Related papers: Constructing many-twist M\"obius bands with small …
The aspect ratio of a (positively) weighted graph $G$ is the ratio of its maximum edge weight to its minimum edge weight. Aspect ratio commonly arises as a complexity measure in graph algorithms, especially related to the computation of…
We study the problem of finding the minimal (maximal) genus for a surface where a given four-valent graph with fixed opposite edge structure can be embedded into. We find several partial relations and give new reformulations in…
Weaving knots are alternating knots with the same projection as torus knots, and were conjectured by X.-S. Lin to be among the maximum volume knots for fixed crossing number. We provide the first asymptotically correct volume bounds for…
We give a characterisation of Bieberbach manifolds which are geodesic boundaries of a compact flat manifold, and discuss the low dimensional cases, up to dimension 4.
Results of classical force field geometry optimizations for twisted graphene nanoribbons with a number of twists $N_t$ varying from 0 to 7 (the case $N_t$=1 corresponds to a half-twist M\"obius nanoribbon) are presented in this work. Their…
Global textures are interesting because they are promising candidates for seeds in the structure formation of the universe. The important configurations are those who will be able to collapse. The type of configurations that I will consider…
Investigating topological effects in materials requires often the modeling of material systems as a whole. Such modeling restricts system sizes, and makes it hard to extract systematic trends. Here, we investigate the effect of M\"obius…
We show that the volumes of certain hyperbolic A-adequate links can be bounded (above and) below in terms of two diagrammatic quantities: the twist number and the number of certain alternating tangles in an A-adequate diagram. We then…
In this paper we use continued fractions to study a partial order on the set of 2-bridge knots derived from the work of Ohtsuki, Riley, and Sakuma. We establish necessary and sufficient conditions for any set of 2-bridge knots to have an…
The resistive and reactive components of magneto-impedance was studied for the as-quenched and microwave annealed amorphous Fe73.5Nb3Cu1Si13.5B9 ribbon as a function of biasing d.c magnetic fields (-60 to +60 Oe) and excitation frequencies…
In this work, we use the warped \( \mu \)-bubble method to study the consequences of a spectral curvature bound. In particular, with a lower spectral Ricci curvature bound and a lower spectral scalar curvature bound, we show that the band…
Band surgery is an operation relating pairs of knots or links in the three-sphere. We prove that if two quasi-alternating knots $K$ and $K'$ of the same square-free determinant are related by a band surgery, then the absolute value of the…
Super-oscillating beams can be used to create light spots whose size is below the diffraction limit with a side ring of high intensity adjacent to them. Optical traps made of the super-oscillating part of such beams exhibit superior…
We establish a Kauffman-Murasugi-Thistlethwaite-type theorem for alternating knots in a solid torus. Specifically, we show that any dotted-reduced alternating diagram of a knot in a handlebody realizes the minimal crossing number, and that…
A novel way of filling high aspect ratio vertical interconnection (microvias) with an aspect ratio of >2:1 is presented. High frequency acoustic streaming at megasonic frequencies enables the decrease of the Nernst-diffusion layer down to…
A graph is called (generically) rigid in R^d if, for any choice of sufficiently generic edge lengths, it can be embedded in R^d in a finite number of distinct ways, modulo rigid transformations. Here, we deal with the problem of determining…
The large tunability of band gaps and optical absorptions of armchair MoS$_2$ nanoribbons of different widths under bending is studied using density functional theory and many-body perturbation GW and Bethe-Salpeter equation approaches. We…
We give a simple obstruction for a knot to be amphichiral, in terms of the homology of the 2-fold branched cover. We work with unoriented knots, and so obstruct both positive and negative amphichirality.
Non-destructive characterization of multi-layered structures that can be accessed from only a single side is important for applications such as well-bore integrity inspection. Existing methods related to Synthetic Aperture Focusing…
Biaxially textured MgO templates have been successfully fabricated on several amorphous polymer films including Kapton tapes, polyimide, Poly(methyl methacrylate) (PMMA), and photoresist films using ion-beam-assisted-deposition (IBAD). With…