Nematic alignment of self-propelled particles: from particle to macroscopic dynamics

Starting from a particle model describing self-propelled particles interacting through nematic alignment, we derive a macroscopic model for the particle density and mean direction of motion. We first propose a mean-field kinetic model of the particle dynamics. After diffusive rescaling of the kinetic equation, we formally show that the distribution function converges to an equilibrium distribution in particle direction, whose local density and mean direction satisfies a cross-diffusion system. We show that the system is consistent with symmetries typical of a nematic material. The derivation is carried over by means of a Hilbert expansion. It requires the inversion of the linearized collision operator for which we show that the generalized collision invariants, a concept introduced to overcome the lack of momentum conservation of the system, plays a central role. This cross-diffusion system poses many new challenging questions

The role of excitons and trions on electron spin polarization in quantum wells

We have studied the time evolution of the electron spin polarization under continuous photoexcitation in remotely n-doped semiconductor quantum wells. The doped region allows us to get the necessary excess of free electrons to form trions. We have considered electron resonant photoexcitation at free, exciton and trion electron energy levels. Also, we have studied the relative effect of photoexcitation energy density and doping concentration. In order to obtain the two-dimensional density evolution of the different species, we have performed dynamic calculations through the matrix density formalism. Our results indicate that photoexcitation of free electron level leads to a higher spin polarization. Also, we have found that increasing the photoexcitation energy or diminishing the doping enhances spin polarization.Comment: 30 pages, 11 figures, 1 tabl

Negative lateral conductivity of hot electrons in a biased superlattice

Nonequilibrium electron distribution in a superlattice subjected to a homogeneous electric field (biased superlattice with equipopulated levels) is studied within the tight-binding approximation, taking into account the scattering by optical and acoustic phonons and by lateral disorder. It is found that the distribution versus the in-plane kinetic energy depends essentially on the ratio between the Bloch energy and the optical phonon energy. The in-plane conductivity is calculated for low-doped structures at temperatures 4.2 K and 20 K. The negative conductivity is found for bias voltages corresponding to the Bloch-phonon resonance condition.Comment: 12 pages, 7 figure

Phase transitions and macroscopic limits in a BGK model of body-attitude coordination

In this article we investigate the phase transition phenomena that occur in a model of self-organisation through body-attitude coordination. Here, the body attitude of an agent is modelled by a rotation matrix in R3 as in Degond et al. (Math Models Methods Appl Sci 27(6):1005–1049, 2017). The starting point of this study is a BGK equation modelling the evolution of the distribution function of the system at a kinetic level. The main novelty of this work is to show that in the spatially homogeneous case, self-organisation may appear or not depending on the local density of agents involved. We first exhibit a connection between body-orientation models and models of nematic alignment of polymers in higher-dimensional space from which we deduce the complete description of the possible equilibria. Then, thanks to a gradient-flow structure specific to this BGK model, we are able to prove the stability and the convergence towards the equilibria in the different regimes. We then derive the macroscopic models associated with the stable equilibria in the spirit of Degond et al. (Arch Ration Mech Anal 216(1):63–115, 2015, Math Models Methods Appl Sci 27(6):1005–1049, 2017)