Macroscopic Limits and Phase Transition in a System of Self-propelled Particles

We investigate systems of self-propelled particles with alignment interaction. Compared to previous work (Degond and Motsch, Math. Models Methods Appl. Sci. 18:1193–1215, 2008a; Frouvelle, Math. Models Methods Appl. Sci., 2012), the force acting on the particles is not normalized, and this modification gives rise to phase transitions from disordered states at low density to aligned states at high densities. This model is the space-inhomogeneous extension of (Frouvelle and Liu, Dynamics in a kinetic model of oriented particles with phase transition, 2012), in which the existence and stability of the equilibrium states were investigated. When the density is lower than a threshold value, the dynamics is described by a nonlinear diffusion equation. By contrast, when the density is larger than this threshold value, the dynamics is described by a similar hydrodynamic model for self-alignment interactions as derived in (Degond and Motsch, Math. Models Methods Appl. Sci. 18:1193–1215, 2008a; Frouvelle, Math. Models Methods Appl. Sci., 2012). However, the modified normalization of the force gives rise to different convection speeds, and the resulting model may lose its hyperbolicity in some regions of the state space.     

Multi-residue analysis of 80 environmental contaminants in honeys, honeybees and pollens by one extraction procedure followed by liquid and gas chromatography coupled with mass spectrometric detection

One of the factors that may explain nowadays honeybees' colonies losses is the increasing presence of chemicals in the environment. The aim of this study is to obtain a global view of the presence of environmental contaminants in beehives and, develop a fast, cheap and sensitive tool to analyze environmental contaminants in apiarian matrices. A multi residue analysis was developed to quantify 80 environmental contaminants, pesticides and veterinary drugs, belonging to different chemical classes, in honeys, honeybees and pollens. It consists in a single extraction, based on a modified "QuEChERS method", followed by gas chromatography coupled with Time of Flight mass spectrometry (GC-ToF) and liquid chromatography coupled with tandem mass spectrometry (LC-MS/MS). The "QuEChERS method" combines salting-out liquid-liquid extraction with acetonitrile and a dispersive-SPE clean up. It was adjusted to honey and especially to honeybee and pollen, by adding a small fraction of hexane in acetonitrile to eliminate lipids that interfere with mass spectrometry analysis. This method, combined with accurate and sensitive detection, allowed quantification and confirmation at levels as low as 10 ng/g, with recoveries between 60 and 120%. Application to more than 100 samples of each matrix was achieved for a global view of pesticide presence in the honeybee environment. Relatively high percentages of honeys, honeybees and pollens were found to be contaminated by pesticides used to combat varroa but also by fungicides like carbendazim and ubiquitous contaminants.     

QSPR modeling: graph connectivity indices versus line graph connectivity indices

Five QSPR models of alkanes were reinvestigated. Properties considered were molecular surface-dependent properties (boiling points and gas chromatographic retention indices) and molecular volume-dependent properties (molar volumes and molar refractions). The vertex- and edge-connectivity indices were used as structural parameters. In each studied case we computed connectivity indices of alkane trees and alkane line graphs and searched for the optimum exponent. Models based on indices with an optimum exponent and on the standard value of the exponent were compared. Thus, for each property we generated six QSPR models (four for alkane trees and two for the corresponding line graphs). In all studied cases QSPR models based on connectivity indices with optimum exponents have better statistical characteristics than the models based on connectivity indices with the standard value of the exponent. The comparison between models based on vertex- and edge-connectivity indices gave in two cases (molar volumes and molar refractions) better models based on edge-connectivity indices and in three cases (boiling points for octanes and nonanes and gas chromatographic retention indices) better models based on vertex-connectivity indices. Thus, it appears that the edge-connectivity index is more appropriate to be used in the structure-molecular volume properties modeling and the vertex-connectivity index in the structure-molecular surface properties modeling. The use of line graphs did not improve the predictive power of the connectivity indices. Only in one case (boiling points of nonanes) a better model was obtained with the use of line graphs.     

Local Stability of Perfect Alignment for a Spatially Homogeneous Kinetic Model

We prove the nonlinear local stability of Dirac masses for a kinetic model of alignment of particles on the unit sphere, each point of the unit sphere representing a direction. A population concentrated in a Dirac mass then corresponds to the global alignment of all individuals. The main difficulty of this model is the lack of conserved quantities and the absence of an energy that would decrease for any initial condition. We overcome this difficulty thanks to a functional which is decreasing in time in a neighborhood of any Dirac mass (in the sense of the Wasserstein distance). The results are then extended to the case where the unit sphere is replaced by a general Riemannian manifold.