Uncovering the Fractal Nature of Water Vapor Distribution above the Surface of the Earth

Fractals have been at the heart of geophysical and geospatial studies in the recent past. We examine the emergent fractal character of water vapor distributions above the surface of the Earth as a function of both image resolution (number of pixels) and moisture content percentile. We calculate physically relevant quantities such as fractal dimension, number of clusters, and size of the largest cluster with varying vapor percentile using computational methods and algorithms. We test the applicability of Korcak's law on our system and determine the quality of the fit using the Kolmogorov-Smirnoff satistic. We show that the fractal character of the distribution is exact as a function of image resolution and approximate in some regimes as a function of the vapor percentiles.Comment: 14 pages, 16 figure

Theoretical and Computational Explorations of Topological Materials

Topological materials are of great interest to condensed matter physicists and engi-neers alike due to their potential application in quantum technology. To this end, two materials in this class, Weyl semimetals and quantum spin liquids, are studied in this dissertation using a set of computational and theoretical techniques. Quantum spin ice models are studied using exact diagonalization, numerical linked cluster expansions, and perturbation theory. We calculate a host of observables like entanglement entropy and Ising correlation, and use them extract the phase bound- aries of these models as a function of model parameters. These results have potential application in the experimental study of rare-earth pyrochlores. We study the Hall transport properties of Weyl and multi-Weyl semimetals un- der the periodic drive of a laser pulse using analytical methods such as the Kubo formalism and the Matsubara Green's function formalism. Physical quantities such as the thermal Hall and Nernst conductivities are extracted for such models. The information obtained is analyzed and we show the characteristics of the transport coecients as a function of monopole charge.

Theoretical and Computational Explorations of Topological Materials

Topological materials are of great interest to condensed matter physicists and engi-neers alike due to their potential application in quantum technology. To this end, two materials in this class, Weyl semimetals and quantum spin liquids, are studied in this dissertation using a set of computational and theoretical techniques. Quantum spin ice models are studied using exact diagonalization, numerical linked cluster expansions, and perturbation theory. We calculate a host of observables like entanglement entropy and Ising correlation, and use them extract the phase bound- aries of these models as a function of model parameters. These results have potential application in the experimental study of rare-earth pyrochlores. We study the Hall transport properties of Weyl and multi-Weyl semimetals un- der the periodic drive of a laser pulse using analytical methods such as the Kubo formalism and the Matsubara Green's function formalism. Physical quantities such as the thermal Hall and Nernst conductivities are extracted for such models. The information obtained is analyzed and we show the characteristics of the transport coecients as a function of monopole charge.