Similar Sublattices and Coincidence Rotations of the Root Lattice A4 and its Dual

A natural way to describe the Penrose tiling employs the projection method on the basis of the root lattice A4 or its dual. Properties of these lattices are thus related to properties of the Penrose tiling. Moreover, the root lattice A4 appears in various other contexts such as sphere packings, efficient coding schemes and lattice quantizers. Here, the lattice A4 is considered within the icosian ring, whose rich arithmetic structure leads to parametrisations of the similar sublattices and the coincidence rotations of A4 and its dual lattice. These parametrisations, both in terms of a single icosian, imply an index formula for the corresponding sublattices. The results are encapsulated in Dirichlet series generating functions. For every index, they provide the number of distinct similar sublattices as well as the number of coincidence rotations of A4 and its dual.Comment: 8 pages, paper presented at ICQ10 (Zurich, Switzerland

86 GHz Very Long Baseline Polarimetry of 3C273 and 3C279 with the Coordinated Millimeter VLBI Array

86 GHz Very Long Baseline Polarimetry probes magnetic field structures within the cores of Active Galactic Nuclei at higher angular resolutions and a spectral octave higher than previously achievable. Observations of 3C273 and 3C279 taken in April 2000 with the Coordinated Millimeter VLBI Array have resulted in the first total intensity (Stokes I) and linear polarization VLBI images reported of any source at 86 GHz. These results reveal the 86 GHz electric vector position angles within the jets of 3C273 and 3C279 to be orthogonal to each other, and the core of 3C273 to be unpolarized. If this lack of polarization is due to Faraday depolarization alone, the dispersion in rotation measure is >=90000 rad/m^2 for the core of 3C273.Comment: AASTeX v5.02; 10 pages; 4 figures; accepted for publication in the Astrophysical Journal Letter

Diffusion of a Janus nanoparticle in an explicit solvent: A molecular dynamics simulation study

Molecular dynamics simulations are carried out to study the translational and rotational diffusion of a single Janus particle immersed in a dense Lennard-Jones fluid. We consider a spherical particle with two hemispheres of different wettability. The analysis of the particle dynamics is based on the time-dependent orientation tensor, particle displacement, as well as the translational and angular velocity autocorrelation functions. It was found that both translational and rotational diffusion coefficients increase with decreasing surface energy at the nonwetting hemisphere, provided that the wettability of the other hemisphere remains unchanged. We also observed that in contrast to homogeneous particles, the nonwetting hemisphere of the Janus particle tends to rotate in the direction of the displacement vector during the rotational relaxation time.Comment: Web reference added for animations:http://www.wright.edu/~nikolai.priezjev/janus/janus.htm

Decomposition of time-covariant operations on quantum systems with continuous and/or discrete energy spectrum

Every completely positive map G that commutes which the Hamiltonian time evolution is an integral or sum over (densely defined) CP-maps G_\sigma where \sigma is the energy that is transferred to or taken from the environment. If the spectrum is non-degenerated each G_\sigma is a dephasing channel followed by an energy shift. The dephasing is given by the Hadamard product of the density operator with a (formally defined) positive operator. The Kraus operator of the energy shift is a partial isometry which defines a translation on R with respect to a non-translation-invariant measure. As an example, I calculate this decomposition explicitly for the rotation invariant gaussian channel on a single mode. I address the question under what conditions a covariant channel destroys superpositions between mutually orthogonal states on the same orbit. For channels which allow mutually orthogonal output states on the same orbit, a lower bound on the quantum capacity is derived using the Fourier transform of the CP-map-valued measure (G_\sigma).Comment: latex, 33 pages, domains of unbounded operators are now explicitly specified. Presentation more detailed. Implementing the shift after the dephasing is sometimes more convenien

Nonlinear Dynamics of Capacitive Charging and Desalination by Porous Electrodes

The rapid and efficient exchange of ions between porous electrodes and aqueous solutions is important in many applications, such as electrical energy storage by super-capacitors, water desalination and purification by capacitive deionization (or desalination), and capacitive extraction of renewable energy from a salinity difference. Here, we present a unified mean-field theory for capacitive charging and desalination by ideally polarizable porous electrodes (without Faradaic reactions or specific adsorption of ions) in the limit of thin double layers (compared to typical pore dimensions). We illustrate the theory in the case of a dilute, symmetric, binary electrolyte using the Gouy-Chapman-Stern (GCS) model of the double layer, for which simple formulae are available for salt adsorption and capacitive charging of the diffuse part of the double layer. We solve the full GCS mean-field theory numerically for realistic parameters in capacitive deionization, and we derive reduced models for two limiting regimes with different time scales: (i) In the "super-capacitor regime" of small voltages and/or early times where the porous electrode acts like a transmission line, governed by a linear diffusion equation for the electrostatic potential, scaled to the RC time of a single pore. (ii) In the "desalination regime" of large voltages and long times, the porous electrode slowly adsorbs neutral salt, governed by coupled, nonlinear diffusion equations for the pore-averaged potential and salt concentration

NG7538 IRS1 N: modeling a circumstellar maser disk

We present an edge-on Keplerian disk model to explain the main component of the 12.2 and 6.7 GHz methanol maser emission detected toward NGC7538-IRS1 N. The brightness distribution and spectrum of the line of bright masers are successfully modeled with high amplification of background radio continuum emission along velocity coherent paths through a maser disk. The bend seen in the position-velocity diagram is a characteristic signature of differentially rotating disks. For a central mass of 30 solar masses, suggested by other observations, our model fixes the masing disk to have inner and outer radii of about 270 AU and 750 AU.Comment: To appear in The Proceedings of the 2004 European Workshop: "Dense Molecular Gas around Protostars and in Galatic Nuclei", Eds. Y. Hagiwara, W.A. Baan, H.J. van Langevelde, 2004, a special issue of ApSS, Kluwe