Exponential Growth of Ponds in Invasion Percolation on Regular Trees

In invasion percolation, the edges of successively maximal weight (the outlets) divide the invasion cluster into a chain of ponds separated by outlets. On the regular tree, the ponds are shown to grow exponentially, with law of large numbers, central limit theorem and large deviation results. The tail asymptotics for a fixed pond are also studied and are shown to be related to the asymptotics of a critical percolation cluster, with a logarithmic correction.     

In situ measurements and modeling of carbon nanotube array growth kinetics during chemical vapor deposition

Direct measurements of carbon nanotube growth kinetics are described based upon time-resolved reflectivity (TRR) of a HeNe laser beam from vertically aligned nanotube arrays (VANTAs) as they grow during chemical vapor deposition (CVD). Growth rates and terminal lengths were measured in situ for VANTAs growing during CVD between 535 °C and 900 °C on Si substrates with evaporated Al/Fe/Mo multi-layered catalysts and acetylene feedstock at different feedstock partial pressures. Methods of analysis of the TRR signals are presented to interpret catalyst particle formation and oxidation, as well as the porosity of the VANTAs. A rate-equation model is developed to describe the measured kinetics in terms of activation energies and rate constants for surface carbon formation and diffusion on the catalyst nanoparticle, nanotube growth, and catalyst over-coating. Taken together with the TRR data, this model enables basic understanding and optimization of growth conditions for any catalyst/feedstock combination. The model lends insight into the main processes responsible for the growth of VANTAs, the measured number of walls in the nanotubes at different temperatures, conditions for growth of single-wall carbon nanotube arrays, and likely catalyst poisoning mechanisms responsible for the sharp decline in growth rates observed at high temperatures. PACS  61.46.+w; 81.07.De; 81.16.Hc     

All-fiber single-mode fiber frequency-modulated continuous-wave Sagnac gyroscope

An all-fiber single-mode fiber unbalanced Sagnac gyroscope is described. The gyroscope is based on optical frequency-modulated continuous-wave interference and consists primarily of four Y-type single-mode fiber directional couplers and a single-mode fiber coil. The rotational velocity of the fiber coil is determined simultaneously by detection of the phase shift of the beat signal. The advantages and limitations of the gyroscope are discussed.     

MR safety and compatibility of a noninvasively expandable total-joint endoprosthesis

A noninvasively expandable total-joint endoprosthesis is now available for pediatric patients; the prosthesis can be lengthened by external application of a magnetic field. We investigated the risks of unintentional heating or lengthening of the prosthesis during MR imaging and evaluated the effect of the device on the diagnostic efficacy of MR imaging of surrounding tissues. We performed MR imaging at 1.5 T by using standard pulse sequences and pulse sequences with high-gradient and high-radiofrequency duty cycle. MR imaging caused no measurable change in prosthesis length, and the temperature of the prosthesis increased by less than 1 degrees C during repeated 14-min exposures. Despite significant signal loss and image distortion around the prosthetic joint, clinically useful images were obtained as close as 12 cm from the ends of the prosthetic stems, measured toward the body of the device. Thus, the prosthesis can be safely exposed to MR imaging pulse sequences at 1.5 T, and the visualization of some tissue surrounding the device is clinically useful.     

Negative and positive mass spectra of some substituted trinitromethanes

The negative and positive ion mass spectra of a series of substituted trinitroalkanes (nitroform, tetranitro methane, methyl, fluoro, chloro, bromo and iodo-trinitro methane) have been measured with an Aatlas CH-4 Mass Spectrometer, under varying electron energies from 70 over the total range at which ions are produced. The modes of decomposition of the compounds are presented. A few metastable transitions are observable in the negative ion spectra, but only at high electron energies (ion pair region) and are very low in intensity. the negative and positive ion clastograms of these polynitro compounds showed little parent-daughter ion correlation. Finally, the negative ions formed appear to contain excess amounts of kinetic energy even at low electron energies; as a retult there is a great deal of overlap in the various mechanisms for the formation of negative ions.     

Gravimetric determination of gold with di-2-thienylketoxime

Di-2-thienylketoxime may be used as a gravimetric reagent to determine gold. The error is of the order of ± 0.3%. There are few interfering ions and simple methods may be used to eliminate these.