Related papers: Wave propagation phenomena in nonlinear hierarchic…
We consider a diffusion process on the edges of a finite network and allow for feedback effects between different, possibly non-adjacent edges. This generalizes the setting that is common in the literature, where the only considered…
This work considers the propagation of high-frequency waves in highly-scattering media where physical absorption of a nonlinear nature occurs. Using the classical tools of the Wigner transform and multiscale analysis, we derive semilinear…
We study inverse problems consisting on determining medium properties using the responses to probing waves from the machine learning point of view. Based on the understanding of propagation of waves and their nonlinear interactions, we…
Waves scattered at a self-oscillating mode can exhibit superradiance, or net amplification of an external harmonic excitation. This exotic behavior, arising from the nonlinear coupling between the mode and the incident wave, is…
Understanding how complex behaviors, opinions, and innovations spread in online social networks remains a central challenge in computational social science. Existing models of complex contagion typically rely on stylized threshold…
We present a theory of electron, electromagnetic, and elastic wave propagation in systems consisting of non-overlapping scatterers in a host medium. The theory provides a framework for a unified description of wave propagation in…
This study explores the use of fractional calculus as a possible tool to model wave propagation in complex, heterogeneous media. We illustrate the methodology by focusing on elastic wave propagation in a one-dimensional periodic rod. The…
We study the onset of the propagation failure of wave fronts in systems of coupled cells. We introduce a new method to analyze the scaling of the critical external field at which fronts cease to propagate, as a function of intercellular…
In the context of epidemic spreading, many intricate dynamical patterns can emerge due to the cooperation of different types of pathogens or the interaction between the disease spread and other failure propagation mechanism. To unravel such…
This paper investigates the propagation characteristics of circular waveguides whose interior surface is coated with a thin metamaterial liner possessing dispersive, negative, and near-zero permittivity. A field analysis of this system…
Using the dynamics of information propagation on a network as our illustrative example, we present and discuss a systematic approach to quantifying heterogeneity and its propagation that borrows established tools from Uncertainty…
Understanding how local perturbations induce the transient dynamics of a network of coupled units is essential to control and operate such systems. Often a perturbation initiated in one unit spreads to other units whose dynamical state they…
Direct numerical simulations are conducted to study the receptivity and transition mechanisms in a solitary wave boundary layer developing over randomly organized wave-like bottom topography. The boundary layer flow shows a selective…
There has been an increasing interest in learning dynamics simulators for model-based control. Compared with off-the-shelf physics engines, a learnable simulator can quickly adapt to unseen objects, scenes, and tasks. However, existing…
Nonlinear reaction-diffusion systems admit a wide variety of spatiotemporal patterns or structures. In this lecture, we point out that there is certain advantage in studying discrete arrays, namely cellular neural/nonlinear networks (CNNs),…
Accurately estimating the refractive environment over multiple frequencies within the marine atmospheric boundary layer is crucial for the effective deployment of radar technologies. Traditional parabolic equation simulations, while…
We present a detailed discussion of scalar wave propagation and light intensity transport in three dimensional random dielectric media with optical gain. The intrinsic length and time scales of such amplifying systems are studied and…
We study the propagation of wave packets for a one-dimensional system of two coupled Schr\"odinger equations with a cubic nonlinearity, in the semi-classical limit. Couplings are induced by the nonlinearity and by the potential, whose…
It is possible to discuss the propagation of an electronic current through certain layered nanostructures modeling them as a collection of random one-dimensional interfaces, through which a coherent signal can be transmitted or reflected…
A general theory of nonlinear signal-noise interactions for wavelength division multiplexed fiber-optic coherent transmission systems is presented. This theory is based on the regular perturbation treatment of the nonlinear Schrodinger…