Vincent Démery

Electrostatic interactions mediated by polarizable counterions: Weak and strong coupling limits

We investigate the statistical mechanics of an inhomogeneous Coulomb fluid composed of charged particles with static polarizability. We derive the weak- and the strong-coupling approximations and evaluate the partition function in a planar dielectric slab geometry with charged boundaries. We investigate the density profiles and the disjoining pressure for both approximations. Comparison to the case of non-polarizable counterions shows that polarizability brings important differences in the counterion density distribution as well as the counterion mediated electrostatic interactions between charged dielectric interfaces.

Generalized Langevin equations for a driven tracer in dense soft colloids: construction and applications

We describe a tracer in a bath of soft Brownian colloids by a particle coupled to the density field of the other bath particles. From the Dean equation, we derive an exact equation for the evolution of the whole system, and show that the density field evolution can be linearized in the limit of a dense bath. This linearized Dean equation with a tracer taken apart is validated by the reproduction of previous results on the mean-field liquid structure and transport properties. Then, the tracer is submitted to an external force and we compute the density profile around it, its mobility and its diffusion coefficient. Our results exhibit effects such as bias enhanced diffusion that are very similar to those observed in the opposite limit of a hard core lattice gas, indicating the robustness of these effects. Our predictions are successfully tested against molecular dynamics simulations.

The one-dimensional Coulomb lattice fluid capacitor

The one-dimensional Coulomb lattice fluid in a capacitor configuration is studied. The model is formally exactly soluble via a transfer operator method within a field theoretic representation of the model. The only interactions present in the model are the one-dimensional Coulomb interaction between cations and anions and the steric interaction imposed by restricting the maximal occupancy at any lattice site to one particle. Despite the simplicity of the model, a wide range of intriguing physical phenomena arise, some of which are strongly reminiscent of those seen in experiments and numerical simulations of three-dimensional ionic liquid based capacitors. Notably, we find regimes where over-screening and density oscillations are seen near the capacitor plates. The capacitance is also shown to exhibit strong oscillations as a function of applied voltage. It is also shown that the corresponding mean-field theory misses most of these effects. The analytical results are confirmed by extensive numerical simulations.

Overscreening in a 1D lattice Coulomb gas model of ionic liquids

Overscreening in the charge distribution of ionic liquids at electrified interfaces is shown to proceed from purely electrostatic and steric interactions in an exactly soluble one-dimensional lattice Coulomb gas model. Being not a mean-field effect, our results suggest that even in higher-dimensional systems the overscreening could be accounted for by a more accurate treatment of the basic lattice Coulomb gas model, that goes beyond the mean-field level of approximation, without any additional interactions.

Drag forces in classical fields.

Inclusions, or defects, moving at constant velocity through free classical fields are shown to be subject to a drag force which depends on the field dynamics and the coupling of the inclusion to the field. The results are used to predict the drag exerted on inclusions, such as proteins, in lipid membranes due to their interaction with height and composition fluctuations. The force, measured in Monte Carlo simulations, on a pointlike magnetic field moving through an Ising ferromagnet is also well explained by these results.

From microstructural features to effective toughness in disordered brittle solids

The relevant parameters at the microstructure scale that govern the macroscopic toughness of disordered brittle materials are investigated theoretically. We focus on a crack propagation that is planar and describe it as the motion of an elastic line within a plane with random distribution of toughness. Our study reveals two regimes: in the collective-pinning regime, the macroscopic toughness can be expressed as a function of a few parameters only, namely the average and the standard deviation of the local toughness distribution and the correlation lengths of the heterogeneous toughness field; in the individual-pinning regime, the passage from micro- to macro-scale is more subtle and the full distribution of local toughness is required to be predictive.

Mechanics of Large Folds in Thin Interfacial Films

A thin film confined to a liquid interface responds to uniaxial compression by wrinkling, and then by folding, that has been solved exactly before self-contact. Here, we address the mechanics of large folds, i.e., folds that absorb a length much larger than the wrinkle wavelength. With scaling arguments and numerical simulations, we show that the antisymmetric fold is energetically favorable and can absorb any excess length at zero pressure. Then, motivated by puzzles arising in the comparison of this simple model to experiments on lipid monolayers or capillary rafts, we discuss how to incorporate film weight, self-adhesion, or energy dissipation.

Geometry-Driven Folding of a Floating Annular Sheet

Predicting the large-amplitude deformations of thin elastic sheets is difficult due to the complications of self contact, geometric nonlinearities, and a multitude of low-lying energy states. We study a simple two-dimensional setting where an annular polymer sheet floating on an air-water interface is subjected to different tensions on the inner and outer rims. The sheet folds and wrinkles into many distinct morphologies that break axisymmetry. These states can be understood within a recent geometric approach for determining the gross shape of extremely bendable yet inextensible sheets by extremizing an appropriate area functional. Our analysis explains the remarkable feature that the observed buckling transitions between wrinkled and folded shapes are insensitive to the bending rigidity of the sheet.

Inferring Bounded Evolution in Phenotypic Characters from Phylogenetic Comparative Data.

Our understanding of phenotypic evolution over macroevolutionary timescales largely relies on the use of stochastic models for the evolution of continuous traits over phylogenies. The two most widely used models, Brownian motion and the Ornstein-Uhlenbeck (OU) process, differ in that the latter includes constraints on the variance that a trait can attain in a clade. The OU model explicitly models adaptive evolution toward a trait optimum and has thus been widely used to demonstrate the existence of stabilizing selection on a trait. Here we introduce a new model for the evolution of continuous characters on phylogenies: Brownian motion between two reflective bounds, or Bounded Brownian Motion (BBM). This process also models evolutionary constraints, but of a very different kind. We provide analytical expressions for the likelihood of BBM and present a method to calculate the likelihood numerically, as well as the associated R code. Numerical simulations show that BBM achieves good performance: parameter estimation is generally accurate but more importantly BBM can be very easily discriminated from both BM and OU. We then analyze climatic niche evolution in diprotodonts and find that BBM best fits this empirical data set, suggesting that the climatic niches of diprotodonts are bounded by the climate available in Australia and the neighboring islands but probably evolved with little additional constraints. We conclude that BBM is a valuable addition to the macroevolutionary toolbox, which should enable researchers to elucidate whether the phenotypic traits they study are evolving under hard constraints between bounds.

Perturbative path-integral study of active- and passive-tracer diffusion in fluctuating fields.

We study the effective diffusion constant of a Brownian particle linearly coupled to a thermally fluctuating scalar field. We use a path-integral method to compute the effective diffusion coefficient perturbatively to lowest order in the coupling constant. This method can be applied to cases where the field is affected by the particle (an active tracer) and cases where the tracer is passive. Our results are applicable to a wide range of physical problems, from a protein diffusing in a membrane to the dispersion of a passive tracer in a random potential. In the case of passive diffusion in a scalar field, we show that the coupling to the field can, in some cases, speed up the diffusion corresponding to a form of stochastic resonance. Our results on passive diffusion are also confirmed via a perturbative calculation of the probability density function of the particle in a Fokker-Planck formulation of the problem. Numerical simulations on simplified systems corroborate our results.