Excitation of Na D-line radiation in collisions of sodium atoms with internally excited H2, D2, and N2

Excitation of D-line radiation in collisions of Na atoms with vibrationally excited N2, H2 and D2 was studied in two modulated crossed beam experiments. In both experiments, the vibrational excitation of the molecules was provided by heating the molecular beam source to temperatures in the range of 2000 to 3000 K, which was assumed to give populations according to the Boltzmann expression. In the first experiment, a total rate coefficient was measured as a function of molecular beam temperature, with absolute calibration of the photon detector being made using the black body radiation from the heated molecular beam source. Since heating affects both the internal energy and the collisional kinetic energy, the first experiment could not determine the relative contributions of internal energy transfer versus collisional excitation. The second experiment achieved partial separation of internal versus kinetic energy transfer effects by using a velocity-selected molecular beam. Using two simple models for the kinetic energy dependence of the transfer cross section for a given change in vibrational quantum number, the data from both experiments were used to determine parameters in the models

Hydromagnetic Instability in plane Couette Flow

We study the stability of a compressible magnetic plane Couette flow and show that compressibility profoundly alters the stability properties if the magnetic field has a component perpendicular to the direction of flow. The necessary condition of a newly found instability can be satisfied in a wide variety of flows in laboratory and astrophysical conditions. The instability can operate even in a very strong magnetic field which entirely suppresses other MHD instabilities. The growth time of this instability can be rather short and reach $\sim 10$ shear timescales.Comment: 6 pages, 5 figures. To appear on PR

A Redshift Survey of Nearby Galaxy Groups: the Shape of the Mass Density Profile

We constrain the mass profile and orbital structure of nearby groups and clusters of galaxies. Our method yields the joint probability distribution of the density slope n, the velocity anisotropy beta, and the turnover radius r0 for these systems. The measurement technique does not use results from N-body simulations as priors. We incorporate 2419 new redshifts in the fields of 41 systems of galaxies with z < 0.04. The new groups have median velocity dispersion sigma=360 km/s. We also use 851 archived redshifts in the fields of 8 nearly relaxed clusters with z < 0.1. Within R < 2 r200, the data are consistent with a single power law matter density distribution with slope n = 1.8-2.2 for systems with sigma < 470 km/s, and n = 1.6-2.0 for those with sigma > 470 km/s (95% confidence). We show that a simple, scale-free phase space distribution function f(E,L^2) ~ (-E)^(alpha-1/2) L^(-2 \beta) is consistent with the data as long as the matter density has a cusp. Using this DF, matter density profiles with constant density cores (n=0) are ruled out with better than 99.7% confidence.Comment: 22 pages; accepted for publication in the Astrophysical Journa

Vorticity Budget of Weak Thermal Convection in Keplerian disks

By employing the equations of mean-square vorticity (enstrophy) fluctuations in strong shear flows, we demonstrate that unlike energy production of turbulent vorticity in nonrotating shear flows, the turbulent vorticity of weak convection in Keplerian disks cannot gain energy from vortex stretching/tilting by background shear unless the asscoiated Reynolds stresses are negative. This is because the epicyclic motion is an energy sink of the radial component of mean-square turbulent vorticity in Keplerian disks when Reynolds stresses are positive. Consequently, weak convection cannot be self-sustained in Keplerian flows. This agrees with the results implied from the equations of mean-square velocity fluctuations in strong shear flows. Our analysis also sheds light on the explanation of the simulation result in which positive kinetic helicity is produced by the Balbus-Hawley instability in a vertically stratified Keplerian disk. We also comment on the possibility of outward angular momentum transport by strong convection based on azimuthal pressure perturbations and directions of energy cascade.Comment: 8 pages, 1 figure, emulateapj.sty, revised version in response to referee's comments, accepted by Ap

On perfect neighborhood sets in graphs

AbstractLet G = (V, E) be a graph and let S ⊆ V.. The set S is a dominating set of G is every vertex of V − S is adjacent to a vertex of S. A vertex v of G is called S-perfect if |N[ν]∩S| = 1 where N[v] denotes the closed neighborhood of v. The set S is defined to be a perfect neighborhood set of G if every vertex of G is S-perfect or adjacent with an S-perfect vertex. We prove that for all graphs G, Θ(G) = Γ(G) where Γ(G) is the maximum cardinality of a minimal dominating set of G and where Θ(G) is the maximum cardinality among all perfect neighborhood sets of G

Letters from William Burnside to Robert Fricke: Automorphic Functions, and the Emergence of the Burnside Problem

Two letters from William Burnside have recently been found in the Nachlass of Robert Fricke that contain instances of Burnside's Problem prior to its first publication. We present these letters as a whole to the public for the first time. We draw a picture of these two mathematicians and describe their activities leading to their correspondence. We thus gain an insight into their respective motivations, reactions, and attitudes, which may sharpen the current understanding of professional and social interactions of the mathematical community at the turn of the 20th century.Comment: documentclass amsart, 17 page