Development and testing of laser Doppler system components for wake vortex monitoring. Volume 1: Scanner development, laboratory and field testing and system modeling

A servo-controlled range/elevation scanner for the laser Doppler velocimeter (LDV) was developed and tested in the field to assess its performance in detecting and monitoring aircraft trailing vortices in an airport environment. The elevation scanner provides a capability to manually point the LDV telescope at operator chosen angles from 3.2 deg. to 89.6 deg within 0.2 deg, or to automatically scan the units between operator chosen limits at operator chosen rates of 0.1 Hz to 0.5 Hz. The range scanner provides a capability to manually adjust the focal point of the system from a range of 32 meters to a range of 896 meters under operator control, or to scan between operator chosen limits and at rates from 0.1 Hz to 6.9 Hz. The scanner controls are designed to allow simulataneous range and elevation scanning so as to provide finger scan patterns, arc scan patterns, and vertical line scan patterns. The development and testing of the unit is discussed, along with a fluid dynamic model of the wake vortex developed in a laser Doppler vortex sensor simulation program

The Quantum Mechanics of Hyperion

This paper is motivated by the suggestion [W. Zurek, Physica Scripta, T76, 186 (1998)] that the chaotic tumbling of the satellite Hyperion would become non-classical within 20 years, but for the effects of environmental decoherence. The dynamics of quantum and classical probability distributions are compared for a satellite rotating perpendicular to its orbital plane, driven by the gravitational gradient. The model is studied with and without environmental decoherence. Without decoherence, the maximum quantum-classical (QC) differences in its average angular momentum scale as hbar^{2/3} for chaotic states, and as hbar^2 for non-chaotic states, leading to negligible QC differences for a macroscopic object like Hyperion. The quantum probability distributions do not approach their classical limit smoothly, having an extremely fine oscillatory structure superimposed on the smooth classical background. For a macroscopic object, this oscillatory structure is too fine to be resolved by any realistic measurement. Either a small amount of smoothing (due to the finite resolution of the apparatus) or a very small amount of environmental decoherence is sufficient ensure the classical limit. Under decoherence, the QC differences in the probability distributions scale as (hbar^2/D)^{1/6}, where D is the momentum diffusion parameter. We conclude that decoherence is not essential to explain the classical behavior of macroscopic bodies.Comment: 17 pages, 24 figure

On the Theory of Relativistic Strong Plasma Waves

The influence of motion of ions and electron temperature on nonlinear one-dimensional plasma waves with velocity close to the speed of light in vacuum is investigated. It is shown that although the wavebreaking field weakly depends on mass of ions, the nonlinear relativistic wavelength essentially changes. The nonlinearity leads to the increase of the strong plasma wavelength, while the motion of ions leads to the decrease of the wavelength. Both hydrodynamic approach and kinetic one, based on Vlasov-Poisson equations, are used to investigate the relativistic strong plasma waves in a warm plasma. The existence of relativistic solitons in a thermal plasma is predicted.Comment: 13 pages, 8 figure

Longitudinal relaxation and thermoactivation of quantum superparamagnets

The relaxation mechanisms of a quantum nanomagnet are discussed in the frame of linear response theory. We use a spin Hamiltonian with a uniaxial potential barrier plus a Zeeman term. The spin, having arbitrary $S$, is coupled to a bosonic environment. From the eigenstructure of the relaxation matrix, we identify two main mechanisms, namely, thermal activation over the barrier, with a time scale \eival_1^{-1}, and a faster dynamics inside the potential wells, with characteristic time \eivalW^{-1}. This allows to introduce a simple analytical formula for the response, which agrees well with the exact numerical results, and cover experiments even under moderate to strong fields in the superparamagnetic range. In passing, we generalize known classical results for a number of quantities (e.g., integral relaxation times, initial decay time, Kramers rate), results that are recovered in the limit $S\to\infty$.Comment: submitted to Phys. Rev.

Electrodynamics of a Clean Vortex Lattice

We report on a microscopic evaluation of electrodynamic response for the vortex lattice state of a model s-wave superconductor. Our calculation accounts self-consistently for both quasiparticle and order parameter response and establishes the collective nature of linear response in the clean limit. We discuss the effects of homogeneous and inhomogeneous pinning on the optical conductivity and the penetration depth, and comment on the relationship between macroscopic and local penetration depths. We find unexpected relationships between pinning arrangements and conductivity due to the strongly non-local response.Comment: 4 pages, 2 figure

Depinning transition in type-II superconductors

The surface impedance Z(f) of conventional isotropic materials has been carefully measured for frequencies f ranging from 1 kHz to 3 MHz, allowing a detailed investigation of the depinning transition. Our results exhibit the irrelevance of classical ideas to the dynamics of vortex pinning. We propose a new picture, where the linear ac response is entirely governed by disordered boundary conditions of a rough surface, whereas in the bulk vortices respond freely. The universal law for Z(f) thus predicted is in remarkable agreement with experiment, and tentatively applies to microwave data in YBaCuO films.Comment: 4 pages, 4 figures, 14 reference

Sharpenings of Li's criterion for the Riemann Hypothesis

Exact and asymptotic formulae are displayed for the coefficients $\lambda_n$ used in Li's criterion for the Riemann Hypothesis. For $n \to \infty$ we obtain that if (and only if) the Hypothesis is true, $\lambda_n \sim n(A \log n +B)$ (with $A>0$ and $B$ explicitly given, also for the case of more general zeta or $L$-functions); whereas in the opposite case, $\lambda_n$ has a non-tempered oscillatory form.Comment: 10 pages, Math. Phys. Anal. Geom (2006, at press). V2: minor text corrections and updated reference

Dynamic vortex mass in clean Fermi superfluids and superconductors

We calculate the dynamic vortex mass for clean Fermi superfluids including both s- and d-wave superconductors as a response to a vortex acceleration. Assuming a finite quasiparticle mean free time, the vortex mass appears to be a tensor. The diagonal component dominates in the limit of long mean free time while the off-diagonal mass takes over in the moderately clean regime.Comment: 4 pages, no figures, typeset using RevTe