54,085 research outputs found

    From large deviations to semidistances of transport and mixing: coherence analysis for finite Lagrangian data

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    One way to analyze complicated non-autonomous flows is through trying to understand their transport behavior. In a quantitative, set-oriented approach to transport and mixing, finite time coherent sets play an important role. These are time-parametrized families of sets with unlikely transport to and from their surroundings under small or vanishing random perturbations of the dynamics. Here we propose, as a measure of transport and mixing for purely advective (i.e., deterministic) flows, (semi)distances that arise under vanishing perturbations in the sense of large deviations. Analogously, for given finite Lagrangian trajectory data we derive a discrete-time and space semidistance that comes from the "best" approximation of the randomly perturbed process conditioned on this limited information of the deterministic flow. It can be computed as shortest path in a graph with time-dependent weights. Furthermore, we argue that coherent sets are regions of maximal farness in terms of transport and mixing, hence they occur as extremal regions on a spanning structure of the state space under this semidistance---in fact, under any distance measure arising from the physical notion of transport. Based on this notion we develop a tool to analyze the state space (or the finite trajectory data at hand) and identify coherent regions. We validate our approach on idealized prototypical examples and well-studied standard cases.Comment: J Nonlinear Sci, 201

    Low cost microminiature refrigerators for large unit volume applications

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    Photolithographic techniques were employed to fabricate small Joule-Thomson refrigerators in laminated substrates. The gas passages of a J-T refrigerator are formed by etching channels as narrow as 50 microns and as shallow as 5 microns in glass plates which are laminated together. Circular refrigerators on the order of 1.5 centimeters in diameter and .75 millimeters thick were produced which cool down to cryogenic temperatures in a few seconds, using Argon or Nitrogen, with no vacuum or radiation insulation. Smaller refrigerators are developed for both faster cooldown and low refrigeration capacity applications. By using this technology, custom refrigerators can be designed to meet specific application requirements
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