Twin disc assessment of wheel/rail adhesion

Loss of adhesion between a railway wheel and the track has implications for both braking and traction. Poor adhesion in braking is a safety issue as it leads to extended stopping distances. In traction, it is a performance issue as it may lead to reduced acceleration which could cause delays. In this work, wheel/rail adhesion was assessed using a twin disc simulation. The effects of a number of contaminants, such as oil, dry and wet leaves and sand were investigated. These have been shown in the past to have significant effect on adhesion, but this has not been well quantified. The results have shown that both oil and water reduce adhesion from the dry condition. Leaves, however, gave the lowest adhesion values, even when dry. The addition of sand, commonly used as a friction enhancer, to leaves, brought adhesion levels back to the levels without leaves present. Adhesion levels recorded, particularly for the wet, dry and oil conditions are in the range seen in field measurements. Relatively severe disc surface damage and subsurface deformation was seen after the addition of sand. Leaves were also seen to cause indents in the disc surfaces. The twin disc approach has been shown to provide a good approach for comparing adhesion levels under a range of wheel/rail contact conditions, with and without contaminants

A discrete linearizability test based on multiscale analysis

In this paper we consider the classification of dispersive linearizable partial difference equations defined on a quad-graph by the multiple scale reduction around their harmonic solution. We show that the A_1, A_2 and A_3 linearizability conditions restrain the number of the parameters which enter into the equation. A subclass of the equations which pass the A_3 C-integrability conditions can be linearized by a Mobius transformation

Market solutions to water allocation in Texas

San Antonio (Tex.) ; Water-supply - Texas ; Federal Reserve District, 11th

Two-dimensional Bloch electrons in perpendicular magnetic fields: an exact calculation of the Hofstadter butterfly spectrum

The problem of two-dimensional, independent electrons subject to a periodic potential and a uniform perpendicular magnetic field unveils surprisingly rich physics, as epitomized by the fractal energy spectrum known as Hofstadter's Butterfly. It has hitherto been addressed using various approximations rooted in either the strong potential or the strong field limiting cases. Here we report calculations of the full spectrum of the single-particle Schr\"{o}dinger equation without further approximations. Our method is exact, up to numerical precision, for any combination of potential and uniform field strength. We first study a situation that corresponds to the strong potential limit, and compare the exact results to the predictions of a Hofstadter-like model. We then go on to analyze the evolution of the fractal spectrum from a Landau-like nearly-free electron system to the Hofstadter tight-binding limit by tuning the amplitude of the modulation potential