Quantitative Concentration Inequalities for Empirical Measures on Non-compact Spaces

We establish quantitative concentration estimates for the empirical measure of many independent variables, in transportation distances. As an application, we provide some error bounds for particle simulations in a model mean field problem. The tools include coupling arguments, as well as regularity and moment estimates for solutions of certain diffusive partial differential equations.     

How regular can the boundary of a quadratic Siegel disk be?

In the family of quadratic polynomials with an irrationally indifferent fixed point, we show the existence of Siegel disks with a fine control on the degree of regularity of the linearizing map on their boundary. A general theorem is stated and proved. As a particular case, we show that in the quadratic family, there are Siegel disks whose boundaries are but not Jordan curves.

     

<Emphasis Type="Italic">m</Emphasis>-Dissipativity of Kolmogorov Operators Corresponding to Burgers Equations with Space-time White Noise

In this article, we prove new a priori estimates on the solutions of the Burgers equation driven by a space-time white noise and on the associated invariant measure. We also prove smoothing properties for the transition semi-group. This is obtained thanks to the introduction of a modified Kolmogorov operator. These results are then used to prove that the Kolmogorov operator associated to the Burgers equation is m-dissipative. This implies several properties on the Kolmogorov equation.      

Monte-Carlo simulation of laser diode sub-Poissonian light generation

When laser diodes are driven by high-impedance electrical sources, the variance of the number of photo-detection events counted over large time durations is less than the average number of events (sub-Poissonian light). This paper presents a Monte-Carlo simulation that keeps track of each level occupancy (0 or 1) in the conduction and valence bands, and of the number of light quanta in the optical cavity. When there is good electron–lattice thermal contact, the electron and hole temperatures remain equal to that of the lattice. In that case, the elementary laser-diode noise theory results are accurately reproduced by the simulation. But when the thermal contact is poor (or, almost equivalently, at high power levels), new effects occur (spectral-hole burning, temperature fluctuations, statistical fluctuations of the optical gain) that are difficult to handle theoretically. Our numerical simulation shows that the frequency domain over which the photo-current spectral density is below the shot-noise level becomes narrower as the optical power increases.     

Effect of high pressure processing on the preservation of frozen and re-thawed sliced cod (Gadus morhua) and salmon (Salmo salar) fillets

Cod and salmon are both widely found in the seafood market, but those products are easily spoiled. This work reports on the investigation of the effects of three moderate pressure values (150, 300 and 450?MPa) applied for 5?min at 20°C on crude sliced cod and salmon fillets. It was found that high pressure processing (HPP) significantly reduced the microbial load during refrigerated storage for up to 14 days. As expected, the most effective treatment was 450?MPa because it inhibited microbial growth. This process affected the hardness, lightness, lipid oxidation, protein denaturation and oxidation. The fish muscle composition (lipid amount and protein profile) played a main role in the changes promoted by pressure. HPP permits the shelf life of the raw product at 4°C to be increased with minimal changes in the organoleptic characteristics and to enable crude consumption.     

Finite size effects on structure and magnetism in mass-selected CoPt nanoparticles

In this paper, the one-way absorption property in one-dimensional dielectric/metal photonic crystal structure with a dielectric defect layer is studied. The effects of incident angle and state of polarization on one-way absorption behaviour of the anti-resonant (AR) mode are investigated. The normally incident wave from left to right propagation is totally allowed to penetrate to the structure but right to left propagation totally reflected at the same wavelength. It is found that, with increasing of the incident angle, the AR mode shifts to the lower wavelengths and its intensity decreases. Simultaneously, another AR mode with reversed one-way property appears at higher wavelength. The one-way behaviour on absorption is observed at the both states of polarizations but is localized on different wavelengths. Those effects, are suggesting that the proposed structure can be used as a direction sense polarization splitter or reflector/antireflector device.     

Time-dependent density functional theory molecular dynamics simulation of doubly charged uracil in gas phase

We use time-dependent density functional theory and Born-Oppenheimer molecular dynamics methods to investigate the fragmentation of doubly ionized uracil in gas phase. Different initial electronic excited states of the dication are obtained by removing electrons from different inner-shell orbitals of the neutral species. We show that shape-equivalent orbitals lead to very different fragmentation patterns revealing the importance of the intramolecular chemical environment. The results are in good agreement with ionion coincidence measurements of uracil collision with 100 keV protons.     

Tetraacylation of isobutene: first synthesis of 1,3,6,8-tetramethyl-2,7-naphthyridine

The tetxaacetylation of isobutene has been perfomed in AlCl₃/AcCl. Treatment of the crude reaction medium with liquid ammonia yields the title compound.     

A difluorosulfide as a Freon-free source of phosphonodifluoromethyl carbanion

The synthesis of difluoromethylphosphonates is becoming difficult due to environmental protective laws restricting the use of HCFCs and CFCs as starting chemicals. To circumvent this limitation, we report the preparation of a thioether as a new source of the lithiodifluoromethylphosphonate. This methodology avoiding the use of HCFCs involves a selective fluorination of sulfide followed by a thiaphilic addition of an organometallic reagent, which offers an alternative route to obtain phosphonodifluoromethyl carbanion. A contrasted reactivity, due to a medium effect, was also noted which allows addition of a wide range of electrophiles including nitroalkenes and DMF to thioethers.     

Cyclizations of 4-pentenyl, 5-hexenyl, 6-heptenyl, and 7-octenyl fluorinated radicals: a density functional theory theoretical study

The cyclization reactions of the 4-pentenyl, 5-hexenyl, 6-heptenyl, and 7-octenyl fluorinated and ether radicals have been studied by a hybrid Hartree-Fock density functional method. The reliability of this approach has been confirmed in agreement with experimental data and post-Hartree-Fock projected M?ller-Plesset second-order method. The analysis of the theoretical results shows that two factors are crucial for the determination of the regiochemistry and the reactivity of these reactions. The first factor is the ability of the starting radical to have a stable conformation in position to form the transition state, and the second one is the enthalpic effect of the reaction through the stability of the resulting cyclized radical. It should be pointed out that these factors are not linked to the polarity of the radicals due to the presence of CF2 groups.