Travelling waves associated with saddle-node bifurcation in weakly coupled CML

Weakly coupled CML can be analytically solved by using perturbative methods. This technique has been recently used to deduce analytical expressions for travelling waves. Nonetheless, the results were limited for periodic solutions far away from saddle-node bifurcation. In this Letter, this problem is solved and periodic solutions, arising from the individual dynamics, are totally characterised.     

The Gauss Theorem for Domain Decompositions in Sobolev Spaces

This paper belongs to a broad line of research leaded by Herrera, which encompasses a good number of numerical methods such as Localized Adjoint Method (LAM), Eulerian-Lagrangian LAM (ELAM) and Trefftz-Herrera Method. The results presented in this paper are required in order to incorporate Herrera's general theory in a Sobolev-space setting. In particular, this article introduces a class of partitions (or domain decompositions) whose internal boundaries belong to a category of manifolds with corners, here also presented. Then a version of Gauss (or divergence) theorem, in a wider sense, is established and an explicit integral formula is associated for any given linear partial differential operator L, its adjoint and concomitant. The structure of the bilinear concomitant induced by L is first determined. Then the required formula is given over that class of domain decompositions. Finally, an integral formula well on the way of the Green-Herrera formula is settled.     

Optimisation of 40 Gb/s wavelength converters based on four-wave mixing in a semiconductor optical amplifier

The optimum operating powers and wavelengths for a 40 Gb/s wavelength converter based on four-wave mixing in a semiconductor optical amplifier are inferred from experimental results. From these measurements, some general rules of thumb are derived for this kind of devices. Generally, the optimum signal power should be 10 dB lower than the pump power (−16 dB conversion efficiency) whereas the wavelength separation between the signal and the pump carrier should not be lower than about four times the signal bitrate (1.3 nm for 40 Gb/s RZ signals).     

Iron nano-clusters in ytterbium films: a 57Fe Mössbauer spectroscopic study

We have performed a Mössbauer study on iron clusters that are formed in ytterbium films prepared by vapor co-deposition onto kapton substrates kept at room temperature. The film thicknesses were chosen in a range between 2.5 and 2.8 $\upmu$ m. XRD of the films reveals a mixture of fcc- and hcp-like ytterbium. Iron concentrations were between 0.3 and 5 at %. All samples reveal hyperfine spectra attributed to only two types of iron clusters with well defined hyperfine parameters. The clusters are supposed to be formed at boundaries of hcp- and fcc-like grains. In addition there is found a small contribution from monomeric iron. Spectra taken at 4.2 K reveal a complex distribution of magnetic hyperfine fields. The dynamic origin of the spectral shape is supported by susceptibility data revealing spin-freezing at temperatures below ca. 10 K. This proves that the iron clusters have sizes on the order of nm.     

Characterization,optimization and surface physics aspects of in situ plasma mirror cleaning

Although the graphitic carbon contamination of synchrotron beamline optics has been an obvious problem for several decades, the basic mechanisms underlying the contamination process as well as the cleaning/remediation strategies are not understood and the corresponding cleaning procedures are still under development. In this study an analysis of remediation strategies all based on in situ low‐pressure RF plasma cleaning approaches is reported, including a quantitative determination of the optimum process parameters and their influence on the chemistry as well as the morphology of optical test surfaces. It appears that optimum results are obtained for a specific pressure range as well as for specific combinations of the plasma feedstock gases, the latter depending on the chemical aspects of the optical surfaces to be cleaned.     

Rank One Discrete Valuations of Power Series Fields

In this article we study rank one discrete valuations of the field k((X ₁,…, X _n )) whose center in k[[X ₁,…, X _n ]] is the maximal ideal. In Sections 2 to 6 we give a construction of a system of parametric equations describing such valuations. This amounts to finding a parameter and a field of coefficients. We devote Section 2 to finding an element of value 1, that is, a parameter. The field of coefficients is the residue field of the valuation, and it is given in Section 5.

The constructions given in these sections are not effective in the general case, because we need either to use Zorn's lemma or to know explicitly a section σ of the natural homomorphism R _v  → Δ _v between the ring and the residue field of the valuation v.

However, as a consequence of this construction, in Section 7, we prove that k((X ₁,…, X _n )) can be embedded into a field L((Y ₁,…, Y _n )), where L is an algebraic extension of k and the “extended valuation” is as close as possible to the usual order function.     

Shear as a source of inhomogeneity in general relativistic stellar models

We investigate the class of spherically symmetric, anisotropic (principal stresses unequal) fluids admitting the existence of a vector field, assumed to be orthogonal to the four velocity of the fluid, and with respect to which the Lie derivative of the metric tensor is proportional to the shear tensor. The physical variables, as well as the evolution equation of the bounday surface, are found for different models.     

Indirect methods of collocation: Trefftz‐Herrera collocation

A nonstandard collocation method (TH‐collocation) is presented, where collocation is used to construct specialized weighting functions instead of the solution itself, as it is usual, so that in this sense it is an indirect method. TH‐collocation is shown to be as accurate as standard collocation, but computationally far more efficient. The present article is the first of a series devoted to explore thoroughly collocation methods. The following classification of collocation methods is introduced: direct‐nonoverlapping; indirect‐nonoverlapping; direct‐overlapping; and indirect‐overlapping. Most of the effort reported in the literature has gone to direct‐nonoverlapping methods. The procedure presented in this article falls into the indirect‐nonoverlapping category and it is based on Trefftz‐Herrera formulation. © 1999 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 15: 709–738, 1999     

Melting a Hubbard dimer: benchmarks of ‘ALDA’ for quantum thermodynamics

The competition between evolution time, interaction strength, and temperature challenges our understanding of many-body quantum systems out-of-equilibrium. Here, we consider a benchmark system, the Hubbard dimer, which allows us to explore all the relevant regimes and calculate exactly the related average quantum work. At difference with previous studies, we focus on the effect of increasing temperature, and show how this can turn the competition between many-body interactions and driving field into synergy. We then turn to use recently proposed protocols inspired by density functional theory to explore if these effects could be reproduced by using simple approximations. We find that, up to and including intermediate temperatures, a method which borrows from ground-state adiabatic local density approximation improves dramatically the estimate for the average quantum work, including, in the adiabatic regime, when correlations are strong. However at high temperature and at least when based on the pseudo-LDA, this method fails to capture the counterintuitive qualitative dependence of the quantum work with interaction strength, albeit getting the quantitative estimates relatively close to the exact results.