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Vincent Rossetto

Publications and source records attributed to Vincent Rossetto.

17 recordsLinked to original sources
arXiv2025

Structure and statistical organization of the stationary state of the Oslo model

In most driven-dissipative sandpile models, the dynamics of the system reaches a critical stationary state. This state displays organization features such as a power-law avalanche spectrum and hyperuniformity, but these features often emerge without a clear path from the microscopic evolution rules. Only in a few cases is there an available description of the stationary state, in other sandpile models the question is open. In this article, we present our result on the stationary state of the Oslo model, a driven-dissipative sandpile model with intrinsic randomness. In order to do so, we use different representations of the system configurations and of the dynamical process. Moving back and forth between these representations allows to identify invariant quantities for each configurations. Moreover, we obtain the detailed statistical description of the stationary state by considering all paths leading to a given configuration at once, and by summing their contributions under the constraint specified by the invariants. As a result, we find that the configurations of the stationary state are structured into a small number of equivalence classes, and that their statistical weights are related to the counting of colored diagrams respecting a small set of rules.

cond-mat.stat-mech↗
arXiv2022

Isotropic radiative transfer as a phase space process: Lorentz covariant Green's functions and first-passage times

The solutions of the radiative transfer equation, known for the energy density, do not satisfy the fundamental transitivity property for Green's functions expressed by Chapman-Kolmogorov's relation. I show that this property is retrieved by considering the radiance distribution in phase space. Exact solutions are obtained in one and two dimensions as probability density functions of continous-time persistent random walks, the Fokker-Planck equation of which is the radiative transfer equation. The expected property of Lorentz covariance is verified. I also discuss the measured signal from a pulse source in one dimension, which is a first-passage time distribution, and unveil an effective random delay when the pulse is emitted away from the observer.

cond-mat.stat-mech↗
arXiv2022

Statistical properties of the gravitational force through ordering statistics

We investigate the statistical distribution of Newtonian gravitational forces acting on a test particle embedded in an infinite, homogeneous, and uncorrelated random gas of point masses. Using order statistics, we derive the probability density functions of distances to the $n$-th nearest neighbors in arbitrary spatial dimensions and analyze their contributions to the total gravitational force. We show that, in three dimensions, the formally divergent variance of the Holtsmark probability density function arises entirely from the first nearest neighbor, while contributions from more distant neighbors remain finite. Our results provide a clear decomposition of local versus distant contributions to the gravitational forces exerted on a test particle, and explore the dominant role of nearest neighbors in the divergence of the Holtsmark distribution's variance.

cond-mat.stat-mech↗
arXiv2021

Eulerian spatio-temporal correlations in passive scalar turbulence

We study the spatio-temporal two-point correlation function of passively advected scalar fields in the inertial-convective range in three dimensions by means of numerical simulations. We show that at small time delays $t$ the correlations decay as a Gaussian in the variable $tp$ where $p$ is the wavenumber. At large time delays, a crossover to an exponential decay in $tp^2$ is expected from a recent functional renormalization group (FRG) analysis. We study this regime for a scalar field advected by a Kraichnan's ``synthetic'' velocity field, and accurately confirm the FRG result, including the form of the prefactor in the exponential. By introducing finite time correlations in the synthetic velocity field, we uncover the crossover between the two regimes.

physics.flu-dyn↗
arXiv2021

Spatio-temporal correlations in 3D homogeneous isotropic turbulence

We use Direct Numerical Simulations (DNS) of the forced Navier-Stokes equation for a 3-dimensional incompressible fluid in order to test recent theoretical predictions. We study the two- and three-point spatio-temporal correlation functions of the velocity field in stationary, isotropic and homogeneous turbulence. We compare our numerical results to the predictions from the Functional Renormalization Group (FRG) which were obtained in the large wavenumber limit. DNS are performed at various Reynolds numbers and the correlations are analyzed in different time regimes focusing on the large wavenumbers. At small time delays, we find that the two-point correlation function decays as a Gaussian in the variable $kt$ where $k$ is the wavenumber and $t$ the time delay. The three-point correlation function, determined from the time-dependent advection-velocity correlations, also follows a Gaussian decay at small $t$ with the same prefactor as the one of the two-point function. These behaviors are in precise agreement with the FRG results, and can be simply understood as a consequence of sweeping. At large time delays, the FRG predicts a crossover to an exponential in $k^2 t$, which we were not able to resolve in our simulations. However, we analyze the two-point spatio-temporal correlations of the modulus of the velocity, and show that they exhibit this crossover from a Gaussian to an exponential decay, although we lack of a theoretical understanding in this case. This intriguing phenomenon calls for further theoretical investigation.

physics.flu-dyn↗
arXiv2020

Analysis of the dissipative range of the energy spectrum in grid turbulence and in direct numerical simulations

We present a statistical analysis of the behavior of the kinetic energy spectrum in the dissipative range of scales of fully developed three-dimensional turbulence. We analyze spectra recorded in experiments of grid turbulence generated in the Modane wind tunnel, and spectra obtained from high-resolution direct numerical simulations of the forced Navier-Stokes equation. We focus on wave-number scales in the near-dissipative range. We find that in this domain, the spectra behave as a stretched exponential with an exponent $α= 0.68 \pm 0.19$. This result corroborates previous DNS studies which found that the spectrum in the near-dissipative range is best modeled by a stretched exponential with $α<1$. Moreover, we here give an estimate for the actual value of $α$, which turns out to be in precise agreement with the theoretical prediction $α=2/3$ from the non-perturbative renormalisation group.

physics.flu-dyn↗
arXiv2020

The one-dimensional asymmetric persistent random walk

Persistent random walks are intermediate transport processes between a uniform rectilinear motion and a Brownian motion. They are formed by successive steps of random finite lengths and directions travelled at a fixed speed. The isotropic and symmetric one-dimensional persistent random walk is governed by the telegrapher's equation, also called hyperbolic heat conduction equation. These equations have been designed to resolve the paradox of the infinite speed in the heat and diffusion equations. The finiteness of both the speed and the correlation length leads to several classes of random walks: Persistent random walk in one dimension can display anomalies that cannot arise for Brownian motion such as anisotropy and asymmetries. In this work we focus on the case where the mean free path is anisotropic, the only anomaly leading to a physics that is different from the telegrapher's case. We derive exact expression of its Green's function, for its scattering statistics and distribution of first-passage time at the origin. The phenomenology of the latter shows a transition for quantities like the escape probability and the residence time. (Second version that corrects the typos of the first version).

cond-mat.stat-mech↗
arXiv2017

Spatiotemporal velocity-velocity correlation function in fully developed turbulence

Turbulence is an ubiquitous phenomenon in natural and industrial flows. Since the celebrated work of Kolmogorov in 1941, understanding the statistical properties of fully developed turbulence has remained a major quest. In particular, deriving the properties of turbulent flows from a mesoscopic description, that is from Navier-Stokes equation, has eluded most theoretical attempts. Here, we provide a theoretical prediction for the {\it space and time} dependent velocity-velocity correlation function of homogeneous and isotropic turbulence from the field theory associated to Navier-Stokes equation with stochastic forcing. This prediction is the analytical fixed-point solution of Non-Perturbative Renormalisation Group flow equations, which are exact in a certain large wave-number limit. This solution is compared to two-point two-times correlation functions computed in direct numerical simulations. We obtain a remarkable agreement both in the inertial and in the dissipative ranges.

physics.flu-dyn↗
arXiv2014

Simultaneous double transformations of functions depending on space and time

It is shown that performing simultaneously two transformations on functions of space and time (for instance a Fourier transform on the space variable and a Laplace transform on the time variable) can be easier than performing them one after the other when the variables are combined in invariant quantities. This is naturally also true when performing two inverse transforms simultaneously, when the conjugated variables are combined into a propagator. An immediate application is found in the computation of the solutions of partial differential equations. This article contains several general examples of such "simultaneous double transforms" for arbitrary analytic functions of space and time.

math-ph↗
arXiv2013

Local time in diffusive media and applications to imaging

Local time is the measure of how much time a random walk has visited a given position. In multiple scattering media, where waves are diffuse, local time measures the sensitivity of the waves to the local medium's properties. Local variations of absorption, velocity and scattering between two measurements yield variations in the wave field. These variations are proportionnal to the local time of the volume where the change happened and the amplitude of variation. The wave field variations are measured using correlations and can be used as input in a inversion algorithm to produce variation maps. The present article gives the expression of the local time in dimensions one, two and three and an expression of its fluctuations, in order to perform such inversions and estimate their accuracy.

cond-mat.stat-mech↗
arXiv2012

Stochastic description of geometric phase for polarized waves in random media

We present a stochastic description of multiple scattering of polarized waves in the regime of forward scattering. In this regime, if the source is polarized, polarization survives along a few transport mean free paths, making it possible to measure an outgoing polarization distribution. We solve the direct problem using compound Poisson processes on the rotation group SO(3) and non-commutative harmonic analysis. The obtained solution generalizes previous works in multiple scattering theory and is used to design an algorithm solving the inverse problem of estimating the scattering properties of the medium from the observations. This technique applies to thin disordered layers, spatially fluctuating media and multiple scattering systems and is based on the polarization but not on the signal amplitude. We suggest that it can be used as a non invasive testing method.

physics.data-an↗
arXiv2012

Observation of a non-adiabatic geometric phase for elastic waves

We report the experimental observation of a geometric phase for elastic waves in a waveguide with helical shape. The setup reproduces the experiment by Tomita and Chiao [A. Tomita, R.Y. Chiao, Phys. Rev. Lett. 57 (1986) 937-940, 2471] that showed first evidence of a Berry phase, a geometric phase for adiabatic time evolution, in optics. Experimental evidence of a non-adiabatic geometric phase has been reported in quantum mechanics. We have performed an experiment to observe the polarization transport of classical elastic waves. In a waveguide, these waves are polarized and dispersive. Whereas the wavelength is of the same order of magnitude as the helix's radius, no frequency dependent correction is necessary to account for the theoretical prediction. This shows that in this regime, the geometric phase results directly from geometry and not from a correction to an adiabatic phase.

physics.class-ph↗
arXiv2010

Locating a weak change using diffuse waves (LOCADIFF) : theoretical approach and inversion procedure

We describe a time-resolved monitoring technique for heterogeneous media. Our approach is based on the spatial variations of the cross-coherence of coda waveforms acquired at fixed positions but at different dates. To locate and characterize a weak change that occurred between successive acquisitions, we use a maximum likelihood approach combined with a diffusive propagation model. We illustrate this technique, called LOCADIFF, with numerical simulations. In several illustrative examples, we show that the change can be located with a precision of a few wavelengths and its effective scattering cross-section can be retrieved. The precision of the method depending on the number of source receiver pairs, time window in the coda, and errors in the propagation model is investigated. Limits of applications of the technique to real-world experiments are discussed.

physics.data-an↗
arXiv2009

A general framework for multiple scattering of polarized waves including anisotropies and Berry phase

We develop a framework for the multiple scattering of a polarized wave. We consider particles with spin propagating in a medium filled with scatterers. We write the amplitudes of each spin eigenstate in a local, mobile frame. One of the axes is in the direction of propagation of the particle. We use this representation to define a directional Green's operator of the homogeneous medium and also to write the spin-dependent scattering amplitudes. We show that this representation reveals a Berry phase. We establish a generalized Green-Dyson equation for the multiple scattering problem in this framework. We show that the generalized Green-Dyson equation can be solved by linear algebra if one uses a representation of the rotations based on Wigner D-matrices. The properties of light scattering are retrieved if we use spin 1 particles. Our theory allows to take into account several kinds of anisotropies like circular or linear dichroism and birefringence, Faraday effects andMie scattering within the same formalism. Several anisotropies can be present at the same time.

cond-mat.other↗
arXiv2004

DNA loop statistics and torsional modulus

The modelling of DNA mechanics under external constraints is discussed. Two analytical models are widely known, but disagree for instance on the value of the torsional modulus. The origin of this embarassing situation is located in the concept of writhe. This letter presents a unified model for DNA establishing a relation between the different approaches. I show that the writhe created by the loops of DNA is at the origin of the discrepancy. To take this into account, I propose a new treatment of loop statistics based on numerical simulations using the most general formula for the writhe, and on analytic calculations with only one fit parameter. One can then compute the value of the torsional modulus of DNA without the need of any cut-off.

cond-mat.soft↗