arXiv subjects

Aline Lefebvre-Lepot

Publications and source records attributed to Aline Lefebvre-Lepot.

7 recordsLinked to original sources

arXiv2026

Microscopic derivation of a one-dimensional lubrication model with roughness

We derive a hydrodynamic model for the motion of inertial particles with a spherical hard core, interacting through lubrication forces and pairwise repulsive forces. The repulsion arises from the assumption that each particle is surrounded by a thin rough layer of reduced permeability. We prove that, as the number of particles tends to infinity (and their size tends to 0), the microscopic dynamics converges to a macroscopic hydrodynamic model in which congestion effects are encoded directly into the macroscopic interaction forces, depending on a local critical density transported by the flow. In particular, we extend the work of Lefebvre-Lepot and Maury where non-inertial particles, submitted to only a lubrication force were considered, and present the convergence proof when inertial effects and roughness are taken into account.

math.AP↗

arXiv2025

Some mathematical models for flagellar activation mechanisms

This paper focuses on studying a model for molecular motors responsible for the bending of the axoneme in the flagella of microorganisms. The model is a coupled system of partial differential equations inspired by Jülicher et al. or Camalet, incorporating two rows of molecular motors between microtubules filaments. Existence and uniqueness of a solution is proved, together with the presence of a supercritical Hopf bifurcation. Additionally, numerical simulations are provided to illustrate the theoretical results. A brief study on the generalization to N-rows is also included.

math.NA↗

arXiv2025

The N-link model for slender rods in a viscous fluid: well-posedness and convergence to classical elastohydrodynamics equations

Flexible fibers at the microscopic scale, such as flagella and cilia, play essential roles in biological and synthetic systems. The dynamics of these slender filaments in viscous flows involve intricate interactions between their mechanical properties and hydrodynamic drag. In this paper, considering a 1D, planar, inextensible Euler-Bernoulli rod in a viscous fluid modeled by Resistive Force Theory, we establish the existence and uniqueness of solutions for the $N$-link model, a mechanical model, designed to approximate the continuous filament with rigid segments. Then, we prove the convergence of the $N$-link model's solutions towards the solutions to classical elastohydrodynamics equations of a flexible slender rod. This provides an existence result for the limit model, comparable to those by Mori and Ohm [Nonlinearity, 2023], in a different functional context and with different methods. Due to its mechanical foundation, the discrete system satisfies an energy dissipation law, which serves as one of the main ingredients in our proofs. Our results provide mathematical validation for the discretization strategy that consists in approximating a continuous filament by the mechanical $N$-link model, which does not correspond to a classical approximation of the underlying PDE.

math.AP↗

arXiv2023

A limiting model for a low Reynolds number swimmer with N passive elastic arms

We consider a low Reynolds number artificial swimmer that consists of an active arm followed by $N$ passive springs separated by spheres. This setup generalizes an approach proposed in Montino and DeSimone, Eur. Phys. J. E, vol. 38, 2015. We further study the limit as the number of springs tends to infinity and the parameters are scaled conveniently, and provide a rigorous proof of the convergence of the discrete model to the continuous one. Several numerical experiments show the performances of the displacement in terms of the frequency or the amplitude of the oscillation of the active arm.

math.NA↗

arXiv2012

Micro-Macro Modelling of an Array of Spheres Interacting Through Lubrication Forces

We consider here a discrete system of spheres interacting through a lubrication force. This force is dissipative, and singular near contact: it behaves like the reciprocal of interparticle distance. We propose a macroscopic constitutive equation which is built as the natural continuous counterpart of this microscopic lubrication model. This model, which is of the newtonian type, relies on an elongational viscosity, which is proportional to the reciprocal of the local fluid fraction. We then establish the convergence in a weak sense of solutions to the discrete problem towards the solution to the partial differential equation which we identified as the macroscopic constitutive equation.

math.AP↗

arXiv2012

A "Necklace" Model for Vesicles Simulations in 2D

The aim of this paper is to propose a new numerical model to simulate 2D vesicles interacting with a newtonian fluid. The inextensible membrane is modeled by a chain of circular rigid particles which are maintained in cohesion by using two different type of forces. First, a spring force is imposed between neighboring particles in the chain. Second, in order to model the bending of the membrane, each triplet of successive particles is submitted to an angular force. Numerical simulations of vesicles in shear flow have been run using Finite Element Method and the FreeFem++[1] software. Exploring different ratios of inner and outer viscosities, we recover the well known "Tank-Treading" and "Tumbling" motions predicted by theory and experiments. Moreover, for the first time, 2D simulations of the "Vacillating-Breathing" regime predicted by theory in [2] and observed experimentally in [3] are done without special ingredient like for example thermal fluctuations used in [4].

math-ph↗

arXiv2010

Existence results for non-smooth second order differential inclusions, Convergence result for a numerical scheme and applications for modelling inelastic collisions

We are interested in existence results for second order differential inclusions, involving finite number of unilateral constraints in an abstract framework. These constraints are described by a set-valued operator, more precisely a proximal normal cone to a time-dependent set. Moreover we extend a numerical scheme, introduced in [8] and proved a convergence result. We propose applications in modelling inelastic collisions between rigid particles too.

math.CA↗