Related papers: Light Propagation through Space-Time Non-Markovian…
Non-local reaction-diffusion partial differential equations (PDEs) involving the fractional Laplacian have arisen in a wide variety of applications. One common tool to analyse the dynamics of classical local PDEs near instability is to…
In weakly nonlinear dispersive wave systems, long-time dynamics are typically governed by time resonances, where wave phases evolve coherently due to exact frequency matching. Recent advances in spatio-temporal spectrum measurements,…
We demonstrate that a model with extra dimensions formulated in Csaki et al. (Phys Rev D 62, 045015), which fatefully reproduces Friedmann-Robertson-Walker (FRW) equations on the brane, allows for an apparent superluminal propagation of…
Light propagating in an optical waveguide can gain or lose power through interaction with a travelling acoustic wave or radio-frequency modulation of permittivity. Here, we model this propagation by considering an optical wave interacting…
We describe a novel approach to statistical learning from particles tracked while moving in a random environment. The problem consists in inferring properties of the environment from recorded snapshots. We consider here the case of a fluid…
Stochastic partial differential equations (SPDEs) represent a very active research field with numerous recent developments and breakthrough results. There are several well-established approaches and methods used to construct solutions for…
Introducing angular dispersion into a pulsed field associates each frequency with a particular angle with respect to the propagation axis. A perennial yet implicit assumption is that the propagation angle is differentiable with respect to…
The developing of (non-Markovian) memory effects strongly depends on the underlying system-environment dynamics. Here we study this problem in multipartite arrangements where all subsystems are coupled to each other by non-diagonal…
Non-equilibrium systems have long-ranged spatial correlations even far away from critical points. This implies that the likelihoods of spatial steady state profiles of physical observables are nonlocal functionals. In this letter, it is…
We propose and demonstrate theoretically a method to achieve and design optical nonlinear responses through a light-mediated spatial hybridization of different standard nonlinearities. The mechanism is based on the fact that optical…
We designed a model-based analysis to predict the occurrence of population patterns in distributed spiking activity. Using a maximum entropy principle with a Markovian assumption, we obtain a model that accounts for both spatial and…
Unidirectional pulse propagation equations [UPPE, Phys. Rev. E 70, 036604 (2004)] have provided a theoretical underpinning for computer-aided investigations into dynamics of high-power ultrashort laser pulses and have been successfully…
We deal with parametric estimation for a parabolic linear second order stochastic partial differential equation (SPDE) with a small dispersion parameter based on high frequency data which are observed in time and space. By using the thinned…
Over the past several decades, phase field modeling has been established as a standard simulation technique for mesoscopic science, allowing for seamless boundary tracking of moving interfaces and relatively easy coupling to other physical…
In this paper we establish the strong existence, pathwise uniqueness and a comparison theorem to a stochastic partial differential equation driven by Gaussian colored noise with non-Lipschitz drift, H\"older continuous diffusion…
Recent experiments have demonstrated that it is possible to alter the dispersion of a medium without significantly altering its absorption or refractive index and that this may be done while a wave propagates through the medium. This…
We provide an introduction to complex photonic media, that is, composite materials with spatial inhomogeneities that are distributed over length scales comparable to or smaller than the wavelength of light. This blossoming field is firmly…
In a series of two papers, we investigate the large deviations and asymptotic behavior of stochastic models of brain neural networks with random interaction coefficients. In this first paper, we take into account the spatial structure of…
In this paper, we address the question of the discretization of Stochastic Partial Differential Equations (SPDE's) for excitable media. Working with SPDE's driven by colored noise, we consider a numerical scheme based on finite differences…
A method is proposed for the analysis of the propagation of electromagnetic waves through a homogeneous slab of a medium with Drude-Lorentz dispersion behavior, and excited by a causal sinusoidal source. An expression of the time dependent…