Phase instabilities in hexagonal patterns

The general form of the amplitude equations for a hexagonal pattern including spatial terms is discussed. At the lowest order we obtain the phase equation for such patterns. The general expression of the diffusion coefficients is given and the contributions of the new spatial terms are analysed in this paper. From these coefficients the phase stability regions in a hexagonal pattern are determined. In the case of Benard-Marangoni instability our results agree qualitatively with numerical simulations performed recently.Comment: 6 pages, 6 figures, to appear in Europhys. Let

Nonlinear Competition Between Small and Large Hexagonal Patterns

Recent experiments by Kudrolli, Pier and Gollub on surface waves, parametrically excited by two-frequency forcing, show a transition from a small hexagonal standing wave pattern to a triangular ``superlattice'' pattern. We show that generically the hexagons and the superlattice wave patterns bifurcate simultaneously from the flat surface state as the forcing amplitude is increased, and that the experimentally-observed transition can be described by considering a low-dimensional bifurcation problem. A number of predictions come out of this general analysis.Comment: 4 pages, RevTex, revised, to appear in Phys. Rev. Let

Bypassing the Inertness of Aziridine/CO2 Systems to Access 5-Aryl-2-Oxazolidinones: Catalyst-Free Synthesis Under Ambient Conditions

The development of sustainable synthetic routes to access valuable oxazolidinones via CO2 fixation is an active research area, and the aziridine/carbon dioxide coupling has aroused a considerable interest. This reaction features a high activation barrier and thus requires a catalytic system, and may present some other critical issues. Here, the straightforward gram-scale synthesis of a series of 5-aryl-2-oxazolidinones was developed at ambient temperature and atmospheric CO2 pressure, in the absence of any catalyst/co-catalyst. The key to this innovative procedure consists in the direct transfer of the pre-formed amine/CO2 adduct (carbamate) to common aziridine precursors (dimethylsulfonium salts), replacing the classical sequential addition of amine (intermediate isolation of aziridine) and then CO2. The reaction mechanism was investigated by NMR spectroscopy and DFT calculations applied to model cases

Optical devices provide unprecedented insights into the laser cleaning of calcium oxalate layers

Abstract Calcium oxalates are insoluble colorless or whitish salts constituting noble patina, on both natural and artificial stone artworks' surfaces, the presence of which is extremely valued. The oxalates are not considered detrimental to the substrate, however, being often accompanied by other substances such as gypsum, silicates, and pigmented particles. They may form very adherent, relatively thick and colored layers creating disfiguring effects and hindering legibility of the pictorial surface. For this reason it may be appropriate to diminish their thickness, but patina's partial preservation is particularly required calling for extremely gradual and controllable cleaning approach. Thinning of calcium oxalate patina from a detached 16th century fresco (from Sansepolcro) was performed through the use of laser (Nd:YAG and Er:YAG) systems and chemical means (Carbogel loaded 5 wt.% of tetrasodium EDTA). Optical coherence tomography (OCT), providing a non-invasive stratigraphic cross-section of the examined surface, allowed to distinguish the oxalate from the underlying original layers and therefore to have an overview about its distribution, to numerically evaluate patina's thickness range and to provide the information on the amount of the material both removed and left on the artwork's surface. Laser scanning conoscopic microprofilometry allowed for a high-density sampling of the artwork's surface providing a three-dimensional model of the surface pattern. The obtained 3D models were used to estimate the amount of material removed and to compare them with those provided by OCT. The successful exploitation of the proposed exceptional cleaning monitoring methodology may be seen as an innovative and valid support for the restorers in the conservation of mural painting or other surfaces covered by oxalate layers and may pilot more targeted, cautious and respectful cleaning intervention

Finite-size effects in the transition from hexagons to rolls in convective systems

The transition thresholds between hexagons and rolls in convective patterns are obtained in the framework of the amplitude equations. We show that the discrepancies between the theoretical thresholds, calculated for unbounded systems, and the experimental ones, made in finite containers, can be partially corrected by a phenomenological argument. The finite-size effects are responsible for the decreasing in the efficiency of the heat transport across the cell. Using this fact we are able to approach the calculated thresholds to those observed in real experiments. The transition between different symmetries in convectiv

Disclosing Jackson Pollock's palette in Alchemy (1947) by non-invasive spectroscopies

Alchemy (1947, Peggy Guggenheim Collection, Venice) is one of the most materic works by J. Pollock, whose palette is extensive, ranging from white to yellow, red, green, violet, blue, black, and silver. Each layer of color was laid on top of a previously dried one and effectively separated from the lower one forming a quite complex stratigraphy with colors intersecting each other. In this study, a non-invasive multi-technique method combining point analysis with Vis–NIR multispectral imaging has been exploited to give insights on the painting technique of the American abstract expressionist. The molecular identification of pigments, colorants and extenders contained in fifteen different paints has been achieved combining key spectral markers from elemental, electronic and vibrational spectroscopies. For those colors exhibiting similar hues but different chemical compositions, a mapping procedure based on false color rendering, obtained by properly mixing three spectral planes from the Vis–NIR multispectral imaging set, has been successfully applied. Relevant for the understanding of the evolution of Pollock's drip technique is the identification of both traditional oil-based paints and oil-modified alkyd media. Point analysis by reflection FTIR scattered throughout the painting enabled mapping the distinct use of traditional and new binding media among painted, squeezed and dripped paints

Elastic properties of grafted microtubules

We use single-particle tracking to study the elastic properties of single microtubules grafted to a substrate. Thermal fluctuations of the free microtubule's end are recorded, in order to measure position distribution functions from which we calculate the persistence length of microtubules with contour lengths between 2.6 and 48 micrometers. We find the persistence length to vary by more than a factor of 20 over the total range of contour lengths. Our results support the hypothesis that shearing between protofilaments contributes significantly to the mechanics of microtubules.Comment: 9 pages, 3 figure

Square to stripe transition and superlattice patterns in vertically oscillated granular layers

We investigated the physical mechanism for the pattern transition from square lattice to stripes, which appears in vertically oscillating granular layers. We present a continuum model to show that the transition depends on the competition between inertial force and local saturation of transport. By introducing multiple free-flight times, this model further enables us to analyze the formation of superlattices as well as hexagonal lattice