Deriving the sampling errors of correlograms for general white noise

We derive the second-order sampling properties of certain autocovariance and autocorrelation estimators for sequences of independent and identically distributed samples. Specifically, the estimators we consider are the classic lag windowed correlogram, the correlogram with subtracted sample mean, and the fixed-length summation correlogram. For each correlogram we derive explicit formulas for the bias, covariance, mean square error and consistency for generalised higher-order white noise sequences. In particular, this class of sequences may have non-zero means, be complexed valued and also includes non-analytical noise signals. We find that these commonly used correlograms exhibit lag dependent covariance despite the fact that these processes are white and hence by definition do not depend on lag.Comment: Submitted to Biometrik

Scanning-electron-microscope used in real-time study of friction and wear

Small friction and wear apparatus built directly into scanning-electron-microscope provides both dynamic observation and microscopic view of wear process. Friction and wear tests conducted using this system have indicated that considerable information can readily be gained

Sampling errors of correlograms with and without sample mean removal for higher-order complex white noise with arbitrary mean

We derive the bias, variance, covariance, and mean square error of the standard lag windowed correlogram estimator both with and without sample mean removal for complex white noise with an arbitrary mean. We find that the arbitrary mean introduces lag dependent covariance between different lags of the correlogram estimates in spite of the lack of covariance in white noise for non-zeros lags. We provide a heuristic rule for when the sample mean should be, and when it should not be, removed if the true mean is not known. The sampling properties derived here are useful is assesing the general statistical performance of autocovariance and autocorrelation estimators in different parameter regimes. Alternatively, the sampling properties could be used as bounds on the detection of a weak signal in general white noise.Comment: 11 pages, 2 figures, To be published in Journal of Time Series Analysi

Ion plating seals microcracks or porous metal components

Description of ion plating process is given. Advantage of this process is that any plating metal or alloy can be selected, whereas, for conventional welding, material selection is limited by compatability

Optimisation in ‘Self-modelling’ Complex Adaptive Systems

When a dynamical system with multiple point attractors is released from an arbitrary initial condition it will relax into a configuration that locally resolves the constraints or opposing forces between interdependent state variables. However, when there are many conflicting interdependencies between variables, finding a configuration that globally optimises these constraints by this method is unlikely, or may take many attempts. Here we show that a simple distributed mechanism can incrementally alter a dynamical system such that it finds lower energy configurations, more reliably and more quickly. Specifically, when Hebbian learning is applied to the connections of a simple dynamical system undergoing repeated relaxation, the system will develop an associative memory that amplifies a subset of its own attractor states. This modifies the dynamics of the system such that its ability to find configurations that minimise total system energy, and globally resolve conflicts between interdependent variables, is enhanced. Moreover, we show that the system is not merely ‘recalling’ low energy states that have been previously visited but ‘predicting’ their location by generalising over local attractor states that have already been visited. This ‘self-modelling’ framework, i.e. a system that augments its behaviour with an associative memory of its own attractors, helps us better-understand the conditions under which a simple locally-mediated mechanism of self-organisation can promote significantly enhanced global resolution of conflicts between the components of a complex adaptive system. We illustrate this process in random and modular network constraint problems equivalent to graph colouring and distributed task allocation problems

Effect of strain hardening on friction behavior of iron lubricated with benzyl structures

Sliding friction experiments were conducted with iron, copper, and aluminum in contact with iron in various states of strain. The surfaces were examined in dry sliding and with various benzyl compounds applied as lubricants. Friction experiments were conducted with a hemispherical rider contacting a flat disk at loads of from 50 to 600 grams with a sliding speed of 0.15 cm/min. Results indicate that straining increases friction for dry sliding and for surfaces lubricated with certain benzyl structures such as dibenzyl disulfide. With other benzyl compounds (e.g., benzyl formate), friction coefficients are lower for strained than for annealed iron

Friction and wear of metals in contact with pyrolytic graphite

Sliding friction experiments were conducted with gold, iron, and tantalum single crystals sliding on prismatic and basal orientations of pyrolytic graphite in various environments, including vacuum, oxygen, water vapor, nitrogen, and hydrogen bromide. Surfaces were examined in the clean state and with various adsorbates present on the graphite surfaces. Auger and LEED spectroscopy, SEM, and EDXA were used to characterize the graphite surfaces. Results indicate that the prismatic and basal orientations do not contain nor do they chemisorb oxygen, water vapor, acetylene, or hydrogen bromide. All three metals exhibited higher friction on the prismatic than on the basal orientation and these metals transferred to the atomically clean prismatic orientation of pyrolytic graphite. No metal transfer to the graphite was observed in the presence of adsorbates at 760 torr. Ion bombardment of the graphite surface with nitrogen ions resulted in the adherence of nitrogen to the surface