On the Jacobi-Metric Stability Criterion

We investigate the exact relation existing between the stability equation for the solutions of a mechanical system and the geodesic deviation equation of the associated geodesic problem in the Jacobi metric constructed via the Maupertuis-Jacobi Principle. We conclude that the dynamical and geometrical approaches to the stability/instability problem are not equivalent.Comment: 14 pages, no figure

A study on the interplay between perturbative QCD and CSS/TMD formalism in SIDIS processes

We study the Semi-Inclusive Deep Inelastic Scattering (SIDIS) cross section as a function of the transverse momentum, $q_T$. In order to describe it over a wide region of $q_T$, soft gluon resummation has to be performed. Here we will use the original Collins-Soper-Sterman (CSS) formalism; however, the same procedure would hold within the improved Transverse Momentum Dependent (TMD) framework. We study the matching between the region where fixed order perturbative QCD can successfully be applied and the region where soft gluon resummation is necessary. We find that the commonly used prescription of matching through the so-called Y-factor cannot be applied in the SIDIS kinematical configurations we examine. In particular, the non-perturbative component of the resummed cross section turns out to play a crucial role and should not be overlooked even at relatively high energies. Moreover, the perturbative expansion of the resummed cross section in the matching region is not as reliable as it is usually believed and its treatment requires special attention.Comment: Two references and an appendix added, 22 pages, 11 figure

Studies on Air Injection in a Wastewater-Fed Subsurface Drip Irrigation System

In 2020, the Ogallala High Plains Aquifer supplied irrigation water for approximately 3.6 million hectares in Nebraska, making it the most irrigated state in the United States. Although Nebraska is highly dependent in groundwater, locations included in the Gering-Fort Laramie Irrigation District (border of Nebraska and Wyoming) rely on surface water resources. In addition to these conventional water sources, using non-conventional alternatives for crop production can be just as important during water shortage times such as the one that e occurred in 2019 with the collapse of the Goshen/Gering-Fort Laramie Canal. Feedlot runoff presents a great opportunity in Nebraska, but it can become a point source pollution of pharmaceutical and personal care products, which could be accumulated in plant tissues and soil. In Chapter 1, we tested how passive air injection to the wastewater-fed SDI system could improve crop yield by increasing soil oxygen content at the root zone. Therefore, the objective of Chapter 1 was to evaluate the effect of air injection on corn and sugar beets yield when using feedlot runoff irrigation in SDI. Results have shown that passive air injection has been effective increasing soil oxygen content in shallow depth. Air injection did not affect sugar beet yield or sucrose content in any growing season, but significantly increased corn yield in the 2021 growing season. In Chapter 2, we evaluated the effects of air injection into subsurface drip irrigation on the soil microbial diversity and the residual of antibiotic residues accumulated in soil pore water, soil, and plant matrices. The objective of Chapter 2 was to evaluate the effects of air injection on the reduction of antibiotic concentrations in the soil environment introduced by irrigation with feedlot wastewater. Results have shown that air injection was not effective in removing or treating antibiotics such as sulfamethoxazole or monensin Na. However, in air-injected sugar beet or corn plots, some microbes had a significantly higher abundance than in non-air-injected plots, revealing potential benefits for crop production. Advisor: Xin Qiao

Sidebranching induced by external noise in solutal dendritic growth

We have studied sidebranching induced by fluctuations in dendritic growth. The amplitude of sidebranching induced by internal (equilibrium) concentration fluctuations in the case of solidification with solutal diffusion is computed. This amplitude turns out to be significantly smaller than values reported in previous experiments.The effects of other possible sources of fluctuations (of an external origin)are examined by introducing non-conserved noise in a phase-field model. This reproduces the characteristics of sidebranching found in experiments. Results also show that sidebranching induced by external noise is qualitatively similar to that of internal noise, and it is only distinguished by its amplitude.Comment: 13 pages, 5 figure