Review of antiskid and brake dynamics research

The behavior of various antiskid systems was investigated under controlled conditions. Results from utilizing a single main wheel of a DC-9 aircraft suggest that the systems investigated perform well under most circumstances but there may be room for improvement. For example, it was demonstrated that pressure bias modulation can adversely affect the response of antiskid systems to rapid changes in the runway friction level. Results also indicate that antiskid systems designed to operate at a slip ratio of approximately 0.1 can provide a maximum braking effort without undue loss in the cornering capability of the tire. Time histories of braking friction coefficient were shown to provide a means of determining antiskid system performance and for systems that employed pressure bias modulation it was shown that performance could also be estimated from time histories of brake pressure and torque

Status of recent aircraft braking and cornering research

The sources of degraded performance which sometimes occurs under adverse runway conditions, are investigated to obtain data necessary to the development of more advanced systems, in an effort to insure safe ground handling operations under all-weather conditions. Tire-to-ground friction characteristics are determined under braking conditions which closely resemble those of airplanes under heavy braking. Braking data from single-wheel landing loads track tests are related with those available from full-scale flight tests

Behavior of aircraft antiskid breaking systems on dry and wet runway surfaces: A slip-ratio-controlled system with ground speed reference from unbraked nose wheel

An experimental investigation was conducted at the Langley aircraft landing loads and traction facility to study the braking and cornering response of a slip ratio controlled aircraft antiskid braking system with ground speed reference derived from an unbraked nose wheel. The investigation, conducted on dry and wet runway surfaces, utilized one main gear wheel, brake, and tire assembly of a DC-9 series 10 airplane. During maximum braking, the average ratio of the drag force friction coefficient developed by the antiskid system to the maximum drag force friction coefficient available was higher on the dry surface than on damp and flooded surfaces, and was reduced with lighter vertical loads, higher yaw angles, and when new tire treads were replaced by worn treads. Similarly, the average ratio of side force friction coefficient developed by the tire under antiskid control to the maximum side force friction coefficient available to a freely rolling yawed tire decreased with increasing yaw angle, generally increased with ground speed, and decreased when tires with new treads were replaced by those with worn treads

Technique for measuring side forces on a banked aircraft with a free-swiveling nose gear

An experimental investigation was conducted at the Langley Research Center to determine a method for towing an aircraft to measure the side forces of a free-swiveling nose gear due to variations in bank angle. A F-106 aircraft and the Space Shuttle orbiter OV-101 were towed to measure side forces on full-size aircraft for bank angles up to 3 deg. These tests indicate that substantial side forces will occur if an aircraft is rolling on a runway in a banked attitude even when the nose gear is free to swivel. Corotation of a twin-tire nose gear appears to cause a substantial increase in side force due to bank angle compared with a nose gear with indepdendently rotating wheels

Improved Bounds on Restricted Isometry Constants for Gaussian Matrices

The Restricted Isometry Constants (RIC) of a matrix $A$ measures how close to an isometry is the action of $A$ on vectors with few nonzero entries, measured in the $\ell^2$ norm. Specifically, the upper and lower RIC of a matrix $A$ of size $n\times N$ is the maximum and the minimum deviation from unity (one) of the largest and smallest, respectively, square of singular values of all ${N\choose k}$ matrices formed by taking $k$ columns from $A$. Calculation of the RIC is intractable for most matrices due to its combinatorial nature; however, many random matrices typically have bounded RIC in some range of problem sizes $(k,n,N)$. We provide the best known bound on the RIC for Gaussian matrices, which is also the smallest known bound on the RIC for any large rectangular matrix. Improvements over prior bounds are achieved by exploiting similarity of singular values for matrices which share a substantial number of columns.Comment: 16 pages, 8 figure

Quantum search algorithms on a regular lattice

Quantum algorithms for searching one or more marked items on a d-dimensional lattice provide an extension of Grover's search algorithm including a spatial component. We demonstrate that these lattice search algorithms can be viewed in terms of the level dynamics near an avoided crossing of a one-parameter family of quantum random walks. We give approximations for both the level-splitting at the avoided crossing and the effectively two-dimensional subspace of the full Hilbert space spanning the level crossing. This makes it possible to give the leading order behaviour for the search time and the localisation probability in the limit of large lattice size including the leading order coefficients. For d=2 and d=3, these coefficients are calculated explicitly. Closed form expressions are given for higher dimensions

Regular quantum graphs

We introduce the concept of regular quantum graphs and construct connected quantum graphs with discrete symmetries. The method is based on a decomposition of the quantum propagator in terms of permutation matrices which control the way incoming and outgoing channels at vertex scattering processes are connected. Symmetry properties of the quantum graph as well as its spectral statistics depend on the particular choice of permutation matrices, also called connectivity matrices, and can now be easily controlled. The method may find applications in the study of quantum random walks networks and may also prove to be useful in analysing universality in spectral statistics.Comment: 12 pages, 3 figure

Mixed Models and Reduction Techniques for Large-Rotation, Nonlinear Analysis of Shells of Revolution with Application to Tires

An effective computational strategy is presented for the large-rotation, nonlinear axisymmetric analysis of shells of revolution. The three key elements of the computational strategy are: (1) use of mixed finite-element models with discontinuous stress resultants at the element interfaces; (2) substantial reduction in the total number of degrees of freedom through the use of a multiple-parameter reduction technique; and (3) reduction in the size of the analysis model through the decomposition of asymmetric loads into symmetric and antisymmetric components coupled with the use of the multiple-parameter reduction technique. The potential of the proposed computational strategy is discussed. Numerical results are presented to demonstrate the high accuracy of the mixed models developed and to show the potential of using the proposed computational strategy for the analysis of tires

Coronal Seismology and the Propagation of Acoustic Waves Along Coronal Loops

We use a combination of analytical theory, numerical simulation, and data analysis to study the propagation of acoustic waves along coronal loops. We show that the intensity perturbation of a wave depends on a number of factors, including dissipation of the wave energy, pressure and temperature gradients in the loop atmosphere, work action between the wave and a flow, and the sensitivity properties of the observing instrument. In particular, the scale length of the intensity perturbation varies directly with the dissipation scale length (i.e., damping length) and the scale lengths of pressure, temperature, and velocity. We simulate wave propagation in three different equilibrium loop models and find that dissipation and pressure and temperature stratification are the most important effects in the low corona where the waves are most easily detected. Velocity effects are small, and cross-sectional area variations play no direct role for lines-of-sight that are normal to the loop axis. The intensity perturbation scale lengths in our simulations agree very well with the scale lengths we measure in a sample of loops observed by TRACE. The median observed value is 4.35x10^9 cm. In some cases the intensity perturbation increases with height, which is likely an indication of a temperature inversion in the loop (i.e., temperature that decreases with height). Our most important conclusion is that thermal conduction, the primary damping mechanism, is accurately described by classical transport theory. There is no need to invoke anomalous processes to explain the observations.Comment: To appear in the Dec. 1, 2004 issue of the Astrophysical Journa

Pulsar Timing Probes of Primordial Black Holes and Subhalos

Pulsars act as accurate clocks, sensitive to gravitational redshift and acceleration induced by transiting clumps of matter. We study the sensitivity of pulsar timing arrays (PTAs) to single transiting compact objects, focusing on primordial black holes and compact subhalos in the mass range from $10^{-12} M _{\odot}$ to well above $100~M_\odot$. We find that the Square Kilometer Array can constrain such objects to be a subdominant component of the dark matter over this entire mass range, with sensitivity to a dark matter sub-component reaching the sub-percent level over significant parts of this range. We also find that PTAs offer an opportunity to probe substantially less dense objects than lensing because of the large effective radius over which such objects can be observed, and we quantify the subhalo concentration parameters which can be constrained.Comment: 18 pages, 6 figure