Related papers: Sensing and Multiscale Structure
The fluctuations in the particle size distribution for processes of fragmentation and aggregation are studied for stationary state regimes. The system is described in terms of a stochastic process over an adequate tree structure. The RMS…
We present a simple and systematic procedure to determine the effective dynamics of a Brownian particle coupled to a rapidly fluctuating correlated medium, modeled as a scalar Gaussian field, under spatial confinement. The method allows us,…
We report an extensive numerical study and supporting experimental results on the spectral characterization of optical aberrations in macroscopic fluidic lenses with tunable focal distance and aperture shape. Using a Shack-Hartmann…
This paper concerns the derivation of radiative transfer equations for acoustic waves propagating in a randomly fluctuating slab (between two parallel planes) in the weak-scattering regime, and the study of boundary effects through an…
Motivated by the modeling of the temporal structure of the velocity field in a highly turbulent flow, we propose and study a linear stochastic differential equation that involves the ingredients of a Ornstein-Uhlenbeck process, supplemented…
In this paper, we investigate the localization properties of optical waves in disordered systems with multifractal scattering potentials. In particular, we apply the localization landscape theory to the classical Helmholtz operator and,…
Density fluctuations of expanding nuclear matter are studied within a mean-field model in which fluctuations are generated by an external stochastic field. Fluctuations develop about a mean one-body phase-space density corresponding to a…
Scattering resonances arise in wave phenomena and play an important role in many applications. While extensive theoretical studies have been conducted, effective numerical computation remains limited, and most existing methods suffer from…
This paper deals with an estimating of the Fractal Dimension of a hydrometeorology variables like an Air temperature or humidity at a different sites in a landscape (and will be further evaluated from the land use point of view). Three…
We derive accurate formulas for thermal fluctuations in multilayer interferometric coating taking into account light propagation inside the coating. In particular, we calculate the reflected wave phase as a function of small displacements…
In this work, we are devoted to the reconstruction of an unknown initial value from the terminal data. The asymptotic and root-distribution properties of Mittag-Leffler functions are used to establish stability of the backward problem.…
We describe the fractal solid by a special continuous medium model. We propose to describe the fractal solid by a fractional continuous model, where all characteristics and fields are defined everywhere in the volume but they follow some…
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…
Scatterometry is a fast, indirect and nondestructive optical method for the quality control in the production of lithography masks. Geometry parameters of line gratings are obtained from diffracted light intensities by solving an inverse…
Numerical simulations of concrete fracture performed with a probabilistic mesoscale discrete model are presented. The model represents a substantial part of material randomness by assigning random locations to the largest aggregates. The…
Miscible tracer dispersion measurements in transparent model fractures with different types of wall roughness are reported. The nature (Fickian or not) of dispersion is determined by studying variations of the mixing front as a function of…
Light transport in superdiffusive media of finite size is studied theoretically. The intensity Green's function for a slab geometry is found by discretizing the fractional diffusion equation and employing the eigenfunction expansion method.…
Scale invariance of intrinsic patterns is an important concept in geology that can be observed in numerous geological objects and phenomena. These geological objects and phenomena are described as containing statistically selfsimilar…
We prove some weighted Fourier restriction estimates using polynomial partitioning and refined Strichartz estimates. As application we obtain improved spherical average decay rates of the Fourier transform of fractal measures, and therefore…
We introduce a robust numerical technique to verify the causality of sampled scattering parameters given on a finite bandwidth. The method is based on a filtered Fourier transform and includes a rigorous estimation of the errors caused by…