Time-dependent density-functional theory beyond the adiabatic approximation: insights from a two-electron model system

Most applications of time-dependent density-functional theory (TDDFT) use the adiabatic local-density approximation (ALDA) for the dynamical exchange-correlation potential Vxc(r,t). An exact (i.e., nonadiabatic) extension of the ground-state LDA into the dynamical regime leads to a Vxc(r,t) with a memory, which causes the electron dynamics to become dissipative. To illustrate and explain this nonadiabatic behavior, this paper studies the dynamics of two interacting electrons on a two-dimensional quantum strip of finite size, comparing TDDFT within and beyond the ALDA with numerical solutions of the two-electron time-dependent Schroedinger equation. It is shown explicitly how dissipation arises through multiple particle-hole excitations, and how the nonadiabatic extension of the ALDA fails for finite systems, but becomes correct in the thermodynamic limit.Comment: 10 pages, 7 figure

Immortal homogeneous Ricci flows

We show that for an immortal homogeneous Ricci flow solution any sequence of parabolic blow-downs subconverges to a homogeneous expanding Ricci soliton. This is established by constructing a new Lyapunov function based on curvature estimates which come from real geometric invariant theory.Comment: Final version, to appear in Invent. Mat

Bayesian weak lensing tomography: Reconstructing the 3D large-scale distribution of matter with a lognormal prior

We present a Bayesian reconstruction algorithm that infers the three-dimensional large-scale matter distribution from the weak gravitational lensing effects measured in the image shapes of galaxies. The algorithm is designed to also work with non-Gaussian posterior distributions which arise, for example, from a non-Gaussian prior distribution. In this work, we use a lognormal prior and compare the reconstruction results to a Gaussian prior in a suite of increasingly realistic tests on mock data. We find that in cases of high noise levels (i.e. for low source galaxy densities and/or high shape measurement uncertainties), both normal and lognormal priors lead to reconstructions of comparable quality, but with the lognormal reconstruction being prone to mass-sheet degeneracy. In the low-noise regime and on small scales, the lognormal model produces better reconstructions than the normal model: The lognormal model 1) enforces non-negative densities, while negative densities are present when a normal prior is employed, 2) better traces the extremal values and the skewness of the true underlying distribution, and 3) yields a higher pixel-wise correlation between the reconstruction and the true density.Comment: 23 pages, 12 figures; updated to match version accepted for publication in PR

Pulsation-Initiated Mass Loss in Luminous Blue Variables: A Parameter Study

Luminous blue variables (LBVs) are characterized by semi-periodic episodes of enhanced mass-loss, or outburst. The cause of these outbursts has thus far been a mystery. One explanation is that they are initiated by kappa-effect pulsations in the atmosphere caused by an increase in luminosity at temperatures near the so-called ``iron bump'' (T ~ 200,000 K), where the Fe opacity suddenly increases. Due to a lag in the onset of convection, this luminosity can build until it exceeds the Eddington limit locally, seeding pulsations and possibly driving some mass from the star. We present some preliminary results from a parameter study focusing on the conditions necessary to trigger normal S-Dor type (as opposed to extreme eta-Car type) outbursts. We find that as Y increases or Z decreases, the pulsational amplitude decreases and outburst-like behavior, indicated by a large, sudden increase in photospheric velocity, becomes likes likely.Comment: 6 pages, 4 figures, to be published in the Proceedings of Massive Stars as Cosmic Engines, IAU Symp 250, ed. F. Bresolin, P. A. Crowther, & J. Puls (Cambridge Univ. Press

Hysteresis of Backflow Imprinted in Collimated Jets

We report two different types of backflow from jets by performing 2D special relativistic hydrodynamical simulations. One is anti-parallel and quasi-straight to the main jet (quasi-straight backflow), and the other is bent path of the backflow (bent backflow). We find that the former appears when the head advance speed is comparable to or higher than the local sound speed at the hotspot while the latter appears when the head advance speed is slower than the sound speed bat the hotspot. Bent backflow collides with the unshocked jet and laterally squeezes the jet. At the same time, a pair of new oblique shocks are formed at the tip of the jet and new bent fast backflows are generated via these oblique shocks. The hysteresis of backflow collisions is thus imprinted in the jet as a node and anti-node structure. This process also promotes broadening of the jet cross sectional area and it also causes a decrease in the head advance velocity. This hydrodynamic process may be tested by observations of compact young jets.Comment: 9 pages, 5 figures, accepted for publication in ApJ