This paper presents an Interactive View-Driven Evenly Spaced Streamline placement algorithm (IVDESS) for 3D explorative visualization of large complex planar or curved surface flows. IVDESS rapidly performs accurate streamline integration in 3D physical space, i.e., the flow field, while achieving high quality streamline density control in 2D view space, i.e., the output image. The corresponden...

Let us consider incompressible and inviscid flows in two-dimensional domains with multiple obstacles. The instantaneous velocity field becomes aHamiltonian vector field defined from the stream function, and it is topologically characterized by the streamline pattern that corresponds to the contour plot of the stream function. The present paper provides us with a procedure to construct structura...

Considering a simple model transport problem, we present a new finite element method. While the new method fits in the class of discontinuous Galerkin (DG) methods, it differs from standard DG and streamline diffusion methods, in that it uses a space of discontinuous trial functions tailored for stability. The new method, unlike the older approaches, yields optimal estimates for the primal vari...

A challenging difficulty in solving the radial Dirac eigenvalue problem numerically is the presence of spurious (unphysical) eigenvalues among the correct ones that are neither related to mathematical interpretations nor to physical explanations. Many attempts have been made and several numerical methods have been applied to solve the problem using finite element method (FEM), finite difference...

Particulate catalysts with streamline shapes have important impacts on fluid-related reactions, and they need to be properly characterized. However, utilization of streamline-shaped catalysts for heterogeneous catalysis has remained an unexplored area due to the lack of easy-to-use techniques to produce such shaped catalysts, especially at the small length scale of the submicron to micron regim...

Carbon nanotubes have an important role in reinforcing nanocomposits. Many experimental observations have shown that in the most nanostructures such as nanocomposites, carbon nanotubes (CNTs) are often characterized by a certain degree of waviness along their axial direction. In the present paper, the effects of initial curvature, influence of surrounding medium that is modeled as Winkler elast...

We further consider the Galerkin method for advective-diiusive equations in two-dimensions. The nite dimensional space employed is of piecewise polynomials enriched with residual-free bubbles (RFB). We show that, in general, this method does not coincide with the SUPG method, unless the piecewise polynomials are spanned by linear functions. Furthermore a simple stability analysis argument displ...

Modeling of a wide class of physical phenomena, such as crystal growth and flame propagation, leads to tracking fronts moving with curvature-dependent speed. When the speed is the curvature this leads to one of the classical degenerate nonlinear second-order differential equations on Euclidean space. One naturally wonders, “What is the regularity of solutions?” A priori solutions are only defin...

The obstacle avoidance problem has been a well researched topic by many robotics researchers. We focus on one popular solution to this problem, the Curvature-Velocity Method(CVM). In Simmons’ original paper [5], differentially steered (DS) robots where not considered thoroughly. This paper presents a variation on CVM, specifically designed for DS robots. We show comparable results to that of Si...