A Van der Pol-Mathieu equation for the dynamics of dust grain charge in dusty plasmas

The chaotic profile of dust grain dynamics associated with dust-acoustic oscillations in a dusty plasma is considered. The collective behaviour of the dust plasma component is described via a multi-fluid model, comprising Boltzmann distributed electrons and ions, as well as an equation of continuity possessing a source term for the dust grains, the dust momentum and Poisson's equations. A Van der Pol–Mathieu-type nonlinear ordinary differential equation for the dust grain density dynamics is derived. The dynamical system is cast into an autonomous form by employing an averaging method. Critical stability boundaries for a particular trivial solution of the governing equation with varying parameters are specified. The equation is analysed to determine the resonance region, and finally numerically solved by using a fourth-order Runge–Kutta method. The presence of chaotic limit cycles is pointed out.

Generalized compound transport of charged particles in turbulent magnetized plasmas

The transport of charged particles in partially turbulent magnetic systems is investigated from first principles. A generalized compound transport model is proposed, providing an explicit relation between the mean-square deviation of the particle parallel and perpendicular to a magnetic mean field, and the mean-square deviation which characterizes the stochastic field-line topology. The model is applied in various cases of study, and the relation to previous models is discussed.

Higher order statistics for lognormal small-scale fading in mobile radio channels

This letter reports the statistical characterization and modeling of the indoor radio channel for a mobile wireless personal area network operating at 868 MHz. Line of sight (LOS) and non-LOS conditions were considered for three environments: anechoic chamber, open office area and hallway. Overall, the Nakagami-m cdf best described fading for bodyworn operation in 60% of all measured channels in anechoic chamber and open office area environments. The Nakagami distribution was also found to provide a good description of Rician distributed channels which predominated in the hallway. Multipath played an important role in channel statistics with the mean recorded m value being reduced from 7.8 in the anechoic chamber to 1.3 in both the open office area and hallway.

Higher order statistics for the κ–μ distribution

Closed-form expressions for the level crossing rate and average fade duration of a kappa–mu distributed fading signal envelope are presented. The proposed equations are validated by reduction to known Rice, Rayleigh and Nakagami-m special cases. They are also compared with measured data obtained from field trials analysing human body to body radio channels and shown to provide good agreement.

The structure of the Statistics Anxiety Rating Scale: A confirmatory factor analysis using UK psychology students

This study aimed to examine the structure of the statistics anxiety rating scale. Responses from 650 undergraduate psychology students throughout the UK were collected through an on-line study. Based on previous research three different models were specified and estimated using confirmatory factor analysis. Fit indices were used to determine if the model fitted the data and a likelihood ratio difference test was used to determine the best fitting model. The original six factor model was the best explanation of the data. All six subscales were intercorrelated and internally consistent. It was concluded that the statistics anxiety rating scale was found to measure the six subscales it was designed to assess in a UK population.

Decompositions of spaces of measures

Let M be the Banach space of sigma-additive complex-valued measures on an abstract measurable space. We prove that any closed, with respect to absolute continuity norm-closed, linear subspace L of M is complemented and describe the unique complement, projection onto L along which has norm 1. Using this fact we prove a decomposition theorem, which includes the Jordan decomposition theorem, the generalized Radon-Nikodym theorem and the decomposition of measures into decaying and non-decaying components as particular cases. We also prove an analog of the Jessen-Wintner purity theorem for our decompositions.

Positive dilations of piecewise monotonic Markov maps

We provide an explicit formula which gives natural extensions of piecewise monotonic Markov maps defined on an interval of the real line. These maps are exact endomorphisms and define chaotic discrete dynamical systems.

Fault reconstruction in linear dynamic systems using multivariate statistics

Treasure et al. (2004) recently proposed a new sub space-monitoring technique, based on the N4SID algorithm, within the multivariate statistical process control framework. This dynamic-monitoring method requires considerably fewer variables to be analysed when compared with dynamic principal component analysis (PCA). The contribution charts and variable reconstruction, traditionally employed for static PCA, are analysed in a dynamic context. The contribution charts and variable reconstruction may be affected by the ratio of the number of retained components to the total number of analysed variables. Particular problems arise if this ratio is large and a new reconstruction chart is introduced to overcome these. The utility of such a dynamic contribution chart and variable reconstruction is shown in a simulation and by application to industrial data from a distillation unit.

Improved reliability in diagnosing faults using multivariate statistics

This paper analyses multivariate statistical techniques for identifying and isolating abnormal process behaviour. These techniques include contribution charts and variable reconstructions that relate to the application of principal component analysis (PCA). The analysis reveals firstly that contribution charts produce variable contributions which are linearly dependent and may lead to an incorrect diagnosis, if the number of principal components retained is close to the number of recorded process variables. The analysis secondly yields that variable reconstruction affects the geometry of the PCA decomposition. The paper further introduces an improved variable reconstruction method for identifying multiple sensor and process faults and for isolating their influence upon the recorded process variables. It is shown that this can accommodate the effect of reconstruction, i.e. changes in the covariance matrix of the sensor readings and correctly re-defining the PCA-based monitoring statistics and their confidence limits. (c) 2006 Elsevier Ltd. All rights reserved.