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

A Comparison between Electroluminescence Models and Experimental Results

Electrical insulation ages and degrades until its eventual failure under electrical stress. One cause of this relates to the movement and accumulation of charge within the insulation. The emission of a low level of light from polymeric materials while under electrical stressing occurs before the onset of currently detectable material degradation. This light is known as electroluminescence (EL) and under an ac electric field is thought to relate to the interaction of charge in close proximity to the electrode-polymer interface. Understanding the cause of this light emission gives a very high-resolution method of monitoring charge interaction and its influence on material ageing. A possible cause of this light emission is the bipolar charge recombination theory. This theory involves the injection, trapping and recombination of charge carriers during each half cycle of the applied field [1]. This work compares two models that to simulate the EL emission according to this bipolar charge recombination theory. Model 1 assumes a fixed space charge region and all injected charge is uniformly distributed in this region with charges able to either become trapped or to recombine with opposite polarity charge carriers [2]. This recombination relates directly the excitation needed for the emission of a photon of light as measured in experiments. Model 2 develops on this by accounting for the transport and extraction of charge with an exponential distribution of trap levels rather than a uniform distribution [3]. Figure 1 shows a good correlation between the two models and experimental data. The full paper will describe the models in more detail and present results comparing the simulated and experimental results under various applied waveforms. Model 1 and model 2 both provide a good correlation with experimental data but model 2 allows a greater understanding of the space charge profile in the region close to the electrodes as well as the shape of the conduction current. Further work involves developing these models to support changes in the charge trapping profiles due to material ageing and supporting simulated results with measured conduction current

On small time asymptotics for rough differential equations driven by fractional Brownian motions

We survey existing results concerning the study in small times of the density of the solution of a rough differential equation driven by fractional Brownian motions. We also slightly improve existing results and discuss some possible applications to mathematical finance.Comment: This is a survey paper, submitted to proceedings in the memory of Peter Laurenc

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

Analyse préliminaire de la situation et des perspectives de la culture du haricot de Lima (Phaseolus lunatus L.) sur la Côte péruvienne (Vallées d'Ica, Pisco et Casma)

Preliminary analysis of the situation and prospects of the Lima bean crop (Phaseolus lunatus L.) in the Peruvian Coast (Valleys of Ica, Pisco and Casma). The Lima bean, Phaseolus lunatus L., is a crop of regional importance on the Peruvian Coast. Within the framework of a collaborative project between the ""faculté universitaire des Sciences agronomiques'"" in Gembloux and the ""Universidad Nacional Agraria La Molina"" in Lima, we carried out a diagnosis of this speculation in the Ica, Pisco and Casma valleys in order to define the constraints which limit crop yields and to suggest improvements within the reach of the smallholders. To achieve these objectives we carried out a formal survey, centred on the Lima bean crop and smallholder relations with the agro-socio-economical environment, and an informal survey, centred on the studied farm systems. To complete these data we met some key informants belonging to all the sectors in contact with agriculture. This study allowed us to identify five undersystems in the farm systems of the Peruvian Coastal Valleys. These undersystems are: cotton, commercial food crops, self-subsistence food crops, livestock and fruit trees. The Lima bean usually belongs to the commercial food crops undersystem. There are two types of constraints. External constraints affect all the components of the farm system and are mainly: end of State support to agriculture, liberalization of trade and unavailability of credit. Internal constraints directly affect the Lima bean crop. Low income leads to a deficiency in pest control and adequate crop management. The Lima bean is also in competition with other components of the system such as cotton and common bean