1,687 research outputs found
On Khovanov's cobordism theory for su(3) knot homology
We reconsider the su(3) link homology theory defined by Khovanov in
math.QA/0304375 and generalized by Mackaay and Vaz in math.GT/0603307. With
some slight modifications, we describe the theory as a map from the planar
algebra of tangles to a planar algebra of (complexes of) `cobordisms with
seams' (actually, a `canopolis'), making it local in the sense of Bar-Natan's
local su(2) theory of math.GT/0410495.
We show that this `seamed cobordism canopolis' decategorifies to give
precisely what you'd both hope for and expect: Kuperberg's su(3) spider defined
in q-alg/9712003. We conjecture an answer to an even more interesting question
about the decategorification of the Karoubi envelope of our cobordism theory.
Finally, we describe how the theory is actually completely computable, and
give a detailed calculation of the su(3) homology of the (2,n) torus knots.Comment: 49 page
A quasi-three-dimensional method for calculating blade surface velocities for an axial flow turbine blade
Quasi-three-dimensional compressible flow analysis for calculating blade surface velocities for axial flow turbine blad
Efficient solution of the Euler and Navier-Stokes equations with a vectorized multiple-grid algorithm
A multiple-grid algorithm for use in efficiently obtaining steady solutions to the Euler and Navier-Stokes equations is presented. The convergence of the explicit MacCormack algorithm on a fine grid is accelerated by propagating transients from the domain using a sequence of successively coarser grids. Both the fine and coarse grid schemes are readily vectorizable. The combination of multiple-gridding and vectorization results in substantially reduced computational times for the numerical solution of a wide range of flow problems. Results are presented for subsonic, transonic, and supersonic inviscid flows and for subsonic attached and separated laminar viscous flows. Work reduction factors over a scalar, single-grid algorithm range as high as 76.8
The Fractured Memory of a Mind’s Eye
The work I create is informed by questioning reality/identity, the fractalizing planes
of existence our essence occupies, and the artifacts of memory experience navigating
through space time. While existing in this realm of oversaturated media and neon
glow, I question the effects of pervasive data systems overloading or programming the
mental software we possess. My work includes humor as a means of exploring these
conventions while also displaying psychedelic surrealist imagery to help break away
from the conscious prison this existence births our concept apparatuses within
X-ray observations of flow patterns in a mercury boiler
X ray observations of two phase flow patterns in metallic, forced flow mercury boile
Numerical Studies of a Supersonic Fluidic Diverter Actuator for Flow Control
The analysis of the internal flow structure and performance of a specific fluidic diverter actuator, previously studied by time-dependent numerical computations for subsonic flow, is extended to include operation with supersonic actuator exit velocities. The understanding will aid in the development of fluidic diverters with minimum pressure losses and advanced designs of flow control actuators. The self-induced oscillatory behavior of the flow is successfully predicted and the calculated oscillation frequencies with respect to flow rate have excellent agreement with our experimental measurements. The oscillation frequency increases with Mach number, but its dependence on flow rate changes from subsonic to transonic to supersonic regimes. The delay time for the initiation of oscillations depends on the flow rate and the acoustic speed in the gaseous medium for subsonic flow, but is unaffected by the flow rate for supersonic condition
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