Nonlinear unbalanced bessel beams: stationary conical waves supported by nonlinear losses

Nonlinear losses accompanying self-focusing substantially impact the dynamic balance of diffraction and nonlinearity, permitting the existence of localized and stationary solutions of the 2D + 1 nonlinear Schr?dinger equation, which are stable against radial collapse. These are featured by linear, conical tails that continually refill the nonlinear, central spot. An experiment shows that the discovered solution behaves as a strong attractor for the self-focusing dynamics in Kerr media.     

Universal statistics of the critical depinning force of elastic systems in random media

We study the rescaled probability distribution of the critical depinning force of an elastic system in a random medium. We put in evidence the underlying connection between the critical properties of the depinning transition and the extreme value statistics of correlated variables. The distribution is Gaussian for all periodic systems, while in the case of random manifolds there exists a family of universal functions ranging from the Gaussian to the Gumbel distribution. Both of these scenarios are a priori experimentally accessible in finite, macroscopic, disordered elastic systems.     

Concise and practical synthesis of C-glycosyl ketones from sugar benzothiazoles and their transformation into chiral tertiary alcohols

[Reaction: see text]. A collection of 13 unsymmetrical ketones, each one featuring a sugar (d-glucosyl, d-galactosyl, d-mannosyl, and l-fucosyl) and an aglycone moiety (phenyl, 2-thiazolyl, TMS-ethynyl, allyl, and 1-propenyl) was prepared by a uniform route based on the use of benzothiazole as a carbonyl group equivalent. Succinctly, C-glycosylbenzothiazoles readily prepared by addition of 2-lithiobenzothiazole to sugar lactones and deoxygenation, were subjected to a one-pot reaction sequence involving N-methylation of the heterocyclic ring by MeOTf, treatment of the N-methylbenzothiazolium salt with a Grignard reagent, and HgCl(2)-promoted hydrolysis of the benzothiazoline thus formed. The resulting ketones were isolated in yields varying from 35 to 80%. Treatment of the sugar ketones with various organometals containing the phenyl, 2-thiazolyl, TMS-ethynyl, or ethynyl group as a substituent afforded chiral tertiary alcohols. These addition reactions were highly stereoselective as observed by crude NMR analysis and isolation of a single epimer in high yield in each case examined. However, because of the complexity of the reagents involved, the stereochemical outcome of these reactions appears to be difficult to rationalize by simple classical steric models, thus, ab initio studies taking into account the role of the sugar fragment are advisable. An interesting synthetic elaboration of a propargylic alcohol containing the thiazole ring into a propargylic alcohol bearing the formyl and carboxylate groups is reported.     

Enantiorecognition on solid chiral selectors using microbatch technology: an example of limitation in case of strong association in the racemate

When they were independently tested, the enantiomers of N,N'-bis(salicylidene)-trans-1,2-cyclohexanediamine showed a large difference in adsorption on new chiral selectors using microbatch technology. Surprisingly, when these enantiomers were applied on the same supports as a racemic mixture, no discrimination was observed even though suitable adsorption existed. When a mixture enriched in one enantiomer (scalemic mixture) was applied, the resulting supernatant contained the racemic form and the enantiomer in excess was adsorbed on the support together with a part of racemate. This behavior, which militates in favor of a strong heterochiral dimer formation in the racemate, was revealed using microbatch technology but remained hidden on classical column chromatography on chiral support. Molecular dynamics calculations corroborate this hypothesis, showing a favorite binding mode of the heterochiral dimer, which is stabilized by various inter- and intramolecular interactions. Our findings may be considered as a new limitation of microbatch technology, but they may have some inference in case of chiral amplification using the N,N'-bis(salicylidene)-trans-1,2-cyclohexanediamine enantiomers as chiral ligands.     

Carbynes phonons: a tight binding force field

Modeling the vibrational structure of linear carbon chains has proved to be a difficult task with present first-principles calculations. This limits their applicability for the interpretation of experimental data, such as Raman scattering experiments on linear carbon chains within nanotubes. These limitations can be overcome by means of a simple tight binding scheme for pi-electrons. In this work a force field for the calculation of longitudinal phonon dispersion branches is built on the basis of bond-bond polarizabilities and just three parameters. The so obtained phonon dispersion branches are in very good agreement with the experimental data on carbynes in different environments and polyynes of any length. The model is discussed in relation to the importance of long range vibrational interactions in carbynes. The physical phenomena affecting their vibrational properties (i.e., Kohn anomaly, electron-phonon coupling) can be accurately and analytically described by the present approach.     

Trajectories of differential inclusions with state constraints

The paper deals with solutions of a differential inclusion constrained to a compact convex set Ω. Here F is a compact, possibly non-convex valued, Lipschitz continuous multifunction, whose convex closure co F satisfies a strict inward pointing condition at every boundary point x∈∂Ω. Given a reference trajectory x^?(⋅) taking values in an ε-neighborhood of Ω, we prove the existence of a second trajectory x:[0,T]?Ω which satisfies . As shown by an earlier counterexample, this bound is sharp.     

On Two Superintegrable Nonlinear Oscillators in N Dimensions

We consider the classical superintegrable Hamiltonian system given by

Chemically controlled self-assembly of [2]pseudorotaxanes based on 1,2-bis(benzimidazolium)ethane cations and 24-crown-8 macrocycles

Cations derived from 1,2-bis(benzimidazolium)ethane can penetrate the cavity of dibenzo-24-crown-8 macrocycles to produce a new family of [2]pseudorotaxanes. These supramolecular structures are held together by a series of charge-assisted hydrogen bonds (+)N-H[dot dot dot]O, ion-dipole and pi-stacking interactions. These new adducts were fully characterised by NMR spectroscopy, ESI mass spectrometry and single-crystal X-ray diffraction. The effect of electron-donating and electron-withdrawing groups on the association constants was also analyzed. Chemical control of the threading/unthreading process was acheived by the alternate addition of acid and base.     

Experimental evidence of localized oscillations in the photosensitive chlorine dioxide-iodine-malonic acid reaction

The interaction between Hopf and Turing modes has been the subject of active research in recent years. We present here experimental evidence of the existence of mixed Turing-Hopf modes in a two-dimensional system. Using the photosensitive chlorine dioxide-iodine-malonic acid reaction (CDIMA) and external constant background illumination as a control parameter, standing spots oscillating in amplitude and with hexagonal ordering were observed. Numerical simulations in the Lengyel-Epstein model for the CDIMA reaction confirmed the results.     

On Stabilized Point Spectra of Multivalued Systems

Let H be an infinite dimensional Hilbert space. Denote by Λ (E, F) the set of all for which the multivalued system 0 ∈ (F − λ E) (x) admits a nonzero solution x ∈ H. One says that Λ (E, F) is the point spectrum of the pair (E, F). It is well known that Λ (E, F) does not behave in a stable manner with respect to perturbations in the argument (E, F). The purpose of this note is to study the outer-semicontinuous hull (or graph-closure) of the mapping Λ.