A cellation of the Grassmann manifold

Motivated by the computation of equilibria in economic models with incomplete asset markets, a cellation of the Grassmann manifold is constructed by restricting a common atlas. The Grassmann manifold ofm-planes inn-dimensional space is shown to be a union ofn choosem congruentm(n−m)-dimensional topological disks whose interiors are disjoint.     

A finite procedure for determining if a quadratic form is bounded below on a closed polyhedral convex set

Mathematical Programming -     

Inference for an anisotropic diffusion model

The vector sum of a white noise in an unknown hyperspace and an Ornstein-Uhlenbeck process in an unknown line is observed through sharp linear test functions over a finite time span. The parameters associated with the white noise (including the hyperplane) are determinable with precision and index the measure-equivalence classes in the relevant sample space. An intraclass relative density provides a basis for Bayesian inference of the remaining parameters.     

Influence of pressure on near nozzle flow field and soot formation in laminar co-flow diffusion flames

Soot formation from combustion devices, which tend to operate at high pressure, is a health and environmental concern, thus investigating the effect of pressure on soot formation is important. While most fundamental studies have utilised the co-flow laminar diffusion flame configuration to study the effect of pressure on soot, there is a lack of investigations into the effect of pressure on the flow field of diffusion flames and the resultant influence on soot formation. A recent work has displayed that recirculation zones can form along the centreline of atmospheric pressure diffusion flames. This present work seeks to investigate whether these zones can form due to higher pressure as well, which has never been explored experimentally or numerically. The CoFlame code, which models co-flow laminar, sooting, diffusion flames, is validated for the prediction of recirculation zones using experimental flow field data for a set of atmospheric pressure flames. The code is subsequently utilised to model ethane-air diffusion flames from 2 to 33 atm. Above 10 atm, recirculation zones are predicted to form. The reason for the formation of the zones is determined to be due to increasing shear between the air and fuel steams, with the air stream having higher velocities in the vicinity of the fuel tube tip than the fuel stream. This increase in shear is shown to be the cause of the recirculation zones formed in previously investigated atmospheric flames as well. Finally, the recirculation zone is determined as a probable cause of the experimentally observed formation of a large mass of soot covering the entire fuel tube exit for an ethane diffusion flame at 36.5 atm. Previously, no adequate explanation for the formation of the large mass of soot existed.