Stability of a premixed flame in stagnation-point flow against general disturbances

Previously, the stability of a premixed flame in a stagnation flow was discussed for a restricted class of disturbances that are self-similar to the basic undisturbed flow; thus, flame fronts with corrugations only in the cross stream direction were considered. Here, we consider a more general class of three-dimensional flame front perturbations which also permits corrugations in the streamwise direction. It is shown that, because of the stretch experienced by the flame, the hydrodynamic instability is limited only to disturbances of short wavelength. If in addition diffusion effects have a stabilizing influence, as would be the case of mixtures with Lewis number greater than one, a stretched flame could be absolutely stable. Instabilities occur when the Lewis number is below some critical value less than one. Neutral stability boundaries are presented in terms of the Lewis number, the strain rate, and the appropriate wavenumbers. Beyond the stability threshold, the two-dimensional self-similar modes always grow first. However, if disturbances of long wavelength are excluded, it is possible for the three-dimensional modes to be the least stable one. Accordingly, the pattern that will be observed on the flame front, at the onset of instability, will consist of either ridges in the direction of stretch or the more common three-dimensional cellular structure

A determinant formula for the Jones polynomial of pretzel knots

This paper presents an algorithm to construct a weighted adjacency matrix of a plane bipartite graph obtained from a pretzel knot diagram. The determinant of this matrix after evaluation is shown to be the Jones polynomial of the pretzel knot by way of perfect matchings (or dimers) of this graph. The weights are Tutte's activity letters that arise because the Jones polynomial is a specialization of the signed version of the Tutte polynomial. The relationship is formalized between the familiar spanning tree setting for the Tait graph and the perfect matchings of the plane bipartite graph above. Evaluations of these activity words are related to the chain complex for the Champanerkar-Kofman spanning tree model of reduced Khovanov homology.Comment: 19 pages, 12 figures, 2 table

Inherently Governmental Functions and Other Work Reserved for Performance by Federal Government Employees: The Obama Administration’s Proposed Policy Letter

[Excerpt] On March 31, 2010, the Office of Federal Procurement Policy (OFPP) in the Office of Management and Budget (OMB) issued a proposed policy letter on inherently governmental functions and other “work reserved for performance by federal government employees.” While not final, the policy letter represents the Obama Administration’s proposed guidance for agencies determining (1) whether particular functions are inherently governmental and (2) when functions closely associated with the performance of inherently governmental functions and critical functions should be performed by government personnel. The proposed policy letter was, in part, issued under the authority of the Duncan Hunter National Defense Authorization Act for FY2009 (NDAA\u2709) and President Obama’s memorandum of March 4, 2009, on government contracting. Section 321 of NDAA\u2709 tasked OMB with (1) reviewing existing definitions of “inherently governmental function” to determine whether such definitions are “sufficiently focused” to ensure that only government personnel perform inherently governmental functions or “other critical functions necessary for the mission of a Federal department or agency;” (2) developing a “single consistent definition” of “inherently governmental function” that would address any deficiencies in the existing definitions, reasonably apply to all agencies, and ensure that agency personnel can identify positions that perform inherently governmental functions; (3) developing criteria for identifying critical functions” that should be performed by government personnel; and (4) developing criteria for identifying positions that government personnel should perform in order to ensure that agencies develop and maintain “sufficient organic expertise and technical capacity” to perform their missions and oversee contractors’ work. President Obama’s March 4, 2009, memorandum similarly charged OMB with clarifying when outsourcing is “appropriate.

Improving the fairness of FAST TCP to new flows

It has been observed that FAST TCP, and the related protocol TCP Vegas, suffer unfairness when many flows arrive at a single bottleneck link, without intervening departures. We show that the effect is even more marked if a new flow arrives when existing flows share bandwidth fairly, and propose a simple method to ameliorate this effect