Threadable Curves

We define a plane curve to be threadable if it can rigidly pass through a point-hole in a line L without otherwise touching L. Threadable curves are in a sense generalizations of monotone curves. We have two main results. The first is a linear-time algorithm for deciding whether a polygonal curve is threadable---O(n) for a curve of n vertices---and if threadable, finding a sequence of rigid motions to thread it through a hole. We also sketch an argument that shows that the threadability of algebraic curves can be decided in time polynomial in the degree of the curve. The second main result is an O(n polylog n)-time algorithm for deciding whether a 3D polygonal curve can thread through hole in a plane in R^3, and if so, providing a description of the rigid motions that achieve the threading.Comment: 16 pages, 12 figures, 12 references. v2: Revised with brief addendum after Mikkel Abrahamsen pointed us to a relevant reference on "sweepable polygons." v3: Major revisio

How a tariff-based trade policy affects domestic prices, import volumes and welfare: an empirical analysis of the eu´s retaliatory tariffs on the Us

This Project examines how the retaliatory tariffs imposed by the EU in response to the US steel and aluminum tariffs affect EU prices and welfare over the period from June 2018 to May 2020. Using a partial equilibrium model that assumes perfect competition, the graphical analysis and the regression show that the prices of the goods subject to the tariffs are fully passed on to EU producers and consumers, suggesting that they bear the full burden of the tariff increase. Consequently, the EU suffers a deadweight welfare lossof almost€144 million over the two years considered

Slip-Stick Contact Conditions for the Thermo-Mechanically Coupled Flow Drill Screw Process

Automakers have adopted a heavy focus towards lightweighting their fleets due to the stringent emission standards placed upon them. Lightweighting can be done using several methods but material substitution is proven to be most effective considering the traditional powertrains are on the border of theoretical limits. Designing multi-material body structures is a recognized strategy, replacing steels with lightweight metals such as aluminum, magnesium, and fiber-reinforced composites. The issue now arises on how to join these materials that possess such varied thermo-mechanical properties, with resistance spot welding (RSW) currently not an option. One of the newly-adopted joining technologies is Flow Drill Screwing (FDS) which is currently the only structurally viable joining technology that does not require access to the back side of the joint. FDS is a coupled thermo-mechanical process due to the frictional behavior between the rotating screw and stationary workpiece. An understanding of the process is limited to empirical methods mainly based on experimental findings with little known about the frictional behavior at the screw-workpiece interface. This lack of understanding not only inhibits the potential of the process, but more importantly, whether its application borders on the edge of reliability; and without an understanding to the transient contact conditions, accurate torque and temperature modeling is not feasible. Current models have limited accuracy as their methodology couples a friction coefficient and material strength term. A modeling approach that incorporates both a slipping and sticking condition is theorized to be more appropriate for frictional processes of this nature, but no coupled models currently exist. The following research aims at integrating these two conditions under a single model to enable more accurate modeling and prediction of the FDS process performance. A secondary objective presented in this research is to determine whether FDS processing time could benefit from the assistance of supplementary energy sources. Replacing RSW with these alternate joining technologies, such as FDS, comes at the expense of an increased process time. This research aims at augmenting FDS with heat to lower the impact of this decreased process efficiency while also testing the potential to open the design space to thicker/stronger materials

Entanglement Length Scale Separates Threading from Branching of Unknotted and Non-concatenated Ring Polymers in Melts

Current theories on the conformation and dynamics of unknotted and non-concatenated ring polymers in melt conditions describe each ring as a tree-like double-folded object. While evidence from simulations supports this picture on a single ring level, other works show pairs of rings also thread each other, a feature overlooked in the tree theories. Here we reconcile this dichotomy using Monte Carlo simulations of the ring melts with different bending rigidities. We find that rings are double-folded (more strongly for stiffer rings) on and above the entanglement length scale, while the threadings are localized on smaller scales. The different theories disagree on the details of the tree structure, i.e., the fractal dimension of the backbone of the tree. In the stiffer melts we find an indication of a self-avoiding scaling of the backbone, while more flexible chains do not exhibit such a regime. Moreover, the theories commonly neglect threadings and assign different importance to the impact of the progressive constraint release (tube dilation) on single ring relaxation due to the motion of other rings. Despite that each threading creates only a small opening in the double-folded structure, the threading loops can be numerous and their length can exceed substantially the entanglement scale. We link the threading constraints to the divergence of the relaxation time of a ring, if the tube dilation is hindered by pinning a fraction of other rings in space. Current theories do not predict such divergence and predict faster than measured diffusion of rings, pointing at the relevance of the threading constraints in unpinned systems as well. Revision of the theories with explicit threading constraints might elucidate the validity of the conjectured existence of topological glass

A Framework for Optical Inspection Applications in Life-Science Automation

This thesis presents possible applications for Computer Vision based systems in the field of Laboratory Automation and applicable camera-based, multi-camera-based or flatbed scanner based imaging devices. A concept of a software framework for CV applications is developed with respect to hardware compatibility, data processing and user interfaces. An application is implemented using the framework. It aims at the detection of low-volume liquids in microtiter plates, a labware standard. Using this algorithm, it is possible to cover a wide range of labware on different imaging hardware

Spectral properties of graphs derived from groups.

This thesis is primarily about spectral measures and walk-generating functions of lattices. Formally a lattice is obtained from a finitely-generated abelian group G, a finite set Y, and a finite subset L of Gxx. Informally a lattice is likely to be some structure in n-dimensional space such as a hexagonal or cubic lattice. Spectral measures and walk-generating functions determine each other, and are relevant to Markov Chains and networks of resistances. Formulae for spectral measures and walk generating functions of lattices are found, and generalised to sum-difference graphs and graphs obtained from groups with large abelian subgroups. Formulae are also found for walk generating functions for modified lattices. Lattices may be modified by a finite set of changes to edges or vertices, but also by an infinite but periodic set of modifications (such as a row of points being removed). For example, this makes it possible to find exact formulae for Markov Chains where two interacting particles move around a lattice. However only one infinite periodic set of modifications can be so handled; we show that with directed lattices with two infinite periodic sets of modifications, even finding if two points are connected can be equivalent to the Halting Problem. New methods are found for discovering what a spectral measure looks like. We develop techniques in the theory of complex functions of several variables to provide criteria which make it possible to show that a spectral measure is well-behaved at some point (in the sense that its density function is analytic) if local properties of certain analytic functions are satisfied globally

Ring Polymers: Threadings, Knot Electrophoresis and Topological Glasses

Elucidating the physics of a concentrated suspension of ring polymers, or of an ensemble of ring polymers in a complex environment, is an important outstanding question in polymer physics. Many of the characteristic features of these systems arise due to topological interactions between polymers, or between the polymers and the environment, and it is often challenging to describe this quantitatively. Here we review recent research which suggests that a key role is played by inter-ring threadings (or penetrations), which become more abundant as the ring size increases. As we discuss, the physical consequences of such threadings are far-reaching: for instance, they lead to a topologically-driven glassy behaviour of ring polymer melts under pinning perturbations, while they can also account for the shape of experimentally observed patterns in two-dimensional gel electrophoresis of DNA knots