Self-Similarity of Volume Measures for Laplacians¶on P. C. F. Self-Similar Fractals

Our main goal in this paper is to obtain a precise analogue of Weyl's asymptotic formula for the eigenvalue distribution of Laplacians on a certain class of “finitely ramified” (or p.c.f.) self-similar fractals, building, in particular, on the work of [7, 9, 22, 24]. Our main result consists in precisely identifying (for the class of “decimable fractals”) the volume measures constructed by the second author in [24] for general p.c.f. fractals and showing that they are self-similar. From a physical point of view, our results should be relevant to the study of the density of states for diffusions and wave propagation in fractal media. Received: 6 September 1999 / Accepted: 7 October 2000     

Numerical predictions and experiments on the free-plate edge mode

In this paper, te edge mode variation is studied with three different methods: the reciprocal work method, already used by Torvik [J. Acoust. Soc. Am. 41 (1967) 346] to model this phenomenon, the S-parameter method and a finite element model that are applied for the first time to the study of the edge resonance. Moreover, laser probe measurements of the edge mode have also been performed and compared to the numerical predictions. The good agreement between the numerical predictions and the experimental data allows full understanding of the resonant phenomenon. The edge resonance is linked to the strong increase in amplitude of two complex Lamb waves, and the edge mode is proved to radiate into the plate as the first symmetrical Lamb mode S(0). Displacements at the edge and away from the edge have been computed and measured to evaluate the spatial and temporal behaviour of the edge mode. The dependence of the edge resonance frequency and amplitude on the Poisson coefficient has also been studied.     

Superparamagnetic iron oxide particles and positive enhancement for myocardial perfusion studies assessed by subsecond T1-weighted MRI

Superparamagnetic iron oxide particles (SPIOs) are usually referred to as T₂ MR contrast agents, reducing signal intensity (SI) on T₂-weighted MR images (negative enhancement). This study reports the original use of SPIOs as T₁-enhancing contrast agents, primarily assessed in vitro, and then applied to an in vivo investigation of a myocardial perfusion defect. Using a strongly T₁-weighted subsecond MR sequence with SPIOs intravenous (IV) bolus injection, MR imaging of myocardial vascularization after reperfusion was performed, on a dog model of coronary occlusion followed by reperfusion. Immediately after the intravenous bolus injection of 20 μmol/kg of SPIOs, a positive signal intensity enhancement was observed respectively, in the right and left ventricular cavity and in the nonischemic left myocardium. Moreover, compared to normal myocardium, the remaining ischemic myocardial region (anterior wall of the left ventricle) appeared as a lower and delayed SI enhancing area (cold spot). Mean peak SIE in the nonischemic myocardium (posterior wall) was significantly higher than in the ischemic myocardium (anterior wall) (110 ± 23% vs. 74 ± 22%, Mann-Whitney test < 1%, n₁ = 6, n₂ − n₁ = 0, U > 2). In conclusion, the T₁ effect of SPIOs at low dose, during their first intravascular distribution, suggests their potential use as positive markers to investigate the regional myocardial blood flow and some perfusion defects such as the “no-reflow phenomenon”.     

Numerical and experimental studies of molten pool formation during an interaction of a pulse laser (Nd:YAG) with a magnesium alloy

A pulse laser (Nd:YAG) interaction with an AZ91 magnesium alloy has been experimentally and numerically studied. A two-dimensional (2D) axisymmetric model of a molten pool created by a laser heat source has been developed. The elaborated model solves the coupled equations of a laminar fluid flow and heat transfer to demonstrate the flow behavior in the pool. This model takes into account the coupled effects of buoyancy and Marangoni forces, the thermophysic variation properties with temperature, and the radiation and convection heat losses. Concerning numerical results, the molten temperature distribution, velocity field and molten shape were discussed. It was noted that the Marangoni flow significantly alters the characteristics of the thawing and solidifying processes, and makes the molten pool wider and shallower. On the other hand, the experimental results showed that the material thermal properties have significant effects on the transport phenomena which takes place in the molten pool, and consequently on the formation as well as the shape of the pool. Finally, a comparison between the numerical and experimental results exhibited a good agreement.     

Dielectric and NMR Studies of the superionic conductor AgI embedded in mesoporous silicate matrices

This paper reports on the results of studies of small particles of the superionic conductor AgI embedded in MCM-41 and SBA-15 molecular sieves with different sizes of pores (channels). The studies are performed by the dielectric and nuclear magnetic resonance techniques. The temperature of the superionic phase transition is shown to increase monotonically with decreasing pore size. The enthalpy of activation of the ion motion in β-AgI in restricted geometry is determined. It is shown that introduction of AgI into pores does not noticeably affect its structure.     

The self-similarity of wall-bounded temporally accelerating turbulent flows

From the study of viscous flow it is known that certain time-dependent laminar problems, such as the impulsively started flat plate and the diffusion of a vortex sheet, possess self-similar solutions. Previous studies of turbulent channel and pipe flows accelerating between two steady states have shown that the flow field evolves in three distinct stages. Furthermore, recent direct numerical simulations have shown that the perturbation velocity, i.e. the surplus velocity from the initial value, in an impulsively accelerating turbulent channel and pipe flow also possesses a self-similar distribution during the initial stage. In here, these results are developed analytically and it is shown that accelerating flows in which the centreline velocity develops as U^∧_c(t) = U₀(t/t₀)^m will possess a self-similar velocity distribution during the initial stage. The displacement thickness of the perturbation velocity is shown to be dependent only on the type of acceleration, and not on the initial Reynolds number, the acceleration rate or the change in Reynolds number. The derived formulas are verified with good agreement against measurements performed in a linearly accelerating turbulent pipe flow and with data from channel flow simulations.     

Probing Proteins in Solution by Xe NMR Spectroscopy

The interaction of xenon with different proteins in aqueous solution is investigated by ¹²⁹Xe NMR spectroscopy. Chemical shifts are measured in horse metmyoglobin, hen egg white lysozyme, and horse cytochrome c solutions as a function of xenon concentration. In these systems, xenon is in fast exchange between all possible environments. The results suggest that nonspecific interactions exist between xenon and the protein exteriors and the data are analyzed in term of parameters which characterize the protein surfaces. The experimental data for horse metmyoglobin are interpreted using a model in which xenon forms a 1:1 complex with the protein and the chemical shift of the complexed xenon is reported (Locci et al., Keystone Symposia “Frontiers of NMR in Molecular Biology VI”, Jan. 9–15, 1999, Breckenridge, CO, Abstract E216, p. 53; Locci et al., XeMAT 2000 “Optical Polarization and Xenon NMR of Materials”, June 28–30, 2000, Sestri Levante, Italy, p. 46).     

Stabilisation of fcc cobalt layers by 0.4 nm thick manganese layers in Co/Mn superlattices

Epitaxial Co/Mn multilayers (0.75 to 6 nm Co, 0.4 nm Mn layer thickness) have been grown on mica substrates covered by a (0002) Ru buffer layer. The structural properties of these layers have been studied using X-ray diffraction, nuclear magnetic resonance (NMR), and high resolution transmission electron microscopy (HRTEM). The Co layers, grown as face centred cubic (fcc), were found to be stabilised by the very thin Mn layers. Data obtained using X-ray diffraction and NMR were analysed and found to be in good agreement, while Monte-Carlo simulations were used to interpret the data and calculate the expected diffracted intensity and NMR spectra. The HRTEM data show that the Mn layers give rise to a large strain contrast extending, in the growth direction, over a distance which exceeds the thickness of the Mn layers. The superlattices could be described as having an fcc structure containing randomly located stacking faults with varying densities. The results verify the presence of a dominant, almost perfect phase of fcc stacking, and of a faulted hcp phase, while the number of defects increases with the Co layer thickness. Received 27 October 1999 and Received in final form 29 May 2000