On some questions related to the Gauss conjecture for function fields

We show that, for any finite field Fq, there exist infinitely many real quadratic function fields over Fq such that the numerator of their zeta function is a separable polynomial. As pointed out by Anglès, this is a necessary condition for the existence, for any finite field Fq, of infinitely many real function fields over Fq with ideal class number one (the so-called Gauss conjecture for function fields). We also show conditionally the existence of infinitely many real quadratic function fields over Fq such that the numerator of their zeta function is an irreducible polynomial.     

The effect of modeled drag reduction on the wall region

The low-dimensional model derived for the wall region of a turbulent boundary layer (Aubry et al., 1988) is applied to a drag-reduced flow. In agreement with some experimental results, drag reduction is modeled by thickening the wall region, which is achieved by applying stretching transformations to the original flow. By application of a Galerkin projection, a set of ordinary differential equations (ODEs) is obtained whose structure is identical to the set corresponding to the unmodified flow. The coefficients of the ODEs are modified in a nontrivial way. The bifurcation diagrams plotted for different values of the stretching parameter are different in detail but the structure is globally the same. In particular, the intermittent behavior which Aubry et al. identified with the cyclic bursting events experimentally observed is still present. The scenario by which intermittency appears through a subcritical Hopf bifurcation in which a heteroclinic cycle is created and disappears through a bifurcation to traveling waves is identical. These results hold for values of the stretching between 1 and 2.65, the value at which the top of the buffer layer reaches the centerline of the pipe. This is in agreement with experimental results for flows whose drag is reduced but which still display intermittency. The bifurcations occur in the stretched flow at increased levels of dissipation (relative to the unstretched flow), consistent with theoretical pictures of drag reduction, in which the increase of scale is due to stabilization by an increase of dissipation in the turbulent part of the flow. Moreover, this method is a systematic way to perturb the coefficients of the ODEs of Aubry et al. (1988). Under this kind of perturbation, the behavior of the solution (in the part of the bifurcation diagram physically relevant) is found to be extremely robust.     

Hemolytic and Antimicrobial Activities Differ Among Saponin-rich Extracts From Guar, Quillaja, Yucca, and Soybean

Hemolytic and antibacterial activities of eight serial concentrations ranged from 5-666 µg/mL of saponin-rich extracts from guar meal (GM), quillaja, yucca, and soybean were tested in 96-well plates and read by enzyme-linked immunosorbent assay plate-well as 650 nm. Hemolytic assay used a 1% suspension of chicken red blood cells with water and phosphate buffered saline as positive and negative controls, respectively. Antibacterial activity against Staphylococcus aureus, Salmonella typhimurium, and Escherichia coli were evaluated using ampicillin and bacteria without saponin-rich extract as positive and negative controls, respectively. The 100% MeOH GM and commercial quillaja saponin-rich extracts were significantly the highest in both hemolytic and antibacterial activities against all bacteria at the same concentration tested. Soybean saponin-rich extract had no antibacterial activity against any of the bacteria at the concentrations tested while yucca saponin-rich extract had no antibacterial activity against the gram-negative bacteria at the concentrations tested. GM and quillaja saponin-rich extracts were hemolytic, while yucca and soybean saponin-rich extracts were not hemolytic at the concentrations tested. No saponin-rich extract source had antibacterial activity against S. typhimurium or E. coli at the concentrations tested. Both GM and quillaja saponin-rich extracts exhibited antibacterial activity against S. aureus. Saponin-rich extracts from different plant sources have different hemolytic and antibacterial activities.     

Multiple scattering of ultrasound in weakly inhomogeneous media: application to human soft tissues

Waves scattered by a weakly inhomogeneous random medium contain a predominant single-scattering contribution as well as a multiple-scattering contribution which is usually neglected, especially for imaging purposes. A method based on random matrix theory is proposed to separate the single- and multiple-scattering contributions. The experimental setup uses an array of sources/receivers placed in front of the medium. The impulse responses between every couple of transducers are measured and form a matrix. Single-scattering contributions are shown to exhibit a deterministic coherence along the antidiagonals of the array response matrix, whatever the distribution of inhomogeneities. This property is taken advantage of to discriminate single- from multiple-scattered waves. This allows one to evaluate the absorption losses and the scattering losses separately, by comparing the multiple-scattering intensity with a radiative transfer model. Moreover, the relative contribution of multiple scattering in the backscattered wave can be estimated, which serves as a validity test for the Born approximation. Experimental results are presented with ultrasonic waves in the megahertz range, on a synthetic sample (agar-gelatine gel) as well as on breast tissues. Interestingly, the multiple-scattering contribution is found to be far from negligible in the breast around 4.3 MHz.     

Adaptive projection method applied to three-dimensional ultrasonic focusing and steering through the ribs

An adaptive projection method for ultrasonic focusing through the rib cage, with minimal energy deposition on the ribs, was evaluated experimentally in 3D geometry. Adaptive projection is based on decomposition of the time-reversal operator (DORT method) and projection on the "noise" subspace. It is shown that 3D implementation of this method is straightforward, and not more time-consuming than 2D. Comparisons are made between adaptive projection, spherical focusing, and a previously proposed time-reversal focusing method, by measuring pressure fields in the focal plane and rib region using the three methods. The ratio of the specific absorption rate at the focus over the one at the ribs was found to be increased by a factor of up to eight, versus spherical emission. Beam steering out of geometric focus was also investigated. For all configurations projecting steered emissions were found to deposit less energy on the ribs than steering time-reversed emissions: thus the non-invasive method presented here is more efficient than state-of-the-art invasive techniques. In fact, this method could be used for real-time treatment, because a single acquisition of back-scattered echoes from the ribs is enough to treat a large volume around the focus, thanks to real time projection of the steered beams.     

Exploiting the time-reversal operator for adaptive optics, selective focusing, and scattering pattern analysis

We report on the experimental measurement of the backscattering matrix of a weakly scattering medium in optics, composed of a few dispersed gold nanobeads. The decomposition of the time-reversal operator is applied to this matrix and we demonstrate selective and efficient focusing on individual scatterers, even through an aberrating layer. Moreover, we show that this approach provides the decomposition of the scattering pattern of a single nanoparticle. These results open important perspectives for optical imaging, characterization, and selective excitation of nanoparticles.     

Kernel Characterization of an Interval Function

This paper proposes a set-membership approach to characterize the kernel of an interval-valued function. In the context of a bounded-error estimation, this formulation makes it possible to embed all uncertainties of the problem inside the interval function and thus to avoid bisections with respect to all these uncertainties. To illustrate the principle of the approach, two testcases taken from robotics will be presented. The first testcase deals with the characterization of all loops of a mobile robot from proprioceptive measurements only. The second testcase is the localization of a robot from range-only measurements.     

Sur le nombre de points rationnels des variétés abéliennes et des Jacobiennes sur les corps finis

We give upper and lower bounds for the number of points on abelian and Jacobian varieties over finite fields. We also determine the values for the maximum and minimum number of points on Jacobian surfaces on a given finite field.     

Absence of wave packet diffusion in disordered nonlinear systems

We study the spreading of an initially localized wave packet in two nonlinear chains (discrete nonlinear Schr?dinger and quartic Klein-Gordon) with disorder. Previous studies suggest that there are many initial conditions such that the second moment of the norm and energy density distributions diverges with time. We find that the participation number of a wave packet does not diverge simultaneously. We prove this result analytically for norm-conserving models and strong enough nonlinearity. After long times we find a distribution of nondecaying yet interacting normal modes. The Fourier spectrum shows quasiperiodic dynamics. Assuming this result holds for any initially localized wave packet, we rule out the possibility of slow energy diffusion. The dynamical state could approach a quasiperiodic solution (Kolmogorov-Arnold-Moser torus) in the long time limit.     

Control of vortex breakdown in a closed cylinder with a rotating lid

The flow within a closed cylinder with a rotating lid is considered as a prototype for fundamental studies of vortex breakdown. Numerical simulations for various parameter values have been carried out to reproduce the known effect of a thin rotating rod positioned along the center axis as well as analyze the influence of local vorticity sources. As expected, the results show that the breakdown bubbles in the steady axisymmetric flow can be affected dramatically, i.e., fully suppressed or significantly enhanced, by rotating the rod. The main contribution of this article is to show that the observed behavior can be explained by the vorticity generated by the rod locally near the rotating lid and near the fixed lid, as analogous behavior is caused by the introduction of local vorticity sources in the flow without a rod. Moreover, we describe the influence on the breakdown bubbles of the vorticity sources by an analytical model. In addition to improving our understanding, this finding should also open the door to other types of flow control devices capable of generating localized vorticity.