Ultra High Pressure Hydrogen Studies

Hydrogen has been called the fuel of the future, and as it’s non- renewable counterparts become scarce the economic viability of hydrogen gains traction. The potential of hydrogen is marked by its high mass specific energy density and wide applicability as a fuel in fuel cell vehicles and homes. However hydrogen’s volume must be reduced via pressurization or liquefaction in order to make it more transportable and volume efficient. Currently the vast majority of industrially produced hydrogen comes from steam reforming of natural gas. This practice yields low-pressure gas which must then be compressed at considerable cost and uses fossil fuels as a feedstock leaving behind harmful CO and CO2 gases as a by-product. The second method used by industry to produce hydrogen gas is low pressure electrolysis. In comparison the electrolysis of water at low pressure can produce pure hydrogen and oxygen gas with no harmful by-products using only water as a feedstock, but it will still need to be compressed before use. Multiple theoretical works agree that high pressure electrolysis could reduce the energy losses due to product gas compression. However these works openly admit that their projected gains are purely theoretical and ignore the practical limitations and resistances of a real life high pressure system. The goal of this work is to experimentally confirm the proposed thermodynamic gains of ultra-high pressure electrolysis in alkaline solution and characterize the behavior of a real life high pressure system.

Solitons in Exciton-Polariton System: Reduced Modelling, Analysis, and Numerical Studies

In this dissertation, we study the behavior of exciton-polariton quasiparticles in semiconductor microcavities, under the sourceless and lossless conditions.

First, we simplify the original model by removing the photon dispersion term, thus effectively turn the PDEs system to an ODEs system,

and investigate the behavior of the resulting system, including the equilibrium points and the wave functions of the excitons and the photons.

Second, we add the dispersion term for the excitons to the original model and prove that the band of the discontinuous solitons now become dark solitons.

Third, we employ the Strang-splitting method to our sytem of PDEs and prove the first-order and second-order error bounds in the $H^1$ norm and the $L_2$ norm, respectively.

Using this numerical result, we analyze the stability of the steady state bright soliton solution. This solution revolves around the $x$-axis as time progresses

and the perturbed soliton also rotates around the $x$-axis and tracks closely in terms of amplitude but lags behind the exact one. Our numerical result shows orbital

stability but no $L_2$ stability.