Homenaje/Homenatge a María Jesús Rubiera Mata.

Sin resume

Solitons in combined linear and nonlinear lattice potentials

We study ordinary solitons and gap solitons (GSs) in the effectively one-dimensional Gross-Pitaevskii equation, with a combination of linear and nonlinear lattice potentials. The main points of the analysis are effects of the (in)commensurability between the lattices, the development of analytical methods, viz., the variational approximation (VA) for narrow ordinary solitons, and various forms of the averaging method for broad solitons of both types, and also the study of mobility of the solitons. Under the direct commensurability (equal periods of the lattices, the family of ordinary solitons is similar to its counterpart in the free space. The situation is different in the case of the subharmonic commensurability, with L_{lin}=(1/2)L_{nonlin}, or incommensurability. In those cases, there is an existence threshold for the solitons, and the scaling relation between their amplitude and width is different from that in the free space. GS families demonstrate a bistability, unless the direct commensurability takes place. Specific scaling relations are found for them too. Ordinary solitons can be readily set in motion by kicking. GSs are mobile too, featuring inelastic collisions. The analytical approximations are shown to be quite accurate, predicting correct scaling relations for the soliton families in different cases. The stability of the ordinary solitons is fully determined by the VK (Vakhitov-Kolokolov) criterion, while the stability of GS families follows an inverted ("anti-VK") criterion, which is explained by means of the averaging approximation.Comment: 9 pages, 6 figure

Modelling biological invasions: individual to population scales at interfaces

Extracting the population level behaviour of biological systems from that of the individual is critical in understanding dynamics across multiple scales and thus has been the subject of numerous investigations. Here, the influence of spatial heterogeneity in such contexts is explored for interfaces with a separation of the length scales characterising the individual and the interface, a situation that can arise in applications involving cellular modelling. As an illustrative example, we consider cell movement between white and grey matter in the brain which may be relevant in considering the invasive dynamics of glioma. We show that while one can safely neglect intrinsic noise, at least when considering glioma cell invasion, profound differences in population behaviours emerge in the presence of interfaces with only subtle alterations in the dynamics at the individual level. Transport driven by local cell sensing generates predictions of cell accumulations along interfaces where cell motility changes. This behaviour is not predicted with the commonly used Fickian diffusion transport model, but can be extracted from preliminary observations of specific cell lines in recent, novel, cryo-imaging. Consequently, these findings suggest a need to consider the impact of individual behaviour, spatial heterogeneity and especially interfaces in experimental and modelling frameworks of cellular dynamics, for instance in the characterisation of glioma cell motility

Dust growth in molecular cloud envelopes: a numerical approach

Variations in the grain size distribution are to be expected in the interstellar medium (ISM) due to grain growth and destruction. In this work, we present a dust collision model to be implemented inside a magnetohydrodynamical (MHD) code that takes into account grain growth and shattering of charged dust grains of a given composition (silicate or graphite). We integrate this model in the MHD code Athena, and builds on a previous implementation of the dynamics of charged dust grains in the same code. To demonstrate the performance of this coagulation model, we study the variations in the grain size distribution of a single-sized population of dust with radius 0.05 $\mu$m inside several dust filaments formed during a 2D MHD simulation. We also consider a realistic dust distribution with sizes ranging from 50 \AA~to 0.25 $\mu$m and analyze both the variations in the size distribution for graphite and silicates, as well as of the far ultraviolet extinction curve. From the obtained results, we conclude that the methodology here presented, based on the MHD evolution of the equation of motion for a charged particle, is optimal for studying the coagulation of charged dust grains in a diffuse regime such as a molecular cloud envelope. Observationally, these variations in the dust size distribution are translated into variations in the far ultraviolet extinction curve, and they are mainly caused by small graphite dust grains.Comment: Accepted for publication in Ap

Flexible magnetoelectronics: some aspects of the development of hibrid thin film structures

This work was developed under support of the “Laboratory of Physical Sensoric” project of Ural Federal University and ACTIMAT-ETORTEK grant of UPV-EHU and The Basque Country Government

Giant magnetoimpedance of FeNi-based nanostructures deposited onto glass and flexible substrates

This work was supported in part by the Basque Government through the Actimat Project under Grant IE13-380

Stable two-dimensional solitons supported by radially inhomogeneous self-focusing nonlinearity

We demonstrate that modulation of the local strength of the cubic self-focusing (SF) nonlinearity in the two-dimensional (2D) geometry, in the form of a circle with contrast $\Delta g$ of the SF coefficient relative to the ambient medium with a weaker nonlinearity, stabilizes a family of fundamental solitons against the critical collapse. The result is obtained in an analytical form, using the variational approximation (VA) and Vakhitov-Kolokolov (VK) stability criterion, and corroborated by numerical computations. For the small contrast, the stability interval of the soliton's norm scales as $\Delta N\sim \Delta g$ (the replacement of the circle by an annulus leads to a reduction of the stability region by perturbations breaking the axial symmetry). To further illustrate this mechanism, we demonstrate, in an exact form, the stabilization of 1D solitons against the critical collapse under the action of a locally enhanced quintic SF nonlinearity.Comment: 3 pages, 2 figure, to appear in Optics Letter

Symbiotic Solitons in Heteronuclear Multicomponent Bose-Einstein condensates

We show that bright solitons exist in quasi-one dimensional heteronuclear multicomponent Bose-Einstein condensates with repulsive self-interaction and attractive inter-species interaction. They are remarkably robust to perturbations of initial data and collisions and can be generated by the mechanism of modulational instability. Some possibilities for control and the behavior of the system in three dimensions are also discussed