Vincent Rossetto

Locating a small change in a multiple scattering environment

This article presents an imaging technique to locate a weak perturbation in a multiple scattering environment. We derive a formula to predict the spatiotemporal decorrelation of diffuse coda waves induced by an extra scatterer. Locating this new defect is formulated as an inverse problem which is solved by a maximum likelihood approach. Using elastic waves in the 50–400 kHz frequency band, we recover the position of a millimetric hole drilled in a concrete sample with a precision of a few centimeter. Note that the size of the defect is comparable to the size of the myriads of heterogeneities constituting the sample.

Locating a weak change using diffuse waves: 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 diffuse waves acquired at fixed positions but at different dates. The technique applies to all kind of waves, provided that waveforms can be acquired with a sampling frequency much larger than the wave frequency. 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 characterize this technique, locating a weak change using diffuse waves, called LOCADIFF, with the aid of numerical simulations. In several illustrative examples, we show that the change can be located with a precision of a few wavelengths and that its effective scattering cross-section can be retrieved. We investigate how the accuracy and precision of the method depends on the number of source-receiver pairs, on the time window used to compute the cross-correlation and on the errors in the propagation model. Applications can be found in nondestructive testing, seismology, radar, and sonar location.

Writhing geometry of open DNA

Motivated by recent experiments on DNA torsion-force-extension characteristics we consider the writhing geometry of open stiff molecules. We exhibit a cyclic motion which allows arbitrarily large twisting of the end of a molecule via an activated process. This process is suppressed for forces larger than femtonewtons which allows us to show that experiments are sensitive to a generalization of the Călugăreanu–White formula for the writhe. Using numerical methods we compare this formulation of the writhe with recent analytic calculations.

Imaging multiple local changes in heterogeneous media with diffuse waves

This study focuses on imaging local changes in heterogeneous media. The method employed is demonstrated and validated using numerical experiments of acoustic wave propagation in a multiple scattering medium. Changes are simulated by adding new scatterers of different sizes at various positions in the medium, and the induced decorrelation of the diffuse (coda) waveforms is measured for different pairs of sensors. The spatial and temporal dependences of the decorrelation are modeled through a diffuse sensitivity kernel, based on the intensity transport in the medium. The inverse problem is then solved with a linear least square algorithm, which leads to a map of scattering cross section density of the changes.

Probing slow dynamics of consolidated granular multicomposite materials by diffuse acoustic wave spectroscopy

The stiffness of a consolidated granular medium experiences a drop immediately after a moderate mechanical solicitation. Then the stiffness rises back toward its initial value, following a logarithmic time evolution called slow dynamics. In the literature, slow dynamics has been probed by macroscopic quantities averaged over the sample volume, for instance, by the resonant frequency of vibrational eigenmodes. This article presents a different approach based on diffuse acoustic wave spectroscopy, a technique that is directly sensitive to the details of the sample structure. The parameters of the dynamics are found to depend on the damage of the medium. Results confirm that slow dynamics is, at least in part, due to tiny structural rearrangements at the microscopic scale, such as inter-grain contacts.

Geometric depolarization in patterns formed by backscattered light.

We formulate a framework to extend the idea of Berrys topological phase to multiple light scattering, and in particular to backscattering of linearly polarized light. We show that the randomization of the geometric Berrys phases in the medium leads to a loss of the polarization degree of the light, i.e., to a depolarization. We use Monte Carlo simulations in which Berrys phase is calculated for each photon path. Then we average over the distribution of the geometric phases to calculate the form of the patterns, which we compare with experimental patterns formed by backscattered light between crossed or parallel polarizers.

Writhing Photons and Berry Phases in Polarized Multiple Scattering

We study theoretically the polarization state of light in multiple scattering media in the limit of low contrast in the refractive index. Linearly polarized photons are randomly rotated due to the Berry phase associated with the scattering path. For circularly polarized light independent speckle patterns are found for the two helical states. The statistics of the geometric phase is related to the writhe distribution of semiflexible polymers such as DNA.

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.

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 Greens 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 such as circular or linear dichroism and birefringence, Faraday effects, and Mie scattering within the same formalism. Several anisotropies can be present at the same time.

LOCADIFF: Locating a weak change with diffuse ultrasound

This article presents an imaging technique to locate a weak perturbation in a multiple scattering environment. We focus on concrete probed by ultrasound. We derive a formula to predict the spatiotemporal decorrelation of diffuse coda waves induced by an extra scatterer. We solve the inverse problem with a maximum likelihood approach. Using elastic waves in the 50-400 kHz frequency band, we recover the position of millimetric holes drilled in a concrete sample with a precision of a few centimeters.