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Three-dimensional magnetic fields: from coils to reconnection
This thesis is a work divided into two parts on aspects of three-dimensional (3D) magnetic fields: (I) magnetic reconnection treated from a strictly 3D viewpoint and (II) the design of coils for producing the 3D magnetic fields of optimized stellarators.
In astrophysical settings, magnetic fields are generically 3D. 3D divergence-free fields have rich topological structures such as magnetic nulls and chaotic field line structures. Standard reconnection literature identifies magnetic nulls as locations of magnetic reconnection, and that intense currents will build up around them. This idea is explored with a key realization that by placing a vanishingly small sphere around the null, boundary conditions on field lines passing through the sphere may be sorted out. The main result here is (1) the dismissal of the notion that nulls are crucial places for magnetic reconnection and current accumulation, instead identifying separatrices of topological type on the boundaries of null-passing field lines to be crucial. Standard reconnection literature dismisses chaotic flows yet 3D fields generically have chaotic flows. An inherent property of chaotic flows is exponentiation. The main result here is (2) the identification of exponentiation as a natural mechanism for magnetic reconnection and that the associated current builds up linearly in time in contradiction to standard results requiring the formation of high-density current sheets.
The magnetic fields of optimized stellarators are intricate, producing complex 3D magnetic surfaces. These fields are conventionally generated by non-planar electromagnetic coils, though these coils are costly to manufacture, slow device assembly, and hinder stellarator maintenance. Part II of this thesis explores methods of stellarator coil simplification that do not involve modular coils. All of this work uses current potentials, which are stream functions of the current sheets that produce magnetic surfaces. We begin with a result found using analytic methods on current potentials that (1) there may be an inherent limitation in the ability of modular coils to produce fields at a distance. This result is not surprising, though further analysis is necessary to work out some complexities of the result.
Next, (2) a novel method to produce localized patches of current potential, representative of patches of current sheets, is developed and used to identify crucial locations of current placement for shaping magnetic surfaces. Most notably, these current sheet patches are able to produce much of the surface shaping while occupying a small fraction of the winding surface, resulting in good open-access stellarator coil configurations. Continuing the trend away from modular coils, (3) helical coils are optimized to support stellarator magnetic fields.
This work agrees with related work on the optimization of helical coils, finding them unsuitable to the precise production of equilibria generated by modular coils. To improve this result, we use coil sets of mixed-type: helical coils with windowpane coils or permanent magnets, to mitigate field error left behind by the helical coils. Finally, (4) the development of a generalized method to cut modular, helical, and windowpane coils out of current potentials and to identify the associated coil currents is developed and used in coil optimization
Covering and Separation for Permutations and Graphs
This is a thesis of two parts, focusing on covering and separation topics of extremal combinatorics and graph theory, two major themes in this area. They entail the existence and properties of collections of combinatorial objects which together either represent all objects (covering) or can be used to distinguish all objects from each other (separation). We will consider a range of problems which come under these areas. The first part will focus on shattering k-sets with permutations. A family of permutations is said to shatter a given k-set if the permutations cover all possible orderings of the k elements. In particular, we investigate the size of permutation families which cover t orders for every possible k-set as well as study the problem of determining the largest number of k-sets that can be shattered by a family with given size. We provide a construction for a small permutation family which shatters every k-set. We also consider constructions of large families which do not shatter any triple. The second part will be concerned with the problem of separating path systems. A separating path system for a graph is a family of paths where, for any two edges, there is a path containing one edge but not the other. The aim is to find the size of the smallest such family. We will study the size of the smallest separating path system for a range of graphs, including complete graphs, complete bipartite graphs, and lattice-type graphs. A key technique we introduce is the use of generator paths - constructed to utilise the symmetric nature of Kn. We continue this symmetric approach for bipartite graphs and study the limitations of the method. We consider lattice-type graphs as an example of the most efficient possible separating systems for any graph
Cycling Through the Pandemic : Tactical Urbanism and the Implementation of Pop-Up Bike Lanes in the Time of COVID-19
Provides an international overview on how tactical urbanism was implemented to give more space to cycling
Demonstrates the conceptual framework surrounding tactical urbanism and how it plays out theoretically
Proposes new methodological insights to understand the effects of tactical urbanism intervention
Essays on Corporate Disclosure of Value Creation
Information on a firm’s business model helps investors understand an entity’s resource requirements, priorities for action, and prospects (FASB, 2001, pp. 14-15; IASB, 2010, p. 12). Disclosures of strategy and business model (SBM) are therefore considered a central element of effective annual report commentary (Guillaume, 2018; IIRC, 2011). By applying natural language processing techniques, I explore what SBM disclosures look like when management are pressed to say something, analyse determinants of cross-sectional variation in SBM reporting properties, and assess whether and how managers respond to regulatory interventions seeking to promote SBM annual report commentary. This dissertation contains three main chapters. Chapter 2 presents a systematic review of the academic literature on non-financial reporting and the emerging literature on SBM reporting. Here, I also introduce my institutional setting. Chapter 3 and Chapter 4 form the empirical sections of this thesis. In Chapter 3, I construct the first large sample corpus of SBM annual report commentary and provide the first systematic analysis of the properties of such disclosures. My topic modelling analysis rejects the hypothesis that such disclosure is merely padding; instead finding themes align with popular strategy frameworks and management tailor the mix of SBM topics to reflect their unique approach to value creation. However, SBM commentary is less specific, less precise about time horizon (short- and long-term), and less balanced (more positive) in tone relative to general management commentary. My findings suggest symbolic compliance and legitimisation characterize the typical annual report discussion of SBM. Further analysis identifies proprietary cost considerations and obfuscation incentives as key determinants of symbolic reporting. In Chapter 4, I seek evidence on how managers respond to regulatory mandates by adapting the properties of disclosure and investigate whether the form of the mandate matters. Using a differences-in-differences research design, my results suggest a modest incremental response by treatment firms to the introduction of a comply or explain provision to provide disclosure on strategy and business model. In contrast, I find a substantial response to enacting the same requirements in law. My analysis provides clear and consistent evidence that treatment firms incrementally increase the volume of SBM disclosure, improve coverage across a broad range of topics as well as providing commentary with greater focus on the long term. My results point to substantial changes in SBM reporting properties following regulatory mandates, but the form of the mandate does matter. Overall, this dissertation contributes to the accounting literature by examining how firms discuss a central topic to economic decision making in annual reports and how firms respond to different forms of disclosure mandate. Furthermore, the results of my analysis are likely to be of value for regulators and policymakers currently reviewing or considering mandating disclosure requirements. By examining how companies adapt their reporting to different types of regulations, this study provides an empirical basis for recalibrating SBM disclosure mandates, thereby enhancing the information set of capital market participants and promoting stakeholder engagement in a landscape increasingly shaped by non-financial information
LIPIcs, Volume 251, ITCS 2023, Complete Volume
LIPIcs, Volume 251, ITCS 2023, Complete Volum
Multi Layer Peeling for Linear Arrangement and Hierarchical Clustering
We present a new multi-layer peeling technique to cluster points in a metric space. A well-known non-parametric objective is to embed the metric space into a simpler structured metric space such as a line (i.e., Linear Arrangement) or a binary tree (i.e., Hierarchical Clustering). Points which are close in the metric space should be mapped to close points/leaves in the line/tree; similarly, points which are far in the metric space should be far in the line or on the tree. In particular we consider the Maximum Linear Arrangement problem [Refael Hassin and Shlomi Rubinstein, 2001] and the Maximum Hierarchical Clustering problem [Vincent Cohen-Addad et al., 2018] applied to metrics.
We design approximation schemes (1-? approximation for any constant ? > 0) for these objectives. In particular this shows that by considering metrics one may significantly improve former approximations (0.5 for Max Linear Arrangement and 0.74 for Max Hierarchical Clustering). Our main technique, which is called multi-layer peeling, consists of recursively peeling off points which are far from the "core" of the metric space. The recursion ends once the core becomes a sufficiently densely weighted metric space (i.e. the average distance is at least a constant times the diameter) or once it becomes negligible with respect to its inner contribution to the objective. Interestingly, the algorithm in the Linear Arrangement case is much more involved than that in the Hierarchical Clustering case, and uses a significantly more delicate peeling
Reuse of Water and Nutrients in Soilless Plant Culture
This dissertation proposes two approaches to mitigating the dependency of soilless culture on scarce mineral fertilisers. The first approach aims to increase the lifetime of the NS used in recirculating hydroponic systems, while the second approach presents a holistic method for the treatment and use of aquacultural sludge as NS for soilless growth systems. This method includes two steps: nutrient mobilisation using aerobic digestion (AD), followed by solids precipitation using the biopolymer chitosan as the flocculant. The recovered NS was used to grow lettuce in a recirculating hydroponic system.
The outcome of the first approach showed that NS can be used for several weeks before discharge, even though many growers discard recycling NS at weekly intervals. In this study, NS was reused for 6 weeks, corresponding to a production of 1 kg lettuce per 10 litres tank volume of NS, in a closed hydroponic system without compromising the yield and apparent quality of lettuce.
The results from the second approach indicated that AD is an efficient method to mobilise nutrients in aquacultural waste to concentrations close to or exceeding the mineral levels recommended for soilless growth systems. In addition, the biopolymer chitosan proved to be an efficient and safe alternative for solids removal from aerobically digested aquacultural waste. The recovered NS was successfully used for lettuce production in a closed hydroponic system, with yield and quality comparable to those of lettuce grown with conventional NS. The results obtained clearly show the possibility of substituting synthetic fertilisers with recovered NS from aquaculture waste, which can be considered an alternative and resource-efficient fertilisation strategy for soilless culture systems.
Both approaches are described in this dissertation, while detailed explanations of the materials and methods used, as well as the obtained results, can be found in the appended papers.publishedVersio
Efficient 1-Laplacian Solvers for Well-Shaped Simplicial Complexes: Beyond Betti Numbers and Collapsing Sequences
We present efficient algorithms for solving systems of linear equations in 1-Laplacians of well-shaped simplicial complexes. 1-Laplacians, or higher-dimensional Laplacians, generalize graph Laplacians to higher-dimensional simplicial complexes and play a key role in computational topology and topological data analysis. Previously, nearly-linear time solvers were developed for simplicial complexes with known collapsing sequences and bounded Betti numbers, such as those triangulating a three-ball in R3 (Cohen, Fasy, Miller, Nayyeri, Peng, and Walkington [SODA’2014], Black, Maxwell, Nayyeri, and Winkelman [SODA’2022], Black and Nayyeri [ICALP’2022]). Furthermore, Nested Dissection provides quadratic time solvers for more general systems with nonzero structures representing well-shaped simplicial complexes embedded in R3. We generalize the specialized solvers for 1-Laplacians to simplicial complexes with additional geometric structures but without collapsing sequences and bounded Betti numbers, and we improve the runtime of Nested Dissection. We focus on simplicial complexes that meet two conditions: (1) each individual simplex has a bounded aspect ratio, and (2) they can be divided into “disjoint” and balanced regions with well-shaped interiors and boundaries. Our solvers draw inspiration from the Incomplete Nested Dissection for stiffness matrices of well-shaped trusses (Kyng, Peng, Schwieterman, and Zhang [STOC’2018]).ISSN:1868-896
Product structure of graph classes with strongly sublinear separators
We investigate the product structure of hereditary graph classes admitting
strongly sublinear separators. We characterise such classes as subgraphs of the
strong product of a star and a complete graph of strongly sublinear size. In a
more precise result, we show that if any hereditary graph class
admits separators, then for any fixed
every -vertex graph in is a subgraph
of the strong product of a graph with bounded tree-depth and a complete
graph of size . This result holds with if
we allow to have tree-depth . Moreover, using extensions of
classical isoperimetric inequalties for grids graphs, we show the dependence on
in our results and the above bound are
both best possible. We prove that -vertex graphs of bounded treewidth are
subgraphs of the product of a graph with tree-depth and a complete graph of
size , which is best possible. Finally, we investigate the
conjecture that for any hereditary graph class that admits
separators, every -vertex graph in is a
subgraph of the strong product of a graph with bounded tree-width and a
complete graph of size . We prove this for various classes
of interest.Comment: v2: added bad news subsection; v3: removed section "Polynomial
Expansion Classes" which had an error, added section "Lower Bounds", and
added a new author; v4: minor revisions and corrections
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