It is well-known that the standing wave u0 for the KPP type convectiondiffusion equation is stable if the perturbations of the initial data are in the weighted function spaces proposed by Sattinger. We study boundary conditions so that in a large finite domain, there is a stable standing wave ũ near u0. The standing wave ũ may not be monotone, and the stability is proved by pseudo exponential d...

Periodic multilayers give rise to enhanced X-ray fluorescence when a regime of standing waves occurs within the structure. This regime may concern the primary radiation used to induce the fluorescence, the secondary radiation of fluorescence or both of them. Until now, existing models only dealt with standing wave regime of primary radiation. We present a theoretical approach based on the oscil...

Multigrid methods are known for their high efficiency in the solution of definite elliptic problems. However, difficulties that appear in highly indefinite problems, such as standing wave equations, cause a total loss of efficiency in the standard multigrid solver. The aim of this paper is to isolate these difficulties, analyze them, suggest how to deal with them, and then test the suggestions ...

Reflection of neutral atoms and molecules by a pulsed standing wave with a duration on the order of nanoseconds is studied. It is shown that, with a suitable choice of the laser parameter values, each period of the standing-wave pattern functions as an independent mirror, thus providing a novel way to manipulate large samples of neutral gas-phase particles even with a single laser pulse. At mod...

We analyze the size limits of coupled map lattices with diffusive coupling at the crossover of low-dimensional to high-dimensional chaos. We investigate the existence of standing-wave-type periodic patterns, within the low-dimensional limit, in addition to the stable synchronous chaotic states depending upon the initial conditions. Further, we bring out a controlling mechanism to explain the em...

X-ray diffraction from crystal surfaces at grazing angles gives rise to X-ray standing waves above and below the surface. Expressions are derived for the fluorescence observed from atoms located on or in a crystal as a result of excitation by the grazing-angle X-ray standing waves. In addition to the dependence of the fluorescence on the position of the atom with regard to the crystal plane tha...

The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. An improved single-cell photonic band-gap (PBG) structure with an inner row of elliptical rods (PBG-E) was tested with high power at a 60 Hz repetition rate at X-band (11.424 GHz), achieving a gradient of 128 MV=m at a breakdown probability of 3:6 Â 10 À3 per pulse per meter at...

A fluorescence correlation spectroscopy experiment that combines two-photon excitation and a standing-wave interference pattern is presented. The experimental correlation function can be analyzed using a simple expression involving (1) an exponential decay with time constant tau(f), which reflects diffusion across the interference fringes, and (2) a longer-lived decay with time constant tau(ome...