New conserved vorticity integrals for moving surfaces in multi-dimensional fluid flow

For inviscid fluid flow in any n-dimensional Riemannian manifold, new conserved vorticity integrals generalizing helicity, enstrophy, and entropy circulation are derived for lower-dimensional surfaces that move along fluid streamlines. Conditions are determined for which the integrals yield constants of motion for the fluid. In the case when an inviscid fluid is isentropic, these new constants of motion generalize Kelvin’s circulation theorem from closed loops to closed surfaces of any dimension.

Predicting performance on fluid intelligence from speed of processing, working memory, and controlled attention

Fluid inteliigence has been defined as an innate ability to reason which is measured commonly by the Raven's Progressive Matrices (RPM). Individual differences in fluid intelligence are currently explained by the Cascade model (Fry & Hale, 1996) and the Controlled Attention hypothesis (Engle, Kane, & Tuholski, 1999; Kane & Engle, 2002). The first theory is based on a complex relation among age, speed, and working memory which is described as a Cascade. The alternative to this theory, the Controlled Attention hypothesis, is based on the proposition that it is the executive attention component of working memory that explains performance on fluid intelligence tests. The first goal of this study was to examine whether the Cascade model is consistent within the visuo-spatial and verbal-numerical modalities. The second goal was to examine whether the executive attention component ofworking memory accounts for the relation between working memory and fluid intelligence. Two hundred and six undergraduate students between the ages of 18 and 28 completed a battery of cognitive tests selected to measure processing speed, working memory, and controlled attention which were selected from two cognitive modalities, verbalnumerical and visuo-spatial. These were used to predict performance on two standard measures of fluid intelligence: the Raven's Progressive Matrices (RPM) and the Shipley Institute of Living Scales (SILS) subtests. Multiple regression and Structural Equation Modeling (SEM) were used to test the Cascade model and to determine the independent and joint effects of controlled attention and working memory on general fluid intelligence. Among the processing speed measures only spatial scan was related to the RPM. No other significant relations were observed between processing speed and fluid intelligence. As 1 a construct, working memory was related to the fluid intelligence tests. Consistent with the predictions for the RPM there was support for the Cascade model within the visuo-spatial modality but not within the verbal-numerical modality. There was no support for the Cascade model with respect to the SILS tests. SEM revealed that there was a direct path between controlled attention and RPM and between working memory and RPM. However, a significant path between set switching and RPM explained the relation between controlled attention and RPM. The prediction that controlled attention mediated the relation between working memory and RPM was therefore not supported. The findings support the view that the Cascade model may not adequately explain individual differences in fluid intelligence and this may be due to the differential relations observed between working memory and fluid intelligence across different modalities. The findings also show that working memory is not a domain-general construct and as a result its relation with fluid intelligence may be dependent on the nature of the working memory modality.

Hydraulic and fluvial geomorphological models for a bedrock channel reach of the Twenty Mile Creek /

Bedrock channels have been considered challenging geomorphic settings for the application of numerical models. Bedrock fluvial systems exhibit boundaries that are typically less mobile than alluvial systems, yet they are still dynamic systems with a high degree of spatial and temporal variability. To understand the variability of fluvial systems, numerical models have been developed to quantify flow magnitudes and patterns as the driving force for geomorphic change. Two types of numerical model were assessed for their efficacy in examining the bedrock channel system consisting of a high gradient portion of the Twenty Mile Creek in the Niagara Region of Ontario, Canada. A one-dimensional (1-D) flow model that utilizes energy equations, HEC RAS, was used to determine velocity distributions through the study reach for the mean annual flood (MAF), the 100-year return flood and the 1,000-year return flood. A two-dimensional (2-D) flow model that makes use of Navier-Stokes equations, RMA2, was created with the same objectives. The 2-D modeling effort was not successful due to the spatial complexity of the system (high slope and high variance). The successful 1 -D model runs were further extended using very high resolution geospatial interpolations inherent to the HEC RAS extension, HEC geoRAS. The modeled velocity data then formed the basis for the creation of a geomorphological analysis that focused upon large particles (boulders) and the forces needed to mobilize them. Several existing boulders were examined by collecting detailed measurements to derive three-dimensional physical models for the application of fluid and solid mechanics to predict movement in the study reach. An imaginary unit cuboid (1 metre by 1 metre by 1 metre) boulder was also envisioned to determine the general propensity for the movement of such a boulder through the bedrock system. The efforts and findings of this study provide a standardized means for the assessment of large particle movement in a bedrock fluvial system. Further efforts may expand upon this standardization by modeling differing boulder configurations (platy boulders, etc.) at a high level of resolution.