We study sustained oscillations in two-dimensional oscillator systems driven by Rayleigh-type negative friction. In particular we investigate the influence of mismatch of the two frequencies. Further we study the influence of external noise and nonlinearity of the conservative forces. Our consideration is restricted to the case that the driving is rather weak and that the forces show only weak ...

We rigorously justify the infinite Prandtl number model of convection as the limit of the Boussinesq approximation to the Rayleigh-Bénard convection as the Prandtl number approaches infinity. This is a singular limit problem involving an initial layer.

1.0 Rayleigh Distribution Using central limit theorem arguments, one can show that the I and Q channels on a mobile radio multipath fading channel are independent Gaussian (normal) random variables. Jakes [1] and others show that the envelope of two independent and identically distributed (iid) Gaussian random variables is Rayleigh distributed.1 Probability Density Function (pdf) (usual form fo...

Abst rac t . In this paper a class of goodness-of-fit tests for the Rayleigh distribution is proposed. The tests are based on a weighted integral involving the empirical Laplace transform. The consistency of the tests as well as their asymptotic distribution under the null hypothesis are investigated. As the decay of the weight function tends to infinity the test statistics approach limit value...

We have previously presented the exponent for an upper bound on the error probability of a “peaky” signaling scheme that achieves the capacity of the Rayleigh fading channel under an average power constraint in the limit of infinite bandwidth. In the present work, we complement this result with a lower bound. We find that the exponents of the upper and lower bounds coincide in the wideband limi...

We study the super-resolution (SR) problem of recovering point sources consisting of a collection of isolated and suitably separated spikes from only the low frequency measurements. If the peak separation is above a factor in (1, 2) of the Rayleigh length (physical resolution limit), L1 minimization is guaranteed to recover such sparse signals. However, below such critical length scale, especia...

The extremely low loss of silica fibers has enabled the telecommunication revolution, but single-mode fiber-optic communication systems have been driven to their capacity limits. As a means to overcome this capacity crunch, space-division multiplexing (SDM) using few-mode fibers (FMF) has been proposed and demonstrated. In single-mode optical fibers, Rayleigh scattering serves as the dominant m...

It is shown that homogeneous Rayleigh-Bénard flow, i.e., Rayleigh-Bénard turbulence with periodic boundary conditions in all directions and a volume forcing of the temperature field by a mean gradient, has a family of exact, exponentially growing, separable solutions of the full nonlinear system of equations. These solutions are clearly manifest in numerical simulations above a computable criti...