Eccentricity Evolution of Extrasolar Multiple Planetary Systems due to the Depletion of Nascent Protostellar Disks

Most extrasolar planets are observed to have eccentricities much larger than those in the solar system. Some of these planets have sibling planets, with comparable masses, orbiting around the same host stars. In these multiple planetary systems, eccentricity is modulated by the planets' mutual secular interaction as a consequence of angular momentum exchange between them. For mature planets, the eigenfrequencies of this modulation are determined by their mass and semi-major axis ratios. But, prior to the disk depletion, self gravity of the planets' nascent disks dominates the precession eigenfrequencies. We examine here the initial evolution of young planets' eccentricity due to the apsidal libration or circulation induced by both the secular interaction between them and the self gravity of their nascent disks. We show that as the latter effect declines adiabatically with disk depletion, the modulation amplitude of the planets' relative phase of periapse is approximately invariant despite the time-asymmetrical exchange of angular momentum between planets. However, as the young planets' orbits pass through a state of secular resonance, their mean eccentricities undergo systematic quantitative changes. For applications, we analyze the eccentricity evolution of planets around Upsilon Andromedae and HD168443 during the epoch of protostellar disk depletion. We find that the disk depletion can change the planets' eccentricity ratio. However, the relatively large amplitude of the planets' eccentricity cannot be excited if all the planets had small initial eccentricities.Comment: 50 pages including 11 figures, submitted to Ap

Thermalization and temperature distribution in a driven ion chain

We study thermalization and non-equilibrium dynamics in a dissipative quantum many-body system -- a chain of ions with two points of the chain driven by thermal bath under different temperature. Instead of a simple linear temperature gradient as one expects from the classical heat diffusion process, the temperature distribution in the ion chain shows surprisingly rich patterns, which depend on the ion coupling rate to the bath, the location of the driven ions, and the dissipation rates of the other ions in the chain. Through simulation of the temperature evolution, we show that these unusual temperature distribution patterns in the ion chain can be quantitatively tested in experiments within a realistic time scale.Comment: 5 pages, 5 figure

Modeling for Active Control of Combustion and Thermally Driven Oscillations

Organized oscillations excited and sustained by high densities of energy release in combustion chambers have long caused serious problems in development of propulsion systems. The amplitudes often become sufficiently large to cause unacceptable structural vibrations. Because the oscillations are self-excited, they reach limiting amplitudes (limit cycles) only because of the action of nonlinear processes. Traditionally, satisfactory behavior has been achieved through a combination of trial-and-error design and testing, with control always involving passive means: geometrical modifications, changes of propellant composition, or devices to enhance dissipation of acoustic energy. Active control has been applied only to small-scale laboratory devices, but the limited success suggests the possibility of serious applications to full-scale propulsion systems. Realization of that potential rests on further experimental work, combined with deeper understanding of the mechanisms causing the oscillations and of the physical behavior of the systems. Effective design of active control systems will require faithful modeling of the relevant processes over broad frequency ranges covering the spectra of natural modes. This paper will cover the general character of the linear and nonlinear behavior of combustion systems, with special attention to acoustics and the mechanisms of excitation. The discussion is intended to supplement the paper by Doyle et al. concerned primarily with controls issues and the observed behavior of simple laboratory devices

Polar plasmas as observed by Dynamics Explorers 1 and 2

Plasma measurements from the Dynamics Explorer 1 and 2 satellites were used to characterize the polar cap environment. Analysis of numerous polar-cap passes indicate that, in general, three major regimes of plasma exist: (1) polar rain--electrons with magnetosheath-like energy spectra but much lower densities, most intense near the cusp and weakening toward the central polar cap; (2) polar wind--low energy upward flowing ions with both field-aligned and conical distributions; and (3) acceleration events--sporadic events consistent with the acceleration of electrons and positive ions by parallel electric fields. (1) to (3) were observed at high altitudes by Dynamics Explorer 1, while (1) and (3) were also observed at low altitudes by Dynamics Explorer 2. The plasma parameters associated with these plasma regimes are presented and discussed in terms of source and acceleration mechanisms

Influence of Correlated Hybridization on the Conductance of Molecular Transistors

We study the spin-1/2 single-channel Anderson impurity model with correlated (occupancy dependent) hybridization for molecular transistors using the numerical renormalization-group method. Correlated hybridization can induce nonuniversal deviations in the normalized zero-bias conductance and, for some parameters, modestly enhance the spin polarization of currents in applied magnetic field. Correlated hybridization can also explain a gate-voltage dependence to the Kondo scale similar to what has been observed in recent experiments.Comment: 4 pages, 5 figure

Collisional Cascades in Planetesimal Disks II. Embedded Planets

We use a multiannulus planetesimal accretion code to investigate the growth of icy planets in the outer regions of a planetesimal disk. In a quiescent minimum mass solar nebula, icy planets grow to sizes of 1000--3000 km on a timescale t = 15-20 Myr (a/30 AU)^3 where a is the distance from the central star. Planets form faster in more massive nebulae. Newly-formed planets stir up leftover planetesimals along their orbits and produce a collisional cascade where icy planetesimals are slowly ground to dust. The dusty debris of planet formation has physical characteristics similar to those observed in beta Pic, HR 4796A, and other debris disks. We derive dust masses for small particles, 1 mm and smaller, and large particles, 1 mm and larger, as a function of the initial conditions in the planetesimal disk. The dust luminosities derived from these masses are similar to those observed in Vega, HR 4796A, and other debris disks. The calculations produce bright rings and dark gaps. Bright rings occur where 1000 km and larger planets have recently formed. Dark gaps are regions where planets have cleared out dust or shadows where planets have yet to form.Comment: to be published in the Astronomical Journal, January 2004; 7 pages of text; 17 figures at http://cfa-www.harvard.edu/~kenyon/pf/emb-planet-figures.pdf; 2 animations at http://cfa-www.harvard.edu/~kenyon/pf/emb-planet-movies.htm

The structure of the central disk of NGC 1068: a clumpy disk model

NGC 1068 is one of the best studied Seyfert II galaxies, for which the blackhole mass has been determined from the Doppler velocities of water maser. We show that the standard $\alpha$-disk model of NGC 1068 gives disk mass between the radii of 0.65 pc and 1.1 pc (the region from which water maser emission is detected) to be about 7x10$^7$ M$_\odot$ (for $\alpha=0.1$), more than four times the blackhole mass, and a Toomre Q-parameter for the disk is $\sim$0.001. This disk is therefore highly self-gravitating and is subject to large-amplitude density fluctuations. We conclude that the standard $\alpha$-viscosity description for the structure of the accretion disk is invalid for NGC 1068. In this paper we develop a new model for the accretion disk. The disk is considered to be composed of gravitationally bound clumps; accretion in this clumped disk model arises because of gravitational interaction of clumps with each other and the dynamical frictional drag exerted on clumps from the stars in the central region of the galaxy. The clumped disk model provides a self-consistent description of the observations of NGC 1068. The computed temperature and density are within the allowed parameter range for water maser emission, and the rotational velocity in the disk falls off as $r^{-0.35}$.Comment: To appear in Ap

Matrix elements of the complete set of \Delta B = 2 and \Delta C = 2 operators in heavy meson chiral perturbation theory

Using heavy meson chiral perturbation theory, we consider the light quark-mass and spatial volume dependence of the matrix elements of \Delta B=2 and \Delta C=2 four-quark operators relevant for B^{0}_{(s)}{-}\bar{B}^{0}_{(s)} and D^{0}{-}\bar{D}^{0} mixing, and the B_{s} meson width difference. Our results for these matrix elements are obtained in the N_{f}=2+1 partially quenched theory, which becomes full QCD in the limit where sea and valence quark masses become equal. They can be used in extrapolation of lattice calculations of these matrix elements to the physical light quark masses and to infinite volume. An important conclusion of this paper is that the chiral extrapolations for matrix elements of heavy-light meson mixing beyond the Standard Model, and those relevant for the B_s width difference are more complicated than that for the Standard Model mixing matrix elements.Comment: 13 pages; version accepted for publicatio