Comment on "Classical Mechanics of Nonconservative Systems"

A Comment on the Letter by C. R. Galley, Phys. Rev. Lett. 110, 174301 (2013)

Chain Paradoxes

For nearly two centuries the dynamics of chains have offered examples of paradoxical theoretical predictions. Here we propose a theory for the dissipative dynamics of one-dimensional continua with singularities which provides a unified treatment for chain problems that have suffered from paradoxical solutions. These problems are duly solved within the present theory and their paradoxes removed---we hope

Dissipative Shocks behind Bacteria Gliding

Gliding is a means of locomotion on rigid substrates utilized by a number of bacteria includingmyxobacteria and cyanobacteria. One of the hypotheses advanced to explain this motility mechanism hinges on the role played by the slime filaments continuously extruded from gliding bacteria. This paper solves in full a non-linear mechanical theory that treats as dissipative shocks both the point where the extruded slime filament comes in contact with the substrate, called the filament's foot, and the pore on the bacterium outer surface from where the filament is ejected. We prove that kinematic compatibility for shock propagation requires that the bacterium uniform gliding velocity (relative to the substrate) and the slime ejecting velocity (relative to the bacterium) must be equal, a coincidence that seems to have already been observed.Comment: arXiv admin note: text overlap with arXiv:1402.636

Dissipative shocks in a chain fountain

The fascinating and anomalous behaviour of a chain that instead of falling straight down under gravity, first rises and then falls, acquiring a steady shape in space that resembles a fountain's sprinkle, has recently attracted both popular and academic interest. The paper presents a complete mathematical solution of this problem, whose distinctive feature is the introduction of a number of dissipative shocks which can be resolved exactly

Octupolar order in two dimensions

Octupolar order is described in two space dimensions in terms of the maxima (and conjugated minima) of the probability density associated with a third-rank, fully symmetric and traceless tensor. Such a representation is shown to be equivalent to diagonalizing the relevant third-rank tensor, an equivalence which however is only valid in the two-dimensional case

How much do children really cost? Maternity benefits and career opportunities of women in academia

Motherhood and professional achievements appear as conflicting goals even for academic women. This project explores this tension by focusing on a set of provisions on parental and maternity leaves across 165 higher education institutions in the UK. Generous maternity provisions generate countervailing incentives for female academics. On the one hand, advantageous policies can foster women’s productivity in terms of research outcomes allowing them to take time out of work without income and career break concerns. On the other hand, women can exploit generous provisions without generating returnable results for the academic institution. We argue that adverse selection problems lead universities to differentiate among academic staff by offering two different types of maternity provisions (more vs less generous maternity leaves) in order to “test” women’s commitment and research ability before offering permanent contracts. Our results support this this line of argumentation. We also find that generous maternity leaves and childcare provisions positively affect the number of women at research and professorship levels

The symmetries of octupolar tensors

Octupolar tensors are third order, completely symmetric and traceless tensors. Whereas in 2D an octupolar tensor has the same symmetries as an equilateral triangle and can ultimately be identified with a vector in the plane, the symmetries that it enjoys in 3D are quite different, and only exceptionally reduce to those of a regular tetrahedron. By use of the octupolar potential that is, the cubic form associated on the unit sphere with an octupolar tensor, we shall classify all inequivalent octupolar symmetries. This is a mathematical study which also reviews and incorporates some previous, less systematic attempts

Explicit excluded volume of cylindrically symmetric convex bodies

We represent explicitly the excluded volume Ve{B1,B2} of two generic cylindrically symmetric, convex rigid bodies, B1 and B2, in terms of a family of shape functionals evaluated separately on B1 and B2. We show that Ve{B1,B2} fails systematically to feature a dipolar component, thus making illusory the assignment of any shape dipole to a tapered body in this class. The method proposed here is applied to cones and validated by a shape-reconstruction algorithm. It is further applied to spheroids (ellipsoids of revolution), for which it shows how some analytic estimates already regarded as classics should indeed be emended