Stochastic microgeometry for displacement mapping

Proceedings of Shape Modeling International 2005, June 2005, pp. 164-173. Retrieved 3/16/2006 from http://www.cs.drexel.edu/~david/Papers/schroeder_SMI05.pdf.Creating surfaces with intricate small-scale features (microgeometry) and detail is an important task in geometric modeling and computer graphics. We present a model processing method capable of producing a wide variety of complex surface features based on displacement mapping and stochastic geometry. The latter is a branch of mathematics that analyzes and characterizes the statistical properties of spatial structures. The technique has been incorporated into an interactive modeling environment that supports the design of stochastic microgeometries. Additionally a tool has been developed that provides random exploration of the technique's entire parameter space by generating sample microgeometry over a broad range of values. We demonstrate the effectiveness of our technique by creating diverse, complex surface structures for a variety of geometric models, e.g. arrowheads, candy bars, busts, planets and coral

Mesoscopic simulations of the counterion-induced electroosmotic flow - a comparative study

We present mesoscopic simulations of the counterion-induced electroosmotic flow in different electrostatic coupling regimes. Two simulation methods are compared, Dissipative Particle Dynamics (DPD) and coupled Lattice-Boltzmann/Molecular Dynamics (LB/MD). A general mapping scheme to match DPD to LB/MD is developed. For the weak-coupling regime, analytic expressions for the flow profiles in the presence of partial-slip as well as no-slip boundary conditions are derived from the Poisson-Boltzmann and Stokes equations, which are in good agreement with the numerical results. The influence of electrofriction and partial slip on the flow profiles is discussed.Comment: 10 pages, 8 figures, 3 tables, additional references and minor changes in the tex

A continuous time random walk model of transport in variably saturated heterogeneous porous media

We propose a unified physical framework for transport in variably saturated porous media. This approach allows fluid flow and solute migration to be treated as ensemble averages of fluid and solute particles, respectively. We consider the cases of homogeneous and heterogeneous porous materials. Within a fractal mobile-immobile (MIM) continuous time random walk framework, the heterogeneity will be characterized by algebraically decaying particle retention-times. We derive the corresponding (nonlinear) continuum limit partial differential equations and we compare their solutions to Monte Carlo simulation results. The proposed methodology is fairly general and can be used to track fluid and solutes particles trajectories, for a variety of initial and boundary conditions.Comment: 12 pages, 9 figure

Partial differential equations for self-organization in cellular and developmental biology

Understanding the mechanisms governing and regulating the emergence of structure and heterogeneity within cellular systems, such as the developing embryo, represents a multiscale challenge typifying current integrative biology research, namely, explaining the macroscale behaviour of a system from microscale dynamics. This review will focus upon modelling how cell-based dynamics orchestrate the emergence of higher level structure. After surveying representative biological examples and the models used to describe them, we will assess how developments at the scale of molecular biology have impacted on current theoretical frameworks, and the new modelling opportunities that are emerging as a result. We shall restrict our survey of mathematical approaches to partial differential equations and the tools required for their analysis. We will discuss the gap between the modelling abstraction and biological reality, the challenges this presents and highlight some open problems in the field

State Lands Energy Resource Optimization Project - 1992 Annual Progress Report

Project SLERO, for which The University of Texas at Austin Bureau of Economic Geology is the lead contractor and coordinating institution, is a five-university consortium study of hydrocarbon resources on Texas State Lands. The five universities are The University of Texas at Austin, Texas A&M University, the University of Houston, Texas Tech University, and Lamar University, and the entire program is aided by the cooperation of the Texas General Land Office. This is a four-year project funded at the level of $16 million,$8 million of which was granted by the Office of the Governor of Texas and $8 million of which is matched by participating academic institutions. Project personnel include geologists, petroleum engineers, geophysicists, and chemists. The interdisciplinary nature of this project is directed toward a more thorough understanding of the geologic controls on production and the development of appropriate recovery technologies to address the specific needs of State Lands reservoirs. Transfer of these technologies to industry, in particular to independent operators, is expected to result in increased efficiency of hydrocarbon recovery from State Lands and increased revenue to the Texas Public School Fund. The project is divided into three parts: (1) play analysis and resource assessment, (2) reservoir characterization, and (3) development of advanced extraction technology. The play analysis and resource assessment part of this research program involves dividing the oil and gas fields on Texas State Lands into geologically based families, such that fields with similar depositional histories, trapping styles, production efficiencies, and extraction difficulties are grouped into "plays." Play analysis provides the framework for making a quantitative assessment of the remaining resources on State Lands. Importantly, even maturely developed oil reservoirs may still contain substantial volumes of both "mobile" oil (oil that is movable at reservoir conditions and that can be conventionally recovered) and "residual" oil (oil that requires expensive and technically complex reservoir stimulation). The relative amounts of these resource types vary among the geologically based plays. Quantifying the amounts of these two types of oil on State Lands, as well as quantifying the remaining natural gas resource, is critical both for designing field development programs and for optimizing the recovery economics of Texas hydrocarbon resources and is the focus of the resource assessment task.Bureau of Economic Geolog

Filtering Non-Linear Transfer Functions on Surfaces

International audienceApplying non-linear transfer functions and look-up tables to procedural functions (such as noise), surface attributes, or even surface geometry are common strategies used to enhance visual detail. Their simplicity and ability to mimic a wide range of realistic appearances have led to their adoption in many rendering problems. As with any textured or geometric detail, proper filtering is needed to reduce aliasing when viewed across a range of distances, but accurate and efficient transfer function filtering remains an open problem for several reasons: transfer functions are complex and non-linear, especially when mapped through procedural noise and/or geometry-dependent functions, and the effects of perspective and masking further complicate the filtering over a pixel's footprint. We accurately solve this problem by computing and sampling from specialized filtering distributions on the fly, yielding very fast performance. We investigate the case where the transfer function to filter is a color map applied to (macroscale) surface textures (like noise), as well as color maps applied according to (microscale) geometric details. We introduce a novel representation of a (potentially modulated) color map's distribution over pixel footprints using Gaussian statistics and, in the more complex case of high-resolution color mapped microsurface details, our filtering is view- and light-dependent, and capable of correctly handling masking and occlusion effects. Our approach can be generalized to filter other physical-based rendering quantities. We propose an application to shading with irradiance environment maps over large terrains. Our framework is also compatible with the case of transfer functions used to warp surface geometry, as long as the transformations can be represented with Gaussian statistics, leading to proper view- and light-dependent filtering results. Our results match ground truth and our solution is well suited to real-time applications, requires only a few lines of shader code (provided in supplemental material), is high performance, and has a negligible memory footprint

Linear Efficient Antialiased Displacement and Reflectance Mapping

International audienceWe present Linear Efficient Antialiased Displacement and Reflectance (LEADR) mapping, a reflectance filtering technique for displacement mapped surfaces. Similarly to LEAN mapping, it employs two mipmapped texture maps, which store the first two moments of the displacement gradients. During rendering, the projection of this data over a pixel is used to compute a noncentered anisotropic Beckmann distribution using only simple, linear filtering operations. The distribution is then injected in a new, physically based, rough surface microfacet BRDF model, that includes masking and shadowing effects for both diffuse and specular reflection under directional, point, and environment lighting. Furthermore, our method is compatible with animation and deformation, making it extremely general and flexible. Combined with an adaptive meshing scheme, LEADR mapping provides the very first seamless and hardware-accelerated multi-resolution representation for surfaces. In order to demonstrate its effectiveness, we render highly detailed production models in real time on a commodity GPU, with quality matching supersampled ground-truth images