Related papers: High viscosity effects on solitary wave propagatio…
Due to the non-linearity of Hertzian contacts, the speed of sound $c$ in granular matter is expected to increase with pressure as $P^{1/6}$. A static layer of grains under gravity is thus stratified so that bulk waves are refracted toward…
We analyze the propagation of elastic waves in soft materials subjected to finite deformations. We derive explicit dispersion relations, and apply these results to study elastic wave propagation in (i) nearly incompressible materials such…
We examine the general question of statistical changes experienced by ensembles of nonlinear random waves propagating in systems ruled by integrable equations. In our study that enters within the framework of integrable turbulence, we…
This paper is concerned with an asymptotic analysis of the dispersion relation for wave propagation in an elastic layer of uniform thickness. The layer is subject to an underlying simple shear deformation accompanied by an arbitrary uniform…
We study dispersion properties of linear surface gravity waves propagating in an arbitrary direction atop a current profile of depth-varying magnitude using a piecewise linear approximation, and develop a robust numerical framework for…
Recent experiments on femtosecond pulses in water displayed long distance propagation analogous to that reported in air. We verify this phenomena numerically and show that the propagation is dynamic as opposed to self-guided. Furthermore,…
Oceanic internal waves often have curvilinear fronts and propagate over various currents. We present the first study of long weakly-nonlinear internal ring waves in a three-layer fluid in the presence of a background linear shear current.…
Large-scale molecular dynamics simulations are used to simulate a layer of nanoparticles diffusing on the surface of a liquid. Both a low viscosity liquid, represented by Lennard-Jones monomers, and a high viscosity liquid, represented by…
We study the propagation of one-dimentional optical beams in a weakly nonlocal medium exhibiting cubic-quintic nonlinearity. A nonlinear equation governing the evolution of the beam intensity in the nonlocal medium is derived thereby which…
Cilia and flagella are hair-like appendages that protrude from the surface of a variety of eukaryotic cells and deform in a wavelike fashion to transport fluids and propel cells. Motivated by the ubiquity of non-Newtonian fluids in biology,…
We report on recent progress in the study of nonlinear diffusion equations involving nonlocal, long-range diffusion effects. Our main concern is the so-called fractional porous medium equation, $\partial_t u +(-\Delta)^{s}(u^m)=0$, and some…
Linear stability of solid body rotating flows with axisymmetric density variations is addressed analytically. Considering inviscid disturbances, a non trivial dispersion relation is obtained and it is shown that the instability is of…
We study water waves propagating over a smooth obstacle in a fluid of varying depth, motivated by the observation that submerged islands in the ocean act as effective lenses that increase the amplitude and destructive power of tsunami waves…
We report experiments on gravity-capillary wave turbulence on the surface of a fluid. The wave amplitudes are measured simultaneously in time and space using an optical method. The full space-time power spectrum shows that the wave energy…
A recent study has demonstrated that phase separation in binary liquid mixtures is arrested in the presence of elastic networks and can lead to a nearly uniformly-sized distribution of the dilute-phase droplets. At longer timescales, these…
The combined impact of axial stretching and cross-stream diffusion on the downstream transport of solute is termed Taylor dispersion. The dispersion of active suspensions is qualitatively distinct: viscous and external torques can establish…
We investigate finite-size effects on diffusion in confined fluids using molecular dynamics simulations and hydrodynamic calculations. Specifically, we consider a Lennard-Jones fluid in slit pores without slip at the interface and show that…
We give a detailed analysis of long range cumulative scattering effects from rough boundaries in waveguides. We assume small random fluctuations of the boundaries and obtain a quantitative statistical description of the wave field. The…
We investigate the effect of dispersion on convection in porous media by performing direct numerical simulations (DNS) in a two-dimensional Rayleigh-Darcy domain. Scaling analysis of the governing equations shows that the dynamics of this…
The problem of front propagation in flowing media is addressed for laminar velocity fields in two dimensions. Three representative cases are discussed: stationary cellular flow, stationary shear flow, and percolating flow. Production terms…