Directly diode-pumped Yb3+:SrY4(SiO4)3O regenerative amplifier

We report a regenerative amplifier based on an Yb-doped apatite crystal: Yb3+:SrY4(SiO4)3O (Yb:SYS). We obtained 420-fs pulses at a central wavelength of 1066 nm with an energy of 100 microJ at 300 Hz after compression. To the best of our knowledge, this system is the first regenerative amplifier based on an Yb:SYS crystal and provides duration among the shortest ones generated by a directly diode-pumped regenerative amplifier.     

Radiation forces on a Rayleigh dielectric sphere in a patterned optical near field

We report on the study of the radiation forces exerted on a Rayleigh dielectric particle by a patterned optical near-field landscape at an interface decorated with resonant gold nanostructures. This configuration allows for the generation of a large array of surface subwavelength optical traps from an extended collimated beam, which may be of interest for parallel optical manipulation and sorting of submicrometer objects.     

Synthesis of new porphyrins with peripheral conjugated chelates and their use for the preparation of porphyrin dimers linked by metal ions

This article describes the preparation of several new porphyrins bearing chelating peripheral groups fully conjugated with the macrocyclic pi-system. Treatment of a 2-nitro-meso-tetraarylporphyrin with phosphite gave a cyclic enamine, whose formylation gave an enaminoaldehyde. The thio analogue was obtained on treatment with Lawesson's reagent. The same reagent was also used to obtain the isomeric thioenaminoketone chelates. A enaminoketone ligand was prepared from a porphyrinic pyrrolone. All these ligands, as internal nickel complexes, could be metalated with palladium to yield porphyrinic dimers. The dimers obtained from enaminoketones and thioketones show a trans geometry, while in the enaminoaldehyde and -thioaldehyde series the cis isomer is thermodynamically favored. The bathochromic shifts of the electronic spectra of the aldehyde-derived dimers illustrate the strong electronic effect of peripheral metalation and dimerization. However, in the case of the pyrrolone-derived ligand, opposite effects were observed, due to partial reconstitution of the porphyrin chromophore on complexation. As with the dimers derived from enaminoketones, the dimers derived from the new ligands show typical splitting (up to 190 mV) of the electrochemical waves confirming large porphyrin-porphyrin interactions.     

New scaffolds for supramolecular chemistry: upper-rim fully tethered 5-methyleneureido-5'-methyl-2,2'-bipyridyl cyclodextrins

Seven upper-rim fully tethered cyclodextrins (URFT-CDs) have been synthesised in a good average coupling yield using the one-step "phosphine imide" approach and their metal complexation behaviour with lanthanides and transition metals was explored. We observed that the A-TE-E light conversion process (antennae effect) occurs in the URFT-CD lanthanide complexes. A molecular redox switch based on the corresponding iron complexes is also reported. A reversible intramolecular translocation of the FeII and FeIII ions, between two distinct binding cavities has been monitored spectroscopically and achieved by chemical triggering. Finally, a negative allosteric control of ion recognition through the formation of a CD pseudocryptand is discussed.     

Modelling of massive particulates for breakwater engineering using coupled FEMDEM and CFD

The seaward slope of many breakwaters consists of thousands of interlocking units of rock or concrete comprising a massive granular system of large elements each weighing tens of tonnes. The dumped quarry materials in the core are protected by progressively coarser particulates. The outer armour layer of freely placed units is intended to both dissipate wave energy and remain structurally stable as strong flows are drawn in and out of the particulate core. Design guidance on the mass and shape of these units is based on empirical equations derived from scaled physical model tests. The main failure mode for armour layers exposed to severe storms is hydraulic instability where the armour units of concrete or rock are subjected to uplift and drag forces which can in turn lead to rocking, displacement and collisions sufficient to cause breakage of units. Recently invented armour unit designs making up such granular layered system owe much of their success to the desirable emergent properties of interlock and porosity and how these combine with individual unit structural strength and inertial mass. Fundamental understanding of the forces governing such wave-structure interaction remains poor. We use discrete element and combined finite-discrete element methods to model the granular solid skeleton of randomly packed units coupled to a CFD code which resolves the wave dynamics through an interface tracking technique. The CFD code exploits several methods including a compressive advection scheme, node movement, and general mesh optimization. We provide the engineering context and report progress towards the numerical modelling of instability in these massive granular systems.     

An example of the complementarity of laser‐induced breakdown spectroscopy and Raman microscopy for wall painting pigments analysis

Laser‐induced breakdown spectroscopy (LIBS) and Raman microscopy were used for the identification of pigments in wall painting. Raman spectroscopy, which provides the molecular ‘fingerprint’ of the compound, is nowadays widely used by the archaeometry community, especially for pigment analysis. LIBS, which provides the elementary composition of samples, is a rapid noncontact method, enabling layer‐by‐layer analysis through a precise laser ablation of the sample. This work deals with the behavior of pigments after a LIBS analysis, by trying to identify the compounds before and after the laser shot. Six commercial pigments prepared with the fresco technique were investigated: ultramarine blue, red lead, charcoal, a yellow and a red ochre, and a green earth. Raman spectra, acquired on the sample surface and in the crater induced by LIBS analysis, were compared. The results show that these pigments are well recognized after a LIBS measurement. The analysis of green earth illustrates that the combination of these two techniques gives complete information from a sample. Copyright © 2007 John Wiley & Sons, Ltd.     

Adaptation of the Generic PDE’s Results to the Notion of Prevalence

Many generic results have been proved, especially concerning the qualitative behaviour of solutions of partial differential equations. Recently, a new notion of “almost always”, the prevalence, has been developed for vectorial spaces. This notion is interesting since, for example, prevalence sets are equivalent to the full Lebesgue measure sets in finite dimensional spaces. The purpose of this article is to adapt the generic PDE’s results to the notion of prevalence. In particular, we consider the cases where Sard–Smale theorems or arguments of analytic perturbations of the parameters are used. Dedicated to Professor Pavol Brunovsky in honor of his 70th birthday.     

Approximation of the Laplace and Stokes operators with Dirichlet boundary conditions through volume penalization: a spectral viewpoint

We report the results of a study on the spectral properties of Laplace and Stokes operators modified with a volume penalization term designed to approximate Dirichlet conditions in the limit when a penalization parameter, \(\eta \) , tends to zero. The eigenvalues and eigenfunctions are determined either analytically or numerically as functions of \(\eta \) , both in the continuous case and after applying Fourier or finite difference discretization schemes. For fixed \(\eta \) , we find that only the part of the spectrum corresponding to eigenvalues \(\lambda \lesssim \eta ^{-1}\) approaches Dirichlet boundary conditions, while the remainder of the spectrum is made of uncontrolled, spurious wall modes. The penalization error for the controlled eigenfunctions is estimated as a function of \(\eta \) and \(\lambda \) . Surprisingly, in the Stokes case, we show that the eigenfunctions approximately satisfy, with a precision \(O(\eta )\) , Navier slip boundary conditions with slip length equal to \(\sqrt{\eta }\) . Moreover, for a given discretization, we show that there exists a value of \(\eta \) , corresponding to a balance between penalization and discretization errors, below which no further gain in precision is achieved. These results shed light on the behavior of volume penalization schemes when solving the Navier–Stokes equations, outline the limitations of the method, and give indications on how to choose the penalization parameter in practical cases.     

Exponentiality of First Passage Times of Continuous Time Markov Chains

Let \((X,\mathbb{P}_{x})\) be a continuous time Markov chain with finite or countable state space S and let T be its first passage time in a subset D of S. It is well known that if μ is a quasi-stationary distribution relative to T, then this time is exponentially distributed under  \(\mathbb {P}_{\mu}\) . However, quasi-stationarity is not a necessary condition. In this paper, we determine more general conditions on an initial distribution μ for T to be exponentially distributed under  \(\mathbb{P}_{\mu}\) . We show in addition how quasi-stationary distributions can be expressed in terms of any initial law which makes the distribution of T exponential. We also study two examples in branching processes where exponentiality does imply quasi-stationarity.