Statistical Mechanics Characterization of Neuronal Mosaics

The spatial distribution of neuronal cells is an important requirement for achieving proper neuronal function in several parts of the nervous system of most animals. For instance, specific distribution of photoreceptors and related neuronal cells, particularly the ganglion cells, in mammal's retina is required in order to properly sample the projected scene. This work presents how two concepts from the areas of statistical mechanics and complex systems, namely the \emph{lacunarity} and the \emph{multiscale entropy} (i.e. the entropy calculated over progressively diffused representations of the cell mosaic), have allowed effective characterization of the spatial distribution of retinal cells.Comment: 3 pages, 1 figure, The following article has been submitted to Applied Physics Letters. If it is published, it will be found online at http://apl.aip.org

On quasi-Jacobi and Jacobi-quasi bialgebroids

We study quasi-Jacobi and Jacobi-quasi bialgebroids and their relationships with twisted Jacobi and quasi Jacobi manifolds. We show that we can construct quasi-Lie bialgebroids from quasi-Jacobi bialgebroids, and conversely, and also that the structures induced on their base manifolds are related via a quasi Poissonization

Effects of Random Biquadratic Couplings in a Spin-1 Spin-Glass Model

A spin-1 model, appropriated to study the competition between bilinear (J_{ij}S_{i}S_{j}) and biquadratic (K_{ij}S_{i}^{2}S_{j}^{2}) random interactions, both of them with zero mean, is investigated. The interactions are infinite-ranged and the replica method is employed. Within the replica-symmetric assumption, the system presents two phases, namely, paramagnetic and spin-glass, separated by a continuous transition line. The stability analysis of the replica-symmetric solution yields, besides the usual instability associated with the spin-glass ordering, a new phase due to the random biquadratic couplings between the spins.Comment: 16 pages plus 2 ps figure

Arbitrary bi-dimensional finite strain crack propagation

In the past two decades numerous numerical procedures for crack propagation have been developed. Lately, enrichment methods (either local, such as SDA or global, such as XFEM) have been applied with success to simple problems, typically involving some intersections. For arbitrary finite strain propagation, numerous difficulties are encountered: modeling of intersection and coalescence, step size dependence and the presence of distorted finite elements. In order to overcome these difficulties, an approach fully capable of dealing with multiple advancing cracks and self-contact is presented (see Fig.1). This approach makes use of a coupled Arbitrary Lagrangian-Eulerian method (ALE) and local tip remeshing. This is substantially less costly than a full remeshing while retaining its full versatility. Compared to full remeshing, angle measures and crack paths are superior. A consistent continuationbased linear control is used to force the critical tip to be exactly critical, while moving around the candidate set. The critical crack front is identified and propagated when one of the following criteria reaches a material limiting value: (i) the stress intensity factor; or (ii) the element-ahead tip stress. These are the control equations. The ability to solve crack intersection and coalescence problems is shown. Additionally, the independence from crack tip and step size and the absence of blade and dagger-shaped finite elements is observed. Classic benchmarks are computed leading to excellent crack path and load-deflection results, where convergence rate is quadratic