A Discrete Hardy-Laptev-Weidl-Type Inequality and Associated Schrödinger-Type Operators

Although the classical Hardy inequality is valid only in the three- and higher dimensional case, Laptev and Weidl established a two-dimensional Hardy-type inequality for the magnetic gradient with an Aharonov-Bohm magnetic potential. Here we consider a discrete analogue, replacing the punctured plane with a radially exponential lattice. In addition to discrete Hardy and Sobolev inequalities, we study the spectral properties of two associated self-adjoint operators. In particular, it is shown that, for suitable potentials, the discrete Schrödingertype operator in the Aharonov-Bohm field has essential spectrum concentrated at 0, and the multiplicity of its lower spectrum satisfies a CLR-type inequality.Although the classical Hardy inequality is valid only in the three- and higher dimensional case, Laptev and Weidl established a two-dimensional Hardy-type inequality for the magnetic gradient with an Aharonov-Bohm magnetic potential. Here we consider a discrete analogue, replacing the punctured plane with a radially exponential lattice. In addition to discrete Hardy and Sobolev inequalities, we study the spectral properties of two associated self-adjoint operators. In particular, it is shown that, for suitable potentials, the discrete Schrödingertype operator in the Aharonov-Bohm field has essential spectrum concentrated at 0, and the multiplicity of its lower spectrum satisfies a CLR-type inequality

Percolative diffusion of CO during CO oxidation on Pt(100)

During CO-oxidation on Pt(100), CO diffuses in a disordered environment produced by a complex pattern of reconstructed and unreconstructed regions of the substrate. Macroscopic diffusion of CO is effectively only possible on percolating 1X1-regions of the substrate. We treat the spatio-temporal behavior observed in this reaction system accounting in the simple way for the percolative nature of CO-diffusion. This is done via incorporation into the reaction-diffusion equations of a suitable chemical diffusion coefficient, exploiting ideas from the theory of transport in disordered media. We use these equations to analyze the propagation of reactive, O-rich pulses into a CO-covered 1X1-background

NASA Image Processing Technology Applied to Medicine: Ten Unsolved Problems in Medical Imaging

The solutions to current diagnostic imaging problems will be found, at least in part, in digital image processing technology developed by NASA. The adaptation of appropriate technology that can be applied clinically to improve the care of patients is a major concern of radiologists. We have considered ten problems with clinical significance in diagnostic medical imaging, and discuss the impact of NASA image processing technology presently and predict future developments in this area

MAGIICAT V. Orientation of Outflows and Accretion Determine the Kinematics and Column Densities of the Circumgalactic Medium

We investigate the dependence of gas kinematics and column densities in the MgII-absorbing circumgalactic medium on galaxy color, azimuthal angle, and inclination to trace baryon cycle processes. Our sample of 30 foreground isolated galaxies at $0.3<z_{\rm gal}<1.0$, imaged with the Hubble Space Telescope, are probed by background quasars within a projected distance of $20<D<110$ kpc. From the high-resolution ($\Delta v\simeq 6.6$ km s$^{-1}$) quasar spectra, we quantify the extent of the absorber velocity structure with pixel-velocity two-point correlation functions. Absorbers with the largest velocity dispersions are associated with blue, face-on ($i<57^{\circ}$) galaxies probed along the projected minor axis ($\Phi \geq 45^{\circ}$), while those with the smallest velocity dispersions belong to red, face-on galaxies along the minor axis. The velocity structure is similar for edge-on ($i \geq 57^{\circ}$) galaxies regardless of galaxy color or azimuthal angle, for red galaxies with azimuthal angle, and for blue and red galaxies probed along the projected major axis ($\Phi<45^{\circ}$). The cloud column densities for face-on galaxies and red galaxies are smaller than for edge-on galaxies and blue galaxies, respectively. These results are consistent with biconical outflows along the minor axis for star-forming galaxies and accreting and/or rotating gas, which is most easily observed in edge-on galaxies probed along the major axis. Gas entrained in outflows may be fragmented with large velocity dispersions, while gas accreting onto or rotating around galaxies may be more coherent due to large path lengths and smaller velocity dispersions. Quiescent galaxies may exhibit little-to-no outflows along the minor axis, while accretion/rotation may exist along the major axis.Comment: 12 pages, 6 figures, 1 table. Accepted for publication in Ap

10 µm minority-carrier diffusion lengths in Si wires synthesized by Cu-catalyzed vapor-liquid-solid growth

The effective electron minority-carrier diffusion length, L_(n,eff), for 2.0 µm diameter Si wires that were synthesized by Cu-catalyzed vapor-liquid-solid growth was measured by scanning photocurrent microscopy. In dark, ambient conditions, L_(n,eff) was limited by surface recombination to a value of ≤ 0.7 µm. However, a value of L_(n,eff) = 10.5±1 µm was measured under broad-area illumination in low-level injection. The relatively long minority-carrier diffusion length observed under illumination is consistent with an increased surface passivation resulting from filling of the surface states of the Si wires by photogenerated carriers. These relatively large L_(n,eff) values have important implications for the design of high-efficiency, radial-junction photovoltaic cells from arrays of Si wires synthesized by metal-catalyzed growth processes