Given a graph, a matching is a set of vertex-disjoint edges. Graph matchings have been well studied, since they play a fundamental role in algorithmic theory as well as motivate many practical applications. Of particular interest is the problem of finding a maximum cardinality matching of a graph. Also of interest is the weighted variant: the problem of computing a minimum-cost maximum cardinality matching. For an arbitrary graph with m edges and n vertices, there are known, long-standing combinatorial algorithms that compute a maximum cardinality matching in O(m\sqrt{n}) time. For graphs with non-negative integer edge costs at most C, it is known how to compute a minimum-cost maximum cardinality matching in roughly O(m\sqrt{n} log(nC)) time using combinatorial methods. While non-combinatorial methods exist, they are generally impractical and not well understood due to their complexity. As a result, there is great interest in obtaining faster matching algorithms that are purely combinatorial in nature. Improving existing combinatorial algorithms for arbitrary graphs is considered to be a very difficult problem. To make the problem more approachable, it is desirable to make some additional assumptions about the graph. For our work, we make two such assumptions. First, we assume the graph is bipartite. Second, we assume that the graph has a small balanced separator, meaning it is possible to split the graph into two roughly equal-size components by removing a relatively small portion of the graph. Several well-studied classes of graphs have separator-like properties, including planar graphs, minor-free graphs, and geometric graphs. For such graphs, we describe a framework, a general set of techniques for designing efficient algorithms. We demonstrate this framework by applying it to yield polynomial-factor improvements for several open-problems in bipartite matching. / Doctor of Philosophy / Assume we are given a list of objects, and a list of compatible pairs of these objects. A matching consists of a chosen subset of these compatible pairs, where each object participates in at most one chosen pair. For any chosen pair of objects, we say the these two objects are matched. Generally, we seek to maximize the number of compatible matches. A maximum cardinality matching is a matching with the largest possible size. In many cases, there are multiple options for maximizing the number of compatible pairings. While maximizing the size of the matching is often the primary concern, one may also seek to minimize the cost of the matching. This is known as the minimum-cost maximum-cardinality matching problem. These two matching problems have been well studied, since they play a fundamental role in algorithmic theory as well as motivate many practical applications. Our interest is in the design of algorithms for both of these problems that are efficiently scalable, even as the number of objects involved grows very large. To aid in the design of scalable algorithms, we observe that some inputs have good separators, meaning that by removing some subset S of objects, one can divide the remaining objects into two sets V and V', where all pairs of objects between V and V' are incompatible. We design several new algorithms that exploit good separators, and prove that these algorithms scale better than previously existing approaches.

The ultimate goal of this work is to facilitate the design of gas turbine engine particle separators by reducing the computational expense to accurately simulate the fluid flow and particle motion inside the separator. It has been well-documented that particle ingestion yields many detrimental impacts for gas turbine engines. The consequences of ice particle ingestion can range from surface-wear abrasion to engine power loss. It is known that sufficiently small particles, characterized by small particle response times (τp), closely follow the fluid trajectory whereas large particles deviate from the streamlines. Rather than manually deriving how the particle acceleration varies from the fluid acceleration, this work chooses to implicitly derive this relationship using machine learning (ML). Inertial particle separators are devices designed to remove particles from the engine intake flow, which contributes to both elongating the lifespan and promoting safer operation of aviation gas turbine engines. Complex flows, such as flow through a particle separator, naturally have rotation and strain present throughout the flow field. This study attempts to understand if the motion of particles within rotational and strained canonical flows can be accurately predicted using supervised ML. This report suggests that preprocessing the ML training data to the fluid streamline coordinates can improve model training. ML models were developed for predicting particle acceleration in laminar, fully rotational/irrotational flows and combined laminar flows with rotation and strain. Lastly, the ML model is applied to particle data extracted from a Computational Fluid Dynamics (CFD) study of particle-laden flow around a louver-geometry. However, the model trained with particle data from combined canonical flows fails to accurately predict particle accelerations in the CFD flow field. / Master of Science / Aviation gas turbine engine particle ingestion is known to reduce engine lifespans and even pose a threat to safe operation in the worst case. Particles being ingested into an engine can be modeled using multiphase flow techniques. Devices called inertial particle separators are designed to remove particles from the flow into the engine. One challenge with designing such a separator is figuring out how to efficiently expel the small particles from the flow while not unnecessarily increasing pressure loss with excessive twists and turns in the geometry. Designers usually have to develop such geometries using multiphase flow computational fluid dynamics (CFD) that solve the fluid and particle dynamics. The abundance of data associated with CFD, and especially multiphase flows make it an ideal application to study with machine learning (ML). Because such multiphase simulations are very computationally expensive, it is desirable to develop "cheaper" methods. This is the long term goal of this work; we want to create ML surrogates that decrease the computational cost of simulating the particle and fluid flow in particle separator geometries such that designs can be iterated more quickly. In this work we introduce how artificial neural networks (ANNs), which are a tool used in ML, can be used to predict particle acceleration in fluid flow. The ANNs are shown to learn the acceleration predictions with acceptable accuracy for the training data generated with canonical flow cases. However, the ML model struggles to become generalizable to actual CFD simulations.

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To prevent oil and light liquids from causing damage at wastewater treatment facilities and the environment, a functional oil separator is important. The purpose of this study is to examine which vehicle operations have an oil separator installed and how they supervise its functionality in Arvidsjaur municipality. A questionnaire was used at the interview with all the owners with an oil separator. For those not able to participate in the interview, the same questionnaire was sent by email. The study showed that 14 of the total 15 owners had oil separator at their property and the majority of those where older ones of gravimetric type. Only 31 % had a regular self-inspection of the oil separator, which include control frequency of alarms, oil- and sludge level. The majority of the oil separators had been emptied at least once a year. Further the interviews indicated deficiencies in the owners existing knowledge, record-keeping and documentation. None of the oil separators had been inspected in the last 5 years. 46 % said that the oil separator lacked oil- and sludge level alarms. Results from a survey of operators self-inspection of oil separators in other municipalities in north of Sweden showed similar results as this study. Finally, examples of actions in accordance with standards and established guidelines are presented, which the regulatory authority may require from the owners with insufficient oil separators.

Thesis (Ph. D.)--Rutgers University, 2009. / "Graduate Program in Civil and Environmental Engineering." Includes bibliographical references (p. 194-203).

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Thesis (MSc.(Metallurgical Engineering)--University of Pretoria, 2007. / Includes bibliographical references.

Thesis (M.S.)--West Virginia University, 2006. / Title from document title page. Document formatted into pages; contains ix, 64 p. : ill. (some col.). Includes abstract. Includes bibliographical references (p. 63-64).

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