Discrete Nodal Domain Theorems

We give a detailed proof for two discrete analogues of Courant's Nodal Domain Theorem

Coordinates of features on the Galilean satellites

The coordinate systems of each of the Galilean satellites are defined and coordinates of features seen in the Voyager pictures of these satellites are presented. The control nets of the satellites were computed by means of single block analytical triangulations. The normal equations were solved by the conjugate iterative method which is convenient and which converges rapidly as the initial estimates of the parameters are very good

Are There Magnetars in High Mass X-ray Binaries? The Case of SuperGiant Fast X-Ray Transients

In this paper we survey the theory of wind accretion in high mass X-ray binaries hosting a magnetic neutron star and a supergiant companion. We concentrate on the different types of interaction between the inflowing wind matter and the neutron star magnetosphere that are relevant when accretion of matter onto the neutron star surface is largely inhibited; these include the inhibition through the centrifugal and magnetic barriers. Expanding on earlier work, we calculate the expected luminosity for each regime and derive the conditions under which transition from one regime to another can take place. We show that very large luminosity swings (~10^4 or more on time scales as short as hours) can result from transitions across different regimes. The activity displayed by supergiant fast X-ray transients, a recently discovered class of high mass X-ray binaries in our galaxy, has often been interpreted in terms of direct accretion onto a neutron star immersed in an extremely clumpy stellar wind. We show here that the transitions across the magnetic and/or centrifugal barriers can explain the variability properties of these sources as a results of relatively modest variations in the stellar wind velocity and/or density. According to this interpretation we expect that supergiant fast X-ray transients which display very large luminosity swings and host a slowly spinning neutron star are characterized by magnetar-like fields, irrespective of whether the magnetic or the centrifugal barrier applies. Supergiant fast X-ray transients might thus provide a new opportunity to detect and study magnetars in binary systems.Comment: Accepted for publication in ApJ. 16 pages, 6 figure

When We Sailed For The U.S.A.

https://digitalcommons.library.umaine.edu/mmb-vp/4840/thumbnail.jp

Fundamental length in quantum theories with PT-symmetric Hamiltonians

The direct observability of coordinates x is often lost in PT-symmetric quantum theories. A manifestly non-local Hilbert-space metric $\Theta$ enters the double-integral normalization of wave functions $\psi(x)$ there. In the context of scattering, the (necessary) return to the asymptotically fully local metric has been shown feasible, for certain family of PT-symmetric toy Hamiltonians H at least, in paper I (M. Znojil, Phys. Rev. D 78 (2008) 025026). Now we show that in a confined-motion dynamical regime the same toy model proves also suitable for an explicit control of the measure or width $\theta$ of its non-locality. For this purpose each H is assigned here, constructively, the complete menu of its hermitizing metrics $\Theta=\Theta_\theta$ distinguished by their optional "fundamental lengths" $\theta\in (0,\infty)$. The local metric of paper I recurs at $\theta=0$ while the most popular CPT-symmetric hermitization proves long-ranged, with $\theta=\infty$.Comment: 31 pp, 3 figure

Influence of organic films on the evaporation and condensation of water in aerosol

Uncertainties in quantifying the kinetics of evaporation and condensation of water from atmospheric aerosol are a significant contributor to the uncertainty in predicting cloud droplet number and the indirect effect of aerosols on climate. The influence of aerosol particle surface composition, particularly the impact of surface active organic films, on the condensation and evaporation coefficients remains ambiguous. Here, we report measurements of the influence of organic films on the evaporation and condensation of water from aerosol particles. Significant reductions in the evaporation coefficient are shown to result when condensed films are formed by monolayers of long-chain alcohols [C(n)H((2n+1))OH], with the value decreasing from 2.4 × 10(−3) to 1.7 × 10(−5) as n increases from 12 to 17. Temperature-dependent measurements confirm that a condensed film of long-range order must be formed to suppress the evaporation coefficient below 0.05. The condensation of water on a droplet coated in a condensed film is shown to be fast, with strong coherence of the long-chain alcohol molecules leading to islanding as the water droplet grows, opening up broad areas of uncoated surface on which water can condense rapidly. We conclude that multicomponent composition of organic films on the surface of atmospheric aerosol particles is likely to preclude the formation of condensed films and that the kinetics of water condensation during the activation of aerosol to form cloud droplets is likely to remain rapid

Heavy meson masses and decay constants from relativistic heavy quarks in full lattice QCD

We determine masses and decay constants of heavy-heavy and heavy-charm pseudoscalar mesons as a function of heavy quark mass using a fully relativistic formalism known as Highly Improved Staggered Quarks for the heavy quark. We are able to cover the region from the charm quark mass to the bottom quark mass using MILC ensembles with lattice spacing values from 0.15 fm down to 0.044 fm. We obtain f_{B_c} = 0.427(6) GeV; m_{B_c} = 6.285(10) GeV and f_{\eta_b} = 0.667(6) GeV. Our value for f_{\eta_b} is within a few percent of f_{\Upsilon} confirming that spin effects are surprisingly small for heavyonium decay constants. Our value for f_{B_c} is significantly lower than potential model values being used to estimate production rates at the LHC. We discuss the changing physical heavy-quark mass dependence of decay constants from heavy-heavy through heavy-charm to heavy-strange mesons. A comparison between the three different systems confirms that the B_c system behaves in some ways more like a heavy-light system than a heavy-heavy one. Finally we summarise current results on decay constants of gold-plated mesons.Comment: 16 pages, 12 figure

Control networks for the Galilean satellites, November 1979

Pictures of the four Galilean satellites taken as the two Voyager spacecraft approached Jupiter during March and July 1979 are presented. Control nets of the Galilean satellites, computed photogrammetrically, and measurements of the mean radii are presented. The pictures in the control nets are identified, the coordinates of the control points are given, and identifications of some of the control points are shown on figures. The use of star field pictures to compute the focal lengths of the camera is discussed and the geometric relationship between the narrow and wide and angle cameras is reported. A description of the coordinate systems of the Galilean satellites is presented and the status of the control net computations is reported

Entanglement assisted alignment of reference frames using a dense covariant coding

We present a procedure inspired by dense coding, which enables a highly efficient transmission of information of a continuous nature. The procedure requires the sender and the recipient to share a maximally entangled state. We deal with the concrete problem of aligning reference frames or trihedra by means of a quantum system. We find the optimal covariant measurement and compute the corresponding average error, which has a remarkably simple close form. The connection of this procedure with that of estimating unitary transformations on qubits is briefly discussed.Comment: 4 pages, RevTeX, Version to appear in PR