Below are the links to each student's AMSC 663-664 project webpage. These will evolve as the projects evolve.
Abstract: The purpose of this proposed research will focus on constructing an innovative powerful and robust hybrid approximation method for numerical geophysical fluid dynamics. To accomplish such a task, we will focus on implementing the hybrid method on the shallow-water equations which provide a useful model to global climate modeling because their solutions include nonlinear effects and wave structures similar to those of the full primitive equations of the atmosphere.
Context: A primary objective of the current climate community and its sponsors is to create accurate predictions of future global climate on decadal to centennial time scales and a broad spectrum of space scales by improving regional scale performance and accuracy. In order to do this, innovative methods for localized approximation and scaling must be considered and coupled with efficient global approximations such as the spectral-element method.
Abstract: The goal of this project is to build a code that can simulate population movement and disease dynamics on a river network. Disease dynamics will be locally described by the SEIR model or variants thereof. The river network will be modeled by a graph, perhaps using fractal geometry to model the tributary network. Population movement will be modeled by discrete convection and diffusion processes on this graph.
Context: Many models of population movement and disease dynamics are coupled system of reaction-convection-diffusion (SEIR) partial differential equations often posed on rectangular spatial domains. These models must be extended to geometries that are better suited for modeling populations on river networks.
Abstract: The question of how many sound sources generated the sound we hear each moment is a difficult one, but one which our auditory system tackles with considerable success consistently. This problem, known as auditory scene analysis, is of import to the design of hearing aids, cochlear implants, speech recognition systems and digital signal processing packages and finds application in fields as diverse as psychology, engineering, national security and intelligence. The proposed project is to develop software implementing a framework for testing models of scene analysis, as well as two current models, on a high-performance machine, namely the IBM SP/2 parallel machine in the Center for Scientific Computation and Mathematical Modeling.
Context: This software project is motivated by the desire to understand how auditory processing happens in the human brain. Scene analysis, a natural, important piece of the puzzle of how we view our environment, is a difficult problem requiring the analysis of several cues, including pitch, onset, spatial location, spectral envelope, and others. Attention and learning mechanisms within the brain also contribute. All of these processes come together to form a complex mechanism which is difficult to reveal. This software will help researchers to better understand the underlying mechanisms by providing a framework in which to test new models, and by providing two current models to test on various stimuli.
Abstract: In this project we will develop software that utilizes aspects of biologically inspired computing as a nontraditional approach to the generation and evolution of artificial neural networks, (neural networks). Specifically, principles from swarm intelligence and genetic algorithms or programming will be applied to generate and evolve a two dimensional neural network into a specified architecture. The model, and the software based on it, will account for the geometry as well as the topology of the network. In addition to providing a novel means of encoding neural networks and exploring different architectures, this project is intended to add to our understanding of the relationship between the microscopic rules governing the interactions of a particle system consisting of locally interacting autonomous agents and the resultant macroscopic behavior.
Context: Many systems in the natural world exhibit very complex behavior. Yet these systems often consist of relatively simple components that interact with each other according to simple rules. Such situations arise frequently in biological systems, where a group of simple, locally interacting creatures behaves in a qualitatively straight forward manner at the level of the individual but the group exhibits very complex behavior and problem solving capabilities. Some examples include, the ability of ants to find the shortest path to a food source and the coordinated movement of schools of fish. This phenomena of simple microscopic rules giving rise to complex macroscopic behavior in groups of living entities is particularly interesting in light of the fact that such systems often lack any centralized control. The underlying principles of many of these "self-organizing" biological systems that exhibit intelligent behavior at the group level, ("swarm intelligence"), are being studied so that they may be implemented in alternative problem solving methods.
Abstract: Adaptive mesh refinement (AMR) enables a spatially discretized grid to be refined in local regions that require finer grids to resolve the flow. Using a block refinement process, the sub-grids naturally decompose the domain, which are used to extend the method to parallel processing. For this project, we propose to implement a second-order projection method to solve the incompressible Navier-Stokes equations. The spatial grid will be adaptively refined using the PARAMESH package, and an iterative multigrid method will be explored for the solution of the method's associated elliptic equation.
Context: Numerical solutions of the incompressible Navier-Stokes equations for flows involving complex geometries are of practical importance in many engineering applications. The computational cost of numerically solving the equations is greatly affected by the spatial grid size required to accurately resolve the complex fluid motions caused by and within the near-wall region. This is especially true as the Reynolds number is increased. However, the flow in the remaining regions of the domain are likely to be relatively smooth over large time intervals. AMR adaptively refines and de-refines local regions of the grid in order to meet the requirements of the flow, without the entire spatial grid resolution being dependent on the regions of complexity.
Abstract: Photogrammetry uses a sequence of images to measure the relative position and orientation of objects with respect to each other or to some specified origin. Manual tracking of these targets is labor intensive, so automated tracking is imperitive. The particle filter provides a robust algorithm to meet automatic visual tracking and recognition needs from a single sensor in two dimensions. The proposed project is to built a tool that extends this technology to multiple sensors, thereby providing postion data in three dimensions.
Context: This project is motivated by the desire to quickly visualize and understand the relationships of important objects in sequences of images. Whether human faces, automobiles, or weapons, this project will give engineers and scientists a tool to aquire necessary data.