National Geodetic Satellite Program, Part II: Smithsonian Astrophysical Observatory

A sequence of advances in the determination of geodetic parameters presented by the Smithsonian Astrophysical Observatory are described. A Baker-Nunn photographic system was used in addition to a ruby-laser ranging system to obtain data for refinement of geodetic parameters. A summary of the data employed to: (1) derive coordinates for the locations of various tracking stations; and (2) determine the gravitational potential of the earth, is presented

Chiral and herringbone symmetry breaking in water-surface monolayers

We report the observation from monolayers of eicosanoic acid in the L′2 phase of three distinct out-of-plane first-order diffraction peaks, indicating molecular tilt in a nonsymmetry direction and hence the absence of mirror symmetry. At lower pressures the molecules tilt in the direction of their nearest neighbors. In this region we find a structural transition, which we tentatively identify as the rotator-herringbone transition L2d−L2h

Metallicity variations in the Type II globular cluster NGC6934

The Hubble Space Telescope photometric survey of Galactic globular clusters (GCs) has revealed a peculiar "chromosome map" for NGC6934. Besides a typical sequence, similar to that observed in Type I GCs, NGC 6934 displays additional stars on the red side, analogous to the anomalous, Type II GCs, as defined in our previous work. We present a chemical abundance analysis of four red giants in this GC. Two stars are located on the chromosome map sequence common to all GCs, and another two on the additional sequence. We find: (i) star-to-star Fe variations, with the two anomalous stars being enriched by ~0.2 dex. Due to our small-size sample, this difference is at the ~2.5 sigma level; (ii) no evidence for variations in the slow neutron-capture abundances over Fe, at odds with what is often observed in anomalous Type II GCs, e.g. M 22 and Omega Centauri; (iii) no large variations in light elements C, O and Na, compatible with the targets location on the lower part of the chromosome map where such variations are not expected. Since the analyzed stars are homogeneous in light elements, the only way to reproduce the photometric splits on the sub-giant (SGB) and the red-giant (RGB) branches is to assume that red-RGB/faint-SGB stars are enhanced in [Fe/H] by ~0.2. This fact corroborates the spectroscopic evidence of a metallicity variation in NGC6934. The observed chemical pattern resembles only partially the other Type II GCs, suggesting that NGC6934 might belong either to a third class of GCs, or be a link between normal Type I and anomalous Type II GCs.Comment: 26 pages, 9 figures, accepted for publication in Ap

Second harmonic generation in SiC polytypes

LMTO calculations are presented for the frequency dependent second harmonic generation (SHG) in the polytypes 2H, 4H, 6H, 15R and 3C of SiC. All independent tensor components are calculated. The spectral features and the ratios of the 333 to 311 tensorial components are studied as a function of the degree of hexagonality. The relationship to the linear optical response and the underlying band structure are investigated. SHG is suggested to be a sensitive tool for investigating the near band edge interband excitations.Comment: 12 pages, 10 figure

Trkalian fields: ray transforms and mini-twistors

We study X-ray and Divergent beam transforms of Trkalian fields and their relation with Radon transform. We make use of four basic mathematical methods of tomography due to Grangeat, Smith, Tuy and Gelfand-Goncharov for an integral geometric view on them. We also make use of direct approaches which provide a faster but restricted view of the geometry of these transforms. These reduce to well known geometric integral transforms on a sphere of the Radon or the spherical Curl transform in Moses eigenbasis, which are members of an analytic family of integral operators. We also discuss their inversion. The X-ray (also Divergent beam) transform of a Trkalian field is Trkalian. Also the Trkalian subclass of X-ray transforms yields Trkalian fields in the physical space. The Riesz potential of a Trkalian field is proportional to the field. Hence, the spherical mean of the X-ray (also Divergent beam) transform of a Trkalian field over all lines passing through a point yields the field at this point. The pivotal point is the simplification of an intricate quantity: Hilbert transform of the derivative of Radon transform for a Trkalian field in the Moses basis. We also define the X-ray transform of the Riesz potential (of order 2) and Biot-Savart integrals. Then, we discuss a mini-twistor respresentation, presenting a mini-twistor solution for the Trkalian fields equation. This is based on a time-harmonic reduction of wave equation to Helmholtz equation. A Trkalian field is given in terms of a null vector in C3 with an arbitrary function and an exponential factor resulting from this reduction.Comment: 37 pages, http://dx.doi.org/10.1063/1.482610

Modulational instability of solitary waves in non-degenerate three-wave mixing: The role of phase symmetries

We show how the analytical approach of Zakharov and Rubenchik [Sov. Phys. JETP {\bf 38}, 494 (1974)] to modulational instability (MI) of solitary waves in the nonlinear Schr\"oedinger equation (NLS) can be generalised for models with two phase symmetries. MI of three-wave parametric spatial solitons due to group velocity dispersion (GVD) is investigated as a typical example of such models. We reveal a new branch of neck instability, which dominates the usual snake type MI found for normal GVD. The resultant nonlinear evolution is thereby qualitatively different from cases with only a single phase symmetry.Comment: 4 pages with figure

Self-Control in Cyberspace: Applying Dual Systems Theory to a Review of Digital Self-Control Tools

Many people struggle to control their use of digital devices. However, our understanding of the design mechanisms that support user self-control remains limited. In this paper, we make two contributions to HCI research in this space: first, we analyse 367 apps and browser extensions from the Google Play, Chrome Web, and Apple App stores to identify common core design features and intervention strategies afforded by current tools for digital self-control. Second, we adapt and apply an integrative dual systems model of self-regulation as a framework for organising and evaluating the design features found. Our analysis aims to help the design of better tools in two ways: (i) by identifying how, through a well-established model of self-regulation, current tools overlap and differ in how they support self-control; and (ii) by using the model to reveal underexplored cognitive mechanisms that could aid the design of new tools.Comment: 11.5 pages (excl. references), 6 figures, 1 tabl

Numerical and Experimental Investigation of Circulation in Short Cylinders

In preparation for an experimental study of magnetorotational instability (MRI) in liquid metal, we explore Couette flows having height comparable to the gap between cylinders, centrifugally stable rotation, and high Reynolds number. Experiments in water are compared with numerical simulations. Simulations show that endcaps corotating with the outer cylinder drive a strong poloidal circulation that redistributes angular momentum. Predicted azimuthal flow profiles agree well with experimental measurements. Spin-down times scale with Reynolds number as expected for laminar Ekman circulation; extrapolation from two-dimensional simulations at $Re\le 3200$ agrees remarkably well with experiment at $Re\sim 10^6$. This suggests that turbulence does not dominate the effective viscosity. Further detailed numerical studies reveal a strong radially inward flow near both endcaps. After turning vertically along the inner cylinder, these flows converge at the midplane and depart the boundary in a radial jet. To minimize this circulation in the MRI experiment, endcaps consisting of multiple, differentially rotating rings are proposed. Simulations predict that an adequate approximation to the ideal Couette profile can be obtained with a few rings

Leading Order Temporal Asymptotics of the Modified Non-Linear Schrodinger Equation: Solitonless Sector

Using the matrix Riemann-Hilbert factorisation approach for non-linear evolution equations (NLEEs) integrable in the sense of the inverse scattering method, we obtain, in the solitonless sector, the leading-order asymptotics as $t$ tends to plus and minus infinity of the solution to the Cauchy initial-value problem for the modified non-linear Schrodinger equation: also obtained are analogous results for two gauge-equivalent NLEEs; in particular, the derivative non-linear Schrodinger equation.Comment: 29 pages, 5 figures, LaTeX, revised version of the original submission, to be published in Inverse Problem