Extensions of some classical local moves on knot diagrams

In the present paper, we consider local moves on classical and welded diagrams: (self-)crossing change, (self-)virtualization, virtual conjugation, Delta, fused, band-pass and welded band-pass moves. Interrelationship between these moves is discussed and, for each of these move, we provide an algebraic classification. We address the question of relevant welded extensions for classical moves in the sense that the classical quotient of classical object embeds into the welded quotient of welded objects. As a by-product, we obtain that all of the above local moves are unknotting operations for welded (long) knots. We also mention some topological interpretations for these combinatorial quotients.Comment: 18 pages; this paper is an entirely new version of "On forbidden moves and the Delta move": the exposition has been totally revised, and several new results have been added; to appear in Michigan Math.

Homotopy classification of ribbon tubes and welded string links

Ribbon 2-knotted objects are locally flat embeddings of surfaces in 4-space which bound immersed 3-manifolds with only ribbon singularities. They appear as topological realizations of welded knotted objects, which is a natural quotient of virtual knot theory. In this paper we consider ribbon tubes and ribbon torus-links, which are natural analogues of string links and links, respectively. We show how ribbon tubes naturally act on the reduced free group, and how this action classifies ribbon tubes up to link-homotopy, that is when allowing each component to cross itself. At the combinatorial level, this provides a classification of welded string links up to self-virtualization. This generalizes a result of Habegger and Lin on usual string links, and the above-mentioned action on the reduced free group can be refined to a general "virtual extension" of Milnor invariants. As an application, we obtain a classification of ribbon torus-links up to link-homotopy.Comment: 33p. ; v2: typos and minor corrections ; v3: Introduction rewritten, exposition revised, references added. Section 5 of the previous version was significantly expanded and was separated into another paper (arXiv:1507.00202) ; v4: typos and minor corrections ; to appear in Annali della scuola Normale Superiore de Pisa (classe de scienze

Understanding Internet Shutdowns: A Case Study from Pakistan

This article provides an overview of Internet shutdowns in Pakistan, which have become an increasingly common phenomenon, with 41 occurring between 2012 and 2017. It argues that to understand how shutdowns became normalized in Pakistan, it is necessary to look at the specific dynamics of how the shutdowns take place. In doing so, the concept of communicative ruptures develops to better understand intentional government shutdowns of communications. The article argues that strategic prevention of mobilization is key for short-term shutdowns, whereas long-term shutdowns can be better explained by looking at disciplinary mechanisms and denying the existence of "others". The article then discusses Internet shutdowns in the wider context of authoritarian practices before concluding with the urgent need for further research on this topic, both in Pakistan and beyond

Design of Leading Edge Vortex Flaps for Delta Wings at Low Speeds

Engineering: 4th Place, Honorable Mention (The Ohio State University Denman Undergraduate Research Forum)Small unmanned aerial vehicles (UAVs) have become increasingly important in the role of tactical reconnaissance. Frontline troops rely on the ability to easily deploy UAVs from any position in order to collect time sensitive intelligence. One of the primary criteria for small UAVs is that of portability. In order to address this need, it has been proposed to design a UAV with a foldable delta wing made of a flexible material. However, delta wings typically suffer from decreased aerodynamic efficiency which is the ratio of the lift created to the drag produced. Poor performance in this regard is especially pronounced at low speeds. Since range is directly proportional to the maximum achievable aerodynamic efficiency, a delta wing equipped UAV would need to expend more propulsive energy to accomplish a given mission in comparison to conventional designs. A potential solution exists in the form of Leading Edge Vortex Flaps (LEVF). Essentially a flap-like control surface attached to the wings leading edge, such devices have been shown to improve aerodynamic efficiency by as much as 20 percent on conventional delta wing aircraft. The objective of this research was to determine an effective flap design with the goal of achieving the same aerodynamic improvements for flexible delta wings at low speeds. A secondary objective relating to the potential use of LEVF devices as a means of vehicle control was also investigated. Using Computational Fluid Dynamic (CFD), two and three dimensional analysis was performed on 30° and 60° delta wings in combination with various LEVF geometries. Effort was given to refining the geometry of a fully three-dimensional flap model as well as to determining the primary flow mechanisms that govern the creation of lift, drag, and ultimately aerodynamic efficiency. The results indicated that, at the low velocities tested, LEVF devices could improve the Aerodynamic Efficiency of a 30° delta wing by 4 percent and a 60° delta wing by as much as 10 percent. While a preliminary investigation into the potential for using LEVF devices as a means of vehicle control produced some encouraging results, additional work would be needed in order to make any definitive conclusions.Academic Major: Aeronautical and Astronautical Engineerin

Application of Ewald's Method for Efficient Summation of Dyon Long-Range Potentials

We study a model of dyons for SU(2) Yang-Mills theory at finite temperature T < T_c, in particular its ability to generate a confining force between a static quark antiquark pair. The interaction between dyons corresponds to a long-range 1/r potential, which in naive treatments with a finite number of dyons typically gives rise to severe finite volume effects. To avoid such effects we apply the so-called Ewald method, which has its origin in solid state physics. The basic idea of Ewald's method is to consider a finite number of dyons inside a finite cubic volume and enforce periodicity of this volume. We explain the technicalities of Ewald's method and outline how the method can be applied to a wider class of 1/r^p long-range potentials.Comment: 8 pages, 4 figures, contribution to conference "Confinement X