DC Microgrid Modeling and Energy Storage Placement to Enhance System Stability

The work of this thesis represents a joint venture between the University of Wisconsin-Milwaukee and the University of Wisconsin-Madison. A DC microgrid is selected for the efficiency benefits, lack of reactive power in the system, and ease of connecting to an AC grid. The system modeling relies on physical parameters and industry standard methods for the estimation of loads and lines. An example model is created for the University of Wisconsin - Milwaukee\u27s Campus. Due to the high penetration of renewable energy sources in the example model, system stability is a concern. To help mitigate stability issues, analysis is performed to have the ideal placement of energy storage. The analysis relies heavily on the deep properties of the system such as Eigenvalues and system controllability. Energy storage placement is verified and evaluated with model simulations

Partitioning Edge-Colored Hypergraphs into Few Monochromatic Tight Cycles

Confirming a conjecture of Gy´arf´as, we prove that, for all natural numbers k and r, the vertices of every r-edge-colored complete k-uniform hypergraph can be partitioned into a bounded number (independent of the size of the hypergraph) of monochromatic tight cycles. We further prove that, for all natural numbers p and r, the vertices of every r-edge-colored complete graph can be partitioned into a bounded number of pth powers of cycles, settling a problem of Elekes, Soukup, Soukup, and Szentmikl´ossy [Discrete Math., 340 (2017), pp. 2053–2069]. In fact we prove a common generalization of both theorems which further extends these results to all host hypergraphs of bounded independence number

Chromatic number, clique subdivisions, and the conjectures of Haj\'os and Erd\H{o}s-Fajtlowicz

For a graph $G$, let $\chi(G)$ denote its chromatic number and $\sigma(G)$ denote the order of the largest clique subdivision in $G$. Let H(n) be the maximum of $\chi(G)/\sigma(G)$ over all $n$-vertex graphs $G$. A famous conjecture of Haj\'os from 1961 states that $\sigma(G) \geq \chi(G)$ for every graph $G$. That is, $H(n) \leq 1$ for all positive integers $n$. This conjecture was disproved by Catlin in 1979. Erd\H{o}s and Fajtlowicz further showed by considering a random graph that $H(n) \geq cn^{1/2}/\log n$ for some absolute constant $c>0$. In 1981 they conjectured that this bound is tight up to a constant factor in that there is some absolute constant $C$ such that $\chi(G)/\sigma(G) \leq Cn^{1/2}/\log n$ for all $n$-vertex graphs $G$. In this paper we prove the Erd\H{o}s-Fajtlowicz conjecture. The main ingredient in our proof, which might be of independent interest, is an estimate on the order of the largest clique subdivision which one can find in every graph on $n$ vertices with independence number $\alpha$.Comment: 14 page

Quantum fingerprinting

Classical fingerprinting associates with each string a shorter string (its fingerprint), such that, with high probability, any two distinct strings can be distinguished by comparing their fingerprints alone. The fingerprints can be exponentially smaller than the original strings if the parties preparing the fingerprints share a random key, but not if they only have access to uncorrelated random sources. In this paper we show that fingerprints consisting of quantum information can be made exponentially smaller than the original strings without any correlations or entanglement between the parties: we give a scheme where the quantum fingerprints are exponentially shorter than the original strings and we give a test that distinguishes any two unknown quantum fingerprints with high probability. Our scheme implies an exponential quantum/classical gap for the equality problem in the simultaneous message passing model of communication complexity. We optimize several aspects of our scheme.Comment: 8 pages, LaTeX, one figur

LittleDarwin: a Feature-Rich and Extensible Mutation Testing Framework for Large and Complex Java Systems

Mutation testing is a well-studied method for increasing the quality of a test suite. We designed LittleDarwin as a mutation testing framework able to cope with large and complex Java software systems, while still being easily extensible with new experimental components. LittleDarwin addresses two existing problems in the domain of mutation testing: having a tool able to work within an industrial setting, and yet, be open to extension for cutting edge techniques provided by academia. LittleDarwin already offers higher-order mutation, null type mutants, mutant sampling, manual mutation, and mutant subsumption analysis. There is no tool today available with all these features that is able to work with typical industrial software systems.Comment: Pre-proceedings of the 7th IPM International Conference on Fundamentals of Software Engineerin

Submonolayer Epitaxy Without A Critical Nucleus

The nucleation and growth of two--dimensional islands is studied with Monte Carlo simulations of a pair--bond solid--on--solid model of epitaxial growth. The conventional description of this problem in terms of a well--defined critical island size fails because no islands are absolutely stable against single atom detachment by thermal bond breaking. When two--bond scission is negligible, we find that the ratio of the dimer dissociation rate to the rate of adatom capture by dimers uniquely indexes both the island size distribution scaling function and the dependence of the island density on the flux and the substrate temperature. Effective pair-bond model parameters are found that yield excellent quantitative agreement with scaling functions measured for Fe/Fe(001).Comment: 8 pages, Postscript files (the paper and Figs. 1-3), uuencoded, compressed and tarred. Surface Science Letters, in press