Steady-periodic method for modeling mode instability in fiber amplifiers

We present a detailed description of the methods used in our model of mode instability in high-power, rare earth-doped, large-mode-area fiber amplifiers. Our model assumes steady-periodic behavior, so it is appropriate to operation after turn on transients have dissipated. It can be adapted to transient cases as well. We describe our algorithm, which includes propagation of the signal field by fast-Fourier transforms, steady-state solutions of the laser gain equations, and two methods of solving the time-dependent heat equation: alternating-direction-implicit integration, and the Green's function method for steady-periodic heating.Comment: 19 pages, 2 figure

Measure based metrics for aggregated data

Aggregated data arises commonly from surveys and censuses where groups of individuals are studied as coherent entities. The aggregated data can take many forms including sets, intervals, distributions and histograms. The data analyst needs to measure the similarity between such aggregated data items and a range of metrics are reported in the literature to achieve this (e.g. the Jaccard metric for sets and the Wasserstein metric for histograms). In this paper, a unifying theory based on measure theory is developed that establishes not only that known metrics are essentially similar but also suggests new metrics