Proposals for a basic theory of air traffic control

This note serves as an introduction to the work on Air Traffic Control currently being carried out at The College of Aeronautics. The basic principles of Air Traffic Control are examined and a mathematical basis for an analysis of the current and future ATC complex is discussed. The theory is based upon feedback control concepts using intermittent data. Examples showing the application to en-route airway and parallel track flying are given. These demonstrate the effect of positional data up-dating rate upon separation minima for both subsonic and supersonic aircraft. Application to both fixed route (Airway Control) and free-route (Area Control) are currently being considered. A full report is to be published at a later date

Non-diffracting Optical Beams in a Three-level Raman System

Diffractionless propagation of optical beams through atomic vapors is investigated. The atoms in the vapor are operated in a three-level Raman configuration. A suitably chosen control beam couples to one of the transitions, and thereby creates a spatially varying index of refraction modulation in the warm atomic vapor for a probe beam which couples to the other transition in the atoms. We show that a Laguerre-Gaussian control beam allows to propagate single Gaussian probe field modes as well as multi-Gaussian modes and non-Gaussian modes over macroscopic distances without diffraction. This opens perspectives for the propagation of arbitrary images through warm atomic vapors.Comment: 8 pages, 7 figure

Exact solutions for equilibrium configurations of charged conducting liquid jets

A wide class of exact solutions is obtained for the problem of finding the equilibrium configurations of charged jets of a conducting liquid; these configurations correspond to the finite-amplitude azimuthal deformations of the surface of a round jet. A critical value of the linear electric charge density is determined, for which the jet surface becomes self-intersecting, and the jet splits into two. It exceeds the density value required for the excitation of the linear azimuthal instability of the round jet. Hence, there exists a range of linear charge density values, where our solutions may be stable with respect to small azimuthal perturbations.Comment: 7 pages, 5 figures, to appear in Physical Review

Experimental investigation and modeling of dynamic performance of wave springs

This paper investigates vibration suppression potentials for a novel frictional system - a wave spring. Two different types of wave springs, crest-to-crest and nested ones, were used in this work. Compared with nested wave springs, crest-to-crest wave springs have lower damping and a larger range for the linear stiffness due to a reduced level of contact. Dynamic compressive tests, subject to different static compression levels, are carried out to investigate the force-displacement hysteresis of individual wave springs. The stiffness is shown to increase up to 800% when the static compression is at 40%. The crest-to-crest wave spring is shown to provide loss factors up to 0.12 while nested ones as high as 0.80. Testing also showed that performance did not degrade between room temperature and 100°C. The effect of different spring materials, inner diameter and flat spring width are also evaluated

Damping of metallic wool with embedded rigid body motion amplifiers

The use of entangled metallic wires as vibrational dampers and shock isolators is of interest in a variety of applications. By taking advantage of the frictional contact between the contiguous wires, it has been shown that significant amounts of energy dissipation can be achieved. The amount of energy dissipation is highly dependent on many factors with one in particular being the excitation amplitude. When the excitation amplitude is low, a combination of the number of contact points, in which have relative motion, and the contact pressure are lessened often leading to a sacrifice in energy dissipation. In this paper, spherical metallic rigid bodies are embedded within metallic wool. These rigid bodies act as motion amplifiers in which, locally within the metallic wool, amplify the excitation amplitude leading to an increase in vibrational damping. Presented are experimental modal results from various metallic wool/embedded rigid body arrangements within a prismatic hollow aluminium tube. It is found that the incorporation of the embedded rigid bodies into the steel wool significantly improves the damping within the system. It is demonstrated that an increase in damping by 2328% has been achieved at only a 3.8% penalty in mass. It is found that the level of damping from the embedded rigid bodies depends not only on the excitation amplitude but their quantity and the accompanying steel wool configuration. A finite element procedure coupled with an analytical model is proposed which accounts for the strain energy produced within the steel wool to estimate the damping effect that this filler material has on the behaviour of the overall structure. The model treats the metallic wool/rigid sphere combination as a homogeneous equivalent solid with amplitude dependent damping properties, thereby reducing the complexities of the physics-based model while still providing an estimate of the vibrational damping while in the frequency domain

Ion-induced nucleation in polar one-component fluids

We present a Ginzburg-Landau theory of ion-induced nucleation in a gas phase of polar one-component fluids, where a liquid droplet grows with an ion at its center. By calculating the density profile around an ion, we show that the solvation free energy is larger in gas than in liquid at the same temperature on the coexistence curve. This difference much reduces the nucleation barrier in a metastable gas.Comment: 9 pagers, 9 figures, to be published in J. Chem. Phy

Offside goals and induced breaches of contract

An analysis of Global Resources Group Ltd v Mackay which explores the possibility of building links between the offside goals rule and nominate delict of inducing breach of contract

Asymptotic behaviour of the Rayleigh--Taylor instability

We investigate long time numerical simulations of the inviscid Rayleigh-Taylor instability at Atwood number one using a boundary integral method. We are able to attain the asymptotic behavior for the spikes predicted by Clavin & Williams\cite{clavin} for which we give a simplified demonstration. In particular we observe that the spike's curvature evolves like $t^3$ while the overshoot in acceleration shows a good agreement with the suggested $1/t^5$ law. Moreover, we obtain consistent results for the prefactor coefficients of the asymptotic laws. Eventually we exhibit the self-similar behavior of the interface profile near the spike.Comment: 4 pages, 6 figure

Quantum Reciprocity Conjecture for the Non-Equilibrium Steady State

By considering the lack of history dependence in the non-equilibrium steady state of a quantum system we are led to conjecture that in such a system, there is a set of quantum mechanical observables whose retarded response functions are insensitive to the arrow of time, and which consequently satisfy a quantum analog of the Onsager reciprocity relations. Systems which satisfy this conjecture can be described by an effective Free energy functional. We demonstrate that the conjecture holds in a resonant level model of a multi-lead quantum dot.Comment: References revised to take account of related work on Onsager reciprocity in mesoscopics by Christen, and in hydrodynamics by Mclennan, Dufty and Rub

Wave attenuation in glasses: Rayleigh and generalized-Rayleigh scattering scaling

The attenuation of long-wavelength phonons (waves) by glassy disorder plays a central role in various glass anomalies, yet it is neither fully characterized, nor fully understood. Of particular importance is the scaling of the attenuation rate $\Gamma(k)$ with small wavenumbers $k\!\to\!0$ in the thermodynamic limit of macroscopic glasses. Here we use a combination of theory and extensive computer simulations to show that the macroscopic low-frequency behavior emerges at intermediate frequencies in finite-size glasses, above a recently identified crossover wavenumber $k_\dagger$, where phonons are no longer quantized into bands. For $k\!<\!k_\dagger$, finite-size effects dominate $\Gamma(k)$, which is quantitatively described by a theory of disordered phonon bands. For $k\!>\!k_\dagger$, we find that $\Gamma(k)$ is affected by the number of quasilocalized nonphononic excitations, a generic signature of glasses that feature a universal density of states. In particular, we show that in a frequency range in which this number is small, $\Gamma(k)$ follows a Rayleigh scattering scaling $\sim\!k^{d+1}$ ($d$ is the spatial dimension), and that in a frequency range in which this number is sufficiently large, the recently observed generalized-Rayleigh scaling of the form $\sim\!k^{d+1}\log\!{(k_0/k)}$ emerges ($k_0\!>k_\dagger$ is a characteristic wavenumber). Our results suggest that macroscopic glasses --- and, in particular, glasses generated by conventional laboratory quenches that are known to strongly suppress quasilocalized nonphononic excitations --- exhibit Rayleigh scaling at the lowest wavenumbers $k$ and a crossover to generalized-Rayleigh scaling at higher $k$. Some supporting experimental evidence from recent literature is presented.Comment: 15 pages, 10 figures (including appendices). v2 includes a new appendix with 2 figures (Fig.7 & Fig.8