We present an alternative method to ray tracing that is based on a phase space description of light propagation. Liouville’s equation geometrical optics describes the evolution basic luminance space. At optical interface, laws describe non-local boundary conditions for luminance. A discontinuous Galerkin employed solve dielectric total internal reflection concentrator.

Aiming at the geomorphological and geometrical features of basin, a recognition approach combined with landform classification discriminant analysis is presented. First, k-means algorithm applied to digital elevation model data. The basic types landforms elevation, slope, relief amplitude are clustered, regions plains, mountains, hills have been separated. Focusing on plain its neighboring regi...

presence of joints and fractures in rocks strongly influences the behavior of the rock mass by dividing the media into smaller units. these structures intensify the potential instability besides the development of sliding and rotational movements. the assumption of discontinuum media changes the whole analysis conditions in relation to the continuum analysis. acquisition of geometrical and stru...

based on the point of view of geometrical representation of an intuitionistic fuzzy set, we take into account all three parameters describing intuitionistic fuzzy set, propose a kind of new method to calculate correlation and correlation coefficient of intuitionistic fuzzy sets which is similar to the cosine of the intersectional angle in finite sets and probability space, respectively. further...

A powerful method to solve nonlinear first-order ordinary differential equations, which is based on a geometrical understanding of the corresponding dynamics of the so-called Lie systems, is developed. This method enables us not only to solve some of these equations, but also gives geometrical explanations for some, already known, ad hoc methods of dealing with such problems. MSC 2000: 34A26 (P...

PURPOSE In the present work, the authors compare geometrical and Monte Carlo projectors in detail. The geometrical projectors considered were the conventional geometrical Siddon ray-tracer (S-RT) and the orthogonal distance-based ray-tracer (OD-RT), based on computing the orthogonal distance from the center of image voxel to the line-of-response. A comparison of these geometrical projectors was...

The buckling torque may be much less than the yield torque in very thin rectangular tubes under torsion. In this paper, simple closed-form formulae are presented for buckling analysis of long hollow rectangular tubes under torsion. By the presented formulae, one can obtain the critical torque or the critical angle of twist of the tube in terms of its geometrical parameters and material constant...