Plasma enhanced chemical vapour deposition carbon nanotubes/nanofibres - How uniform do they grow?

The ability to grow carbon nanotubes/nanofibres (CNs) with a high degree of uniformity is desirable in many applications. In this paper, the structural uniformity of CNs produced by plasma enhanced chemical vapour deposition is evaluated for field emission applications. When single isolated CNs were deposited using this technology, the structures exhibited remarkable uniformity in terms of diameter and height (standard deviations were 4.1 and 6.3% respectively of the average diameter and height). The lithographic conditions to achieve a high yield of single CNs are also discussed. Using the height and diameter uniformity statistics, we show that it is indeed possible to accurately predict the average field enhancement factor and the distribution of enhancement factors of the structures, which was confirmed by electrical emission measurements on individual CNs in an array.

Uniform stability of a particle approximation of the optimal filter derivative

Sequential Monte Carlo methods, also known as particle methods, are a widely used set of computational tools for inference in non-linear non-Gaussian state-space models. In many applications it may be necessary to compute the sensitivity, or derivative, of the optimal filter with respect to the static parameters of the state-space model; for instance, in order to obtain maximum likelihood model parameters of interest, or to compute the optimal controller in an optimal control problem. In Poyiadjis et al. [2011] an original particle algorithm to compute the filter derivative was proposed and it was shown using numerical examples that the particle estimate was numerically stable in the sense that it did not deteriorate over time. In this paper we substantiate this claim with a detailed theoretical study. Lp bounds and a central limit theorem for this particle approximation of the filter derivative are presented. It is further shown that under mixing conditions these Lp bounds and the asymptotic variance characterized by the central limit theorem are uniformly bounded with respect to the time index. We demon- strate the performance predicted by theory with several numerical examples. We also use the particle approximation of the filter derivative to perform online maximum likelihood parameter estimation for a stochastic volatility model.