Charge transport in a semiconductor structure with heterojunction is described by a multiscale partial differential equation model. This model can be used, e.g., for the design of more efficient solar cells. Phenomena at the heterojunction must be resolved at the angstrom scale while the size of the device is that...
In this dissertation, we consider two problems in number theory, both relating to modular forms. First we consider when a given modular form can be expressed as a quotient in Dedekind's $\eta$ function. Rouse and Webb \cite{RW} have determined the integers $N \leq 500$ such that the graded ring of...
The formation of carbonaceous and silicate precursor molecules to astrophysical dust grains is investigated. Using density functional theory (DFT) in combination with global optimization techniques, the ground-state binding energies of dust precursors are determined. These results are employed in atomistic nucleation theory (ANT) to predict the critical size and nucleation...
Organic semiconductors are used in a wide variety of applications including transistors,solar cells, and light emitting diodes. These materials are solution-processable,low cost, and tunable. Many successful organic optoelectronic materials utilizeblends of several types of molecules (such as donors and acceptors) in order topromote charge generation. As blends are an inherently...
Functional control at the nanoscale forms the foundation of biological systems. These work at the cellular level by manipulating ions and molecules. Nanoscale devices that give functional control at this scale are also becoming an important component in diverse fields such as electronics, medicine, engineering, and manufacturing. Moreover, scientific advances...
The photophysical properties of two-dimensional (2D) layered van der Waals (vdW) materials, and their heterostructures are manifestly distinct from crystalline bulk materials. Recently, the discovery of new 2D vdW materials and strongly-bound interlayer excitons in these materials has created a new branch in nanoscience. As such, there are a number...
The ability for individual cells and multicellular networks to process information contained in perceived stimuli is of vital importance to their proper functioning and ultimately their cellular fate. The primary mechanism employed by cells to this end is the use of biochemical signaling in which a series of molecular events...
Time-dependent electronic transport is increasingly important to the state-of-the-art device design and fabrication. The development of nanoscale sensing, the harnessing and control of structural fluctuations, and the advancement of next-generation materials all require a treatment of quantum dynamics beyond the level of traditional methods and a more nuanced approach to...
Single-scattering tomography describes a model of photon transfer through a object in which photons are assumed to scatter at most once. The Broken Ray transform arises from this model, and was first investigated by Lucia Florescu, Vadim A. Markel, and John C. Schotland, [2], in 2010, followed by an inversion,...
The continued development of organic semiconductor materials relies on an understanding of the relationship between optoelectronic properties, molecular structure, and molecular interaction. Several detailed studies of electronic properties in functionalized polyacene materials are presented. A computational model which allows the extraction of charge generation and transport properties from experimental data...