On the variational structure of breather solutions

In this paper we give a systematic and simple account that put in evidence that many breather solutions of integrable equations satisfy suitable variational elliptic equations, which also implies that the stability problem reduces in some sense to $(i)$ the study of the spectrum of explicit linear systems (\emph{spectral stability}), and $(ii)$ the understanding of how bad directions (if any) can be controlled using low regularity conservation laws. We exemplify this idea in the case of the modified Korteweg-de Vries (mKdV), Gardner, and sine-Gordon (SG) equations. Then we perform numerical simulations that confirm, at the level of the spectral problem, our previous rigorous results, where we showed that mKdV breathers are $H^2$ and $H^1$ stable, respectively. In a second step, we also discuss the Gardner and the Sine-Gordon cases, where the spectral study of a fourth-order linear matrix system is the key element to show stability. Using numerical methods, we confirm that all spectral assumptions leading to the $H^2\times H^1$ stability of SG breathers are numerically satisfied, even in the ultra-relativistic, singular regime. In a second part, we study the periodic mKdV case, where a periodic breather is known from the work of Kevrekidis et al. We rigorously show that these breathers satisfy a suitable elliptic equation, and we also show numerical spectral stability. However, we also identify the source of nonlinear instability in the case described in Kevrekidis et al. Finally, we present a new class of breather solution for mKdV, believed to exist from geometric considerations, and which is periodic in time and space, but has nonzero mean, unlike standard breathers.Comment: 55 pages; This paper is an improved version of our previous paper 1309.0625 and hence we replace i

Orbital eigenchannel analysis for ab-initio quantum transport calculations

We show how to extract the orbital contribution to the transport eigenchannels from a first-principles quantum transport calculation in a nanoscopic conductor. This is achieved by calculating and diagonalizing the first-principles transmission matrix reduced to selected scattering cross-sections. As an example, the orbital nature of the eigenchannels in the case of Ni nanocontacts is explored, stressing the difficulties inherent to the use of non-orthogonal basis sets and first-principles Hamiltonians.Comment: 5 pages, 5 figurs; replaced with final version, introduction revised; to be published in PR

Modeling contact formation between atomic-sized gold tips via molecular dynamics

The formation and rupture of atomic-sized contacts is modelled by means of molecular dynamics simulations. Such nano-contacts are realized in scanning tunnelling microscope and mechanically controlled break junction experiments. These instruments routinely measure the conductance across the nano-sized electrodes as they are brought into contact and separated, permitting conductance traces to be recorded that are plots of conductance versus the distance between the electrodes. One interesting feature of the conductance traces is that for some metals and geometric configurations a jump in the value of the conductance is observed right before contact between the electrodes, a phenomenon known as jump-to-contact. This paper considers, from a computational point of view, the dynamics of contact between two gold nano-electrodes. Repeated indentation of the two surfaces on each other is performed in two crystallographic orientations of face-centred cubic gold, namely (001) and (111). Ultimately, the intention is to identify the structures at the atomic level at the moment of first contact between the surfaces, since the value of the conductance is related to the minimum cross-section in the contact region. Conductance values obtained in this way are determined using first principles electronic transport calculations, with atomic configurations taken from the molecular dynamics simulations serving as input structures.Comment: 6 pages, 4 figures, conference submissio

New determination of abundances and stellar parameters for a set of weak G-band stars

Weak G-band (wGb) stars are very peculiar red giants almost devoided of carbon and often mildly enriched in lithium. Despite their very puzzling abundance patterns, very few detailed spectroscopic studies existed up to a few years ago, preventing any clear understanding of the wGb phenomenon. We recently proposed the first consistent analysis of published data for 28 wGb stars and identified them as descendants of early A-type to late B-type stars, without being able to conclude on their evolutionary status or the origin of their peculiar abundance pattern. We used newly obtained high-resolution and high SNR spectra for 19 wGb stars in the southern and northern hemisphere to homogeneously derive their fundamental parameters, metallicities, as well as the spectroscopic abundances for Li, C, N, O, Na, Sr, and Ba. We also computed dedicated stellar evolution models that we used to determine the masses and to investigate the evolutionary status and chemical history of the stars in our sample. We confirm that the wGb stars are stars in the mass range 3.2 to 4.2 M$_\odot$. We suggest that a large fraction could be mildly evolved stars on the SGB currently undergoing the 1st DUP, while a smaller number of stars are more probably in the core He burning phase at the clump. After analysing their abundance pattern, we confirm their strong N enrichment anti-correlated with large C depletion, characteristic of material fully processed through the CNO cycle to an extent not known in other evolved intermediate-mass stars. However, we demonstrate here that such a pattern is very unlikely due to self-enrichment. In the light of the current observational constraints, no solid self-consistent pollution scenario can be presented either, leaving the wGb puzzle largely unsolved.Comment: 19 pages , 14 figures, accepted for publication in Astronomy & Astrophysic

Charging of highly resistive granular metal films

We have used the Scanning Kelvin probe microscopy technique to monitor the charging process of highly resistive granular thin films. The sample is connected to two leads and is separated by an insulator layer from a gate electrode. When a gate voltage is applied, charges enter from the leads and rearrange across the sample. We find very slow processes with characteristic charging times exponentially distributed over a wide range of values, resulting in a logarithmic relaxation to equilibrium. After the gate voltage has been switched off, the system again relaxes logarithmically slowly to the new equilibrium. The results cannot be explained with diffusion models, but most of them can be understood with a hopping percolation model, in which the localization length is shorter than the typical site separation. The technique is very promising for the study of slow phenomena in highly resistive systems and will be able to estimate the conductance of these systems when direct macroscopic measurement techniques are not sensitive enough.Comment: 8 pages, 7 figure

Magnetic and orbital blocking in Ni nanocontacts

We address the fundamental question of whether magneto-resistance (MR) of atomic-sized contacts of Nickel is very large because of the formation of a domain wall (DW) at the neck. Using {\em ab initio} transport calculations we find that, as in the case of non-magnetic electrodes, transport in Ni nanocontacts depends very much on the orbital nature of the electrons. Our results are in agreement with several experiments in the average value of the conductance. On the other hand, contrary to existing claims, DW scattering does {\em not} account for large MR in Ni nanocontacts.Comment: 5 pages, 3 Figure