Possible Research will include the following

1. Models in quantum optics (Faculty Mentor: Dr. G. O. Ariunbold, Physics)

   Controlling macroscopic quantum coherence of quantum particles is one of the fundamental working principles required for quantum devices. Dr. Ariunbold's research focuses on generating and controlling macroscopic quantum coherence in atomic, molecular and polaronic systems. In this project REU students will explore mathematical models for quantum optics systems using MATLAB.

2. Electron-electron correlation physics (Faculty Mentor: Dr. R. T. Clay, Physics)

   Dr. Clay's research is aimed at understanding the effect of electron-electron interactions in materials. Electrons in materials determine many important properties of the material, for example whether the material is conducting, insulating, or semiconducting. Electrons are charged particles and interact with each other through the Coulomb interaction. In many materials, the approximation that electrons do not interact with each other works surprisingly well. However, in some cases this approximation breaks down. Often such "strongly correlated" materials exhibit very unusual electronic properties such as antiferromagnetism or superconductivity.

   While the Schroedinger equation describing electrons in a material can be written down, a solution of the full problem is not feasible. However, much simpler model systems can be used to understand the essential effects electron-electron interactions that determine the properties of materials. The most well-known of these models is the Hubbard model, which keeps electron-electron interactions at only very short distances. These models can still not be solved analytically, and much of our knowledge of them comes from numerical solutions. Dr. Clay develops numerical methods to solve these interacting models. Some of the current topics under research in his group are the effect of electron-electron interactions on superconducting pairing, the effect of phonons (crystal vibrations) on electronic properties, and electronic transitions in multi-band systems.

3. Interfacial properties in high-performance composite materials (Faculty mentor: Dr. S. Gwaltney, Chemistry)

   A key to designing high-performance materials, especially composites, is to understand and control the interface between the various components of the system. Gwaltney and his colleagues have successfully modeled the interfaces between graphitic sheets and vinyl ester resins and between graphitic sheets and polyethylene. Part of this effort involved developing a unique algorithm to include chemical kinetics and selectivity into modeling the curing process. This algorithm, the Relative Reactivity Volume (RRV) model, has now been built into the commercial materials modeling software MAPS.

   The next step is to apply these methods to the interface between graphitic sheets and epoxy resins. The REU student, under the guidance of a graduate student with experience in materials modeling, will build models of the graphitic sheets in the presence of uncured epoxy resin. After equilibrating the resin, the RRV algorithm will be used to cure the resin to a variety of conversion percentages typical of epoxies found in real composites. The physical and mechanical properties of these cured resins will then be determined. Parameters of interest include densities, glass transition temperatures, Youngs moduli, and yield stress and strain. It is not currently well understood how these properties vary with conversion percentage and with temperature. Subsequent REU students will then determine how these properties vary with epoxy resin and with pretreatment of the graphitic sheets (for example, oxidized versus pristine sheets).

4. Image denoising and segmentation methods for material analysis (Faculty mentor: Dr. H. Lim, Mathematics)

   A large range of denoising and segmentation methods cover various fields of mathematics and engineering. However, conventional methods do not work very well on complex material images since they can involve different types of noise and unclear edges. If a conventional segmentation method is used to detect the edges of pores on the X-ray image of a steel sample, annular pattern artificial noise can be produced due to the artifacts which inevitably appear in the original image during the X-ray process. This could result in inaccurate measurements of pore statistics. Partial differential equation (PDE) based denoising methods can effectively remove noise but there are still some remaining artifacts which cannot be removed using conventional denoising methods.

   For the REU projects, we will develop new models and their associated algorithms for denoising and segmentation on material images. One non-conventional denoising/segmentation method that we can consider for material images is by treating the noise as being multiplicative. The programming language for our research project is MATLAB. During the first few weeks of the program, the REU fellows will learn basic tools on MATLAB and test simple codes to get familiar with MATLAB programming. The participants will also learn about the conventional denoising/segmentation methods during these weeks. Once the students get familiar with the use of MATLAB with developing simple codes, they will start writing their own codes for conventional methods and test the numerical examples using materials images. Students will be intensively discussing the development of the new methods/algorithms to overcome the drawbacks on traditional methods for materials images. The newly developed methods will be numerically tested and compared to the conventional methods.

5. Advanced numerical methods for time-dependent multiphysics problems (Faculty mentor: Dr. Vu Thai Luan, Mathematics)

   Many problems in science and engineering involve multi-physical processes, where complex interactions between these components can result in dynamics evolving on different time scales (also known as stiff problems). They arise from a wide range of fields such as meteorology (weather prediction), plasma physics (electricity and magnetism with hydrodynamics), combustion (chemical reaction with transport), astrophysics (radiation with hydrodynamics), and geophysics (ocean-atmosphere dynamics), just to mention a few. The evolution of such problems can often be described by parabolic or hyperbolic nonlinear partial differential equations (PDEs). Since it is typically impossible to solve these nonlinear models exactly, numerical methods are applied to discretize the models in space and time in order to approximate solutions. The major challenge in time domain simulation lies in a significant growing number of changing time scales in dynamics of problems. A prominent example is in numerical weather prediction (NWP), where acoustic and gravity waves travel much faster than advection/convection processes, thereby preventing the use of longer time steps which poses difficulties for real-time simulation of weather conditions. The challenge will increase with future models which resolve very fine-scale processes. As such, developing fast and accurate time integration methods is crucial for a wide range of applications that rely on simulations of complex multiphysics problems.

   In this project, REU students will first learn basic/classical numerical methods for solving ordinary and time-dependent PDEs. This would require studying related materials in Numerical Analysis/Linear Algebra, and Differential Equations. The students would then apply this knowledge to work with more advanced methods for solving stiff problems such as exponential integrators. The goal is to develop novel methods and perform numerical experiments (in MATLAB or Python) for some test problems and applications (such as in NWP or computational biology).

6. Quantum Computing (Faculty mentor: Dr. G. Rupak, Physics))

   Description will be updated shortly

7. Photophysical properties of novel PAHs and their complexes (Faculty mentor: Dr. C. E. Webster, Chemistry)

   Polycyclic aromatic hydrocarbons (PAHs) have gained significant attention in materials chemistry for their unique photophysical properties useful for organic light emitting diodes (OLEDs), photovoltaics, field-effect transistors, organic electronics, and sensors. Pyrene, a highly aromatic molecule comprised of four fused benzene rings, is a ubiquitous building block for synthesizing exceptionally conjugated compounds, or polymeric materials. While many of these fused-ring systems are planar, nonplanar or twisted conjugated molecules are rapidly emerging due to new applications in nonlinear optics, semiconductors, OLEDs and electronic devices. Notably, twisted molecules have displayed improved stability, enhanced solubility, and provide chiroptical properties deeming them versatile in new materials. A new category of distorted ribbon-like PAHs termed pyrene-fused twistacenes has recently been developed and shows imminent promise toward incorporation in OLED devices. Twisted pyrene-fused molecules are often characterized by the degree of their torsion angle at the carbon atoms in the K-region of pyrene.

   In collaboration with Professor Robert Gilliard (University of Virginia) whose groups work on the synthesis of these novel materials, we will study the molecular and electronic structure of these class of molecules with respect to their light emitting properties. In this project undergraduate students will be introduced to main-group organometallic chemistry, data organization and scripting, computational methodologies for electronic structure.