Ricci solitons on singly warped product manifolds and applications

TThe purpose of this article is to study the inheritance properties of Ricci soliton warped product manifolds by their factor manifolds. First, it is proved that being a Ricci soliton is an inheritance property. Then we study Ricci soliton on warped product manifolds admitting either a conformal vector field or a concurrent vector field. Finally, we study Ricci soliton on some warped product space-times

Conformal vector fields on doubly warped product manifolds and applications

In this article, we present a complete study of two disjoint classes of conformal vector fields on doubly warped product manifolds as well as on doubly warped space-times. Then we study Ricci solitons on doubly warped product manifollds admitting these types of conformal vector fields

Optimization and visualization of rapid prototyping process parameters.

The optimal selection of rapid prototyping (RP) process parameters is a great concern to RP designers. When dealing with this problem, different build objectives have to be taken into consideration. Using virtual rapid prototyping (VRP) systems as a visualization tool to verify the optimally selected process parameters will assist designers in taking critical decisions regarding modeling of prototypes. This will lead to substantial improvements in part accuracy using minimal number of iterations, and no physical fabrication until confident enough to do so. The purpose of this thesis is to demonstrate that virtual validation of optimally selected process parameters can significantly reduce time and effort spent on traditional RP experimentation. To achieve the goal of this thesis, a multi-objective optimization technique is proposed and a model is generated taking into consideration different build objectives, which are surface roughness, support structure volume, build time and dimensional accuracy. The multi-objective method used is the weighted sum method, where a single utility function has been formulated, which combines all the objective functions together. The orders of magnitudes have been normalized, and finally weights have been assigned for each objective function in order to create the general formulation. (Abstract shortened by UMI.)Dept. of Industrial and Manufacturing Systems Engineering. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis2004 .E47. Source: Masters Abstracts International, Volume: 43-03, page: 0959. Adviser: Waguih ElMaraghy. Thesis (M.A.Sc.)--University of Windsor (Canada), 2004

Derivation of Bearing Capacity Equation for a Two Layered System of Weak Clay Layer Overlaid by Dense Sand Layer

Calculation of the ultimate bearing capacity of shallow footing on a two layered system of soil depends on the pattern of the failure surface that develops below the footing. For a weak clay layer overlaid by a top dense sand layer, previous studies assumed that the failure surface is a punching shear failure through the upper sand layer and Prandtl's failure mode in the bottom weak clay layer. By adapting this assumption in this study, the ultimate bearing capacity equation was derived as a function of the properties of soils, the footing width, and the topsoil thickness. The paper presents a detailed parametric study of the design parameters including the effect of angle of friction, the ratio of the thickness of sand layer to the footing width, the ratio of the depth of embedment to the footing width, and the ratio of the clay soil cohesion to the product of the clay unit weight by the footing width. Design charts were developed in dimensionless form for very wide ranges of design parameters. The available method based on the limit equalibrium analysis was developed in dimensionlised form and for a limited range of design parametrs. The new charts give another option for those who believe that the design charts developed based on the upper limit analysis overestimate the bearing capacity due to the very nature of the upper bound solution. The new design charts are limited to shallow footings