On the isoperimetric problem with respect to a mixed Euclidean–Gaussian density

The isoperimetric problem with respect to the product-type density on the Euclidean space Rh×Rk is studied. In particular, existence, symmetry and regularity of minimizers is proved. In the special case k=1, also the shape of all the minimizers is derived. Finally, a conjecture about the minimality of large cylinders in the case k>1 is formulated.     

Superconductors in parallel field: Electromagnetic properties at the surface

Summary In the framework of the boson transformation method, a general approach to the study of finite-dimensionality superconductors is applied to the investigation of the electromagnetic properties of a semiinfinite superconductor and of a film of arbitrary thickness in the presence of a parallel external magnetic field. The magnetic-field and current density distributions near the surfaces are computed and numerical results are given for some typical cases. As an application, an estimation of the superheating field for type-II superconductor is obtained and compared with previous results.

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Riassunto Nell'àmbito del metodo della trasformazione bosonica, una tecnica generale per lo studio di superconduttori a dimensione finita è applicata allo studio delle proprietà elettromagnetiche di un superconduttore semi-infinito e di un film di spessore arbitrario. Sono calcolate le distribuzioni del campo magnetico e della densità di corrente, e sono riportati risultati numerici per qualche caso tipico. Infine, si ottiene, e si confronta con precedenti risultati, una stima del campo di surriscaldamento per superconduttori del II tipo.

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Резюме В рамках метода бозонного преобразования общий подход для исследования конечно-мерных сверхпроводников применяется к изучению электромагнитных свойств полубесконечного сверхпроводника и пленки произвольной толщины в присутствии параллельного внешнего магнитного поля. Вычисляются распределения магнитного поля и плотности тока вблизи поверхностей. Приводятся численные результаты для некоторых типичных случаев. Оценивается поле супернагревания для сверхпроводника второго рода. Оценка сравнивается с имеющимися результатами.

     

Electrosprayed Shrimp and Mushroom Nanochitins on Cellulose Tissue for Skin Contact Application

Cosmetics has recently focused on biobased skin-compatible materials. Materials from natural sources can be used to produce more sustainable skin contact products with enhanced bioactivity. Surface functionalization using natural-based nano/microparticles is thus a subject of study, aimed at better understanding the skin compatibility of many biopolymers also deriving from biowaste. This research investigated electrospray as a method for surface modification of cellulose tissues with chitin nanofibrils (CNs) using two different sources—namely, vegetable (i.e., from fungi), and animal (from crustaceans)—and different solvent systems to obtain a biobased and skin-compatible product. The surface of cellulose tissues was uniformly decorated with electrosprayed CNs. Biological analysis revealed that all treated samples were suitable for skin applications since human dermal keratinocytes (i.e., HaCaT cells) successfully adhered to the processed tissues and were viable after being in contact with released substances in culture media. These results indicate that the use of solvents did not affect the final cytocompatibility due to their effective evaporation during the electrospray process. Such treatments did not also affect the characteristics of cellulose; in addition, they showed promising anti-inflammatory and indirect antimicrobial activity toward dermal keratinocytes in vitro. Specifically, cellulosic substrates decorated with nanochitins from shrimp showed strong immunomodulatory activity by first upregulating then downregulating the pro-inflammatory cytokines, whereas nanochitins from mushrooms displayed an overall anti-inflammatory activity via a slight decrement of the pro-inflammatory cytokines and increment of the anti-inflammatory marker. Electrospray could represent a green method for surface modification of sustainable and biofunctional skincare products.     

The limit of <Emphasis Type="Italic">W</Emphasis><Superscript>1,1</Superscript> homeomorphisms with finite distortion

We show that the limit f of a weakly convergent sequence of W ^1,1 homeomorphisms f _j with finite distortion has finite distortion as well, provided that it is a homeomorphism. Moreover, the lower semicontinuity of the distortions is deduced both in case of outer and inner distortion.     

Concerning the reactivity of dioxiranes. Observations from experiments and theory

The challenging hypothesis of a "biphilic" (i.e., electrophilic vs nucleophilic) character for dioxirane reactivity, which envisages that electron-poor alkenes are attacked by dioxiranes in a nucleophilic fashion, could not be sustained experimentally. Rate data, which estimate Hammett "rho" values for the epoxidation of 3- or 4-substituted cinnamonitriles X x Ph-CH=CH-CN, unequivocally allow one to establish that dioxiranes epoxidize electrophilically even alkenes carrying electron-withdrawing groups. The greater propensity of methyl(trifluoromethyl)dioxirane TFDO (1b) to act as an electrophilic oxidant with respect to dimethyldioxirane DDO (1a) parallels the cathode reduction potentials for the two dioxiranes, as measured by cyclic voltammetry. A simple FMO approach for alkene epoxidation is helpful to conceive a likely rationale for the greater oxidizing power of TFDO as compared to DDO.     

Wavefront sensing issues in MCAO

The problematic of wavefront sensing in Multiconjugate Adaptive Optics (MCAO) is addressed in this article. We first focus on the sky coverage estimation which drives, in particular, the choice between natural and laser guide stars and therefore has a major impact on wavefront sensor design. Then a comparison between star oriented and layer oriented concepts is proposed. Analytical developments and optimization of the concepts are derived in the simplest MCAO case: the ground layer AO system. From this study, advantages and drawbacks of each concept are highlighted. To cite this article: T. Fusco et al., C. R. Physique 6 (2005).     

Enhanced downconversion of UV light by resonant scattering of aluminum nanoparticles

Metallic nanoparticles are known to enhance nonlinear optical processes due to a local enhancement of the optical field. This strategy has been proposed to enhance downconversion in thin film solar cells, but has various disadvantages, among which is the fact that the enhancement occurs only in a tiny volume close to the particles. We report on a very different physical mechanism that can lead to significant downconversion enhancement, namely, that of resonant light scattering, and which is a large volume effect. We show that only a tiny amount of resonantly scattering metallic (aluminum) nanoparticles is enough to create a significant enhancement of the fluorescence of dye molecules in the visible wavelength range. The strategy can be applied in general to increase the emission of UV-absorbing constituents, and is of particular use for solar energy.