相关论文: Multi-scale analysis implies strong dynamical loca…
The propagation of waves in highly inhomogeneous media is a problem of interest in multiple fields including seismology, acoustics and electromagnetism. It is also relevant for technological applications such as the design of sound…
We present some recent results concerning the persistence of dynamical localization for disordered systems of n particles under weak interactions.
Wave localization is a ubiquitous phenomenon. It refers to situations that transmitted waves in scattering media are trapped in space and remain confined in the vicinity of the initial site until dissipated. Based on a scaling analysis, the…
We apply variational-wavelet approach for constructing multiscale high-localized eigenmodes expansions in different models of nonlinear waves. We demonstrate appearance of coherent localized structures and stable pattern formation in…
We propose a multiscale approach for predicting quantities in dynamical systems which is explicitly structured to extract information in both fine-to-coarse and coarse-to-fine directions. We envision this method being generally applicable…
Many complex systems exhibit hydrodynamic (or macroscopic) behavior at large scales characterized by few variables such as the particle number density, temperature and pressure obeying a set of hydrodynamic (or macroscopic) equations. Does…
We adapt a simplified version of the Multi-Scale Analysis presented in \cite{C11} to multi-particle tight-binding Anderson models. Combined with a recent eigenvalue concentration bound for multi-particle systems \cite{C10}, the new method…
Waves traveling through random media exhibit random focusing that leads to extremely high wave intensities even in the absence of nonlinearities. Although such extreme events are present in a wide variety of physical systems and the…
We establish a theory for multivariate extreme value analysis of dynamical systems. Namely, we provide conditions adapted to the dynamical setting which enable the study of dependence between extreme values of the components of…
This paper generalises dynamic factor models for multidimensional dependent data. In doing so, it develops an interpretable technique to study complex information sources ranging from repeated surveys with a varying number of respondents to…
Nonlinear dynamical stochastic models are ubiquitous in different areas. Excitable media models are typical examples with large state dimensions. Their statistical properties are often of great interest but are also very challenging to…
This article illustrates the application of multiple scales analysis to two archetypal quasilinear systems; i.e. to systems involving fast dynamical modes, called fluctuations, that are not directly influenced by fluctuation--fluctuation…
Wave localization is ubiquitous in disordered media -- from amorphous materials, where soft-mode localization is closely related to materials failure, to semi-conductors, where Anderson localization leads to metal-insulator transition. Our…
We prove that once one has the ingredients of a ``single-energy multiscale analysis (MSA) result'' on the $\mathbb{Z}^d$ lattice, several spectral and dynamical localization results can be derived, the most prominent being strong dynamical…
We study acoustic propagation in one dimensional water ducts containing many air-filled blocks. The acoustic band structures for the periodic arrangements of the blocks is calculated, whereas the transmission for various random…
We introduce a method to efficiently study the dynamical properties of many-body localized systems in the regime of strong disorder and weak interactions. Our method reproduces qualitatively and quantitatively the real-time evolution with a…
Motivated by previous investigations on the radiative effects of the electric dipoles embedded in structured cavities, localization of electromagnetic waves in two dimensions is studied {\it ab initio} for a system consisting of many…
We theoretically study the Anderson localization of a matter wave packet in a one-dimensional disordered potential. We develop an analytical model which includes the initial phase-space density of the matter wave and the spectral broadening…
We study the spatial structure of wave functions with exceptionally high local amplitudes in the Anderson model of localisation. By means of exact diagonalisations of finite systems, we obtain and analyse images of these wave functions: we…
In this note we show that in any dimension $d$, the strong disorder property implies the strong localization property. This is established for a continuous time model of directed polymers in a random environment : the parabolic Anderson…