Monte Carlo simulation study of exchange biased hysteresis loops in nanoparticles

We present the results of Monte Carlo simulations of the magnetic properties of a model for a single nanoparticle consisting in a ferromagnetic core surrounded by an antiferromagnetic shell. The simulations of hysteresis loops after cooling in a magnetic field display exchange bias effects. In order to understand the origin of the loop shifts, we have studied the thermal dependence of the shell and interface magnetizations under field cooling. These results, together with inspection of the snapshots of the configurations attained at low temperature, show the existence of a net magnetization at the interface which is responsible for the bias of the hysteresis loops.Comment: 9 pages, 3 figures embedded. To be published in Physica

Contact manifolds and generalized complex structures

We give simple characterizations of contact 1-forms in terms of Dirac structures. We also relate normal almost contact structures to the theory of Dirac structures.Comment: 12 pages, typos correcte

Living in an Irrational Society: Wealth Distribution with Correlations between Risk and Expected Profits

Different models to study the wealth distribution in an artificial society have considered a transactional dynamics as the driving force. Those models include a risk aversion factor, but also a finite probability of favoring the poorer agent in a transaction. Here we study the case where the partners in the transaction have a previous knowledge of the winning probability and adjust their risk aversion taking this information into consideration. The results indicate that a relatively equalitarian society is obtained when the agents risk in direct proportion to their winning probabilities. However, it is the opposite case that delivers wealth distribution curves and Gini indices closer to empirical data. This indicates that, at least for this very simple model, either agents have no knowledge of their winning probabilities, either they exhibit an ``irrational'' behavior risking more than reasonable.Comment: 7 pages, 8 figure

Modelling exchange bias in core/shell nanoparticles

We present an atomistic model of a single nanoparticle with core/shell structure that takes into account its lattice strucutre and spherical geometry, and in which the values of microscopic parameters such as anisotropy and exchange constants can be tuned in the core, shell and interfacial regions. By means of Monte Carlo simulations of the hysteresis loops based on this model, we have determined the range of microscopic parameters for which loop shifts after field cooling can be observed. The study of the magnetic order of the interfacial spins for different particles sizes and values of the interfacial exchange coupling have allowed us to correlate the appearance of loop asymmetries and vertical displacements to the existence of a fraction of uncompensated spins at the shell interface that remain pinned during field cycling, offering new insight on the microscopic origin of the experimental phenomenology.Comment: 7 pages, 3 figures. Contribution presented at HMM 2007 held at Napoli 4-6 June 2007. To be published in J. Phys. Condens. Matte

A regularizing iterative ensemble Kalman method for PDE-constrained inverse problems

We introduce a derivative-free computational framework for approximating solutions to nonlinear PDE-constrained inverse problems. The aim is to merge ideas from iterative regularization with ensemble Kalman methods from Bayesian inference to develop a derivative-free stable method easy to implement in applications where the PDE (forward) model is only accessible as a black box. The method can be derived as an approximation of the regularizing Levenberg-Marquardt (LM) scheme [14] in which the derivative of the forward operator and its adjoint are replaced with empirical covariances from an ensemble of elements from the admissible space of solutions. The resulting ensemble method consists of an update formula that is applied to each ensemble member and that has a regularization parameter selected in a similar fashion to the one in the LM scheme. Moreover, an early termination of the scheme is proposed according to a discrepancy principle-type of criterion. The proposed method can be also viewed as a regularizing version of standard Kalman approaches which are often unstable unless ad-hoc fixes, such as covariance localization, are implemented. We provide a numerical investigation of the conditions under which the proposed method inherits the regularizing properties of the LM scheme of [14]. More concretely, we study the effect of ensemble size, number of measurements, selection of initial ensemble and tunable parameters on the performance of the method. The numerical investigation is carried out with synthetic experiments on two model inverse problems: (i) identification of conductivity on a Darcy flow model and (ii) electrical impedance tomography with the complete electrode model. We further demonstrate the potential application of the method in solving shape identification problems by means of a level-set approach for the parameterization of unknown geometries

Discussing the nature of the EU: from the inter-state model to global constitutionalism

Historically, the European Union has been characterized by different legal formulations. Positions are divided, broadly speaking, between those that understand this entity as an international organization in the classical sense, to those others which claim that its features are actually of a Statenature, and that the obvious model of evolution would be the Federal State. In the end, all this leads us, undoubtedly, to the European constitutional project. In this work we give a brief account of all these proposals, and then we try to adopt a different point of view: for us, the nature of the European Union should not be looked for in the legal configuration of the political project, but also in the silent evolution -and not so silent- of a legal order, the European legal order, that is increasingly systematic, and that must boast a key position on the evolution towards a higher level of legal organization, global constitutionalism. In the building up of this proposal, we will appeal to the concept of global ethics and to the recent example of the CETA case of TJUE, which opens the European Legal system to alien influences.Históricamente, se ha caracterizado la Unión Europea mediante diversas fórmulas jurídicas. Las posiciones se dividen, a grandes rasgos, entre aquellas que conciben esta entidad como una organización internacional en sentido clásico, hasta aquellas que propugnan que sus rasgos son los propios de un Estado, y que su modelo evidente de evolución sería el Estado Federal. En el fondo de la cuestión se encuentra, sin duda, el proyecto constitucional europeo. En el presente trabajo damos breve cuenta de estas propuestas, para después optar por un punto de vista distinto de ellas: para nosotros, la naturaleza de la Unión Europea no debe buscarse sólo en la configuración jurídica del proyecto político, sino también en la propia evolución silenciosa -o no tanto- de un ordenamiento, el de la Unión Europea, que va ganando forma sistemática, y que debe ostentar una posición clave en la evolución hacia un nivel de organización jurídica mayor, el constitucionalismo global. En la construcción de esta propuesta, recurriremos al concepto de ética mundial y al ejemplo reciente del caso CETA del TJUE, que abre el sistema jurídico europeo a influencias externas