Browsing by Subject "low-density"

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    Data and R code to support: Estimating densities of zebra mussels (Dreissena polymorpha) in early invasions using distance sampling
    (2019-01-18) Ferguson, Jake M; Fieberg, John R; McCartney, Michael A.; Blinick, Naomi S.; Schroeder, Leslie; jakeferg@umn.edu; Ferguson, Jake M; Minnesota Aquatic Invasive Species Research Center (MAISRC)
    These files are the data and code needed to reproduce the analysis of the manuscript "Estimating densities of zebra mussels (Dreissena polymorpha) in early invasions using distance sampling". The data include spatial coordinates of transects used to survey for zebra mussels in Lake Sylvia and Lake Burgan in the summer of 2017, the counts of zebra mussels on each transect, and environmental covariates collected along transects and at each detection. We also provide the R code needed to process and analyze these data following the distance survey approach described in the manuscript. We provide code for a straightforward distance survey, which doesn't include any spatial covariate information, as well as a more computationally intensive analysis that does include spatial covariates.
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    Superconductivity Away From the High-Density Limit
    (2023-05) Phan, Dan
    In this dissertation, I study how superconductivity evolves away from the high-density weak-coupling limit. In recent years, there has been a resurgence of interest in superconductivity at low carrier density, propelled by experimental advances in a number of materials. These advances have led theorists to re-analyze the assumptions of traditional Bardeen-Cooper-Schrieffer (BCS) theory, and investigate how these assumptions break down at low densities. The first study I discuss in my thesis pertains to the calculation of the superconducting transition temperature Tc in a phonon-mediated superconductor. Taking the weak-coupling limit and working in two dimensions, I obtain Tc not only in the adiabatic limit where the Fermi energy is much larger than the phonon frequency, but also in the opposite anti-adiabatic limit. In doing so, I include Kohn-Luttinger-type corrections to the pairing interaction which must be included to obtain the correct prefactor for Tc. Afterwards, I turn to the issue of repulsive interactions and how they affect superconductivity at low density. In particular, I study a three-dimensional system with a Bardeen-Pines-like interaction in the low-density limit, where the chemical potential mu is much smaller than the phonon frequency. Parameterizing the strength of the repulsion by a dimensionless parameter f, I find that Tc approaches a nonzero value in the mu = 0 limit as long as f is below a certain threshold f*. In this limit, I find that Tc goes to zero as a power of f*-f, in contrast to the high-density limit, where Tc goes to zero exponentially quickly as f approaches f*. I then discuss my work investigating the Higgs (amplitude) mode, and how its dispersion, damping rate, and residue vary away from the high-density limit in a two-dimensional superconductor. I also study how the Higgs mode is affected by the long-range Coulomb interactions between electrons, finding that the Higgs mode is unaffected by the long-range Coulomb interaction in both two and three dimensions.