Visualizing the Template of a Chaotic Attractor

Chaotic attractors are solutions of deterministic processes, of which the topology can be described by templates. We consider templates of chaotic attractors bounded by a genus-1 torus described by a linking matrix. This article introduces a novel and unique tool to validate a linking matrix, to optimize the compactness of the corresponding template and to draw this template. The article provides a detailed description of the different validation steps and the extraction of an order of crossings from the linking matrix leading to a template of minimal height. Finally, the drawing process of the template corresponding to the matrix is saved in a Scalable Vector Graphics (SVG) file.Comment: Appears in the Proceedings of the 26th International Symposium on Graph Drawing and Network Visualization (GD 2018

Sexual Dimorphism of the Zebra Finch Syrinx Indicates Adaptation for High Fundamental Frequencies in Males

In many songbirds the larger vocal repertoire of males is associated with sexual dimorphism of the vocal control centers and muscles of the vocal organ, the syrinx. However, it is largely unknown how these differences are translated into different acoustic behavior.Here we show that the sound generating structures of the syrinx, the labia and the associated cartilaginous framework, also display sexual dimorphism. One of the bronchial half rings that position and tense the labia is larger in males, and the size and shape of the labia differ between males and females. The functional consequences of these differences were explored by denervating syringeal muscles. After denervation, both sexes produced equally low fundamental frequencies, but the driving pressure generally increased and was higher in males. Denervation strongly affected the relationship between driving pressure and fundamental frequency.The syringeal modifications in the male syrinx, in concert with dimorphisms in neural control and muscle mass, are most likely the foundation for the potential to generate an enhanced frequency range. Sexually dimorphic vocal behavior therefore arises from finely tuned modifications at every level of the motor cascade. This sexual dimorphism in frequency control illustrates a significant evolutionary step towards increased vocal complexity in birds

The problem of sharp notch in microstructured solids governed by dipolar gradient elasticity

In this paper, we deal with the asymptotic problem of a body of infinite extent with a notch (re-entrant corner) under remotely applied plane-strain or anti-plane shear loadings. The problem is formulated within the framework of the Toupin-Mindlin theory of dipolar gradient elasticity. This generalized continuum theory is appropriate to model the response of materials with microstructure. A linear version of the theory results by considering a linear isotropic expression for the strain-energy density that depends on strain-gradient terms, in addition to the standard strain terms appearing in classical elasticity. Through this formulation, a microstructural material constant is introduced, in addition to the standard Lamé constants . The faces of the notch are considered to be traction-free and a boundary-layer approach is followed. The boundary value problem is attacked with the asymptotic Knein-Williams technique. Our analysis leads to an eigenvalue problem, which, along with the restriction of a bounded strain energy, provides the asymptotic fields. The cases of a crack and a half-space are analyzed in detail as limit cases of the general notch (infinite wedge) problem. The results show significant departure from the predictions of the standard fracture mechanics