|Office:||Weber Building, room 113 Department of Mathematics, (970) 491-0549|
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There are several topics I have worked with or am currently researching.
Current seawater desalination techniques are highly inefficient, and require an inordinate amount of energy, well beyond that theoretically required by the laws of Thermodynamics.
The ions in seawater will respond well to applied electric charge, and the inherent thermal motion of the ions will allow magnetic fields to affect their propagation as well. However, the sheer number of ions in a reasonable sized sample of seawater make direct separation through electrostatic means impossible.
My Masters work looked at techniques for amplifying the removal capabilities of electrostatic methods, using magnetic fields to manipulate ion concentrations, and combining these techniques with current dialysis techniques to improve efficiencies. The analysis showed that this is not a particularly promising approach, but advances in magnetic field control based on photonic crystals and nano-engineered structures may make this a viable solution in the future.
Molecular dynamics simulations are used to model and understand the evolution and behavior of systems ranging from chemicals in solution to small biological molecules and systems. Where the number of molecules exceeds the capabilities of this direct approach, multi-scale models can use molecular modeling to establish material properties, then bulk material modeling can be used at larger scales, refining the solution at points of interest using targeted modeling at finer scales.
As computing power increases, these techniques will be applied to larger biological systems as well as the engineering of custom nanomachines and nanobiological structures such as engineered drug treatments.
My interest is in methods to incorporate more and more accuracy and quantum effects into the models, which are today pseudo-classical and based largely on empirical interaction potentials. They do not deal well with atomic bond formation and breaking and dynamic transfer of energy from place to place within complex structures (like what occurs in the photosynthesis process). I also want to develop systems to dynamically apply multi-scale simulations based on system behavior, optimizing the transition between scales to the problem domain.
Solar cells are limited by the fact that a fraction of solar radiation falls above the band gap energy of silicon, and only photons above that energy can generate free electrons (which then have to fight diffusion and recombination on their way to a conducting electrode).
Meanwhile, blackbody radiation has a profile of photon energies that is entirely temperature-based, and by elevating the temperature of a blackbody cavity to a particular level, the distribution of the resulting photon energies can be controlled.
I want to research whether it is possible to use solar radiation to heat a blackbody to temperatures at which it radiates a higher percentage of its spectrum in energies that lie above the silicon bandgap, effectively making a larger percentage of the light energy available to solar cells.
Neural networks have long been used for image processing and pattern recognition, and various systems have been studied that exhibit learning and adaptation. These systems have, however, been aimed at taking some set of inputs (pixels of an image, samples of a voice, values of securities over time, etc.) and generate a set of outputs (a "yes/no" pattern detection signal, a prediction of future behavior, or a way of filling in missing or noisy information in the input signal).
I plan to research the results of allowing these networks to have outputs that can feed back to their inputs, then allow them to self organize and self-learn, and observe what sorts of patterns they form in their outputs over time.
One of the goals of modern physics is a geometric theory of spacetime that predicts both quantum field theory (QFT) and general relativity. Many of the theories that have been put forth in this pursuit have been based on additional dimensions that are not visible or appant to our perception, due to their scale or their topology.
The development and extension of techniques that allow a hypothesized geometric structure of extra dimensions to drive predicted physical laws is a broad area in which I want to begin research.