Quartz crystal and superconductive resonators and oscillators

A general overview of piezoelectric resonators is given with emphasis on evolution of the resonator design. Superconducting cavities and crystals at low temperature and the use of resonant frequencies are also discussed

Simulation of a Hybrid Optical/Radio/Acoustic Extension to IceCube for EeV Neutrino Detection

Astrophysical neutrinos at $\sim$EeV energies promise to be an interesting source for astrophysics and particle physics. Detecting the predicted cosmogenic (``GZK'') neutrinos at 10$^{16}$ - 10$^{20}$ eV would test models of cosmic ray production at these energies and probe particle physics at $\sim$100 TeV center-of-mass energy. While IceCube could detect $\sim$1 GZK event per year, it is necessary to detect 10 or more events per year in order to study temporal, angular, and spectral distributions. The IceCube observatory may be able to achieve such event rates with an extension including optical, radio, and acoustic receivers. We present results from simulating such a hybrid detector.Comment: 4 pages, 2 figures; to appear in the Proceedings of the 29th ICRC, Pune, Indi

Addendum to "Coherent radio pulses from GEANT generated electromagnetic showers in ice"

We reevaluate our published calculations of electromagnetic showers generated by GEANT 3.21 and the radio frequency pulses they produce in ice. We are prompted by a recent report showing that GEANT 3.21-modeled showers are sensitive to internal settings in the electron tracking subroutine. We report the shower and pulse characteristics obtained with different settings of GEANT 3.21 and with GEANT 4. The default setting of electron tracking in GEANT 3.21 we used in previous work speeds up the shower simulation at the cost of information near the end of the tracks. We find that settings tracking electron and positron to lower energy yield a more accurate calculation, a more intense shower, and proportionately stronger radio pulses at low frequencies. At high frequencies the relation between shower tracking algorithm and pulse spectrum is more complex. We obtain radial distributions of shower particles and phase distributions of pulses from 100 GeV showers that are consistent with our published results.Comment: 4 pages, 3 figure

Stabilized Schemes for the Hydrostatic Stokes Equations

Some new stable finite element (FE) schemes are presented for the hydrostatic Stokes system or primitive equations of the ocean. It is known that the stability of the mixed formulation ap- proximation for primitive equations requires the well-known Ladyzhenskaya–Babuˇska–Brezzi condi- tion related to the Stokes problem and an extra inf-sup condition relating the pressure and the vertical velocity. The main goal of this paper is to avoid this extra condition by adding a residual stabilizing term to the vertical momentum equation. Then, the stability for Stokes-stable FE combinations is extended to the primitive equations and some error estimates are provided using Taylor–Hood P2 –P1 or miniele- ment (P1 +bubble)–P1 FE approximations, showing the optimal convergence rate in the P2 –P1 case. These results are also extended to the anisotropic (nonhydrostatic) problem. On the other hand, by adding another residual term to the continuity equation, a better approximation of the vertical derivative of pressure is obtained. In this case, stability and error estimates including this better approximation are deduced, where optimal convergence rate is deduced in the (P 1 +bubble)–P1 case. Finally, some numerical experiments are presented supporting previous results

Charm meson resonances in D→PℓνD \to P \ell \nu decays

Motivated by recent experimental results we reconsider semileptonic $D \to P \ell \nu_{\ell}$ decays within a model which combines heavy quark symmetry and properties of the chiral Lagrangian. We include excited charm meson states, some of them recently observed, in our Lagrangian and determine their impact on the charm meson semileptonic form factors. We find that the inclusion of excited charm meson states in the model leads to a rather good agreement with the experimental results on the $q^2$ shape of the $F_+(q^2)$ form factor. We also calculate branching ratios for all $D \to P \ell \nu_{\ell}$ decays.Comment: 9 pages, 4 figures; minor corrections, added some discussion, version as publishe

Local monotonicity of Riemannian and Finsler volume with respect to boundary distances

We show that the volume of a simple Riemannian metric on $D^n$ is locally monotone with respect to its boundary distance function. Namely if $g$ is a simple metric on $D^n$ and $g'$ is sufficiently close to $g$ and induces boundary distances greater or equal to those of $g$, then $vol(D^n,g')\ge vol(D^n,g)$. Furthermore, the same holds for Finsler metrics and the Holmes--Thompson definition of volume. As an application, we give a new proof of the injectivity of the geodesic ray transform for a simple Finsler metric.Comment: 13 pages, v3: minor corrections and clarifications, to appear in Geometriae Dedicat

Nonlinear Competition Between Small and Large Hexagonal Patterns

Recent experiments by Kudrolli, Pier and Gollub on surface waves, parametrically excited by two-frequency forcing, show a transition from a small hexagonal standing wave pattern to a triangular ``superlattice'' pattern. We show that generically the hexagons and the superlattice wave patterns bifurcate simultaneously from the flat surface state as the forcing amplitude is increased, and that the experimentally-observed transition can be described by considering a low-dimensional bifurcation problem. A number of predictions come out of this general analysis.Comment: 4 pages, RevTex, revised, to appear in Phys. Rev. Let