Simple approach for charge renormalization in highly charged macroions

We revisit the notion of renormalized charge, which is a concept of central importance in the field of highly charged colloidal or polyelectrolyte solutions. Working at the level of a linear Debye-Hückel-like theory only, we propose a versatile method to predict the saturated amount of charge renormalization, which is, however, a nonlinear effect arising at strong electrostatic coupling. The results are successfully tested against nonlinear Poisson-Boltzmann theory for polyions of various shapes (planar, cylindrical, and spherical), both in the infinite dilution limit or in confined geometry, with or without added electrolyte. Our approach, accurate for monovalent microions in solvents such as water, is finally confronted against experimental results on charged colloids and B-DNA solutions.     

Microelectrode study of single cavitational bubbles induced by 500 kHz ultrasound

Insight is gained into about the processes governing cavitational activity and acoustic streaming induced by high frequency (500 kHz) ultrasound by the use of microelectrodes with short time resolution electrochemical equipment to allow monitoring of the activity of single cavitating bubbles. Current transients are interpreted as showing the flux of solution towards the electrode surface due to microstreaming. In order to explain the current amplitude, a simplified model is produced. Important parameters such as bubble size and shape on the surface as well as the boundary layer thickness for microstreaming are taken into account. This model leads to the amplitude of the oscillations of the cavitating bubble. Introducing realistic bubble sizes, this amplitude is found to be in the order of 1 micron. The conclusions arising from this work allow a further interpretation of previous observations at millimeter scale electrodes.     

Fusion of conventional ultrasound imaging and acousto-optic sensing by use of a standard pulsed-ultrasound scanner

Acousto-optic sensing (AOS) is a dual-wave sensing technique based on the ultrasound modulation of diffuse light in a turbid medium. We experimentally demonstrate the feasibility of combining AOS and conventional ultrasound imaging by use of a commercially available pulsed-ultrasound scanner coupled with a photorefractive crystal-based optical interferometry system. Optically absorbing targets embedded in highly diffusive phantoms (mus'= 10 cm(-1)) are imaged through a thickness of 27 mm with millimeter resolution. The acousto-optic images are intrinsically coregistered with the ultrasound images.     

Phase-sensitive optical low-coherence reflectometry technique applied to the characterization of photonic crystal fiber properties

Localized measurements of group-velocity dispersion and birefringence of photonic crystal fibers are achieved with a phase-sensitive optical low-coherence reflectometry technique. This technique is efficient for fiber samples no longer than 1 m. Theoretical simulations are in good agreement with experimental results. As a result, the stress-induced birefringence proves to be at most 1 order of magnitude below the geometrical-shape birefringence.     

Theory of spin hall conductivity in n-doped GaAs

We develop a theory of extrinsic spin currents in semiconductors, resulting from spin-orbit coupling at charged scatterers, which leads to skew-scattering and side-jump contributions to the spin-Hall conductivity. Applying the theory to bulk n-GaAs, without any free parameters, we find spin currents that are in reasonable agreement with experiments by Kato et al. [Science 306, 1910 (2004)].     

Huge fluctuations in weight measurements at the bottom of a two-dimensional vertical sheet of grains

Weight measurements at the bottom of a quasi-2D vertical sheet of static cohesionless grains are carried out. The grains are held between two coaxial cylinders. This peculiar setup allows us to set either periodic or fixed lateral boundary conditions. Huge relative fluctuations in weight measurements appear in case of fixed lateral walls. This may be related to some indetermination in the mobilization state of friction forces on lateral walls. This argument would hold for any piling, but would lead to huge fluctuations in 2D systems only, because of averaging effects in 3D.     

Measures on the Splitting Subspaces of an Inner Product Space

Let S be an inner product space and let E(S) (resp. F(S)) be the orthocomplemented poset of all splitting (resp. orthogonally closed) subspaces of S. In this article we study the possible states/charges that E(S) can admit. We first prove that when S is an incomplete inner product space such that dim S/S < , then E(S) admits at least one state with a finite range. This is very much in contrast to states on F(S). We then go on showing that two-valued states can exist on E(S) not only in the case when E(S) consists of the complete/cocomplete subspaces of S. Finally we show that the well known result which states that every regular state on L(H) is necessarily -additive cannot be directly generalized for charges and we conclude by giving a sufficient condition for a regular charge on L(H) to be -additive.     

Hydrodynamics within the electric double layer on slipping surfaces

We show, using extensive molecular dynamics simulations, that the dynamics of the electric double layer (EDL) is very much dependent on the wettability of the charged surface on which the EDL develops. For a wetting surface, the dynamics, characterized by the so-called zeta potential, is mainly controlled by the electric properties of the surface, and our work provides a clear interpretation for the traditionally introduced immobile Stern layer. In contrast, the immobile layer disappears for nonwetting surfaces, and the zeta potential deduced from electrokinetic effects is considerably amplified by the existence of a slippage at the solid substrate.     

Une Conjecture de Lebesgue

Let A > 0 be an integer. The equation x⁵–y⁵ = Az⁵ wasfirst studied by Dirichlet and Lebesgue. Lebesgue conjecturedin 1843 that if A has no prime divisors of the form 10k+1, theequation has no solutions except the visible ones. Partial resultswere obtained by Lebesgue and by Terjanian in 1987. The purposeof the paper is to prove Lebesgue's conjecture. The main toolused is the method known as the elliptic Chabauty method.     

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.