Description: Wavelets are currently used to solve complex 3D time-dependent problems in areas of geophysics, for example, in mantle convection. Their ability to express a function as a linear combination of locally supported basis functions translated in space and frequency endows them with strong compression properties. By tracking only the wavelets whose coefficients are sufficiently large, savings of up to 95 percent can be achieved in computational time and memory use. The wavelets that are kept define an adaptive mesh that can evolve in time. We are developing volume time-dependent rendering algorithms that can operate directly on the adaptive mesh, taking the wavelet expansion into account. This will be achieved through a judicious use of data structures and a proper choice of wavelet representations. Issues that must be addressed are real-time sorting, data representation, thresholding and user perception.

Code: Students will start with existing code, in a very early stage of development

Some knowledge of basis function expansions, object-oriented C++ programming is preferable.

2. Project: Numerical Experiments in Electromagnetics

Description: When electromagnetic waves travel through different materials they do so at different speeds. These changes in speeds lead to reflection and diffraction of the waves. Similarly, when waves propagate around obstacles or though gaps in a large sheet like pinholes or slits, the waves are scattered and diffracted. In this project we will develop and use highly accurate numerical methods to study the propagation of electromagnetic waves in multiple material situations. Possible applications range from the effects of a building’s structure on cell phone reception to the propagation of light waves in a fiber optic cable.

Code: Students will modify and run existing FORTRAN code.

Preferred Academic background: A&M and PDES

3. Project: Computational Finance

Description: When Grandma bought that bond years ago she didn’t pay the face value. How did they figure out how much to charge her for it? How much should one invest in order to ensure a comfortable retirement? What are options and how are they priced? In the past, personal financial planners would use some typical numbers like average interest and inflation rates and typical growth of the stock market, etc. to answer questions like these. However, one interesting and fundamental characteristic of financial problems is uncertainty – The stock market goes up, but in a very erratic pattern. We can’t predict what interest rates will be in the future either. Today, we’re seeing the use of simulation methods that take uncertainly into account being used more and more. This project will develop and use computational methods to simulate problems in finance.

Code: Light coding in either FORTRAN or CTT

Some knowledge of probability, ordinary differential equations is preferable.

4. Project: Direct numerical simulation of extrusion processes

Description: The manufacturing process is important in the development of high performance materials (e.g. materials that are very good heat conductors/insulators, or very light/strong or taste really good). In particular, manufacturing companies seek to optimize the “extrusion” process in which materials in “liquid form” are extruded through a die and then pulled during the creation of fiber strands. This process is applied to materials such as wheat dough, aluminum, complex polymers and plastics. In this setting, it is very important to predict the local stresses in materials as they are pulled and also predict whether unstable phenomena like “necking” or “die swell” occur. As the extrusion problem is a multiphase flow problem (flow involving gas/liquid/solid), it is a very difficult problem to solve. This REU project involves the direct application of a cutting edge, 3d, adaptive, multiphase numerical method to extrusion processes. The REU student shall apply advanced numerical methodology in order to predict “die swell” or “necking.”

Code: Students might be required to modify existing code by writing small fortran subroutines

Some knowledge of fluid mechanics is preferable.

5. Project: Network Survivability

Description: Various activities in a modern high-technological society rely drastically on continuity of communication and power services. Therefore, there is a high demand for reliable communication and power systems able to survive various types of damage. Networks are an essential part of both systems. The goal of the project is to familiarize students with different network topologies and to provide insight into the network survivability theory and the percolation theory in application to networks. Research will be focused on testing survivability of a few network topologies under multiple damage in a simple power system configuration. The project includes theoretical and computational stages.

Code: from scratch, not extensive (depends on students’ skills)

Some knowledge of FORTRAN or C and programming skills, combinatorics, probability theory is preferable.

6. Project: Numerical Investigations of Chemical Vapor Infiltration in Fabricating Bipolar Plates

Description: Reducing the overall cost and weight of Polymer Electrolyte Membrane (PEM) Fuel Cells calls for low-cost, high-performance bipolar plates. THC Carbon/carbon-composite bipolar plate appears promising due to its relatively low cost, its stability in moist atmosphere and its high electrical conductivity. However, the slurry molded fiber preform bipolar plate is porous and it has to be sealed to prevent the leaking of hydrogen or oxygen from one cell to the other. To this end, we propose chemical vapor infiltration (CVI) technique in which methane is made to flow over the plate at high temperature to deposit carbon on the inner surfaces of pores in the fiber preforms. One of the primary objectives of the investigation is to maximize the deposition rate and to minimize density gradients in the deposited carbon. To this end, a numerical single-pore model that describes species diffusion and chemical reactions is developed within the framework of the Navier-Stocks equations for multispecies transport.

Code: The student will make minor adaptations to the existing user-defined functions. He/She will study the influence of operation conditions, such as temperature and pressure, on the carbon deposition rate and the gradient. He/She will also focus on data visualization.

Some knowledge of reacting flows is preferable.

Description: Particle contamination is a significant problem in the semiconductor manufacturing industry. Currently, the minimum feature size of an integrated circuit is in the order of 100 nanometers and it is necessary to remove particles down to 10-25 nanometers in diameter. In the cleaning process, laser energy is used to heat the system that includes a substrate, the particle and an energy transfer medium, which is a thin liquid film or a droplet. The particles are removed through the explosive boiling of the energy transfer medium. In this study, we will use a molecular dynamics approach to analyze the effects of several processing parameters such as temperature, heating rate and thickness of the liquid film on the particle removal.

Code: The students will be asked to make minor modifications to an existing program that is in fortran.

Some knowledge of mathematical materials science is preferable.

8. Project: Laser Diffusive turbulence in a confined jet

Description: The turbulent transport is one of the most challenging phenomena to model in the context of turbulent flows. Risso & Fabre (JFM, 1997) proposed a new experiment, consisting of a jet entering a confined closed tube. Though the mean velocity on the axis vanishes, the flow turns into a pure turbulent transport process. The aim of this project is to study the existing one point turbulence models and their ability to predict this kind of flow. Large eddy simulations (LES) will also be conducted.

Preferred Academic background: Some knowledge of fluid turbulence is preferable.

9. Project: Visoplastic Model’s Parameters Estimation Using Extended Kalman Filter

Description: The durability of structural materials is best captured through the formulation by the theory of viscoplasicty. A viscoplastic constitutive law is used to model the constitutive behavior of time and rate dependent materials. The objective of this project is to present a method for estimating the parameters in a material constitutive model. Estimation of parameters in time and rate dependent materials is frequently performed by least squares regression. Time and rate dependent material models are represented mathematically by systems of differential equations. To calibrate the model, namely to identify model parameters, a fully numerical approach is proposed. This approach is centered on the extended Kalman filter (EKF) and on an approximate methodology to compute the sensitivity of the structural response to model parameters. The project will include a comparison between the proposed method and standard least squares regression.

Code: from scratch, not extensive (depends on students’ skills)

Some knowledge of estimation theory, control systems (state-space formulation) is preferable.

11. MODELING LASER-ASSISTED PARTICLE REMOVAL

• Set ALLOWTOPICCHANGE = ReuGroup

Last changed: 09 Jun 2005