < 3$ to demonstrate the ability of the PAHs to derive accurate SFRs. We also demonstrate that because the PAH features dominate the mid-IR fluxes, broad-band mid-IR photometric measurements from \jwst\ will trace both the SFR and provide a way to exclude galaxies dominated by an AGN.Comment: Accepted for publication in Ap

How to observe a non-Kerr spacetime

We present a generic criterion which can be used in gravitational-wave data analysis to distinguish an extreme-mass-ratio inspiral into a Kerr background spacetime from one into a non-Kerr background spacetime. The criterion exploits the fact that when an integrable system, such as the system that describes geodesic orbits in a Kerr spacetime, is perturbed, the tori in phase space which initially corresponded to resonances disintegrate so as to form the so called Birkhoff chains on a surface of section, according to the Poincar\'{e}-Birkhoff theorem. The KAM curves of these islands in such a chain share the same ratio of frequencies, even though the frequencies themselves vary from one KAM curve to another inside an island. On the other hand, the KAM curves, which do not lie in a Birkhoff chain, do not share this characteristic property. Such a temporal constancy of the ratio of frequencies during the evolution of the gravitational-wave signal will signal a non-Kerr spacetime which could then be further explored.Comment: 4 pages, 2 figure

Development of a combined surface plasmon resonance/surface acoustic wave device for the characterization of biomolecules

It is known that acoustic sensor devices, if operated in liquid phase, are sensitive not just to the mass of the analyte but also to various other parameters, such as size, shape, charge and elastic constants of the analyte as well as bound and viscously entrained water. This can be used to extract valuable information about a biomolecule, particularly if the acoustic device is combined with another sensor element which is sensitive to the mass or amount of analyte only. The latter is true in good approximation for various optical sensor techniques. This work reports on the development of a combined surface plasmon resonance/surface acoustic wave sensor system which is designed for the investigation of biomolecules such as proteins or DNA. Results for the deposition of neutravidin and DNA are reported

Computing the entropy of user navigation in the web

Navigation through the web, colloquially known as "surfing", is one of the main activities of users during web interaction. When users follow a navigation trail they often tend to get disoriented in terms of the goals of their original query and thus the discovery of typical user trails could be useful in providing navigation assistance. Herein, we give a theoretical underpinning of user navigation in terms of the entropy of an underlying Markov chain modelling the web topology. We present a novel method for online incremental computation of the entropy and a large deviation result regarding the length of a trail to realize the said entropy. We provide an error analysis for our estimation of the entropy in terms of the divergence between the empirical and actual probabilities. We then indicate applications of our algorithm in the area of web data mining. Finally, we present an extension of our technique to higher-order Markov chains by a suitable reduction of a higher-order Markov chain model to a first-order one

A Method of Mass Measurement in Black Hole Binaries Using Timing and High Resolution X-ray Spectroscopy

In X-ray binaries, several percent of the compact object luminosity is intercepted by the surface of the normal companion and re-radiated through Compton reflection and the K-fluorescence. This reflected emission follows the variability of the compact object with a delay approximately equal to the orbital radius divided by the speed of light. This provides the possibility of measuring the orbital radius and thus substantially refining the compact object mass determination compared to using optical data alone. We demonstrate that it may be feasible to measure the time delay between the direct and reflected emission using cross-correlation of the light curves observed near the Kalpha line and above the K-edge of neutral iron. In the case of Cyg X-1, the time delay measurement is feasible with a 300--1000 ksec observation by a telescope with a 1000 cm^2 effective area near 6.4 keV and with a ~5eV energy resolution. With longer exposures, it may be possible to obtain mass constraints even if an X-ray source in the binary system lacks an optical counterpart.Comment: ApJ Letters, in press. 4 pages, 3 figures, uses emulateapj.st