The expansion of a gas within a piston-cylinder arrangement is studied in order to obtain a better understanding of the heat transfer which occurs during this process. While the situation of heat transfer during the expansion of a gas has received considerable attention, the process is still not very well...
The nonlinear Schrödinger equation is a well-known partial differential equation that provides a successful model in nonlinear optic theory, as well as other applications. In this dissertation, following a survey of mathematical literature, the geometric theory of differential equations is applied to the nonlinear Schrödinger equation. The main result of...
There has been a lot of work done in recent decades in the field of symbolic dynamics.
Much attention has been paid to the so-called "complexity" function, which gives a sense
of the rate at which the number of words in the system grow. In this paper, we explore this...
In this dissertation, my research work on excited state dynamics of small organic molecules in solutions is presented. Using femtosecond stimulated Raman spectroscopy (FSRS) as the main experimental tool, the excited state hydrogen-bonding dynamics (ESHBD) of Coumarin 102, a common laser dye molecule, in ethanol solution is examined with <150...
The flow of incompressible, viscous fluids in R³ is governed by the non-linear Navier-Stokes equations. Two common linearizations of the Navier-Stokes equations, the Stokes equations and the Oseen equations, are studied in this thesis using probabilistic methods.
The incompressibility condition presents new challenges for the well known theory relating partial...
In this dissertation, I present electronic spectra of a few polycyclic aromatic hydrocarbons (PAHs): tetracene, pentacene, pyrene, benzo[g,h,i]perylene and benzo[a]pyrene using resonantly enhanced multiphoton ionization (REMPI) and zero kinetic energy (ZEKE) photoelectron spectroscopy. The work of tetracene and pentacene also combine a laser desorption source with a ZEKE spectrometer, demonstrating...