Drawing bobbin lace graphs, or, Fundamental cycles for a subclass of periodic graphs

In this paper, we study a class of graph drawings that arise from bobbin lace patterns. The drawings are periodic and require a combinatorial embedding with specific properties which we outline and demonstrate can be verified in linear time. In addition, a lace graph drawing has a topological requirement: it contains a set of non-contractible directed cycles which must be homotopic to $(1,0)$, that is, when drawn on a torus, each cycle wraps once around the minor meridian axis and zero times around the major longitude axis. We provide an algorithm for finding the two fundamental cycles of a canonical rectangular schema in a supergraph that enforces this topological constraint. The polygonal schema is then used to produce a straight-line drawing of the lace graph inside a rectangular frame. We argue that such a polygonal schema always exists for combinatorial embeddings satisfying the conditions of bobbin lace patterns, and that we can therefore create a pattern, given a graph with a fixed combinatorial embedding of genus one.Comment: Appears in the Proceedings of the 25th International Symposium on Graph Drawing and Network Visualization (GD 2017

Three-Dimensional Fiber Segment Orientation Distribution Using X-Ray Microtomography

The orientation of fibers in assemblies such as nonwovens has a major influence on the anisotropy of properties of the bulk structure and is strongly influenced by the processes used to manufacture the fabric. To build a detailed understanding of a fabric’s geometry and architecture it is important that fiber orientation in three dimensions is evaluated since out-of-plane orientations may also contribute to the physical properties of the fabric. In this study, a technique for measuring fiber segment orientation as proposed by Eberhardt and Clarke is implemented and experimentally studied based on analysis of X-ray computed microtomographic data. Fiber segment orientation distributions were extracted from volumetric X-ray microtomography data sets of hydroentangled nonwoven fabrics manufactured from parallel-laid, cross-laid, and air-laid webs. Spherical coordinates represented the orientation of individual fibers. Physical testing of the samples by means of zero-span tensile testing and z-directional tensile testing was employed to compare with the computed results

Very fast kicker for accelerator applications

We describe a very fast kicker with unique combination of high repetition rate and short pulse width. Constructionally, the device is a counter traveling wave strip-line kicker fed by semiconductor high-voltage pulse generator. Experimentally tested kicker has a full pulse width of about 7 ns, 1.4 MHz repetition rate and maximum kick strength of the order of 3 G m. Recent achievements in high-voltage semiconductor field-effect-transistors (FET) technology and goal-specific optimization of the kicker parameters allow many-fold increase of the strength, and the kicker can be a very useful tool for bunch-by-bunch injection/extraction and other accelerator applications

Testing for unit and fractional orders of integration in the trend and seasonal components of US monetary aggregates

Monthly seasonally unadjusted data can exhibit roots with possibly fractional orders of integration, corresponding to the monthly but also to the quarterly and to the long-run or trending components of the series. In this paper we use a procedure which is suitable to test simultaneously for the order of integration of each of these components and apply it to several US monetary aggregates