Electrostatic fluctuations in cavities within polar liquids and thermodynamics of polar solvation

We present the results of numerical simulations of fluctuations of the electrostatic potential and electric field inside cavities created in the fluid of dipolar hard spheres. We found that the thermodynamics of polar solvation dramatically changes its regime when the cavity size becomes about 4-5 times larger than the size of the liquid particle. The range of small cavities can be reasonably understood within the framework of current solvation models. On the contrary, the regime of large cavities is characterized by a significant softening of the cavity interface resulting in a decay of the fluctuation variances with the cavity size much faster than anticipated by both the continuum electrostatics and microscopic theories. For instance, the variance of potential decays with the cavity size $R_0$ approximately as $1/R_0^{4-6}$ instead of the $1/R_0$ scaling expected from standard electrostatics. Our results suggest that cores of non-polar molecular assemblies in polar liquids lose solvation strength much faster than is traditionally anticipated.Comment: 10 pp, 10 fig

Old puzzle, new insights: a lithium rich giant quietly burning helium in its core

About 1% of giant stars have been shown to have large surface Li abundances, which is unexpected according to standard stellar evolution models. Several scenarios for lithium production have been proposed, but it is still unclear why these Li-rich giants exist. A missing piece in this puzzle is the knowledge of the exact stage of evolution of these stars. Using low-and-high-resolution spectroscopic observations, we have undertaken a survey of lithium-rich giants in the Kepler field. In this letter, we report the finding of the first confirmed Li-rich core-helium-burning giant, as revealed by asteroseismic analysis. The evolutionary timescales constrained by its mass suggest that Li-production most likely took place through non-canonical mixing at the RGB-tip, possibly during the helium flash.Comment: 16 pages, 4 figures, 1 table, accepted in ApJ Letter

Laboratory Experiments, Numerical Simulations, and Astronomical Observations of Deflected Supersonic Jets: Application to HH 110

Collimated supersonic flows in laboratory experiments behave in a similar manner to astrophysical jets provided that radiation, viscosity, and thermal conductivity are unimportant in the laboratory jets, and that the experimental and astrophysical jets share similar dimensionless parameters such as the Mach number and the ratio of the density between the jet and the ambient medium. Laboratory jets can be studied for a variety of initial conditions, arbitrary viewing angles, and different times, attributes especially helpful for interpreting astronomical images where the viewing angle and initial conditions are fixed and the time domain is limited. Experiments are also a powerful way to test numerical fluid codes in a parameter range where the codes must perform well. In this paper we combine images from a series of laboratory experiments of deflected supersonic jets with numerical simulations and new spectral observations of an astrophysical example, the young stellar jet HH 110. The experiments provide key insights into how deflected jets evolve in 3-D, particularly within working surfaces where multiple subsonic shells and filaments form, and along the interface where shocked jet material penetrates into and destroys the obstacle along its path. The experiments also underscore the importance of the viewing angle in determining what an observer will see. The simulations match the experiments so well that we can use the simulated velocity maps to compare the dynamics in the experiment with those implied by the astronomical spectra. The experiments support a model where the observed shock structures in HH 110 form as a result of a pulsed driving source rather than from weak shocks that may arise in the supersonic shear layer between the Mach disk and bow shock of the jet's working surface.Comment: Full resolution figures available at http://sparky.rice.edu/~hartigan/pub.html To appear in Ap

Implementation of an Optimal First-Order Method for Strongly Convex Total Variation Regularization

We present a practical implementation of an optimal first-order method, due to Nesterov, for large-scale total variation regularization in tomographic reconstruction, image deblurring, etc. The algorithm applies to $\mu$-strongly convex objective functions with $L$-Lipschitz continuous gradient. In the framework of Nesterov both $\mu$ and $L$ are assumed known -- an assumption that is seldom satisfied in practice. We propose to incorporate mechanisms to estimate locally sufficient $\mu$ and $L$ during the iterations. The mechanisms also allow for the application to non-strongly convex functions. We discuss the iteration complexity of several first-order methods, including the proposed algorithm, and we use a 3D tomography problem to compare the performance of these methods. The results show that for ill-conditioned problems solved to high accuracy, the proposed method significantly outperforms state-of-the-art first-order methods, as also suggested by theoretical results.Comment: 23 pages, 4 figure

A Bichromatic Incidence Bound and an Application

We prove a new, tight upper bound on the number of incidences between points and hyperplanes in Euclidean d-space. Given n points, of which k are colored red, there are O_d(m^{2/3}k^{2/3}n^{(d-2)/3} + kn^{d-2} + m) incidences between the k red points and m hyperplanes spanned by all n points provided that m = \Omega(n^{d-2}). For the monochromatic case k = n, this was proved by Agarwal and Aronov. We use this incidence bound to prove that a set of n points, no more than n-k of which lie on any plane or two lines, spans \Omega(nk^2) planes. We also provide an infinite family of counterexamples to a conjecture of Purdy's on the number of hyperplanes spanned by a set of points in dimensions higher than 3, and present new conjectures not subject to the counterexample.Comment: 12 page

Parity violating elastic electron scattering and neutron density distributions in the Relativistic Hartree-Bogoliubov model

Parity violating elastic electron scattering on neutron-rich nuclei is described in the framework of relativistic mean-field theory. Self-consistent ground state density distributions of Ne, Na, Ni and Sn isotopes are calculated with the relativistic Hartree- Bogoliubov model, and the resulting neutron radii are compared with available experimental data. For the elastic scattering of 850 MeV electrons on these nuclei, the parity-violating asymmetry parameters are calculated using a relativistic optical model with inclusion of Coulomb distortion effects. The asymmetry parameters for chains of isotopes are compared, and their relation to the Fourier transforms of neutron densities is studied. It is shown that parity-violating asymmetries are sensitive not only to the formation of the neutron skin, but also to the shell effects of the neutron density distribution.Comment: RevTeX 17 pages, 18 eps figs, submitted to Phys. Rev.