Gerardo J. Vázquez

Continuous opinion model in small-world directed networks

In the compromise model of continuous opinions proposed by Deffuant et al., the states of two agents in a network can start to converge if they are neighbors and if their opinions are sufficiently close to each other, below a given threshold of tolerance ϵ. In directed networks, if agent i is a neighbor of agent j,j need not be a neighbor of i. In Watts–Strogatz networks we performed simulations to find the averaged number of final opinions 〈F〉 and their distribution as a function of ϵ and of the network structural disorder. In directed networks 〈F〉 exhibits a rich structure, being larger than in undirected networks for higher values of ϵ, and smaller for lower values of ϵ.

Interaction between an icosahedron Li 13 cluster and a graphene layer doped with a hydrogen atom

It is known that graphene reacts with atomic hydrogen to form a hydrogenated sheet of graphene. In order to understand the nature of the interaction between hydrogen and lithium in hydrogenated samples, we have carried out first principle calculations. Density functional theory and molecular dynamics were used to study the interaction between an icosahedron Li13 cluster, and a graphene layer doped with a hydrogen atom. It was found that a hydrogen atom is levitated from the graphene layer and absorbed into the cluster of Li at 300xa0K and atmospheric pressure, with a binding energy far exceeding that of the adsorption energy of a hydrogen atom on the graphene layer.

Stark effect in a wedge-shaped quantum box

Abstract The effect of an external applied electric field on the electronic ground-state energy of a quantum box with a geometry defined by a wedge is studied by carrying out a variational calculation. This geometry could be used as an approximation for a tip of a cantilever of an atomic force microscope. We study theoretically the Stark effect as function of the parameters of the wedge: its diameter, angular aperture and thickness; as well as function of the intensity of the external electric field applied along the axis of the wedge in both directions; pushing the carrier towards the wider or the narrower parts. A confining electronic effect, which is sharper as the wedge dimensions are smaller, is clearly observed for the first case. Besides, the sign of the Stark shift changes when the angular aperture is changed from small angles to angles θ > π . For the opposite field, the electronic confinement for large diameters is very small and it is also observed that the Stark shift is almost independent with respect to the angular aperture.

Stark effect on a geometry defined by a cake's slice

By using a variational calculation, we study the effect of an external applied electric field on the ground state of electrons confined in a quantum box with a geometry defined by a slice of a cake. This geometry is a first approximation for a tip of a cantilever of an atomic force microscope. By modeling the tip with the slice, we calculate the electronic ground-state energy as a function of the slices diameter, its angular aperture, its thickness and the intensity of the external electric field applied along the slice. For the applied field pointing to the wider part of the slice, a confining electronic effect in the opposite side is clearly observed. This effect is sharper as the angular slices aperture is smaller and there is more radial space to manifest itself.

Transition radiation in cholesteric liquid crystal

ABSTRACT We consider a constant velocity charged particle travelling in an arbitrary direction by a cholesteric liquid crystal. We calculate the time-dependent-induced polarisation in the cholesteric by the electric field generated by the charged particle. Thus, we express the radiation field originated by the induced dipole distribution in the cholesteric in terms of the cholesteric susceptibility. To simplify our procedure, we write Maxwell equations and the constitutive non-local equation for the cholesteric, in the Fourier space since in this representation the equations turn to be simple difference equations. We solve these equations iteratively by assuming small values for the cholesteric birefringence to find the first-order electric field produced by the charge particle immersed in the cholesteric. This allows us to obtain the dominant contributions of the radiation field one of which is the usual Cherenkov effect. We focus in the terms occurring for hypoluminic charged particle and calculate the radiated energy as a function of observing angle, frequency, velocity and direction with respect to the cholesteric axis. Graphical Abstract