The TASEP speed process

In the multi-type totally asymmetric simple exclusion process (TASEP) on the line, each site of Z is occupied by a particle labeled with some number, and two neighboring particles are interchanged at rate one if their labels are in increasing order. Consider the process with the initial configuration where each particle is labeled by its position. It is known that in this case a.s. each particle has an asymptotic speed which is distributed uniformly on [-1,1]. We study the joint distribution of these speeds: the TASEP speed process. We prove that the TASEP speed process is stationary with respect to the multi-type TASEP dynamics. Consequently, every ergodic stationary measure is given as a projection of the speed process measure. This generalizes previous descriptions restricted to finitely many classes. By combining this result with known stationary measures for TASEPs with finitely many types, we compute several marginals of the speed process, including the joint density of two and three consecutive speeds. One striking property of the distribution is that two speeds are equal with positive probability and for any given particle there are infinitely many others with the same speed. We also study the partially asymmetric simple exclusion process (ASEP). We prove that the states of the ASEP with the above initial configuration, seen as permutations of Z, are symmetric in distribution. This allows us to extend some of our results, including the stationarity and description of all ergodic stationary measures, also to the ASEP.Comment: Published in at http://dx.doi.org/10.1214/10-AOP561 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Built-in templates speed up process for making accurate models

From accurate scale drawings of a model, photographic negatives of the cross sections are printed on thin sheets of aluminum. These cross-section images are cut out and mounted, and mahogany blocks placed between them. The wood can be worked down using the aluminum as a built-in template

High Speed Sintering – Continuing Research into a New Rapid Manufacturing Process

High Speed Sintering (HSS) is an emerging layer manufacturing technique aiming to break into the lucrative field of Rapid Manufacturing (RM). The process is likened to Selective Laser Sintering (SLS), however, instead of a laser dictating the sintered cross sectional area of each layer, the desired area is first printed using a Radiation Absorbing Material (RAM) and then sintered using an inexpensive infrared lamp. This paper begins by describing the sintering process in more detail and then outlining the overall manufacturing cycle. It then continues by describing the experiments performed to investigate the current problem concerning the hardness of excess powder within the powder bed. This problem arose due to the continual exposure of the whole bed to infrared radiation from the lamp. The experiments showed that as the power of the IR lamp increased, the hardness of the bed also increased. Furthermore, at higher IR power levels it was found the excess powder produced a solid tile which could only be broken down by a glass bead blaster.Mechanical Engineerin

Finite-size corrections to the speed of a branching-selection process

We consider a particle system studied by E. Brunet and B. Derrida, which evolves according to a branching mechanism with selection of the fittest keeping the population size fixed and equal to $N$. The particles remain grouped and move like a travelling front driven by a random noise with a deterministic speed. Because of its mean-field structure, the model can be further analysed as $N \to \infty$. We focus on the case where the noise lies in the max-domain of attraction of the Weibull extreme value distribution and show that under mild conditions the correction to the speed has universal features depending on the tail probabilities

Gravitational redshift and the vacuum index of refraction

A physical process of the gravitational redshift was described in an earlier paper (Wilhelm & Dwivedi 2014) that did not require any information for the emitting atom neither on the local gravitational potential U nor on the speed of light c. Although it could be shown that the correct energy shift of the emitted photon resulted from energy and momentum conservation principles and the speed of light at the emission site, it was not obvious how this speed is controlled by the gravitational potential. The aim of this paper is to describe a physical process that can accomplish this control. We determine the local speed of light c by deducing a gravitational index of refraction nG as a function of the potential U assuming a specific aether model, in which photons propagate as solitons. Even though an atom cannot locally sense the gravitational potential U (cf. Muller et al. 2010), the gravitational redshift will nevertheless be determined by U (cf. Wolf et al. 2010)- mediated by the local speed of light c.Comment: 8 Page