Interplay between sublattice and spin symmetry breaking in graphene

We study the effect of sublattice symmetry breaking on the electronic, magnetic, and transport properties of two-dimensional graphene as well as zigzag terminated one- and zero-dimensional graphene nanostructures. The systems are described with the Hubbard model within the collinear mean field approximation. We prove that for the noninteracting bipartite lattice with an unequal number of atoms in each sublattice, in-gap states still exist in the presence of a staggered on-site potential ±Δ/2. We compute the phase diagram of both 2D and 1D graphene with zigzag edges, at half filling, defined by the normalized interaction strength U/t and Δ/t, where t is the first neighbor hopping. In the case of 2D we find that the system is always insulating, and we find the Uc(Δ) curve above which the system goes antiferromagnetic. In 1D we find that the system undergoes a phase transition from nonmagnetic insulator for Umoment in the system is zero. We compute the transport properties of a heterojunction with two magnetic graphene ribbon electrodes connected to a finite length armchair ribbon and we find a strong spin filter effect.

Magnetism in graphene nanoislands

We study the magnetic properties of nanometer-sized graphene structures with triangular and hexagonal shapes terminated by zigzag edges. We discuss how the shape of the island, the imbalance in the number of atoms belonging to the two graphene sublattices, the existence of zero-energy states, and the total and local magnetic moment are intimately related. We consider electronic interactions both in a mean-field approximation of the one-orbital Hubbard model and with density functional calculations. Both descriptions yield values for the ground state total spin S consistent with Lieb’s theorem for bipartite lattices. Triangles have a finite S for all sizes whereas hexagons have S=0 and develop local moments above a critical size of ≈1.5  nm.

Logic-Based Outer Approximation for the Design of Discrete-Continuous Dynamic Systems with Implicit Discontinuities

We address the optimization of discrete-continuous dynamic optimization problems using a disjunctive multistage modeling framework, with implicit discontinuities, which increases the problem complexity since the number of continuous phases and discrete events is not known a-priori. After setting a fixed alternative sequence of modes, we convert the infinite-dimensional continuous mixed-logic dynamic (MLDO) problem into a finite dimensional discretized GDP problem by orthogonal collocation on finite elements. We use the Logic-based Outer Approximation algorithm to fully exploit the structure of the GDP representation of the problem. This modelling framework is illustrated with an optimization problem with implicit discontinuities (diver problem).

Logic-Based Outer-Approximation Algorithm for Solving Discrete-Continuous Dynamic Optimization Problems

We present an extension of the logic outer-approximation algorithm for dealing with disjunctive discrete-continuous optimal control problems whose dynamic behavior is modeled in terms of differential-algebraic equations. Although the proposed algorithm can be applied to a wide variety of discrete-continuous optimal control problems, we are mainly interested in problems where disjunctions are also present. Disjunctions are included to take into account only certain parts of the underlying model which become relevant under some processing conditions. By doing so the numerical robustness of the optimization algorithm improves since those parts of the model that are not active are discarded leading to a reduced size problem and avoiding potential model singularities. We test the proposed algorithm using three examples of different complex dynamic behavior. In all the case studies the number of iterations and the computational effort required to obtain the optimal solutions is modest and the solutions are relatively easy to find.

Méthode Fanjul: dosage pondéral des bétons légers et lourds

La détermination directe des caractéristiques de cisaillement des bétons par des essais universels est un problème qui reste encore une préoccupation majeure des chercheurs. La plupart des études disponibles consistent à appliquer un couple de torsion à un cylindre creux ayant un rapport épaisseur/rayon le plus faible possible. Ceci pour pouvoir élaborer un critère lié au comportement du matériau et non de la structure (Fourd et al. 1982). Cependant, ces essais peuvent présenter des dispersions liées aux problèmes de fragilité à la rupture ou de non homogénéité du matériau au sein de la paroi (Gotuwka et al. 1999). Pour cela, un dispositif expérimental original a été utilisé et qui consiste en la création de deux zones de contrainte nulle par l’emplacement de corps déformables au moment du coulage de l’éprouvette. De nouvelles conditions aux frontières sont créées permettant de transformer la sollicitation de compression en cisaillement plan sur une zone bien déterminée. L’utilisation de cette technique permet la détermination de l’influence de l’inclinaison du plan de rupture sur le comportement du béton en cisaillement. Le dispositif permet d’assurer la perpendicularité NOvEMBRE 2012 5 des génératrices du cylindre ainsi que la répartition et l’homogénéité des contraintes.

A Belief System's Organization Based on a Computational Model of the Dynamic Context: First Approximation

In this article we present a model of organization of a belief system based on a set of binary recursive functions that characterize the dynamic context that modifies the beliefs. The initial beliefs are modeled by a set of two-bit words that grow, update, and generate other beliefs as the different experiences of the dynamic context appear. Reason is presented as an emergent effect of the experience on the beliefs. The system presents a layered structure that allows a functional organization of the belief system. Our approach seems suitable to model different ways of thinking and to apply to different realistic scenarios such as ideologies.

On the Result of Invariance of the Closure Set of the Real Projections of the Zeros of an Important Class of Exponential Polynomials

In this paper we provide the proof of a practical point-wise characterization of the set RP defined by the closure set of the real projections of the zeros of an exponential polynomial P(z) = Σn j=1 cjewjz with real frequencies wj linearly independent over the rationals. As a consequence, we give a complete description of the set RP and prove its invariance with respect to the moduli of the c′ js, which allows us to determine exactly the gaps of RP and the extremes of the critical interval of P(z) by solving inequations with positive real numbers. Finally, we analyse the converse of this result of invariance.

Experiències senzilles de física recreativa: Conservació del moment lineal, efecte Coandă i emissió atòmica

La realització pràctica d’experiments és fonamental en qualsevol disciplina científica. Per això, en aquest treball exposem una sèrie d’experiències de física senzilles i sorprenents que ens permetran reforçar diversos conceptes físics d’una manera amena, utilitzant materials molt assequibles i barats. Amb la realització d’aquests experiments volem estimular la curiositat de l’alumnat i el plaer per la investigació i el descobriment de nous fenòmens físics. Aquestes experiències estan adreçades tant a estudiants d’educació secundària i batxillerat com a alumnes dels primers cursos d’universitat. Hem dissenyat i dut a terme experiències de diversos camps de la física, entre els quals hi ha algunes pràctiques per a posar de manifest la conservació del moment lineal, o l’efecte Coandă en fluids en moviment, i també experiments de física atòmica relacionats amb l’emissió atòmica en l’espectre visible, que posen de manifest la quantització de l’energia dels nivells atòmics. Amb aquestes experiències volem motivar els alumnes en l’estudi i l’interès per la física des d’una perspectiva diferent de l’habitual.