Core of the Magnetic Obstacle

Rich recirculation patterns have been recently discovered in the electrically conducting flow subject to a local external magnetic termed "the magnetic obstacle" [Phys. Rev. Lett. 98 (2007), 144504]. This paper continues the study of magnetic obstacles and sheds new light on the core of the magnetic obstacle that develops between magnetic poles when the intensity of the external field is very large. A series of both 3D and 2D numerical simulations have been carried out, through which it is shown that the core of the magnetic obstacle is streamlined both by the upstream flow and by the induced cross stream electric currents, like a foreign insulated insertion placed inside the ordinary hydrodynamic flow. The closed streamlines of the mass flow resemble contour lines of electric potential, while closed streamlines of the electric current resemble contour lines of pressure. New recirculation patterns not reported before are found in the series of 2D simulations. These are composed of many (even number) vortices aligned along the spanwise line crossing the magnetic gap. The intensities of these vortices are shown to vanish toward to the center of the magnetic gap, confirming the general conclusion of 3D simulations that the core of the magnetic obstacle is frozen. The implications of these findings for the case of turbulent flow are discussed briefly.Comment: 14 pages, 9 figures, submitted to Journal of Turbulenc

Non-invasive methods of identifying and tracking wild squid

The ability to identify individual free-living animals in the field is an important method for studying their behavior. Apart from invasive external or internal tags, which may cause injury or abnormal behavior, most cephalopods cannot be tagged, as their skin is too soft and delicate for tag retention. Additionally, cephalopods remove many types of tags. However, body markings have been successfully used as a non invasive method to identify individuals of many different species of animals, including whale sharks, grey whales, seals, and zebras. We developed methods to sex and individually identify Caribbean reef squid, Sepiotheuthis sepioidea. Males showed distinct bright dots on their fins on a Basic Brown background and have a light line at the fin edge while the females had a gradual transition from Brown to Pale towards the edge of their fins without showing distinct fin-dots or lines. In the field we used four characters to distinguish individual S. sepioidea from each other – sex, relative size to each other, scars, and patterns of light-colored dots on their mantles and fins. These dot patterns are individually unique and constant in location through time. Observations in the field were backed up by an image database using illustrations and photography

Non-invasive methods of identifying and tracking wild squid

The ability to identify individual free-living animals in the field is an important method for studying their behavior. Apart from invasive external or internal tags, which may cause injury or abnormal behavior, most cephalopods cannot be tagged, as their skin is too soft and delicate for tag retention. Additionally, cephalopods remove many types of tags. However, body markings have been successfully used as a non invasive method to identify individuals of many different species of animals, including whale sharks, grey whales, seals, and zebras. We developed methods to sex and individually identify Caribbean reef squid, Sepiotheuthis sepioidea. Males showed distinct bright dots on their fins on a Basic Brown background and have a light line at the fin edge while the females had a gradual transition from Brown to Pale towards the edge of their fins without showing distinct fin-dots or lines. In the field we used four characters to distinguish individual S. sepioidea from each other – sex, relative size to each other, scars, and patterns of light-colored dots on their mantles and fins. These dot patterns are individually unique and constant in location through time. Observations in the field were backed up by an image database using illustrations and photography

On the analogy between streamlined magnetic and solid obstacles

Analogies are elaborated in the qualitative description of two systems: the magnetohydrodynamic (MHD) flow moving through a region where an external local magnetic field (magnetic obstacle) is applied, and the ordinary hydrodynamic flow around a solid obstacle. The former problem is of interest both practically and theoretically, and the latter one is a classical problem being well understood in ordinary hydrodynamics. The first analogy is the formation in the MHD flow of an impenetrable region -- core of the magnetic obstacle -- as the interaction parameter $N$, i.e. strength of the applied magnetic field, increases significantly. The core of the magnetic obstacle is streamlined both by the upstream flow and by the induced cross stream electric currents, like a foreign insulated insertion placed inside the ordinary hydrodynamic flow. In the core, closed streamlines of the mass flow resemble contour lines of electric potential, while closed streamlines of the electric current resemble contour lines of pressure. The second analogy is the breaking away of attached vortices from the recirculation pattern produced by the magnetic obstacle when the Reynolds number $Re$, i.e. velocity of the upstream flow, is larger than a critical value. This breaking away of vortices from the magnetic obstacle is similar to that occurring past a real solid obstacle. Depending on the inlet and/or initial conditions, the observed vortex shedding can be either symmetric or asymmetric.Comment: minor changes, accepted for PoF, 26 pages, 7 figure

The generalized Robinson-Foulds metric

The Robinson-Foulds (RF) metric is arguably the most widely used measure of phylogenetic tree similarity, despite its well-known shortcomings: For example, moving a single taxon in a tree can result in a tree that has maximum distance to the original one; but the two trees are identical if we remove the single taxon. To this end, we propose a natural extension of the RF metric that does not simply count identical clades but instead, also takes similar clades into consideration. In contrast to previous approaches, our model requires the matching between clades to respect the structure of the two trees, a property that the classical RF metric exhibits, too. We show that computing this generalized RF metric is, unfortunately, NP-hard. We then present a simple Integer Linear Program for its computation, and evaluate it by an all-against-all comparison of 100 trees from a benchmark data set. We find that matchings that respect the tree structure differ significantly from those that do not, underlining the importance of this natural condition.Comment: Peer-reviewed and presented as part of the 13th Workshop on Algorithms in Bioinformatics (WABI2013

Regularity for eigenfunctions of Schr\"odinger operators

We prove a regularity result in weighted Sobolev spaces (or Babuska--Kondratiev spaces) for the eigenfunctions of a Schr\"odinger operator. More precisely, let K_{a}^{m}(\mathbb{R}^{3N}) be the weighted Sobolev space obtained by blowing up the set of singular points of the Coulomb type potential V(x) = \sum_{1 \le j \le N} \frac{b_j}{|x_j|} + \sum_{1 \le i < j \le N} \frac{c_{ij}}{|x_i-x_j|}, x in \mathbb{R}^{3N}, b_j, c_{ij} in \mathbb{R}. If u in L^2(\mathbb{R}^{3N}) satisfies (-\Delta + V) u = \lambda u in distribution sense, then u belongs to K_{a}^{m} for all m \in \mathbb{Z}_+ and all a \le 0. Our result extends to the case when b_j and c_{ij} are suitable bounded functions on the blown-up space. In the single-electron, multi-nuclei case, we obtain the same result for all a<3/2.Comment: to appear in Lett. Math. Phy

An adaptive numerical method for the Vlasov equation based on a multiresolution analysis.

International audienceIn this paper, we present very first results for the adaptive solution on a grid of the phase space of the Vlasov equation arising in particles accelarator and plasma physics. The numerical algorithm is based on a semi-Lagrangian method while adaptivity is obtained using multiresolution analysis

Pharmacological Alterations of Anxious Behaviour in Mice Depending on Both Strain and the Behavioural Situation

A previous study comparing non-emotive mice from the strain C57BL/6/ByJ with ABP/Le mice showed ABP/Le to be more anxious in an open-field situation. In the present study, several compounds affecting anxiety were assayed on ABP/Le and C57BL/6/ByJ mice using three behavioural models of anxiety: the elevated plus-maze, the light-dark discrimination test and the free exploratory paradigm. The compounds used were the full benzodiazepine receptor agonist, chlordiazepoxide, and the antagonist, flumazenil, the GABAA antagonist, bicuculline, the full 5-HT1A agonist 8-OH-DPAT, and the mixed 5-HT1A/5-HT1B agonist, RU 24969. Results showed the effect of the compounds to be dependent on both the strain and the behavioural task. Several compounds found to be anxiolytic in ABP/Le mice had an anxiogenic effect on C57BL/6/ByJ mice. More behavioural changes were observed for ABP/Le in the elevated plus-maze, but the clearest findings for C57BL/6/ByJ mice were observed in the light-dark discrimination apparatus. These data demonstrate that anxious behaviour is a complex phenomenon which cannot be described by a single behavioural task nor by the action of a single compound

Interfacial separation between elastic solids with randomly rough surfaces: comparison between theory and numerical techniques

We study the distribution of interfacial separations P(u) at the contact region between two elastic solids with randomly rough surfaces. An analytical expression is derived for P(u) using Persson's theory of contact mechanics, and is compared to numerical solutions obtained using (a) a half-space method based on the Boussinesq equation, (b) a Green's function molecular dynamics technique and (c) smart-block classical molecular dynamics. Overall, we find good agreement between all the different approaches.Comment: 25 pages, 12 figure

Numerical Computations with H(div)-Finite Elements for the Brinkman Problem

The H(div)-conforming approach for the Brinkman equation is studied numerically, verifying the theoretical a priori and a posteriori analysis in previous work of the authors. Furthermore, the results are extended to cover a non-constant permeability. A hybridization technique for the problem is presented, complete with a convergence analysis and numerical verification. Finally, the numerical convergence studies are complemented with numerical examples of applications to domain decomposition and adaptive mesh refinement.Comment: Minor clarifications, added references. Reordering of some figures. To appear in Computational Geosciences, final article available at http://www.springerlink.co