Buckling of elastic filaments by discrete magnetic moments

We study the buckling of an idealized, semiflexible filament along whose contour magnetic moments are placed. {We give analytic expressions for the critical stiffness of the filament below which it buckles due to the magnetic compression. For this, we consider various scenarios of the attachment of the magnetic particles to the filament. One possible application for this model are the magnetosome chains of magnetotactic bacteria. An estimate of the critical bending stiffness indicates that buckling may occur within the range of biologically relevant parameters and suggests a role for the bending stiffness of the filament to stabilize the filament against buckling, which would compromise the functional relevance of the bending stiffness of the used filament.Comment: accepted for publication in EPJ

The Burbea-Rao and Bhattacharyya centroids

We study the centroid with respect to the class of information-theoretic Burbea-Rao divergences that generalize the celebrated Jensen-Shannon divergence by measuring the non-negative Jensen difference induced by a strictly convex and differentiable function. Although those Burbea-Rao divergences are symmetric by construction, they are not metric since they fail to satisfy the triangle inequality. We first explain how a particular symmetrization of Bregman divergences called Jensen-Bregman distances yields exactly those Burbea-Rao divergences. We then proceed by defining skew Burbea-Rao divergences, and show that skew Burbea-Rao divergences amount in limit cases to compute Bregman divergences. We then prove that Burbea-Rao centroids are unique, and can be arbitrarily finely approximated by a generic iterative concave-convex optimization algorithm with guaranteed convergence property. In the second part of the paper, we consider the Bhattacharyya distance that is commonly used to measure overlapping degree of probability distributions. We show that Bhattacharyya distances on members of the same statistical exponential family amount to calculate a Burbea-Rao divergence in disguise. Thus we get an efficient algorithm for computing the Bhattacharyya centroid of a set of parametric distributions belonging to the same exponential families, improving over former specialized methods found in the literature that were limited to univariate or "diagonal" multivariate Gaussians. To illustrate the performance of our Bhattacharyya/Burbea-Rao centroid algorithm, we present experimental performance results for $k$-means and hierarchical clustering methods of Gaussian mixture models.Comment: 13 page

Aerodynamic characteristics of an F-8 aircraft configuration with a variable camber wing at Mach numbers from 0.70 to 1.15

A 0.1-scale model of an F-8 aircraft was tested in the Ames 14-Foot Transonic Wind Tunnel at Mach numbers from 0.7 to 1.15. Angle of attack was varied from -2 deg. to 22 deg. at sideslip angles of 0 deg and -5 deg. Reynolds number, dictated by the atmospheric stagnation pressure, varied with Mach number from 3.4 to 4.0 million based on mean aerodynamic chord. The model was configured with a wing designed to simulate the downward deflection of the leading and trailing edges of an advanced-technology-conformal-variable camber wing. This wing was also equipped with conventional (simple hinge) flaps. In addition, the model was tested with the basic F-8 wing to provide a reference for extrapolating to flight data. In general, at all Mach numbers the use of conformal flap deflections at both the leading edge and trailing edge resulted in slightly higher maximum lift coefficients and lower drag coefficients than with the use of simple hinge flaps. There were also found to be small improvements in the pitching-moment characteristics with the use of conformal flaps