RESEARCH - MATH of UA

Multi-scale modeling, simulation and experiments of coating growth on nanofibers

The coating of nanoscale structures and the evolution of crystalline structure at the nanoscale are and will continue to be important issues. Our efforts in this area include a coordinated experimental and modeling program for the synthesis of core/clad and hollow nanowire structures. Physical vapor deposition techniques are used to apply coatings to electrospun polymer nanofibers. These fibers are coated with films of copper, aluminum, titanium, zirconium and aluminum nitride by using a plasma enhanced physical vapor deposition (PEPVD) sputtering process.

<< Readmore

Two-dimensional heat transfer and thermal stress analysis in float glass processing

Two-dimensional heat transfer in a float glass process is considered. Specifically, we consider the processing region where the glass is floating on a tin layer and the temperature of the cooling air above the glass sheet is controllable. Two float glass systems, a one-layer and a multi-layer system, are considered. The one layer system consists of a pure glass layer.

<< Readmore

Modeling of calcium carbonate precipitation in natural karst environments under hydrodynamic and chemical kinetic control

This work addresses some of the fundamental unanswered questions concerning the physics and chemistry of rimstone formation. Rimstone (travertine) dams and flowstone formations are mineral deposits that are found on the land surface, in caves, and in other settings. These formations appear to evolve under geochemical and hydrodynamic control.

<< Readmore

Modeling a porous slider bearing with an external reservoir

The use of porous bearings is widespread throughout industry. In classical cases, the porous medium can be thought of as an external reservoir and so their use is ideal for applications where an external oil supply is undesirable, impractical, or too costly. In these cases, as the bearing moves and creates a pressure gradient, the fluid from inside the porous layer is drawn into the film, further enabling lubrication.

<< Readmore

Directional solidification

Directional solidification techniques are the most widely used methods for preparing high quality single crystals of metallic, electronic, and opto-electronic materials. In order to obtain optimum microstructure and properties in the solidified material, it is important to maintain a uniform distribution of solute/dopants and a flat solidification interface during a growth process. Such ideal conditions are difficult to achieve in practice because of an unavoidable heat exchange between the crucible and the sample.

<< Readmore

Simulation of traffic flow through a highway interchange

Understanding the flow of traffic through a highway interchange system is important for the design process and the smooth operation of the roadway. Currently, traffic engineers ignore entrance and exit ramps in the models by placing sensors upstream from exit ramps and downstream from entrance ramps.

<< Readmore

Mathematical modeling of fiber reinforced composites with linear grading

Many materials are fabricated using fiber reinforced composite materials, which consist of a set of aligned stiff fibers embedded in a softer matrix. A common example is the automobile tire. It is becoming increasingly common for composites manufacturers to add a thin linearly graded coating to improve the bulk properties of the composite, but very little modeling of linearly graded materials has been done.

<< Readmore

Scanned probe oxidation

Scanned probe oxidation is a local surface oxidation induced by an electrically biased Atomic Force Microscope (AFM) tip. The AFM tip is typically a cone-shaped probe that is brought either close to or into direct contact with a substrate. The probe is attached to the end of a cantilever that bends as the tip moves across the substrate's surface. By increasing the voltage bias between the tip and the surface, the tip acts as an ion source that can be used to grow nanoscale oxide features on the substrate.

<< Readmore

Modeling of nanofiber-based devices for efficient thermophotovoltaic energy conversion

Thermophotovoltaics (TPV) is a promising energy conversion technology for producing electricity from sources of thermal energy. The efficient recovery of waste heat is a key goal of TPV. The TPV process comprises three conceptual stages, in which an emitter first converts a source of thermal energy into infrared light, which is propagated to a collector stage and is subsequently converted into electrical energy.

<< Readmore

Wreath Product Finite p-Groups and their Subgroups

Much of my current research is related to the study of the subgroups of iterated wreath product finite p-groups and their automorphism groups. In particular, I am working on classification problems involving the monolithic subgroups H of groups of the form P=(A wr B) or P=((A wr B) wr C), where A, B, and C are cyclic groups of prime-power order, and X wr Y denotes the regular wreath product of X by Y.

<< Readmore

Mechanics of Graphene and Carbon Nanotubes

Graphene layers and carbon nanotube are novel, nanoscale structures exhibiting remarkable mechanical properties, most notably an extraordinary tensile strength combined with the flexibility to sustain large compressive loads and bending deformations elastically. These properties naturally suggest certain applications, for example, using nanotubes as reinforcing fibers in composite materials or as probes in atomic force microscopy.

<< Readmore