The biomechanical role of extra-axonemal structures in shaping the flagellar beat of Euglena gracilis

We propose and discuss a model for flagellar mechanics inEuglena gracilis. We show that the peculiar non-planar shapes of its beating flagellum, dubbed 'spinning lasso', arise from the mechanical interactions between two of its inner components, namely, the axoneme and the paraflagellar rod. The spontaneous shape of the axoneme and the resting shape of the paraflagellar rod are incompatible. Thus, the complex non-planar configurations of the coupled system emerge as the energetically optimal compromise between the two antagonistic components. The model is able to reproduce the experimentally observed flagellar beats and the characteristic geometric signature of spinning lasso, namely, traveling waves of torsion with alternating sign along the length of the flagellum.

Manufactured Cracks in Pipe Used to Evaluate ILI Measurement Performance

Recently, transmission pipeline operators have started designing pipe spools with manufactured cracks of very precise size and orientation for the purpose of qualifying measurement technologies. The manufactured cracks are very similar to naturally occurring cracks and can be made to have varied profiles and off-planar shapes (like hook cracks). The manufactured spools are installed on a transmission pipeline at either the pipe launcher, the receiver or in-line such that an in-line inpsection (ILI) tool passes through it during a transmission pipeline ILI field run. This produces highly valuable data to evaluate measurement performance because the crack sizes are precisely known, crack morphologies are similar to realistic cracks and the ILI tool is tested in field conditions. This paper describes the effect on the estimated ILI tool measurement performance for various combinations of manufactured cracks in a pipe spool. The cases described vary the number of manufactured cracks in the spool to estimate the value of each additional crack and vary the distribution of cracks sizes to compare the value of large versus small cracks.

Mitered Offsets and Skeletons for Circular Arc Polygons

The offsetting process that defines straight skeletons of polygons is generalized to arc polygons, i.e., to planar shapes with piecewise circular boundaries. The offsets are obtained by shrinking or expanding the circular arcs on the boundary in a co-circular manner, and tracing the paths of their endpoints. These paths define the associated shape-preserving skeleton, which decomposes the input object into patches. While the skeleton forms a forest of trees, the patches of the decomposition have a radial monotonicity property. Analyzing the events that occur during the offsetting process is non-trivial; the boundary of the offsetting object may get into self-contact and may even splice. This leads us to an event-driven algorithm for offset and skeleton computation. Several examples (both manually created ones and approximations of planar free-form shapes by arc spline curves) are analyzed to study the practical performance of our algorithm.