A note on the motion of surfaces

We study the motion of surfaces in an intrinsic formulation in which the surface is described by its metric and curvature tensors. The evolution equations for the six quantities contained in these tensors are reduced in number in two cases: (i) for arbitrary surfaces, we use principal coordinates to obtain two equations for the two principal curvatures, highlighting the similarity with the equations of motion of a plane curve; and (ii) for surfaces with spatially constant negative curvature, we use parameterization by Tchebyshev nets to reduce to a single evolution equation. We also obtain necessary and sufficient conditions for a surface to maintain spatially constant negative curvature as it moves. One choice for the surface's normal motion leads to the modified-Korteweg de Vries equation,the appearance of which is explained by connections to the AKNS hierarchy and the motion of space curves.Comment: 10 pages, compile with AMSTEX. Two figures available from the author

Solitary Waves in Optical Fibers Governed by Higher Order Dispersion

An exact solitary wave solution is presented for the nonlinear Schrodinger equation governing the propagation of pulses in optical fibers including the effects of second, third and fourth order dispersion. The stability of this soliton-like solution with sech2 shape is proven by the sign-definiteness of the operator and an integral of the Sobolev type. The main criteria governing the existence of such stable localized pulses propagating in optical fibers are also formulated. A unique feature of these soliton-like optical pulses propagating in a fiber with higher order dispersion is that their parameters satisfy efficient scaling relations. The main soliton solution term given by perturbation theory is also presented when absorption or gain is included in the nonlinear Schrodinger equation. We anticipate that this type of stable localized pulses could find practical applications in communications, slow-light devices and ultrafast lasers.Comment: 4 pages 3 Figure

Pushing up the daisies

When components of an interacting dynamical system (such as organs within an organism, or daisies within the Daisyworld model) have a limited range of viability to changes in some essential variable, intuition suggests that increasing any individual range of viability will also increase viability in the context of the whole system. We show circumstances in which the reverse is true

The Gomi legacy

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Ranking social bookmarks using topic models

Ranking of resources in social tagging systems is a difficult problem due to the inherent sparsity of the data and the vo- cabulary problems introduced by having a completely unre- stricted lexicon. In this paper we propose to use hidden topic models as a principled way of reducing the dimensionality of this data to provide more accurate resource rankings with higher recall. We first describe Latent Dirichlet Allocation (LDA) and then show how it can be used to rank resources in a social bookmarking system. We test the LDA tagging model and compare it with 3 non-topic model baselines on a large data sample obtained from the Delicious social book- marking site. Our evaluations show that our LDA-based method significantly outperforms all of the baselines

Infrared observations of OB star formation in NGC 6334

Infrared photometry and maps from 2 to 100 microns are presented for three of the principal far infrared sources in NGC 6334. Each region is powered by two or more very young stars. The distribution of dust and ionized gas is probably strongly affected by the presence of the embedded stars; one of the sources is a blister H II region, another has a bipolar structure, and the third exhibits asymmetric temperature structure. The presence of protostellar objects throughout the region suggests that star formation has occurred nearly simultaneously in the whole molecular cloud rather than having been triggered sequentially from within

Wind tunnel blockage tests at Mach 5 of vacuum duct models for two sound radiation shields

Two sound shield models with dummy vacuum exhaust ducts were tested in a Mach 5 pilot quiet tunnel. The first model simulates a new sound shield of 3 in. (7.62 cm) inside diameter and the second model is a shield of 4 in. (10.16 cm) inside diameter. The dummy vacuum exhaust ducts were attached to the external housing of the models. The flow in the first model, which had a by pass mass flow ratio of about 0.6, could not be started except at the two highest test Reynolds numbers where only the central core flow region was started. The flow in the second model with a mass ratio of approximately 0.3 was fully started except at the lowest unit Reynolds number where some unsteadiness and partial flow separation at the wall was observed. Since the external housing and dummy vacuum ducts were the same for both models, these results indicate that the ratio of by pass mass flow to total mass flow for a wind tunnel sound shield of this particular design must be less than about 0.3. Hence, a lower limit is imposed on the inlet diameter of the sound shield in relation to the exit diameter of the wind tunnel nozzle. This lower limit on the inlet diameter may possibly be reduced by improvements in streamlining of the external housing and ducts, by reductions in blockage area, or by the use of external ducting shrouds

Space nuclear reactor shields for manned and unmanned applications

Missions which use nuclear reactor power systems require radiation shielding of payload and/or crew areas to predetermined dose rates. Since shielding can become a significant fraction of the total mass of the system, it is of interest to show the effect of various parameters on shield thickness and mass for manned and unmanned applications. Algorithms were developed to give the thicknesses needed if reactor thermal power, separation distances, and dose rates are given as input. The thickness algorithms were combined with models for four different shield geometries to allow tradeoff studies of shield volume and mass for a variety of manned and unmanned missions. Shield design tradeoffs presented in this study include the effects of: higher allowable dose rates; radiation hardened electronics; shorter crew exposure times; shield geometry; distance of the payload and/or crew from the reactor; and changes in the size of the shielded area. Specific NASA missions that were considered in this study include unmanned outer planetary exploration, manned advanced/evolutionary space station, and advanced manned lunar base

Forecast Encompassing Tests and Probability Forecasts

We consider tests of forecast encompassing for probability forecasts, for both quadratic and logarithmic scoring rules. We propose test statistics for the null of forecast encompassing, present the limiting distributions of the test statistics, and investigate the impact of estimating the forecasting models’ parameters on these distributions. The small-sample performance of the various statistics is investigated, both in terms of small numbers of forecasts and model estimation sample sizes. Two empirical applications show the usefulness of the tests for the evaluation of recession probability forecasts from logit models with different leading indicators as explanatory variables, and for evaluating survey-based probability forecasts. Probability forecasts ; encompassing tests ; recession probabilities