Pattern formation driven by cross-diffusion in a 2D domain

In this work we investigate the process of pattern formation in a two dimensional domain for a reaction–diffusion system with nonlinear diffusion terms and the competitive Lotka–Volterra kinetics. The linear stability analysis shows that cross-diffusion, through Turing bifurcation, is the key mechanism for the formation of spatial patterns. We show that the bifurcation can be regular, degenerate non-resonant and resonant. We use multiple scales expansions to derive the amplitude equations appropriate for each case and show that the system supports patterns like rolls, squares, mixed-mode patterns, supersquares, and hexagonal patterns.     

Analytical characterization of corrosion products of copper and its alloys on stained stone surfaces

Monuments, where stone and metals or metallic alloys are used together, are very frequently met in all historical periods and in all countries. In the case of bronze and other copper alloys, their corrosion products can be dissolved by the action of acid rain and thus reach the porous building materials in contact with (or near to) the metallic structures. Once absorbed by the stone, they precipitate on the external stone surface and inside its porous space. As the majority of these products are coloured, their precipitates may produce stains, which are perceived as unpleasant alterations of the original ‘values’ of the stone monuments. The removal of stains is therefore required on the occasion of conservation treatments. The paper reports on the characterisation of copper corrosion products found on two, very different, monuments in Rome: ‘Fontana delle Tartarughe’ (by T. Landini, last quarter of the 16th century) and ‘Statua dello Studente’ (by A. Cataldi, 1920). To identify the speciation of copper compounds in their carbonate matrices, different techniques [X‐ray diffraction, X‐ray fluorescence, SEM/energy‐dispersive X‐ray spectroscopy (EDS), micro‐Raman and XPS] had to be employed. To further confirm the identification of the chemical species, SEM/EDS data were also processed by principal component analysis. Copyright © 2013 John Wiley & Sons, Ltd.     

SQUID-based measuring systems

A program has been developed and initiated at the Indira Gandhi Centre for Atomic Research (IGCAR) for the utilization of SQUID sensors in various application areas. DC SQUID sensors based on Nb-AlO _x -Nb Josephson junctions have been designed and developed inhouse along with associated flux-locked loop (FLL) electronics. A compact low field SQUID magnetometer insertible in a liquid helium storage dewar has also been developed inhouse and is in use. Efforts to build a high field SQUID magnetometer, SQUID-DAC system, are in progress. A planar gradiometric DC SQUID sensor for non-destructive evaluation (NDE) application to be used in relatively unshielded environment has been designed and developed. An easily portable NDE cryostat with a small lift-off distance, to be used in external locations has been designed and tested. The magnetic field produced by a given two-dimensional current density distribution is inverted using the Fourier transform technique.     

Nanoelectromechanical systems

Nanoelectromechanical systems (NEMS) are nano-to-micrometer scale mechanical resonators coupled to electronic devices of similar dimensions. NEMS show promise for fast, ultrasensitive force microscopy and for deepening our understanding of how classical dynamics arises by approximation to quantum dynamics. This article begins with a survey of NEMS and then describes certain aspects of their classical dynamics. In particular, we show that for weak coupling the action of the electronic device on the mechanical resonator can be effectively that of a thermal bath, this despite the device being a driven, far-from-equilibrium system.     

The boundary layer analysis for stokes equations on a half space

The time dependent Stokes equations on a half space are considered. We decompose the solution of these equations in an inviscid solution: a boundary layer solution and a correction. Bounds on these solutions are given, in the appropriate Sobolev spaces, in terms of the norms of the initial and boundary data. The correction is shown to be of the same order of magnitude of the square root of the viscosity.