Related papers: Dispersive Lamb Systems
Lamb waves are trapped acoustic-gravity waves that propagate energy over great distances along a solid boundary in density stratified, compressible fluids. They constitute useful indicators of explosions in planetary atmospheres. When the…
We study the propagation of transient waves under the action of a vertical step point load on the surface of a half-space filled by a block medium. The block medium is modeled by a square lattice of masses connected by springs in the…
From a simple model for the driven motion of a planar interface under the influence of a diffusion field we derive a damped nonlinear oscillator equation for the interface position. Inside an unstable regime, where the damping term is…
We identify a new type of pattern formation in spatially distributed active systems. We simulate one-dimensional two-component systems with predator-prey local interaction and pursuit-evasion taxis between the components. In a sufficiently…
We derive the general solution of the unsteady Stokes equations for an unbounded fluid in spherical polar coordinates, in both time and frequency domains. The solution is an expansion in vector spherical harmonics and given as a sum of a…
The phase diffusion in a self-sustained oscillator, which produces oscillator's spectral linewidth, is inherently governed by a nonlinear Langevin equation. Over past 40 years, the equation has been treated with linear approximation,…
When a two level system (TLS) is coupled to an electromagnetic resonator, its transition frequency changes in response to the quantum vacuum fluctuations of the electromagnetic field, a phenomenon known as the Lamb shift. Remarkably, by…
We study the problem of a temporal discontinuity in the permittivity of an unbounded medium with Lorentzian dispersion. More specifically, we tackle the situation in which a monochromatic plane wave forward-travelling in a (generally lossy)…
This paper presents a simple model for such processes as chaos spreading or turbulence spillover into stable regions. In this simple model the essential transport occurs via inelastic resonant interactions of waves on a lattice. The process…
Using a two-fluid approach, we consider the properties of relativistically nonlinear (arbitrary $a_0$), circularly polarized \EM\ waves propagating along magnetic field in electron-ion and pair plasmas. Dispersion relations depend on how…
In this paper, the Talbot effect for the multi-component linear and nonlinear systems of the dispersive evolution equations on a bounded interval subject to periodic boundary conditions and discontinuous initial profiles is investigated.…
We analyze theoretically and experimentally how nonlinear differential-transmission spectroscopy of a lambda-system medium can provide quantitative understanding of the optical dipole moments and transition energies. We focus on the…
Evolution of the main signal in a Lorentz dispersive medium is considered. The signal propagating in the medium is excited by a sine-modulated pulse signal, with its envelope described by a hyperbolic tangent function. Both uniform and…
We study statistical models for one-dimensional diffusions which are recurrent null. A first parameter in the drift is the principal one, and determines regular varying rates of convergence for the score and the information process. A…
The temporal Talbot effect refers to the periodic revivals of a pulse train propagating in a dispersive medium, and is a temporal analog of the spatial Talbot effect with group-velocity dispersion in time replacing diffraction in space.…
Laminar-turbulent pattern formation is a distinctive feature of the intermittency regime in subcritical plane shear flows. By performing extensive numerical simulations of the plane channel flow, we show that the pattern emerges from a…
We analyze some specific features of the beam-plasma instability. In particular, non-perturbative effects in the dispersion relation are studied when the standard perturbative inverse Landau damping treatment breaks down. We also elucidate…
Dispersion lies at the heart of real-time signal processing systems across the entire electromagnetic spectrum from radio to optics. However, the performance and applicability of such systems have been severely plagued by distortions due to…
The issue of the observability of the Lamb shift in systems with non-degenerate energy levels is put to question. To this end, we compute the Lamb shift of such systems in the electromagnetic environment provided by two infinite parallel…
In this paper, we investigate the dichotomous behavior of solutions to the Kawahara equation with bounded variation initial data, analogous to the Talbot effect. Specifically, we observe that the solution is quantized at rational times,…