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Current Research

These computational and mathematical methodologies drive a variety of applications.

Design of New Materials: Navigating Molecular Worms Inside Chemical Labyrinths

Access of a molecule to a particular site or place in a chemical system is important in chemistry and material science. For example, a substrate has to have access to an active site of an enzyme (catalyst) before the enzymatic (catalytic) reaction can take place. The “accessible volume” which is available to a penetrating molecule is useful in discussing physical properties such as diffusion, viscosity, and electrical conductivity in glasses, polymers and porous materials. Predicting if a… Read More »

Granular Flow: Coal Hoppers and Pebble Bed Reactors

Granular materials, common in everyday experience, are critical in many industrial processes, and exhibit complex mixed liquid-like/solid-like behavior and microscale stress inhomogeneities. Together with Sandia National Lab, we have built large-scale simulations of an experimental pebblebed nuclear reactor design, featuring 440,000 6 cm spherical particles that are slowly cycled through a cylindrical container, to analyze particle mixing between fuel and moderator. Our 3D homogenized… Read More »

High-Throughput Data Extraction from DOE Advanced Light Source User Facility

We have built fast, automatic algorithms to extract data from synchrotron light sources. These methods, which combine PDE-based image segmentation with statistical methods, assembled 2D data slices in 3D, and extract relevant structures. The left shows channels, voids, and internal structures from rock data obtained from the ALS and is used to analyze materials for carbon… Read More »

Seismic imaging: Reconstruction of the earth from surface recordings

In order to reconstruct seismic velocities from reflected wave surface recordings, common seismic imaging “time-migration” techniques assume horizontal layers. With even mild lateral velocity variations, this significantly distorts subsurface structures. They also produce images in “time migration coordinates”, which gives velocities at points reached by rays from the Earth’s surface at a given time. For laterally varying velocities, the relation between this somewhat unnatural… Read More »

Assimilating ocean and geophysics data

A key problem in many sciences is data assimilation- using a model (maybe an uncertain model) and data (maybe noisy data) to assess the state of a system. Our work on implicit sampling makes it possible to produce sample states that have a consistently high probability, reducing by a large factor the exploratory computing that needs to be done to eliminate unlikely possibilities. This is a major breakthrough. We have applied the new methods to problems that range from determining the biological… Read More »

Curved Meshing for Fixed and Deforming Boundaries Using Elasticity

We have applied our new methodology for building curved unstructured meshes on fixed and deforming boundaries, using an elasticity formulation, on a collection of coupled interacting fluid/solid body problems. These include meshing of moving wings in unmanned aerial vehicles. Read More »

Modeling of Industrial Printing and Nano-Jetting Spray Delivery

We built a computational environment to model two-phase microjetting in manufacturing and industrial devices. The code is a fully three-dimensional computational model simulating both Newtonian and Oldroyd-B viscoelastic fluids in two-phase immiscible incompressible flows with surface tension and both viscosity/density jumps across interfaces separating viscoelastic fluid from air. This model includes a contact model for air/wall/fluid interactions, and incorporates complex geometries. The… Read More »

Etching and Deposition in Semiconductor Process Manufacturing

We built a complete suite of mathematical and algorithmic tools to model etching and deposition in semiconductor manufacturing. Level set methods for interface motion are coupled to empirical flux laws, material-depending etch and deposition rates, re-emission profiles and pattern masks. These allow tracking of complex interfaces in plasma-enhanced chemical vapor deposition, ion-milling, and photolithography. Results were validated through careful comparison with experiment, and show the… Read More »

Grain Boundaries and Stresses: Microchip Component Failure and Electromigration

We recently developed a continuum model of mass transport phenomena in microelectronic circuits due to high current densities (electromigration) and gradients in normal stress along grain boundaries. As microelectronic circuits become smaller and current densities become higher, failure due to electromigration damage is an ever-increasing problem in the design of circuits. Our work, performed in close collaboration with physicists and materials scientists at Motorola, is the first systematic… Read More »

Fluid Pinch-off and Sprays

Fluid pinchoff is a highly challenging problem: computational techniques either break down when topological change occurs, or become highly inaccurate and miss most of the subtle dynamics. We have built a new mathematical model applicable to a host of fluid breakage issues. Our new approach relies on embedding the interface, the velocity, and the potential in higher dimensional implicit forms, and then solving a coupled set of PDEs which naturally transition through fluid breakup. Using this… Read More »