arXiv subjects

Antoine Fruleux

Publications and source records attributed to Antoine Fruleux.

5 recordsLinked to original sources

arXiv2021

Cellular Fourier analysis for geometrically disordered materials

Many media are divided into elementary units with irregular shape and size, as exemplified by domains in magnetic materials, bubbles in foams, or cells in biological tissues. Such media are essentially characterized by geometrical disorder of their elementary units, which we term cells. Cells set a reference scale at which are often assessed parameters and fields reflecting material properties and state. Here, we consider the spectral analysis of spatially varying fields. Such analysis is difficult in geometrically disordered media, because space discretization based on standard coordinate systems is not commensurate with the natural discretization into geometrically disordered cells. Indeed, we found that two classical spectral methods, the Fast Fourier Transform and the Graph Fourier transform, fail to reproduce all expected properties of spectra of plane waves and of white noise. We therefore built a method, which we call Cellular Fourier Transform (CFT), to analyze cell-scale fields, which comprise both discrete fields defined only at cell level and continuous fields smoothed out from their sub-cell variations. Our approach is based on the construction of a discrete operator suited to the disordered geometry and on the computation of its eigenvectors, which, respectively, play the same role as the Laplace operator and sine waves in Euclidean coordinate systems. We show that CFT has the expected behavior for sinusoidal fields and for random fields with long-range correlations. Our approach for spectral analysis is suited to any geometrically disordered material, such as a biological tissue with complex geometry, opening the path to systematic multiscale analyses of material behavior.

physics.bio-ph↗

arXiv2016

Mesoscopic formulas of linear and angular momentum fluxes

Many approaches of coarse-graining have been developed under the names of Cosserat theory or polar-fluid theory, for those materials in which some component elements undergo non-affine deformations, such as elastic materials with inclusions or granular matters. For the complex elements such as living cells, however, the microscopic variables and their dynamics are often unknown, and there have been no systematic theory of coarse-graining from the microscales, nor the formulas like Irving-Kirkwood formula that constitutes the macroscopic stress or couple-stress in terms of some microscale quantities. We show that, for the quasi-steady states, the coarse-graining procedure must generally provides with the Cosserat-type balance equations as long as the procedure keeps track of the conservation of linear and angular momenta, and that the fluxes of these conserved quantities should generally be expressed in the Irving-Kirkwood-type formulas, where the inter- particle distance or forces/torques should be replaced by those associated to the pair of neighboring coarse-graining volumes. This framework, which refers to no particular micro-variables or dynamics, is valid for active complex matters out of equilibrium and with any multi-body interactions.

cond-mat.soft↗

arXiv2013

From adiabatic piston to non-equilibrium hydrodynamics

Based on the new concept of the {\it momentum transfer deficiency due to dissipation} (MDD), the physical basis of the mechanism of ``adiabatic piston'' is explained. The implication of MDD in terms of hydrodynamics under non-equilibrium steady state also discussed.

cond-mat.stat-mech↗

arXiv2012

A hard disk analysis of momentum deficit due to dissipation

When a Brownian object is in a nonequilibrium steady state, actual force exerted on it is different from one in a thermal equilibrium. In our previous paper [Phys. Rev. Lett. 108 (2012), 160601] we discovered a general principle which relates the missing force to dissipation rates through a concept of momentum deficit due to dissipation (MDD). In this article, we examine the principle using various models based on hard disk gases and Brownian pistons. Explicit expressions of the forces are obtained analytically and the results are compared with molecular dynamics simulations. The good agreement demonstrates the validity of MDD.

cond-mat.stat-mech↗

arXiv2012

Momentum transfer in non-equilibrium steady states

When a Brownian object interacts with non-interacting gas particles under non-equilibrium conditions, the energy dissipation associated to the Brownian motion causes an additional force on the object as a `momentum transfer deficit'. This principle is demonstrated first by a new NESS model and then applied to several known models such as adiabatic piston for which simple explanation has been lacking.

cond-mat.stat-mech↗