Colloquium: Comparison of Astrophysical and Terrestrial Frequency Standards

We have re-analyzed the stability of pulse arrival times from pulsars and white dwarfs using several analysis tools for measuring the noise characteristics of sampled time and frequency data. We show that the best terrestrial artificial clocks substantially exceed the performance of astronomical sources as time-keepers in terms of accuracy (as defined by cesium primary frequency standards) and stability. This superiority in stability can be directly demonstrated over time periods up to two years, where there is high quality data for both. Beyond 2 years there is a deficiency of data for clock/clock comparisons and both terrestrial and astronomical clocks show equal performance being equally limited by the quality of the reference timescales used to make the comparisons. Nonetheless, we show that detailed accuracy evaluations of modern terrestrial clocks imply that these new clocks are likely to have a stability better than any astronomical source up to comparison times of at least hundreds of years. This article is intended to provide a correct appreciation of the relative merits of natural and artificial clocks. The use of natural clocks as tests of physics under the most extreme conditions is entirely appropriate; however, the contention that these natural clocks, particularly white dwarfs, can compete as timekeepers against devices constructed by mankind is shown to be doubtful.Comment: 9 pages, 2 figures; presented at the International Frequency Control Symposium, Newport Beach, Calif., June, 2010; presented at Pulsar Conference 2010, October 12th, Sardinia; accepted 13th September 2010 for publication in Reviews of Modern Physic

Asymptotics of Eigenvalues and Eigenfunctions for the Laplace Operator in a Domain with Oscillating Boundary. Multiple Eigenvalue Case

We study the asymptotic behavior of the solutions of a spectral problem for the Laplacian in a domain with rapidly oscillating boundary. We consider the case where the eigenvalue of the limit problem is multiple. We construct the leading terms of the asymptotic expansions for the eigenelements and verify the asymptotics

Scanning Probe Techniques for Characterization of Vertically Aligned Carbon Nanotubes

This chapter presents the results of experimental studies of the electrical, mechanical and geometric parameters of vertically aligned carbon nanotubes (VA CNTs) using scanning probe microscopy (SPM). This chapter also presents the features and difficulties of characterization of VA CNTs in different scanning modes of the SPM. Advanced techniques for VA CNT characterization (the height, Young’s modulus, resistivity, adhesion and piezoelectric response) taking into account the features of the SPM modes are described. The proposed techniques allow to overcome the difficulties associated with the vertical orientation and high aspect ratio of nanotubes in determining the electrical and mechanical parameters of the VA CNTs by standard methods. The results can be used in the development of diagnostic methods as well as in nanoelectronics and nanosystem devices based on vertically aligned carbon nanotubes (memory elements, adhesive structures, nanoelectromechanical switches, emission structures, etc.)

Vibrational instability, two-level systems and Boson peak in glasses

We show that the same physical mechanism is fundamental for two seemingly different phenomena such as the formation of two-level systems in glasses and the Boson peak in the reduced density of low-frequency vibrational states g(w)/w^2. This mechanism is the vibrational instability of weakly interacting harmonic modes. Below some frequency w_c << w_0 (where w_0 is of the order of Debye frequency) the instability, controlled by the anharmonicity, creates a new stable universal spectrum of harmonic vibrations with a Boson peak feature as well as double-well potentials with a wide distribution of barrier heights. Both are determined by the strength of the interaction I ~ w_c between the oscillators. Our theory predicts in a natural way a small value for the important dimensionless parameter C ~ 10^{-4} for two-level systems in glasses. We show that C ~ I^{-3} and decreases with increasing of the interaction strength I. We show that the number of active two-level systems is very small, less than one per ten million of oscillators, in a good agreement with experiment. Within the unified approach developed in the present paper the density of the tunneling states and the density of vibrational states at the Boson peak frequency are interrelated.Comment: 28 pages, 3 figure

The Vega Debris Disk -- A Surprise from Spitzer

We present high spatial resolution mid- and far-infrared images of the Vega debris disk obtained with the Multiband Imaging Photometer for Spitzer (MIPS). The disk is well resolved and its angular size is much larger than found previously. The radius of the disk is at least 43" (330 AU), 70"(543 AU), and 105" (815 AU) in extent at 24, 70 and 160 um, respectively. The disk images are circular, smooth and without clumpiness at all three wavelengths. The radial surface brightness profiles imply an inner boundary at a radius of 11"+/-2" (86 AU). Assuming an amalgam of amorphous silicate and carbonaceous grains, the disk can be modeled as an axially symmetric and geometrically thin disk, viewed face-on, with the surface particle number density following an r^-1 power law. The disk radiometric properties are consistent with a range of models using grains of sizes ~1 to ~50 um. We find that a ring, containing grains larger than 180 um and at radii of 86-200 AU from the star, can reproduce the observed 850 um flux, while its emission does not violate the observed MIPS profiles. This ring could be associated with a population of larger asteroidal bodies analogous to our own Kuiper Belt. Cascades of collisions starting with encounters amongthese large bodies in the ring produce the small debris that is blown outward by radiation pressure to much larger distances where we detect its thermal emission. The dust production rate is >~10^15 g/s based on the MIPS results. This rate would require a very massive asteroidal reservoir for the dust to be produced in a steady state throughout Vega's life. Instead, we suggest that the disk we imaged is ephemeral and that we are witnessing the aftermath of a large and relatively recent collisional event, and subsequent collisional cascade.Comment: 13 pages, 17 figures, accepted for publication in ApJ. (Figures 2, 3a, 3b and 4 have been degraded to lower resolutions.

Hard loss of stability in Painlev\'e-2 equation

A special asymptotic solution of the Painlev\'e-2 equation with small parameter is studied. This solution has a critical point $t_*$ corresponding to a bifurcation phenomenon. When $t<t_*$ the constructed solution varies slowly and when $t>t_*$ the solution oscillates very fast. We investigate the transitional layer in detail and obtain a smooth asymptotic solution, using a sequence of scaling and matching procedures

Anharmonic vs. relaxational sound damping in glasses: II. Vitreous silica

The temperature dependence of the frequency dispersion in the sound velocity and damping of vitreous silica is reanalyzed. Thermally activated relaxation accounts for the sound attenuation observed above 10 K at sonic and ultrasonic frequencies. Its extrapolation to the hypersonic regime reveals that the anharmonic coupling to the thermal bath becomes important in Brillouin-scattering measurements. At 35 GHz and room temperature, the damping due to this anharmonicity is found to be nearly twice that produced by thermally activated relaxation. The analysis also reveals a sizeable velocity increase with temperature which is not related with sound dispersion. This suggests that silica experiences a gradual structural change that already starts well below room temperature.Comment: 13 pages with 8 figure

Generation of small-scale structures in the developed turbulence

The Navier-Stokes equation for incompressible liquid is considered in the limit of infinitely large Reynolds number. It is assumed that the flow instability leads to generation of steady-state large-scale pulsations. The excitation and evolution of the small-scale turbulence is investigated. It is shown that the developed small-scale pulsations are intermittent. The maximal amplitude of the vorticity fluctuations is reached along the vortex filaments. Basing on the obtained solution, the pair correlation function in the limit $r\to 0$ is calculated. It is shown that the function obeys the Kolmogorov law $r^{2/3}$.Comment: 18 page

Effects of Electron-Electron and Electron-Phonon Interactions in Weakly Disordered Conductors and Heterostuctures

We investigate quantum corrections to the conductivity due to the interference of electron-electron (electron-phonon) scattering and elastic electron scattering in weakly disordered conductors. The electron-electron interaction results in a negative $T^2 \ln T$-correction in a 3D conductor. In a quasi-two-dimensional conductor, $d < v_F/T$ ($d$ is the thickness, $v_F$ is the Fermi velocity), with 3D electron spectrum this correction is linear in temperature and differs from that for 2D electrons (G. Zala et. al., Phys. Rev.B {\bf 64}, 214204 (2001)) by a numerical factor. In a quasi-one-dimensional conductor, temperature-dependent correction is proportional to $T^2$. The electron interaction via exchange of virtual phonons also gives $T^2$-correction. The contribution of thermal phonons interacting with electrons via the screened deformation potential results in $T^4$-term and via unscreened deformation potential results in $T^2$-term. The interference contributions dominate over pure electron-phonon scattering in a wide temperature range, which extends with increasing disorder.Comment: 6 pages, 2figure