Jacobi Structures in R3\mathbb{R}^3

The most general Jacobi brackets in $\mathbb{R}^3$ are constructed after solving the equations imposed by the Jacobi identity. Two classes of Jacobi brackets were identified, according to the rank of the Jacobi structures. The associated Hamiltonian vector fields are also constructed

Magnetic structure and orbital ordering in BaCoO3 from first-principles calculations

Ab initio calculations using the APW+lo method as implemented in the WIEN2k code have been used to describe the electronic structure of the quasi-one-dimensional system BaCoO3. Both, GGA and LDA+U approximations were employed to study different orbital and magnetic orderings. GGA predicts a metallic ground state whereas LDA+U calculations yield an insulating and ferromagnetic ground state (in a low-spin state) with an alternating orbital ordering along the Co-Co chains, consistent with the available experimental data.Comment: 8 pages, 9 figure

Integration of Dirac-Jacobi structures

We study precontact groupoids whose infinitesimal counterparts are Dirac-Jacobi structures. These geometric objects generalize contact groupoids. We also explain the relationship between precontact groupoids and homogeneous presymplectic groupoids. Finally, we present some examples of precontact groupoids.Comment: 10 pages. Brief changes in the introduction. References update

Magnetic Field scaling of Relaxation curves in Small Particle Systems

We study the effects of the magnetic field on the relaxation of the magnetization of small monodomain non-interacting particles with random orientations and distribution of anisotropy constants. Starting from a master equation, we build up an expression for the time dependence of the magnetization which takes into account thermal activation only over barriers separating energy minima, which, in our model, can be computed exactly from analytical expressions. Numerical calculations of the relaxation curves for different distribution widths, and under different magnetic fields H and temperatures T, have been performed. We show how a \svar scaling of the curves, at different T and for a given H, can be carried out after proper normalization of the data to the equilibrium magnetization. The resulting master curves are shown to be closely related to what we call effective energy barrier distributions, which, in our model, can be computed exactly from analytical expressions. The concept of effective distribution serves us as a basis for finding a scaling variable to scale relaxation curves at different H and a given T, thus showing that the field dependence of energy barriers can be also extracted from relaxation measurements.Comment: 12 pages, 9 figures, submitted to Phys. Rev.

Emergence of communities on a coevolutive model of wealth interchange

We present a model in which we investigate the structure and evolution of a random network that connects agents capable of exchanging wealth. Economic interactions between neighbors can occur only if the difference between their wealth is less than a threshold value that defines the width of the economic classes. If the interchange of wealth cannot be done, agents are reconnected with another randomly selected agent, allowing the network to evolve in time. On each interaction there is a probability of favoring the poorer agent, simulating the action of the government. We measure the Gini index, having real world values attached to reality. Besides the network structure showed a very close connection with the economic dynamic of the system.Comment: 5 pages, 7 figure

Jacobi-Nijenhuis algebroids and their modular classes

Jacobi-Nijenhuis algebroids are defined as a natural generalization of Poisson-Nijenhuis algebroids, in the case where there exists a Nijenhuis operator on a Jacobi algebroid which is compatible with it. We study modular classes of Jacobi and Jacobi-Nijenhuis algebroids