Related papers: Multi-scale analysis implies strong dynamical loca…
We show that the sensitivity of wave speckle patterns in disordered nonlinear media to changes of scattering potential increases with sample size. For large enough sample size this quantity diverges, which implies that at given coherent…
We give a short analytic proof of local large deviations for i.i.d. random variables in the domain of a multivariate $\alpha$-stable law, $\alpha\in(0,1)\cup(1,2]$. Our method simultaneously covers lattice and nonlattice distributions (and…
In this work we study oceanic waves in a shallow water flow subject to strong wind forcing and rotation, and linearized around a inhomogeneous (non zonal) stationary profile. This extends the study \cite{CGPS}, where the profile was assumed…
We develop a theoretical model to investigate wave propagation in media with random time-varying properties, where temporal fluctuations lead to complex scattering dynamics. Focusing on the ensemble-averaged field, we derive an exact…
We consider a linear system that consists of a linear wave equation on a horizontal hypersurface and a parabolic equation in the half space below. The model describes longitudinal elastic waves in organic monolayers at the water-air…
We study two-dimensional wave propagation in materials whose properties vary periodically in one direction only. High order homogenization is carried out to derive a dispersive effective medium approximation. One-dimensional materials with…
It is found that there exist composite media that exhibit strong spatial dispersion even in the very large wavelength limit. This follows from the study of lattices of ideally conducting parallel thin wires (wire media). In fact, our…
We study a system of forced viscous shallow water equations with nontrivial bathymetry in two spatial dimensions. We develop a well-posedness theory for small but arbitrary forcing data, as well as for a fixed data profile but large…
We present a novel methodology based on filtered data and moving averages for estimating effective dynamics from observations of multiscale systems. We show in a semi-parametric framework of the Langevin type that our approach is…
An analytical theory, based on the perturbative treatment of the disorder and extended into a self-consistent set of equations for the dynamical density correlations, is developed and applied to the prototype one-dimensional model of…
Causal representation learning promises to extend causal models to hidden causal variables from raw entangled measurements. However, most progress has focused on proving identifiability results in different settings, and we are not aware of…
Scientists have observed and studied diffusive waves in contexts as disparate as population genetics and cell signaling. Often, these waves are propagated by discrete entities or agents, such as individual cells in the case of cell…
We establish the complete spectral exponential, and the strong Hilbert-Schmidt dynamical localization for the one-dimensional multi-particle Anderson tight-binding model and for weakly interacting particles system. In other words, we show…
The article summarizes the studies of wave fields in structured non-equilibrium media describing by means of nonlocal hydrodynamic models. Due to the symmetry properties of models, we derived the invariant wave solutions satisfying…
We consider the use of the energy density for describing a localization of relativistic particles. This method is consistent with the causality requirements. The related positive operator valued measure is presented. The probability…
We study the propagation and scattering of electromagnetic waves by random arrays of dipolar cylinders in a uniform medium. A set of self-consistent equations, incorporating all orders of multiple scattering of the electromagnetic waves, is…
This work relates quantitatively homogenization to Anderson localization for acoustic operators in disordered media. By blending dispersive estimates for homogenized operators and quantitative homogenization of the wave equation, we derive…
Partial-wave analysis is one step in a process connecting experimental measurements to the N* states we are studying. Progress has been made in the area of `model-independent' analysis. However, more model-dependent approaches are needed to…
Multi-scale wave propagation problems are computationally costly to solve by traditional techniques because the smallest scales must be represented over a domain determined by the largest scales of the problem. We have developed and…
We consider wave models with lower order terms and recollect some recent results on energy and dispersive estimates for their solution based on symbolic type estimates for coefficients and partly stabilisation conditions. The exposition is…