Browsing by Author "Babalola, David"
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Item Convection in a differentially heated rotating spherical shell of Boussinesq fluid with radiative forcing(2012-12-01) Babalola, David; Lewis, GregIn this study we investigate the flow of a Boussinesq fluid contained in a rotating, differentially heated spherical shell. Previous work, on the spherical shell of Boussinesq fluid, differentially heated the shell by prescribing temperature on the inner boundary of the shell, setting the temperature deviation from the reference temperature to vary proportionally with -cos 20, from the equator to the pole. We change the model to include an energy balance equation at the earth's surface, which incorporates latitudinal solar radiation distribution and ice-albedo feedback mechanism with moving ice boundary. For the fluid velocity, on the inner boundary, two conditions are considered: stress-free and no-slip. However, the model under consideration contains only simple representations of a small number of climate variables and thus is not a climate model per se but rather a tool to aid in understanding how changes in these variables may affect our planet's climate. The solution of the model is followed as the differential heating is changed, using the pseudo arc-length continuation method, which is a reliable method that can successfully follow a solution curve even at a turning point. Our main result is in regards to hysteresis phenomenon that is associated with transition from one to multiple convective cells, in a dfferentially heated, co-rotating spherical shell. In particular, we find that hysteresis can be observed without transition from one to multiple convective cells. Another important observation is that the transition to multiple convective cells is significantly suppressed altogether, in the case of stress-free boundary conditions on the fluid velocity. Also, the results of this study will be related to our present-day climate.Item Towards molecular reconstruction in Coulomb explosion imaging(2021-02-01) Babalola, David; Bohun, SeanThe interaction of a fast laser with molecules at the femtosecond time scale, leads to the latter losing most of its valence electrons and become positively charged. The molecule which was initially in an equilibrium state, undergoes internal repulsion which leads to fragmentation of the molecule into constituent ions and other neutral fragments. The unidirectional electric field in lens accelerates the charged ions towards a position-sensitive detector, and their arrivals are based on their charge per mass ratio. The ion with the highest ratio of charge per mass arrives first at the detector; its time-of-flight and position of impact on the detector by the ion is recorded. The same information is recorded for subsequent ions that arrive at the detector. This research attempts to reconstruct the molecular structure prior to a Coulomb explosion of the ionized molecule using only the information available at the detector. There are broadly two components to the approach examined here: the forward and the backward (inverse) problems. In the forward problem, we develop a model using the classical equations of motion to describe the time evolution of the constituent ions immediately after the fragmentation of the parent molecule. The goal being to accurately reproduce a given impact pattern on the target screen, consistent with the ions time of arrival. The inverse problem uses the positions and time-of-flights of the constituent ions to systematically predict the original molecular structure. The inverse problem is characterized by a shortage of information from the detector due to the fact that not all the atoms of the molecule become ionized during any particular laser-molecule interaction and the electric field is inhomogeneous. Therefore, one way to reconstruct the initial positions of the photo-fragments is to simulate the inhomogeneous field and reverse the paths of detected ions.