Local Lagrangian Approximations for the Evolution of the Density Distribution Function in Large-Scale Structure

We examine local Lagrangian approximations for the gravitational evolution of the density distribution function. In these approximations, the final density at a Lagrangian point q at a time t is taken to be a function only of t and of the initial density at the same Lagrangian point. A general expression is given for the evolved density distribution function for such approximations, and we show that the vertex generating function for a local Lagrangian mapping applied to an initially Gaussian density field bears a simple relation to the mapping itself. Using this result, we design a local Lagrangian mapping which reproduces nearly exactly the hierarchical amplitudes given by perturbation theory for gravitational evolution. When extended to smoothed density fields and applied to Gaussian initial conditions, this mapping produces a final density distribution function in excellent agreement with full numerical simulations of gravitational clustering. We also examine the application of these local Lagrangian approximations to non-Gaussian initial conditions.Comment: LaTeX, 22 pages, and 11 postscript figure

Mott metal-insulator transition on compressible lattices

The critical properties of the finite temperature Mott endpoint are drastically altered by a coupling to crystal elasticity, i.e., whenever it is amenable to pressure tuning. Similar as for critical piezoelectric ferroelectrics, the Ising criticality of the electronic system is preempted by an isostructural instability, and long-range shear forces suppress microscopic fluctuations. As a result, the endpoint is governed by Landau criticality. Its hallmark is thus a breakdown of Hooke's law of elasticity with a non-linear strain-stress relation characterized by a mean-field exponent. Based on a quantitative estimate, we predict critical elasticity to dominate the temperature range DeltaT/Tc ~ 8% close to the Mott endpoint of kappa-(BEDT-TTF)2X.Comment: 4 pages, 6 figure

Skewness of the Large-Scale Velocity Divergence from Non-Gaussian Initial Conditions

We compute the skewness $t_3$ and the corresponding hierarchical amplitude $T_3$ of the divergence of the velocity field for arbitrary non-Gaussian initial conditions. We find that $T_3$ qualitatively resembles the corresponding hierarchical amplitude for the density field, $S_3$, in that it contains a term proportional to the initial skewness, which decays inversely as the linear growth factor, plus a constant term which differs from the corresponding Gaussian term by a complex function of the initial three- and four- point functions. We extend the results for $S_3$ and $T_3$ with non-Gaussian initial conditions to evolved fields smoothed with a spherical tophat window function. We show that certain linear combinations, namely $S_3 + {1 \over 2} T_3$, $S_3 + T_3$, and $s_3 + t_3$, lead to expressions which are much simpler, for non-Gaussian initial conditions, than $S_3$ and $T_3$ (or $s_3$ and $t_3$) considered separately.Comment: 13 pages, latex, no figure

Astrometric Positions and Proper Motions of 19 Radio Stars

We have used the Very Large Array, linked with the Pie Town Very Long Baseline Array antenna, to determine astrometric positions of 19 radio stars in the International Celestial Reference Frame (ICRF). The positions of these stars were directly linked to the positions of distant quasars through phase referencing observations. The positions of the ICRF quasars are known to 0.25 mas, thus providing an absolute reference at the angular resolution of our radio observations. Average values for the errors in our derived positions for all sources were 13 mas and 16 mas in R.A. and declination respectively, with accuracies approaching 1-2 mas for some of the stars observed. Differences between the ICRF positions of the 38 quasars, and those measured from our observations showed no systematic offsets, with mean values of -0.3 mas in R.A. and -1.0 mas in declination. Standard deviations of the quasar position differences of 17 mas and 11 mas in R.A. and declination respectively, are consistent with the mean position errors determined for the stars. Our measured positions were combined with previous Very Large Array measurements taken from 1978-1995 to determine the proper motions of 15 of the stars in our list. With mean errors of approximately 1.6 mas/yr, the accuracies of our proper motions approach those derived from Hipparcos, and for a few of the stars in our program, are better than the Hipparcos values. Comparing the positions of our radio stars with the Hipparcos catalog, we find that at the epoch of our observations, the two frames are aligned to within formal errors of approximately 3 mas. This result confirms that the Hipparcos frame is inertial at the expected level.Comment: 20 pages, 9 figures Accepted by the Astronomical Journal, 2003 March 1

All-Sky spectrally matched UBVRI-ZY and u'g'r'i'z' magnitudes for stars in the Tycho2 catalog

We present fitted UBVRI-ZY and u'g'r'i'z' magnitudes, spectral types and distances for 2.4M stars, derived from synthetic photometry of a library spectrum that best matches the Tycho2 BtVt, NOMAD Rn and 2MASS JHK_{2/S} catalog magnitudes. We present similarly synthesized multi-filter magnitudes, types and distances for 4.8M stars with 2MASS and SDSS photometry to g<16 within the Sloan survey region, for Landolt and Sloan primary standards, and for Sloan Northern (PT) and Southern secondary standards. The synthetic magnitude zeropoints for BtVt, UBVRI, ZvYv, JHK_{2/S}, JHK_{MKO}, Stromgren uvby, Sloan u'g'r'i'z' and ugriz are calibrated on 20 calspec spectrophotometric standards. The UBVRI and ugriz zeropoints have dispersions of 1--3%, for standards covering a range of color from -0.3 < V-I < 4.6; those for other filters are in the range 2--5%. The spectrally matched fits to Tycho2 stars provide estimated 1-sigma errors per star of ~0.2, 0.15, 0.12, 0.10 and 0.08 mags respectively in either UBVRI or u'g'r'i'z'; those for at least 70% of the SDSS survey region to g<16 have estimated 1-sigma errors per star of ~0.2, 0.06, 0.04, 0.04, 0.05 in u'g'r'i'z' or UBVRI. The density of Tycho2 stars, averaging about 60 stars per square degree, provides sufficient stars to enable automatic flux calibrations for most digital images with fields of view of 0.5 degree or more. Using several such standards per field, automatic flux calibration can be achieved to a few percent in any filter, at any airmass, in most workable observing conditions, to facilitate inter-comparison of data from different sites, telescopes and instruments.Comment: 36 pages, 30 figures, 3 printed tables, several electronic tables, accepted PASP Dec 201

Heat conductivity of DNA double helix

Thermal conductivity of isolated single molecule DNA fragments is of importance for nanotechnology, but has not yet been measured experimentally. Theoretical estimates based on simplified (1D) models predict anomalously high thermal conductivity. To investigate thermal properties of single molecule DNA we have developed a 3D coarse-grained (CG) model that retains the realism of the full all-atom description, but is significantly more efficient. Within the proposed model each nucleotide is represented by 6 particles or grains; the grains interact via effective potentials inferred from classical molecular dynamics (MD) trajectories based on a well-established all-atom potential function. Comparisons of 10 ns long MD trajectories between the CG and the corresponding all-atom model show similar root-mean-square deviations from the canonical B-form DNA, and similar structural fluctuations. At the same time, the CG model is 10 to 100 times faster depending on the length of the DNA fragment in the simulation. Analysis of dispersion curves derived from the CG model yields longitudinal sound velocity and torsional stiffness in close agreement with existing experiments. The computational efficiency of the CG model makes it possible to calculate thermal conductivity of a single DNA molecule not yet available experimentally. For a uniform (polyG-polyC) DNA, the estimated conductivity coefficient is 0.3 W/mK which is half the value of thermal conductivity for water. This result is in stark contrast with estimates of thermal conductivity for simplified, effectively 1D chains ("beads on a spring") that predict anomalous (infinite) thermal conductivity. Thus, full 3D character of DNA double-helix retained in the proposed model appears to be essential for describing its thermal properties at a single molecule level.Comment: 16 pages, 12 figure

Signal Structure of the Starlink Ku-Band Downlink

We develop a technique for blind signal identification of the Starlink downlink signal in the 10.7 to 12.7 GHz band and present a detailed picture of the signal's structure. Importantly, the signal characterization offered herein includes the exact values of synchronization sequences embedded in the signal that can be exploited to produce pseudorange measurements. Such an understanding of the signal is essential to emerging efforts that seek to dual-purpose Starlink signals for positioning, navigation, and timing, despite their being designed solely for broadband Internet provision