Heterobimetallic conducting polymers based on salophen complexes via electrosynthesis

In this work, we report the first electrochemical synthesis of two copolymeric bimetallic conducting polymers by a simple anodic electropolymerization method. The adopted precursors are electroactive transition metal (M = Ni, Cu and Fe) salophen complexes, which can be easily obtained by direct chemical synthesis. The resulting films, labeled poly-NiCu and poly-CuFe, were characterized by cyclic voltammetry in both organic and aqueous media, attenuated total reflectance Fourier transform infrared spectroscopy, UV-vis spectroscopy, scanning electron microscopy, and coupled energy dispersive X-ray spectroscopy. The films are conductive and exhibit great electrochemical stability in both organic and aqueous media (resistant over 100 cycles without significant loss in current response or changes in electrochemical behavior), which makes them good candidates for an array of potential applications. Electrochemical detection of ascorbic acid was performed using both materials

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

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

Regularized Linear Inversion with Randomized Singular Value Decomposition

In this work, we develop efficient solvers for linear inverse problems based on randomized singular value decomposition (RSVD). This is achieved by combining RSVD with classical regularization methods, e.g., truncated singular value decomposition, Tikhonov regularization, and general Tikhonov regularization with a smoothness penalty. One distinct feature of the proposed approach is that it explicitly preserves the structure of the regularized solution in the sense that it always lies in the range of a certain adjoint operator. We provide error estimates between the approximation and the exact solution under canonical source condition, and interpret the approach in the lens of convex duality. Extensive numerical experiments are provided to illustrate the efficiency and accuracy of the approach.Comment: 20 pages, 4 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

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

Tips for implementing multigrid methods on domains containing holes

As part of our development of a computer code to perform 3D `constrained evolution' of Einstein's equations in 3+1 form, we discuss issues regarding the efficient solution of elliptic equations on domains containing holes (i.e., excised regions), via the multigrid method. We consider as a test case the Poisson equation with a nonlinear term added, as a means of illustrating the principles involved, and move to a "real world" 3-dimensional problem which is the solution of the conformally flat Hamiltonian constraint with Dirichlet and Robin boundary conditions. Using our vertex-centered multigrid code, we demonstrate globally second-order-accurate solutions of elliptic equations over domains containing holes, in two and three spatial dimensions. Keys to the success of this method are the choice of the restriction operator near the holes and definition of the location of the inner boundary. In some cases (e.g. two holes in two dimensions), more and more smoothing may be required as the mesh spacing decreases to zero; however for the resolutions currently of interest to many numerical relativists, it is feasible to maintain second order convergence by concentrating smoothing (spatially) where it is needed most. This paper, and our publicly available source code, are intended to serve as semi-pedagogical guides for those who may wish to implement similar schemes.Comment: 18 pages, 11 figures, LaTeX. Added clarifications and references re. scope of paper, mathematical foundations, relevance of work. Accepted for publication in Classical & Quantum Gravit