On the independence ratio of distance graphs

A distance graph is an undirected graph on the integers where two integers are adjacent if their difference is in a prescribed distance set. The independence ratio of a distance graph $G$ is the maximum density of an independent set in $G$. Lih, Liu, and Zhu [Star extremal circulant graphs, SIAM J. Discrete Math. 12 (1999) 491--499] showed that the independence ratio is equal to the inverse of the fractional chromatic number, thus relating the concept to the well studied question of finding the chromatic number of distance graphs. We prove that the independence ratio of a distance graph is achieved by a periodic set, and we present a framework for discharging arguments to demonstrate upper bounds on the independence ratio. With these tools, we determine the exact independence ratio for several infinite families of distance sets of size three, determine asymptotic values for others, and present several conjectures.Comment: 39 pages, 12 figures, 6 table

Modelling and simulations of a narrow track tilting vehicle

Narrow track tilting vehicle is a new category of vehicle that combines the dynamical abilities of a passenger car with a motorcycle. In the presence of overturning moments during cornering, an accurate assessment of the lateral dynamics plays an important role to improve their stability and handling. In order to stabilise or control the narrow tilting vehicle, the demand tilt angle can be calculated from the vehicle’s lateral acceleration and controlled by either steering input of the vehicle or using additional titling actuator to reach this desired angle. The aim of this article is to present a new approach for developing the lateral dynamics model of a narrow track tilting vehicle. First, this approach utilises the well-known geometry ‘bicycle model’ and parameter estimation methods. Second, by using a tuning method, the unknown and uncertainties are taken into account and regulated through an optimisation procedure to minimise the model biases in order to improve the modelling accuracy. Therefore, the optimised model can be used as a platform to develop the vehicle control strategy. Numerical simulations have been performed in a comparison with the experimental data to validate the model accuracy

Optical nanolithography using a scanning near-field probe with an integrated light source

An ultracompact near-field optical probe is described that is based on a single, integrated assembly consisting of a gallium nitride (GaN) light-emitting diode (LED), a microlens, and a cantilever assembly containing a hollow pyramidal probe with a subwavelength aperture at its apex. The LED emits ultraviolet light and may be used as a light source for near-field photolithographic exposure. Using this simple device compatible with many commercial atomic force microscope systems, it is possible to form nanostructures in photoresist with a resolution of 35 nm, corresponding to λ/10. © 2008 American Institute of Physics

High performance, accelerometer-based control of the Mini-MAST structure at Langley Research Center

Many large space system concepts will require active vibration control to satisfy critical performance requirements such as line of sight pointing accuracy and constraints on rms surface roughness. In order for these concepts to become operational, it is imperative that the benefits of active vibration control be shown to be practical in ground based experiments. The results of an experiment shows the successful application of the Maximum Entropy/Optimal Projection control design methodology to active vibration control for a flexible structure. The testbed is the Mini-Mast structure at NASA-Langley and has features dynamically traceable to future space systems. To maximize traceability to real flight systems, the controllers were designed and implemented using sensors (four accelerometers and one rate gyro) that are actually mounted to the structure. Ground mounted displacement sensors that could greatly ease the control design task were available but were used only for performance evaluation. The use of the accelerometers increased the potential of destabilizing the system due to spillover effects and motivated the use of precompensation strategy to achieve sufficient compensator roll-off

Detecting Gear Tooth Fatigue Cracks in Advance of Complete Fracture

Results of using vibration-based methods to detect gear tooth fatigue cracks are presented. An experimental test rig was used to fail a number of spur gear specimens through bending fatigue. The gear tooth fatigue crack in each test was initiated through a small notch in the fillet area of a tooth on the gear. The primary purpose of these tests was to verify analytical predictions of fatigue crack propagation direction and rate as a function of gear rim thickness. The vibration signal from a total of three tests was monitored and recorded for gear fault detection research. The damage consisted of complete rim fracture on the two thin rim gears and single tooth fracture on the standard full rim test gear. Vibration-based fault detection methods were applied to the vibration signal both on-line and after the tests were completed. The objectives of this effort were to identify methods capable of detecting the fatigue crack and to determine how far in advance of total failure positive detection was given. Results show that the fault detection methods failed to respond to the fatigue crack prior to complete rim fracture in the thin rim gear tests. In the standard full rim gear test all of the methods responded to the fatigue crack in advance of tooth fracture; however, only three of the methods responded to the fatigue crack in the early stages of crack propagation

Hydrothermal activity lowers trophic diversity in Antarctic sedimented hydrothermal vents

Sedimented hydrothermal vents are those in which hydrothermal fluid vents through sediment and are among the least studied deep-sea ecosystems. We present a combination of microbial and biochemical data to assess trophodynamics between and within hydrothermally active and off-vent areas of the Bransfield Strait (1050–1647 m depth). Microbial composition, biomass and fatty acid signatures varied widely between and within vent and non-vent sites and provided evidence of diverse metabolic activity. Several species showed diverse feeding strategies and occupied different trophic positions in vent and non-vent areas and stable isotope values of consumers were generally not consistent with feeding structure morphology. Niche area and the diversity of microbial fatty acids reflected trends in species diversity and was lowest at the most hydrothermally active site. Faunal utilisation of chemosynthetic activity was relatively limited but was detected at both vent and non-vent sites as evidenced by carbon and sulphur isotopic signatures, suggesting that the hydrothermal activity can affect trophodynamics over a much wider area than previously thought

Multi-layered Spectral Formation in SNe Ia Around Maximum Light

We use the radiative transfer code PHOENIX to study the line formation of the wavelength region 5000-7000 Angstroms. This is the region where the SNe Ia defining Si II feature occurs. This region is important since the ratio of the two nearby silicon lines has been shown to correlate with the absolute blue magnitude. We use a grid of LTE synthetic spectral models to investigate the formation of line features in the spectra of SNe Ia. By isolating the main contributors to the spectral formation we show that the ions that drive the spectral ratio are Fe III, Fe II, Si II, and S II. While the first two strongly dominate the flux transfer, the latter two form in the same physical region inside of the supernova. We also show that the naive blackbody that one would derive from a fit to the observed spectrum is far different than the true underlying continuum.Comment: 35 pages, 15 figures, ApJ (2008) 684 in pres