Riemann zeros, prime numbers and fractal potentials

Using two distinct inversion techniques, the local one-dimensional potentials for the Riemann zeros and prime number sequence are reconstructed. We establish that both inversion techniques, when applied to the same set of levels, lead to the same fractal potential. This provides numerical evidence that the potential obtained by inversion of a set of energy levels is unique in one-dimension. We also investigate the fractal properties of the reconstructed potentials and estimate the fractal dimensions to be $D=1.5$ for the Riemann zeros and $D = 1.8$ for the prime numbers. This result is somewhat surprising since the nearest-neighbour spacings of the Riemann zeros are known to be chaotically distributed whereas the primes obey almost poisson-like statistics. Our findings show that the fractal dimension is dependent on both the level-statistics and spectral rigidity, $\Delta_3$, of the energy levels.Comment: Five postscript figures included in the text. To appear in Phys. Rev.

Defect chemistry and transport properties of BaxCe0.85M0.15O3-d

The site-incorporation mechanism of M3+ dopants into A2+B4+O3 perovskites controls the overall defect chemistry and thus their transport properties. For charge-balance reasons, incorporation onto the A2+-site would require the creation of negatively charged point defects (such as cation vacancies), whereas incorporation onto the B4+-site is accompanied by the generation of positively charged defects, typically oxygen vacancies. Oxygen-vacancy content, in turn, is relevant to proton-conducting oxides in which protons are introduced via the dissolution of hydroxyl ions at vacant oxygen sites. We propose here, on the basis of x-ray powder diffraction studies, electron microscopy, chemical analysis, thermal gravimetric analysis, and alternating current impedance spectroscopy, that nominally B-site doped barium cerate can exhibit dopant partitioning as a consequence of barium evaporation at elevated temperatures. Such partitioning and the presence of significant dopant concentrations on the A-site negatively impact proton conductivity. Specific materials examined are BaxCe0.85M0.15O3-d (x = 0.85 - 1.20; M = Nd, Gd, Yb). The compositional limits for the maximum A-site incorporation are experimentally determined to be: (Ba0.919Nd0.081)(Ce0.919Nd0.081)O3, (Ba0.974Gd0.026)(Ce0.872Gd0.128)O2.875, and Ba(Ce0.85Yb0.15)O2.925. As a consequence of the greater ability of larger cations to exist on the Ba site, the H2O adsorption and proton conductivities of large-cation doped barium cerates are lower than those of small-cation doped analogs

Coal/rock interface detection by sensitized pick, part A

In order to increase the operating margins of the detector for safe, reliable operation under difficult in-mine conditions the transmitted signal strength was increased to provide additional signal margin for in-mine conditions and the transmitter section was redesigned to reduce frequency pulling of the transmitter frequency with variations in antenna load. The linearity of the pick load SCO signal with true pick load was increased, and hysteresis effects were minimized. The sensitized pick hardware was ruggedized for rough inmine use. The sensitized pick and telemetry system provided excellent, high quality signals proportional to cutting load under all conditions experienced during testing