Motivated by current interest in understanding statistical properties of random landscapes high-dimensional spaces, we consider a model the landscape $\mathbb{R}^N$ obtained superimposing $M>N$ plane waves wavevectors and amplitudes. For this show how to compute "annealed complexity" controlling asymptotic growth rate mean number stationary points as $N\to \infty$ at fixed ratio $\alpha=M/N>1$....

This paper presents new laboratory data on long-wave (surf-beat) forcing by the random breaking of shorter gravity water waves on a plane beach. The data include incident and outgoing wave amplitudes, together with shoreline oscillation amplitudes at long-wave frequencies, from which the correlation between forced long waves and short-wave groups is examined. A detailed analysis of the cross-sh...

The polymerization of actin via branching at a cell membrane containing nucleation-promoting factors is simulated using a stochastic-growth methodology. The polymerized-actin distribution displays three types of behavior: (a) traveling waves, (b) moving patches, and (c) random fluctuations. Increasing actin concentration causes a transition from patches to waves. The waves and patches move by a...

We consider classical acoustic waves in a medium described by a position dependent mass density %(x). We assume that %(x) is a random perturbation of a periodic function % 0 (x) and that the periodic acoustic operator A 0 = ?r 1 % 0 (x) r has a gap in the spectrum. We prove the existence of localized waves, i.e., nite energy solutions of the acoustic equations with the property that almost all ...

We study the quasi-random choice method (QRCM) for the Liouville equation of geometrical optics with discontinuous local wave speed. This equation arises in the phase space computation of high frequency waves through interfaces, where waves undergo partial transmissions and reflections. The numerical challenges include interface, contact discontinuities, and measure-valued solutions. The so-cal...

In this paper we present a simple and robust random projection method for underresolved numerical simulation of stii detonation waves in chemically reacting ows. This method is based on the random projection method proposed by the authors for general hyperbolic systems with stii reaction terms 1], where the ignition temperature is randomized in a suitable domain. It is simpliied using the equat...

Much is known about the propagation of waves through periodic arrangements of identical scatterers, such as through a photonic crystal. Here, we consider a simple realization: scalar waves through a regular two-dimensional array of identical small circles. We are interested in the effect of random disorder: the circles remain identical, but their centres are given small random displacements. We...