Some remarks on the visible points of a lattice

We comment on the set of visible points of a lattice and its Fourier transform, thus continuing and generalizing previous work by Schroeder and Mosseri. A closed formula in terms of Dirichlet series is obtained for the Bragg part of the Fourier transform. We compare this calculation with the outcome of an optical Fourier transform of the visible points of the 2D square lattice.Comment: 9 pages, 3 eps-figures, 1 jpeg-figure; updated version; another article (by M. Baake, R. V. Moody and P. A. B. Pleasants) with the complete solution of the spectral problem will follow soon (see math.MG/9906132

Magnetic Field Uniformity Across the GF 9-2 YSO, L1082C Dense Core, and GF 9 Filamentary Dark Cloud

The orientation of the magnetic field (B-field) in the filamentary dark cloud GF 9 was traced from the periphery of the cloud into the L1082C dense core that contains the low-mass, low-luminosity Class 0 young stellar object (YSO) GF 9-2 (IRAS 20503+6006). This was done using SOFIA HAWC+ dust thermal emission polarimetry (TEP) at 216 um in combination with Mimir near-infrared background starlight polarimetry (BSP) conducted at H-band (1.6 um) and K-band (2.2 um). These observations were augmented with published I-band (0.77 um) BSP and Planck 850 um TEP to probe B-field orientations with offset from the YSO in a range spanning 6000 AU to 3 pc. No strong B-field orientation change with offset was found, indicating remarkable uniformity of the B-field from the cloud edge to the YSO environs. This finding disagrees with weak-field models of cloud core and YSO formation. The continuity of inferred B-field orientations for both TEP and BSP probes is strong evidence that both are sampling a common B-field that uniformly threads the cloud, core, and YSO region. Bayesian analysis of Gaia DR2 stars matched to the Mimir BSP stars finds a distance to GF 9 of 270 +/- 10 pc. No strong wavelength dependence of B-field orientation angle was found, contrary to previous claims.Comment: 18 pages, 6 figures ApJ, accepte

Air hydrodynamics of the ultrafast laser-triggered spark gap

We present space and time resolved measurements of the air hydrodynamics induced by ultrafast laser pulse excitation of the air gap between two electrodes at high potential difference. We explore both plasma-based and plasma-free gap excitation. The former uses the plasma left in the wake of femtosecond filamentation, while the latter exploits air heating by multiple-pulse resonant excitation of quantum molecular wavepackets. We find that the cumulative electrode-driven air density depression channel initiated by the laser plays the dominant role in the gap evolution leading to breakdown

Time--Evolving Statistics of Chaotic Orbits of Conservative Maps in the Context of the Central Limit Theorem

We study chaotic orbits of conservative low--dimensional maps and present numerical results showing that the probability density functions (pdfs) of the sum of $N$ iterates in the large $N$ limit exhibit very interesting time-evolving statistics. In some cases where the chaotic layers are thin and the (positive) maximal Lyapunov exponent is small, long--lasting quasi--stationary states (QSS) are found, whose pdfs appear to converge to $q$--Gaussians associated with nonextensive statistical mechanics. More generally, however, as $N$ increases, the pdfs describe a sequence of QSS that pass from a $q$--Gaussian to an exponential shape and ultimately tend to a true Gaussian, as orbits diffuse to larger chaotic domains and the phase space dynamics becomes more uniformly ergodic.Comment: 15 pages, 14 figures, accepted for publication as a Regular Paper in the International Journal of Bifurcation and Chaos, on Jun 21, 201

Rapid and accurate polarimetric radar measurements of ice crystal fabric orientation at the Western Antarctic Ice Sheet (WAIS) Divide ice core site

The crystal orientation fabric (COF) of ice sheets records the past history of ice sheet deformation and influences present-day ice flow dynamics. Though not widely implemented, coherent ice-penetrating radar is able to detect bulk anisotropic fabric patterns by exploiting the birefringence of ice crystals at radar frequencies, with the assumption that one of the crystallographic axes is aligned in the vertical direction. In this study, we conduct a suite of quad-polarimetric measurements consisting of four orthogonal antenna orientation combinations near the Western Antarctic Ice Sheet (WAIS) Divide Ice Core site. From these measurements, we are able to quantify the azimuthal fabric asymmetry at this site to a depth of 1400 m at a bulk-averaged resolution of up to 15 m. Our estimates of fabric asymmetry closely match corresponding fabric estimates directly measured from the WAIS Divide Ice Core. While ice core studies are often unable to determine the absolute fabric orientation due to core rotation during extraction, we are able to identify and conclude that the fabric orientation is depth-invariant to at least 1400 m, equivalent to 6700 years BP (years before 1950), and aligns closely with the modern surface strain direction at WAIS Divide. Our results support the claim that the deformation regime at WAIS Divide has not changed substantially through the majority of the Holocene. Rapid polarimetric determination of bulk fabric asymmetry and orientation compares well with much more laborious sample-based COF measurements from thin ice sections. Because it is the bulk-averaged fabric that ultimately influences ice flow, polarimetric radar methods provide an opportunity for its accurate and widespread mapping and its incorporation into ice flow models.Natural Environment Research Council (NERC) research grant NE/S006788/1 National Science Foundation (NSF) research grant #173902

Enhancing proton acceleration by using composite targets

Efficient laser ion acceleration requires high laser intensities, which can only be obtained by tightly focusing laser radiation. In the radiation pressure acceleration regime, where the tightly focused laser driver leads to the appearance of the fundamental limit for the maximum attainable ion energy, this limit corresponds to the laser pulse group velocity as well as to another limit connected with the transverse expansion of the accelerated foil and consequent onset of the foil transparency. These limits can be relaxed by using composite targets, consisting of a thin foil followed by a near critical density slab. Such targets provide guiding of a laser pulse inside a self-generated channel and background electrons, being snowplowed by the pulse, compensate for the transverse expansion. The use of composite targets results in a significant increase in maximum ion energy, compared to a single foil target case.Comment: 16 pages, 9 figure