Approximation of a compressible Navier-Stokes system by non-linear acoustical models

We analyse the existing derivation of the models of non-linear acoustics such as the Kuznetsov equation, the NPE equation and the KZK equation. The technique of introducing a corrector in the derivation ansatz allows to consider the solutions of these equations as approximations of the solution of the initial system (a com-pressible Navier-Stokes/Euler system). The validation of the approximation ansatz is given for the KZK equation case

Spatial correlations of the spontaneous decay rate as a probe of dense and correlated disordered materials

We study theoretically and numerically a new kind of spatial correlation for waves in disordered media. We define $C_{\Gamma}$ as the correlation function of the fluorescent decay rate of an emitter at two different positions inside the medium. We show that the amplitude and the width of $C_{\Gamma}$ provide decoupled information on the structural correlation of the disordered medium and on the local environment of the emitter. This result may stimulate the emergence of new imaging and sensing modalities in complex media

Polarization and spatial coherence of electromagnetic waves in uncorrelated disordered media

Spatial field correlation functions represent a key quantity for the description of mesoscopic phenomena in disordered media and the optical characterization of complex materials. Yet many aspects related to the vector nature of light waves have not been investigated so far. We study theoretically the polarization and coherence properties of electromagnetic waves produced by a dipole source in a three-dimensional uncorrelated disordered medium. The spatial field correlation matrix is calculated analytically using a multiple scattering theory for polarized light. This allows us to provide a formal description of the light depolarization process in terms of "polarization eigenchannels" and to derive analytical formulas for the spatial coherence of multiply-scattered light

Short time heat diffusion in compact domains with discontinuous transmission boundary conditions

We consider a heat problem with discontinuous diffusion coefficientsand discontinuous transmission boundary conditions with a resistancecoefficient. For all compact $(\epsilon,\delta)$-domains $\Omega\subset\mathbb{R}^n$ with a $d$-set boundary (for instance, aself-similar fractal), we find the first term of the small-timeasymptotic expansion of the heat content in the complement of$\Omega$, and also the second-order term in the case of a regularboundary. The asymptotic expansion is different for the cases offinite and infinite resistance of the boundary. The derived formulasrelate the heat content to the volume of the interior Minkowskisausage and present a mathematical justification to the de Gennes'approach. The accuracy of the analytical results is illustrated bysolving the heat problem on prefractal domains by a finite elementsmethod

Multiple scattering of polarized light in disordered media exhibiting short-range structural correlations

We develop a model based on a multiple scattering theory to describe the diffusion of polarized light in disordered media exhibiting short-range structural correlations. Starting from exact expressions of the average field and the field spatial correlation function, we derive a radiative transfer equation for the polarization-resolved specific intensity that is valid for weak disorder and we solve it analytically in the diffusion limit. A decomposition of the specific intensity in terms of polarization eigenmodes reveals how structural correlations, represented via the standard anisotropic scattering parameter $g$, affect the diffusion of polarized light. More specifically, we find that propagation through each polarization eigenchannel is described by its own transport mean free path that depends on $g$ in a specific and non-trivial way

Cross density of states and mode connectivity: Probing wave localization in complex media

We introduce the mode connectivity as a measure of the number of eigenmodes of a wave equation connecting two points at a given frequency. Based on numerical simulations of scattering of electromagnetic waves in disordered media, we show that the connectivity discriminates between the diffusive and the Anderson localized regimes. For practical measurements, the connectivity is encoded in the second-order coherence function characterizing the intensity emitted by two incoherent classical or quantum dipole sources. The analysis applies to all processes in which spatially localized modes build up, and to all kinds of waves