Function Of Spatial Distance Research Articles

Canonical functions for dispersal-induced synchrony.

Two processes are universally recognized for inducing spatial synchrony in abundance: dispersal and correlated environmental stochasticity. In the present study we seek the expected relationship between synchrony and distance in populations that are synchronized by density-independent dispersal. In the absence of dispersal, synchrony among populations with simple dynamics has been shown to echo the correlation in the environment. We ask what functional form we may expect between synchrony and distance when dispersal is the synchronizing agent. We formulate a continuous-space, continuous-time model that explicitly represents the time evolution of the spatial covariance as a function of spatial distance. Solving this model gives us two simple canonical functions for dispersal-induced covariance in spatially extended populations. If dispersal is rare relative to birth and death, then covariances between nearby points will follow the dispersal distance distribution. At long distances, however, the covariance tails off according to exponential or Bessel functions (depending on whether the population moves in one or two dimensions). If dispersal is common, then the covariances will follow the mixture distribution that is approximately Gaussian around the origin and with an exponential or Bessel tail. The latter mixture results regardless of the original dispersal distance distribution. There are hence two canonical functions for dispersal-induced synchrony

Microstructural and compositional variations in laser-deposited superconducting thin films

We have investigated thickness and composition variations in laser-deposited superconducting thin films and their effects on the microstructure development after subsequent annealing to recover the superconducting properties. Superconducting thin films were deposited on magnesium oxide substrates using a pulsed excimer laser (λ=308 nm, τ=45×10−9 s). These films were annealed at about 900 °C in helium and oxygen atmospheres followed by slow cooling to room temperature. The forward directed nature of the laser-induced deposition process in controlling the spatial variation in thickness of the film was examined using gas dynamics of the laser generated plasma. The compositional variation as a function of spatial distance was determined by Rutherford backscattering spectrometry. Correlation of the presence of different phases with the average composition in the film was done using transmission electron microscopy combined with x-ray microanalysis techniques. The slight enrichment of yttrium in the film resulted in yttrium-rich phases in the microstructure.