Subelliptic Li-Yau estimates on three dimensional model spaces

We describe three elementary models in three dimensional subelliptic geometry which correspond to the three models of the Riemannian geometry (spheres, Euclidean spaces and Hyperbolic spaces) which are respectively the SU(2), Heisenberg and SL(2) groups. On those models, we prove parabolic Li-Yau inequalities on positive solutions of the heat equation. We use for that the $\Gamma_{2}$ techniques that we adapt to those elementary model spaces. The important feature developed here is that although the usual notion of Ricci curvature is meaningless (or more precisely leads to bounds of the form $-\infty$ for the Ricci curvature), we describe a parameter $\rho$ which plays the same role as the lower bound on the Ricci curvature, and from which one deduces the same kind of results as one does in Riemannian geometry, like heat kernel upper bounds, Sobolev inequalities and diameter estimates

Droplets displacement and oscillations induced by ultrasonic surface acoustic waves: a quantitative study

We present an experimental study of a droplet interacting with an ultrasonic surface acoustic wave (SAW). Depending on the amplitude of the wave, the drop can either experience an internal flow with its contact-line pinned, or (at higher amplitude) move along the direction of the wave also with internal flow. Both situations appear together with oscillations of the drop free-surface. The physical origins of the internal mixing flow as well as the drop displacement and surface waves are still not well understood. In order to give insights of the underlying physics involved in these phenomena, we carried out an experimental and numerical study. The results suggest that the surface deformation of the drop can be related as a combination between acoustic streaming effect and radiation pressure inside the drop.Comment: 9 pages, 14 figures. To appear in Physical Review

Acoustic Tweezers for Particle and Fluid Micromanipulation

International audienc

The air-liquid flow in a microfluidic airway tree

This paper was presented at the 2nd Micro and Nano Flows Conference (MNF2009), which was held at Brunel University, West London, UK. The conference was organised by Brunel University and supported by the Institution of Mechanical Engineers, IPEM, the Italian Union of Thermofluid dynamics, the Process Intensification Network, HEXAG - the Heat Exchange Action Group and the Institute of Mathematics and its Applications.Microfluidic techniques are employed to investigate air-liquid flows in the pulmonary airway tree. A network of microchannels with five generations is made and used as a simplified model of the pulmonary airway tree. Liquid plugs are injected into the network and pushed by air flow to divide at every bifurcation before reaching the exits. The resistance associated with the presence of one plug in a given generation is defined to establish a linear relation between the driving pressure and the total flow rate in the network. Based on this resistance, we have good predictions of the flow of two successive plugs in the network. For two-plug flows under the same driving pressure, the total flow rate depends not only on the lengths of the plugs but also the initial distance between the two. Strong long range interactions are found between daughter plugs, especially when they are flowing through the bifurcations. We also observe different flow patterns under different pushing conditions. Under a constant pressure forcing, the flow develops symmetrically while a constant flow rate push achieves an asymmetric flow.This study is funded by the ANR under the “Sante-Environnement et Sante-Travail” programme

Humanitarian Demining and Robotics

Mines were used for the first time during the American Civil War in the United States (1861-1865). Anti-tank mines were later ameliorated and laid on the battlefields of the First World War. Mine clearing operations did not pose major problems with those visible and easy-to-detect anti-tank mines. The reason why Anti-personnel mines have been conceived and systematically used on the anti-tank minefields during the Second World War was because such mines prevented the enemy from easy demining of the defense system

The subelliptic heat kernel on SU(2): Representations, Asymptotics and Gradient bounds

The Lie group SU(2) endowed with its canonical subriemannian structure appears as a three-dimensional model of a positively curved subelliptic space. The goal of this work is to study the subelliptic heat kernel on it and some related functional inequalities.Comment: Update: Added section + Correction of typo

Analysis of incompatibility barriers during cross-pollinations among Phaseolus L. and other leguminous plants

Plant breeding is intended to seek for ways of realizing a genetic structure adapted to criteria and population needs. In this context, cross-pollinations are for great interest. They offer the means of creating a wide genotypic variability. However, a limited number of species are able to undergo hybridization studies. In Phaseolus L., improvement can be envisioned by either exploiting the primary genetic pool of the species, or the genetic variability of other species. In fact, there are wild or wild-like species more resistant to stresses or diseases than the cultivated ones. The methods of embryo rescues facilitate the interspecific crosses and contribute to exploiting the available genetic diversity within plant germplasm. Difficulties related to obtaining hybrids in grain legumes, and Phaseolus L. in particular, are reported in this research. It is possible to avoid the incompatibility barriers based on their appearance time. When they are pre-zygotic, the use of growth regulators during pollination is recommended. The in vitro explants culture is the most usual method to overcome the post-zygotic barriers. The mechanisms leading to abortion of hybrid embryos, as well as adequate methods to overcome the interspecific incompatibilities should be subjected to further studies.Keywords: Abortion, hybridization, interspecific barriers, Phaseolus L., plant embryos