MRICOM–MRI COntrast Modelling using 2D T1–T2 correlation spectra and relaxation signatures

Image contrast is calculated by inputting experimental 2D T₁–T₂ relaxation spectra into the ODIN software interface. The method involves characterising a magnetic resonance imaging pulse sequence with a “relaxation signature” which describes the sensitivity of the sequence to relaxation and is independent of sample parameters. Maximising (or minimising) the overlap between the experimental 2D T₁–T₂ relaxation spectra and the relaxation signature can then be used to maximise image contrast. The concept is illustrated using relaxation signatures for the echo planar imaging and Turbo spin-echo imaging sequences, together with in-vitro 2D T₁–T₂ spectra for liver and cartilage.     

Reflectometric measurement of birefringence rotation in single-mode optical fibers

We present a novel reflectometric technique for the measurement of orientation and modulus of the linear birefringence vector in single-mode optical fibers. The technique provides information also on circular birefringence, although this component, if present, appears as a rotation of the linear birefringence. A detailed theoretical analysis is reported and validated by experimental results.     

Global existence via Ginzburg-Landau formalism and pseudo-orbits of Ginzburg-Landau approximations

The so-called Ginzburg-Landau formalism applies for parabolic systems which are defined on cylindrical domains, which are, close to the threshold of instability, and for which the unstable Fourier modes belong to non-zero wave numbers. This formalism allows to describe an attracting set of solutions by a modulation equation, here the Ginzburg-Landau equation. If the coefficient in front of the cubic term of the formally derived Ginzburg-Landau equation has negative real part the method allows to show global existence in time in the original system of all solutions belonging to small initial conditions, inL . Another aim of this paper is to construct a pseudo-orbit of Ginzburg-Landau approximations which is close to a solution of the original system up tot=. We consider here as an example the socalled Kuramoto-Shivashinsky equation to explain the methods, but it applies also to a wide class of other problems, like e.g. hydrodynamical problems or reaction-diffusion equations, too.     

Cation disorder in NaW2O6+δ·nH2−zO post-ion exchange with K, Rb, Sr, and Cs

The structure of the defect pyrochlore NaW₂O_6+δ·nH_2−zO after ion exchange with K, Rb, Sr or Cs for Na has been investigated using thermal analysis, solid-state nuclear magnetic resonance, laboratory X-ray and neutron diffraction methods. Neutron diffraction studies show that both the A-type cations (Na⁺, K⁺, Rb⁺, and/or Cs⁺) and the water molecules reside within the channels that form in the 111 direction of the W₂O₆ framework and that these strongly interact. The analytical results suggest that the water and A-type cations compete for space in the tunnels within the W₂O₆ pyrochlore framework, with the total number of water molecules and cations being approximately constant in the six samples investigated. The interplay between the cations and water explains the non-linear dependence of the a lattice parameter on the choice of cation. It appears that the ion-exchange capacity of the material will be controlled by the amount of water initially present in the sample.     

Angular Momentum Effects in Michelson–Morley Type Experiments

The effect of the angular momentum density of a gravitational source on the times of flight of light rays in an interferometer is analyzed. The calculation is made imagining that the interferometer is at the equator of an axisymmetric steadily rotating gravity source. In order to evaluate the size of the effect in the case of the Earth a weak field approximation for the metric elements is introduced. For laboratory scales and non-geodesic paths the correction due to the angular momentum turns out to be comparable with the sensitivity expected in gravitational waves interferometric detectors, whereas it drops under the threshold of detectability when using free (geodesic) light rays.     

A version of Stöber synthesis enabling the facile prediction of silica nanospheres size for the fabrication of opal photonic crystals

A sol-gel synthesis procedure based on the method proposed by Stöber et al. (J Colloid Interface Sci 26:302–315, 1968) has been adopted for the one-step preparation of mono-dispersed silica nanospheres. An excellent control of the particle diameter over a wide range is obtained by varying the amount of silicon alkoxide only, while the concentration of all other components is kept fixed: this allows the fabrication of artificial opals with a finely tuned and precisely predictable lattice parameter.     

On continuation of inviscid vortex patches

This investigation concerns solutions of the steady-state Euler equations in two dimensions featuring finite area regions with constant vorticity embedded in a potential flow. Using elementary methods of the functional analysis we derive precise conditions under which such solutions can be uniquely continued with respect to their parameters, valid also in the presence of the Kutta condition concerning a fixed separation point. Our approach is based on the Implicit Function Theorem and perturbation equations derived using shape-differentiation methods. These theoretical results are illustrated with careful numerical computations carried out using the Steklov–Poincaré method which show the existence of a global manifold of solutions connecting the point vortex and the Prandtl–Batchelor solution, each of which satisfies the Kutta condition.     

Searching for protostars

Summary We present molecular-line observations of young stellar objects (YSOs) suspected to be protostars in the main accretion phase. The aim of this work is to define a list of the best protostellar candidates to be observed in the near future with the ISO spectrometers with the precise scope of searching for the final proof of the infall, theHoly Grail of astrophysics. The sources were mapped in the CS 3?2 and CO 3?2 lines; our data were used to investigate the presence of clumps of materials around these objects and the amount of this material, as well as to detect outflows associated with these objects that would enormously complicate the interpretation of further dynamics studies. Only one of our sources suspected to be protostars resulted to have a good chance of being in the accretion phase and to deserve further spectroscopic measurements. Paper presented at the 6th Cosmic Physics National Conference, Palermo, 3–7 November 1992.