On the distribution of sequences of the form (qny)(q_ny)

We study the distribution of sequences of the form $(q_ny)_{n=1}^\infty$, where $(q_n)_{n=1}^\infty$ is some increasing sequence of integers. In particular, we study the Lebesgue measure and find bounds on the Hausdorff dimension of the set of points $\gamma \in [0,1)$ which are well approximated by points in the sequence $(q_ny)_{n=1}^\infty$. The bounds on Hausdorff dimension are valid for almost every $y$ in the support of a measure of positive Fourier dimension. When the required rate of approximation is very good or if our sequence is sufficiently rapidly growing, our dimension bounds are sharp. If the measure of positive Fourier dimension is itself Lebesgue measure, our measure bounds are also sharp for a very large class of sequences. We also give an application to inhomogeneous Littlewood type problems.Comment: 15 pages. Niclas Technau pointed out to us that Theorems 1 and 2 in the original version were in fact consequences of arXiv:2307.14871 . In this revised version, we have strengthened both theorems to cover a wider class of sequence

The luminosity function of the brightest galaxies in the IRAS survey

Results from a study of the far infrared properties of the brightest galaxies in the IRAS survey are described. There is a correlation between the infrared luminosity and the infrared to optical luminosity ratio and between the infrared luminosity and the far infrared color temperature in these galaxies. The infrared bright galaxies represent a significant component of extragalactic objects in the local universe, being comparable in space density to the Seyferts, optically identified starburst galaxies, and more numerous than quasars at the same bolometric luminosity. The far infrared luminosity in the local universe is approximately 25% of the starlight output in the same volume

Nitrogen hydrides in interstellar gas: Herschel/HIFI observations towards G10.6-0.4 (W31C)

The HIFI instrument on board the Herschel Space Observatory has been used to observe interstellar nitrogen hydrides along the sight-line towards G10.6−0.4 in order to improve our understanding of the interstellar chemistry of nitrogen. We report observations of absorption in NH N = 1 ← 0, J = 2 ← 1 and ortho-NH_2 1_(1,1) ← 0_(0,0). We also observed ortho-NH_3 1_0 ← 0_0, and 2_0 ← 1_0, para-NH_3 2_1 ← 1_1, and searched unsuccessfully for NH^+. All detections show emission and absorption associated directly with the hot-core source itself as well as absorption by foreground material over a wide range of velocities. All spectra show similar, non-saturated, absorption features, which we attribute to diffuse molecular gas. Total column densities over the velocity range 11−54 km s^(−1) are estimated. The similar profiles suggest fairly uniform abundances relative to hydrogen, approximately 6 × 10^(−9), 3 × 10^(−9), and 3 × 10^(−9) for NH, NH_2, and NH_3, respectively. These abundances are discussed with reference to models of gas-phase and surface chemistry

Evidence for the absence of regularization corrections to the partial-wave renormalization procedure in one-loop self energy calculations in external fields

The equivalence of the covariant renormalization and the partial-wave renormaliz ation (PWR) approach is proven explicitly for the one-loop self-energy correction (SE) of a bound electron state in the presence of external perturbation potentials. No spurious correctio n terms to the noncovariant PWR scheme are generated for Coulomb-type screening potentia ls and for external magnetic fields. It is shown that in numerical calculations of the SE with Coulombic perturbation potential spurious terms result from an improper treatment of the unphysical high-energy contribution. A method for performing the PWR utilizing the relativistic B-spline approach for the construction of the Dirac spectrum in external magnetic fields is proposed. This method is applied for calculating QED corrections to the bound-electron $g$-factor in H-like ions. Within the level of accuracy of about 0.1% no spurious terms are generated in numerical calculations of the SE in magnetic fields.Comment: 22 pages, LaTeX, 1 figur

Cloud and boundary layer interactions over the Arctic sea ice in late summer

Observations from the Arctic Summer Cloud Ocean Study (ASCOS), in the central Arctic sea-ice pack in late summer 2008, provide a detailed view of cloud- atmosphere-surface interactions and vertical mixing processes over the sea-ice environment. Measurements from a suite of ground-based remote sensors, near-surface meteorological and aerosol instruments, and profiles from radiosondes and a helicopter are combined to characterize a weeklong period dominated by low-level, mixed-phase, stratocumulus clouds. Detailed case studies and statistical analyses are used to develop a conceptual model for the cloud and atmosphere structure and their interactions in this environment. Clouds were persistent during the period of study, having qualities that suggest they were sustained through a combination of advective influences and in-cloud processes, with little contribution from the surface. Radiative cooling near cloud top produced buoyancy-driven, turbulent eddies that contributed to cloud formation and created a cloud-driven mixed layer. The depth of this mixed layer was related to the amount of turbulence and condensed cloud water. Coupling of this cloud-driven mixed layer to the surface boundary layer was primarily determined by proximity. For 75%of the period of study, the primary stratocumulus cloud-driven mixed layer was decoupled from the surface and typically at a warmer potential temperature. Since the near-surface temperature was constrained by the ocean-ice mixture, warm temperatures aloft suggest that these air masses had not significantly interacted with the sea-ice surface. Instead, backtrajectory analyses suggest that these warm air masses advected into the central Arctic Basin from lower latitudes. Moisture and aerosol particles likely accompanied these air masses, providing necessary support for cloud formation. On the occasions when cloud-surface coupling did occur, back trajectories indicated that these air masses advected at low levels, while mixing processes kept the mixed layer in equilibrium with the near-surface environment. Rather than contributing buoyancy forcing for the mixed-layer dynamics, the surface instead simply appeared to respond to the mixedlayer processes aloft. Clouds in these cases often contained slightly higher condensed water amounts, potentially due to additional moisture sources from below

Dynamical transitions and sliding friction in the two-dimensional Frenkel-Kontorova model

The nonlinear response of an adsorbed layer on a periodic substrate to an external force is studied via a two dimensional uniaxial Frenkel-Kontorova model. The nonequlibrium properties of the model are simulated by Brownian molecular dynamics. Dynamical phase transitions between pinned solid, sliding commensurate and incommensurate solids and hysteresis effects are found that are qualitatively similar to the results for a Lennard-Jones model, thus demonstrating the universal nature of these features.Comment: 11 pages, 12 figures, to appear in Phys. Rev.

Whispering gallery modes in open quantum billiards

The poles of the S-matrix and the wave functions of open 2D quantum billiards with convex boundary of different shape are calculated by the method of complex scaling. Two leads are attached to the cavities. The conductance of the cavities is calculated at energies with one, two and three open channels in each lead. Bands of overlapping resonance states appear which are localized along the convex boundary of the cavities and contribute coherently to the conductance. These bands correspond to the whispering gallery modes appearing in the classical calculations.Comment: 9 pages, 3 figures in jpg and gif forma

On the semi-classical analysis of the groundstate energy of the Dirichlet Pauli operator in non-simply connected domains

We consider the Dirichlet Pauli operator in bounded connected domains in the plane, with a semi-classical parameter. We show, in particular, that the ground state energy of this Pauli operator will be exponentially small as the semi-classical parameter tends to zero and estimate this decay rate. This extends our results, discussing the results of a recent paper by Ekholm--Kova\v{r}\'ik--Portmann, to include also non-simply connected domains.Comment: 15 pages, 4 figure

Astrid-2, an advanced microsatellite for auroral research

International audienceThe successful launch of the Swedish microsatellite Astrid-2 in December 1998 began a new era of auroral research, with advanced microprobes of 30 kg or less used as research tools. Innovative technologies and low-mass solutions were used for the sensors and deployment systems to allow a fairly complete set of scientific instruments within the 10 kg allocated for the scientific payload. A newly developed wire boom deployment system proved to function excellently. During its seven month lifetime Astrid-2 collected more than 26 Gbytes of high-quality data of auroral electric and magnetic fields, and auroral particle and plasma characteristics from approximately 3000 orbits at an inclination of 83° and an altitude of about 1000 km. Scientific results cover a broad range of topics, from the physics of energization of auroral particles to how the magnetosphere responds to the energy input from the solar wind and global magnetic field modelling. The fulfilment of both the technological and the scientific mission objectives has opened entirely new possibilities to carry out low-budget multipoint measurements in near-Earth space