Large particle number limit in rain

International audienceThe way we conceptualize rain is fundamental in many branches of science since it provides the basis not only for rain modeling notably in meteorology and hydrology, but also for interpreting rain data (from gauges and radars). In order to empirically address this question, we use stereophotographic data to measure the positions and volumes of raindrops from similar to10 m(3) regions containing 5000-15 000 of these drops. By determining the drop statistics in spheres of increasing size, we conduct a basic continuum mechanics thought experiment. We show that-presumably due to turbulence-there is no microscale-macroscale separation. We find that the large particle number (N) limit in rain is not a homogeneous continuum, but rather it is nonclassical, strongly inhomogeneous, and approaching a multifractal discontinuum

SIMULTANEOUS LOCOMOTIVE AND CAR ASSIGNMENT AT VIA RAIL CANADA

Given a periodic train schedule and a fleet composed of several types of equipment, the simultaneous locomotive and car assignment problem is to determine a set of minimum cost equipment cycles such that every train is assigned appropriate equipment and some side constraints are satisfied. The authors present a model and heurisitic solution approach based on mathematical optimization to solve the problem of assigning locomotives and cars to passenger trains. They first present a basic formulation that translates maintenance requirements and other fundamental difficulties of the problem. Next, they discuss several extensions, such as substitution possibilities and the minimization of switching operations, which are required in a real-life application. The resulting model is optimized through a branch-and-bound method in which the linear relaxations are solved by column generation. The model and solution strategy were tested on data from VIA Rail in Canada and a complete system based on this approach is now implemented ate the company

OPERATIONAL CAR ASSIGNMENT AT VIA RAIL CANADA

Increasing the utilization of the rolling stock by better assignment of available locomotives and cars to scheduled trains could possibly reduce costs and improve service for passenger railroads. This paper presents a modeling and solution methodology for a car assignment problem that arises when individual car routings that satisfy all operational constraints must be determined. This methodology considers typical constraints such as maintenance requirements as well as more complex constraints such as minimum connection times that depend on the positions of the individual cars in a train consist (i.e., units of equipment assigned to the train). The problem is solved heuristically by a branch-and-bound method in which the linear relaxations are solved by column generation. Simulation results show that the solution approach quickly yields quality solutions. VIA Rail Canada is currently evaluating a software system based on this approach

Physiological Functioning of Carbonic Anhydrase in the Hydrothermal Vent Tubeworm Riftia Pachyptila

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