University of Colorado Boulder

About: University of Colorado Boulder is a education organization based out in Boulder, Colorado, United States. It is known for research contribution in the topics: Population & Galaxy. The organization has 48794 authors who have published 115151 publications receiving 5387328 citations. The organization is also known as: CU Boulder & UCB.

On pressure boundary conditions for the incompressible Navier‐Stokes equations

Abstract: The pressure is a somewhat mysterious quantity in incompressible flows. It is not a thermodynamic variable as there is no ‘equation of state’ for an incompressible fluid. It is in one sense a mathematical artefact—a Lagrange multiplier that constrains the velocity field to remain divergence-free; i.e., incompressible—yet its gradient is a relevant physical quantity: a force per unit volume. It propagates at infinite speed in order to keep the flow always and everywhere incompressible; i.e., it is always in equilibrium with a time-varying divergence-free velocity field. It is also often difficult and/or expensive to compute. While the pressure is perfectly well-defined (at least up to an arbitrary additive constant) by the governing equations describing the conservation of mass and momentum, it is (ironically) less so when more directly expressed in terms of a Poisson equation that is both derivable from the original conservation equations and used (or misused) to replace the mass conservation equation. This is because in this latter form it is also necessary to address directly the subject of pressure boundary conditions, whose proper specification is crucial (in many ways) and forms the basis of this work. Herein we show that the same principles of mass and momentum conservation, combined with a continuity argument, lead to the correct boundary conditions for the pressure Poisson equation: viz., a Neumann condition that is derived simply by applying the normal component of the momentum equation at the boundary. It usually follows, but is not so crucial, that the tangential momentum equation is also satisfied at the boundary.

Reading Comprehension Tests Vary in the Skills They Assess: Differential Dependence on Decoding and Oral Comprehension.

Abstract: Comprehension tests are often used interchangeably, suggesting an implicit assumption that they are all measuring the same thing. We examine the validity of this assumption by comparing some of the most popular reading comprehension measures used in research and clinical practice in the United States: the Gray Oral Reading Test (GORT), the two assessments (retellings and comprehension questions) from the Qualitative Reading Inventory (QRI), the Woodcock–Johnson Passage Comprehension subtest (WJPC), and the Reading Comprehension test from the Peabody Individual Achievement Test (PIAT). Modest intercorrelations among the tests suggested that they were measuring different skills. Regression analyses showed that decoding, not listening comprehension, accounts for most of the variance in both the PIAT and the WJPC; the reverse holds for the GORT and both QRI measures. Large developmental differences in what the tests measure were found for the PIAT and the WJPC, but not the other tests, both when development w...

Mechanical and metabolic determinants of the preferred step width in human walking.

Abstract: We studied the selection of preferred step width in human walking by measuring mechanical and metabolic costs as a function of experimentally manipulated step width (0.00^0.45L, as a fraction of leg length L). We estimated mechanical costs from individual limb external mechanical work and metabolic costs using open circuit respirometry. The mechanical and metabolic costs both increased substantially (54 and 45%, respectively) for widths greater than the preferred value (0.15^0.45L) and with step width squared (R 2 ˆ 0.91 and 0.83, respectively). As predicted by a three-dimensional model of walking mechanics, the increases in these costs appear to be a result of the mechanical work required for redirecting the centre of mass velocity during the transition between single stance phases (step-to-step transition costs). The metabolic cost for steps narrower than preferred (0.10^0.00L) increased by 8%, which was probably as a result of the added cost of moving the swing leg laterally in order to avoid the stance leg (lateral limb swing cost). Trade-ois between the step-to-step transition and lateral limb swing costs resulted in a minimum metabolic cost at a step width of 0.12L, which is not signi¢cantly diierent from foot width (0.11L) or the preferred step width (0.13L). Humans appear to prefer a step width that minimizes metabolic cost.

Randomized algorithms for the low-rank approximation of matrices

Abstract: We describe two recently proposed randomized algorithms for the construction of low-rank approximations to matrices, and demonstrate their application (inter alia) to the evaluation of the singular value decompositions of numerically low-rank matrices. Being probabilistic, the schemes described here have a finite probability of failure; in most cases, this probability is rather negligible (10−17 is a typical value). In many situations, the new procedures are considerably more efficient and reliable than the classical (deterministic) ones; they also parallelize naturally. We present several numerical examples to illustrate the performance of the schemes.