Secular Instability and Planetesimal Formation in the Dust Layer

Late in the gaseous phase of a protostellar disk, centimeter-sized bodies probably settle into a thin ``dust layer'' at the midplane. A velocity difference between the dust layer and the gas gives rise to turbulence, which prevents further settling and direct gravitational instability of the layer. The associated drag on the surface of the layer causes orbital decay in a few thousand years---as opposed to a few hundred years for an isolated meter-sized body. Within this widely-accepted theoretical framework, we show that the turbulent drag causes radial instabilities even if the selfgravity of the layer is negligible. We formulate axisymmetric, height-integrated dynamical equations for the layer that incorporate turbulent diffusion of mass and momentum in radius and height, vertical settling, selfgravity, and resistance to compression due to gas entrained within the dust layer. In steady-state, the equations describe the inward radial drift of a uniform dust layer. In perturbation, overdense rings form on an orbital timescale with widths comparable to the dust-layer thickness. Selfgravity is almost irrelevant to the linear growth rate but will eventually fragment and collapse the rings into planetesimals larger than a kilometer. We estimate that the drag instability is most efficient at 1 AU when most of the ``dust'' mass lies in the size range 0.1-10 meters.Comment: 25 pp., 2 figures. Uses aastex version 5.0

Scintillation Caustics in Planetary Occultation Light Curves

We revisit the GSC5249-01240 light curve obtained during its occultation by Saturn's North polar region. In addition to refractive scintillations, the power spectrum of intensity fluctuations shows an enhancement of power between refractive and diffractive regimes. We identify this excess power as due to high amplitude spikes in the light curve and suggest that these spikes are due to caustics associated with ray crossing situations. The flux variation in individual spikes follows the expected caustic behavior, including diffraction fringes which we have observed for the first time in a planetary occultation light curve. The presence of caustics in scintillation light curves require an inner scale cut off to the power spectrum of underlying density fluctuations associated with turbulence. Another possibility is the presence of gravity waves in the atmosphere. While occultation light curves previously showed the existence of refractive scintillations, a combination of small projected stellar size and a low relative velocity during the event have allowed us to identify caustics in this occultation. This has led us to re-examine previous data sets, in which we have also found likely examples of caustics.Comment: 4 pages, 3 figures; ApJL submitte

A geometric approach to high resolution TVD schemes

A geometric approach, similar to Van Leer's MUSCL schemes, is used to construct a second-order accurate generalization of Godunov's method for solving scalar conservation laws. By making suitable approximations, a scheme is obtained which is easy to implement and total variation diminishing. The entropy condition is also investigated from the standpoint of the spreading of rarefaction waves. Quantitative information is obtained for Godunov's method on the rate of spreading which explain the kinks in rarefaction waves often observed at the sonic point

Correlations and fluctuations of a confined electron gas

The grand potential $\Omega$ and the response $R = - \partial \Omega /\partial x$ of a phase-coherent confined noninteracting electron gas depend sensitively on chemical potential $\mu$ or external parameter $x$. We compute their autocorrelation as a function of $\mu$, $x$ and temperature. The result is related to the short-time dynamics of the corresponding classical system, implying in general the absence of a universal regime. Chaotic, diffusive and integrable motions are investigated, and illustrated numerically. The autocorrelation of the persistent current of a disordered mesoscopic ring is also computed.Comment: 12 pages, 1 figure, to appear in Phys. Rev.

Interstellar Scintillations of Polarization of Compact Sources

We demostrate that the measurement of fluctuations of polarization due to the galactic interstellar scintillations may be used to study the structure of the radiation field at compact radio sources. We develop a mathematical formalism and demonstrate it on a simple analytical model in which the scale of the polarization variation through the source is comparable to the source size. The predicted amplitude of modulation of the polarized radiation flux is ~20% x (pi_s) x (m_sc), where (pi_s) is the characteristic degree of polarization of radiation at the source and (m_sc) is the typical modulation index due to scattering, i.e., (m_sc)~1 for diffractive scintillations and (m_sc)<1 for refractive scintillations.Comment: 5 pages, 2 figures, emilateapj.sty. Submitted to ApJ

The stationary phase point method for transitional scattering: diffractive radio scintillation for pulsar

The stationary phase point (SPP) method in one-dimensional case is introduced to treat the diffractive scintillation. From weak scattering, where the SPP number N=1, to strong scattering (N$\gg$1), via transitional scattering regime (N$\sim$2,3), we find that the modulation index of intensity experiences the monotonically increasing from 0 to 1 with the scattering strength, characterized by the ratio of Fresnel scale \rf to diffractive scale \rdiff.Comment: Hanas Meeting paper, appear in ChJAA, 2006, 6, Su

Radio Scintillation due to Discontinuities in the Interstellar Plasma Density

We develop the theory of interstellar scintillation as caused by an irregular plasma having a power-law spatial density spectrum with a spectral exponent of 4 corresponding to a medium with abrupt changes in its density. An ``outer scale'' is included in the model representing the typical scale over which the density of the medium remains uniform. Such a spectrum could be used to model plasma shock fronts in supernova remnants or other plasma discontinuities. We investigate and develop equations for the decorrelation bandwidth of diffractive scintillations and the refractive scintillation index and compare our results with pulsar measurements. We consider both a medium concentrated in a thin layer and an extended irregular medium. We conclude that the discontinuity model gives satisfactory agreement for many diffractive measurements, in particular the VLBI meaurements of the structure function exponent between 5/3 and 2. However, it gives less satisfactory agreement for the refractive scintillation index than does the Kolmogorov turbulence spectrum. The comparison suggests that the medium consists of a pervasive background distribution of turbulence embedded with randomly placed discrete plasma structures such as shocks or HII regions. This can be modeled by a composite spectrum following the Kolmogorov form at high wavenumbers and steepening at lower wavenumbers corresponding to the typical (inverse) size of the discrete structures. Such a model can also explain the extreme scattering events. However, lines of sight through the enhanced scattering prevalent at low galactic latitudes are accurately described by the Kolmogorov spectrum in an extended medium and do not appear to have a similar low-wavenumber steepening.Comment: Accpeted for ApJ vol 531, March 200

Multiangle static and dynamic light scattering in the intermediate scattering angle range

We describe a light scattering apparatus based on a novel optical scheme covering the scattering angle range 0.5\dg \le \theta \le 25\dg, an intermediate regime at the frontier between wide angle and small angle setups that is difficult to access by existing instruments. Our apparatus uses standard, readily available optomechanical components. Thanks to the use of a charge-coupled device detector, both static and dynamic light scattering can be performed simultaneously at several scattering angles. We demonstrate the capabilities of our apparatus by measuring the scattering profile of a variety of samples and the Brownian dynamics of a dilute colloidal suspension

Surface-Enhanced Plasmon Splitting in a Liquid-Crystal-Coated Gold Nanoparticle

We show that, when a gold nanoparticle is coated by a thin layer of nematic liquid crystal, the deformation produced by the nanoparticle surface can enhance the splitting of the nanoparticle surface plasmon. We consider three plausible liquid crystal director configurations in zero electric field: boojum pair (north-south pole configuration), baseball (tetrahedral), and homogeneous. From a calculation using the Discrete Dipole Approximation, we find that the surface plasmon splitting is largest for the boojum pair, intermediate for the homogeneous, and smallest for the baseball configuration. The boojum pair results are in good agreement with experiment. We conclude that the nanoparticle surface has a strong effect on the director orientation, but, surprisingly, that this deformation can actually enhance the surface plasmon splitting.Comment: 5 pages, 3 figures To be published in PR