This study develops a general discrete flow model which is
discrete both in time and space. A stirred tank network model
(continuous time compartment model) is summarized and then compared
with the discrete flow model. Both models make use of a
fractional input matrix with elements representing the fraction of...
A concept image is that collection of all images, pictures, symbols, definitions
and properties associated with any given mathematical concept. One of the
most important components in the mental representation of concepts in the concept
image of advanced mathematical thinkers is visualization. This component, in
turn, is indispensable in the...
Traditional application of Voronoi diagrams for space partitioning creates Voronoi regions, with areas determined by the generators’ relative locations and weights. Especially in the area of information space (re)construction, however, there is a need for inverse solutions; i.e., finding weights that result in regions with predefined areas. In this thesis,...
Open Source software gives users the freedom to copy, modify and redistribute source code without legal entanglements. The evolution of these software communities usually depend a lot on how the participating developers and users interact and co-operate with each other. Over the past few years, open source software have become...
While individual portfolio diversity analysis is a well-studied problem in visualization, the visual analysis of individual or groups of portfolios, over time, has received little attention. Such analysis, however, is important to researchers who are interested in better understanding portfolio management behavior of experts as well as novices. We conducted...
Many applications in computer graphics and geometry processing rely on the ability to
locally orient 2D and 3D entities on a surface, or inside a volume, such as the sinusoidal
kernels in Gabor noise, the color and geometry textures in pattern synthesis, and the
finite elements in remeshing. In these...
The study of the diversity of multivariate objects shares common characteristics across disciplines, including ecology and organizational management. Nevertheless, experts in these two disciplines have adopted somewhat separate diversity concepts and analysis techniques, limiting the ability of potentially sharing and cross comparing these concerns. Moreover, while complex diversity data may...
Design and control of vector fields is critical for many visualization and graphics tasks such as vector field visualization, fluid simulation, and texture synthesis. The fundamental qualitative structures associated with vector fields are fixed points, periodic orbits, and separatrices. In this paper we provide a new technique that allows for...
Asymmetric tensor fields are useful for understanding fluid flow and solid deformation. They present new challenges, however, for traditional tensor field visualization techniques such as hyperstreamline placement and glyph packing. This is because the physical behavior of tensors inside real domains where eigenvalues are real is fundamentally different from the...
Analysis, visualization, and design of vector fields on surfaces have a wide variety of major applications in both scientific visualization and computer graphics. On the one hand, analysis and visualization of vector fields provide critical insights to the flow data produced from simulation or experiments of various engineering processes. On...
