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Byline: Yifan Chen (1), Vimal K. Dubey (1) Keywords: azimuth-frequency domain channel characterization; geometric channel model; propagation aspects; ultrawideband systems Abstract: An azimuth-frequency domain (AFD) geometric channel model aimed at establishing the fundamental propagation characteristics for an ultrawideband (UWB) time-invariant channel is proposed. This modeling approach envisages the spatial pattern of scatterer distribution in a hypothetical azimuth-frequency space. One of the main advantages of this approach is the availability of analytical expressions relating signal properties in the AFD to channel properties. A further virtue of this method is to exploit the geometric distribution of scatterers for different spectral components from a physical wave-propagation viewpoint. The workhorse is the wideband semi-geometrically based statistical model and three heuristic rules proposed, which are an extension of the rules presented in the previous work. These rules are so proposed as to provide the underlying connection between the canonical model and the physical channel it represents. The important channel properties such as power azimuthal spectrum (PAS) and power delay spectrum (PDS) are calculated using this model and compared with the published data in the existing literature. Author Affiliation: (1) Positioning and Wireless Technology Centre, School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore Article History: Registration Date: 01/01/2004

This paper presents a study of streamer propagation in transformer oil, with point-plane and semi-uniform geometry. The latter is constituted of parallel plane electrodes, with a thin triggering point of calibrated size. By reducing the length of the point, it is possible to move progressively from a point-plane geometry to a quasi uniform geometry. The propagation of streamers is impeded by the presence of a metallic plane behind the triggering point, that reduces the field on propagating streamers. The effect varies widely according to the streamer type considered. The propagation of negative and fast positive streamers is nearly quenched, whereas slower filamentary positive streamers (usually responsible for breakdown in oil) are less affected. This shows that many results obtained in point-plane geometry can not be simply extrapolated to the more realistic case of uniform field.

The 3D passive earth pressure problem is investigated by the upper-bound method in limit analysis. Three kinematically admissible failure mechanisms referred to as M1, Mn, and Mnt are considered for the calculation schemes. The M1 mechanism is an extension into three dimensions of the classical 2D Coulomb mechanism. The Mn mechanism is a generalization of the M1 mechanism and is composed of a sequence of rigid blocks. Finally, the Mnt mechanism is a more elaborate mechanism in which the final block of the Mn mechanism is truncated by two portions of right circular cones. The lowest upper-bound solutions given by the present analysis are compared with other authors' results and presented in a form of design tables relating the geometrical parameters, soil properties, and the 3D passive earth pressure coefficients.

We compute the sign of Gaussian curvature using a purely geometric definition. Consider a point p on a smooth surface S and a closed curve y on S which encloses p. The image of [Gamma] on the unit normal Gaussian sphere is a new curve [Beta]. The Gaussian curvature at p is defined as the ratio of the area enclosed by [Gamma] over the area enclosed by [Beta] as [Gamma] contracts to p. The sign of Gaussian curvature at p is determined by the relative orientations of the closed curves [Gamma] and [Beta]. We directly compute the relative orientation of two such curves from intensity data. We employ three unknown illumination conditions to create a photometric scatter plot. This plot is in one-to-one correspondence with the subset of the unit Gaussian sphere containing the mutually illuminated surface normals. This permits direct computation of the sign of Gaussian curvature without the recovery of surface normals. Our method is albedo invariant. We assume diffuse reflectance, but the nature of the diffuse reflectance can be general and unknown. Error analysis on simulated images shows the accuracy of our technique. We also demonstrate the performance of this methodology on empirical data. Index Terms - Gaussian curvature, differential geometry, photometric invariant, photometric data, shape recovery, curve orientation.

This study aimed to model phenomenologically the dynamics of arterial wall remodeling under hypertensive conditions. Sustained hypertension was simulated by a step increase in blood pressure. The arterial wall was considered to be a thick-walled tube made of nonlinear elastic incompressible material. Remodeling rate equations were postulated for the evolution of the geometric dimensions of the hypertensive artery at the zero-stress state, as well as for one of the material constants in the constitutive equations. The driving stimuli for the geometric adaptation are the normalized deviations of wall stresses from their values under normotensive conditions. The geometric dimensions are modulated by the evolution of the deformed inner radius, which serves to restore the level of the flow-induced shear stresses at the arterial endothelium. Mechanical adaptation is driven by the difference between the area compliance under hypertensive and normotensive conditions. The predicted time course of the geometry and mechanical properties of arterial wall are in good qualitative agreement with published experimental findings. The model predicts that the geometric adaptation maintains the stress distribution in arterial wall to its control level, while the mechanical adaptation restores the normal arterial function under induced hypertension.

The path-following algorithm that can be used to solve signomial geometric programming (GP) dual problems is found to yield better quality and globally optimal results, given a relaxed stopping criterion for early posynomial GP problems in the sequence. The method can be employed to either the original nonconvex problem or to each of a sequence of convex posynomial GP problems nearly equalling the original problem.

The effects of geometrical and material parameters of fluence transmission experiments were studied for glasses with a variety of compositions using a tight focus geometry.The greatest thermal lensing properties were found in lead silicate glasses and it was assumed that glass materials should have high values of absorption coefficient, small valuesfor specific heat capacity and a random network structure with a maximum numberof degrees of freedom to maximize thermal lensing.

The elliptic functions provide an effective tool for describing geometric objects. The recollections of the Elliptical functions are described.