Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 15 of 15 for “"Discrete Geometry"”.
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Semi-algebraic graphs and hypergraphs in incidence geometry
… we discuss three problems in incidence geometry where the bounds for semi-algebraic (hyper)graphs are generally better than the ones for arbitrary (hyper)graphs : (1) what is the maximum number of hyperedges in a hypergraph forbidding some pattern? (2) what is the most compact way to …
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Flexural Mechanics of Creased Thin Metallic Strips
… springs is unclear. In reality, creases have a discrete geometry based on the method they were formed. This dissertation investigates the flexural behaviour of a creased thin metallic strip and the influence of the crease geometry. When a strip is bent perpendicular to the crease, putting the …
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Discrete Differential Geometry of Thin Materials for Computational Mechanics
… to the problem first, and then compute with the discrete geometry. This structure-respecting discrete-differential-geometric (DDG) approach often leads to new algorithms that more accurately track the physically behavior of the system with less computational effort. Thin objects, such as pieces …
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Bounds on extremal functions of forbidden patterns
… 1 matrices have applications to many problems in discrete geometry and enumerative combinatorics. We present a new computational method for deriving upper bounds on extremal functions of forbidden sequences. Then we use this method to prove tight bounds on the extremal functions of sequences of …
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Computer-assisted proofs in geometry and physics
… proof techniques to two problems, one in discrete geometry and one in celestial mechanics. Our main tool is an effective inverse function theorem which shows that, in favorable conditions, the existence of an approximate solution to a system of equations implies the existence of an exact …
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Convexification and Global Optimization of Problems Involving the Euclidean Norm
… but also appear in applications including discrete geometry and operations research, and the question of certifying global optimality remains open even for small instances. We identify the simultaneous elimination of Euclidean and permutational symmetry groups, as well as the …
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Geometric Graph Theory and Wireless Sensor Networks
… Using tools from extremal graph theory and discrete geometry, we obtain for every constant <em>h</em> that the number of <em>n</em>-vertex graphs that admit representations with <em>h</em> obstacles is 2<sup>o(n<sup>2</sup>)</sup>. We improve this bound to show that graphs requiring …
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Atom-Based Geometrical Fingerprinting of Conformal Two-Dimensional Materials
… bonds. Therefore the study of local shape and geometry of two-dimensional materials is a fundamental prerequisite to investigate physical and chemical properties. Hereby the use of discrete geometry to discuss the shape of two-dimensional materials is initiated. </p> <p>The local geometry of a …
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Equilibrium graphs on the flat torus or finding zen amidst the bull
… in many areas, including, but not limited to, discrete geometry, planar graph theory, graphics, surface parametrization, mechanical engineering, and graphical statics. In his 1963 paper, Tutte observed, “[W]e may remark that very little is known about representations of graphs in the protective …
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A novel diagnostic fracture injection test workflow considering natural fractures
… integrated workflow. This work uses an embedded discrete geometry simulation (EDGS) and embedded discrete fracture model (EDFM) to add natural fracture complexity into a new DFIT model. Incorporating fracture modeling tools will enhance the existing reservoir model by creating a more accurate …
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Reciprocal classes of continuous time Markov Chains
… showing some interesting connections with discrete geometry. Examples of such formulas are given in the framework of counting processes and random walks on Abelian groups, where the set of loops has a group structure. In addition to this global description, we propose a second approach by …
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Extremal problems on hypergraphs and set families
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2025-10-19 without embargo terms
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Problems and Results in Discrete and Computational Geometry
Let S be a set of n points in R^3 , no three collinear and not all coplanar. Ifat most n - k are coplanar and n is sufficiently large, the total number ofplanes determined is at least 1 + k * binom(n-k,2) - ((n-k)/2) * binom(k, 2). For similar conditions and sufficiently large n, (inspired by the …
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In pursuit of linear complexity in discrete and computational geometry
Many computational problems arise naturally from geometric data. In this thesis, we consider three such problems: (i) distance optimization problems over point sets, (ii) computing contour trees over simplicial meshes, and (iii) bounding the expected complexity of weighted Voronoi diagrams. While …
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Develpoment of advanced structural multifield models for the study of smart wing
… lift device, such as flap or slat that provide discrete geometry changes cannot be considered as morphing. Otherwise from the conventional solution the shape morphing required: distributed high-power density actuation, structural mechanization, flexible skins, and control law development. In …