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.

Cryogenic loss monitors with FPGA TDC signal processing

Radiation hard helium gas ionization chambers capable of operating in vacuum at temperatures ranging from 5K to 350K have been designed, fabricated and tested and will be used inside the cryostats at Fermilab's Superconducting Radiofrequency beam test facility. The chamber vessels are made of stainless steel and all materials used including seals are known to be radiation hard and suitable for operation at 5K. The chambers are designed to measure radiation up to 30 kRad/hr with sensitivity of approximately 1.9 pA/(Rad/hr). The signal current is measured with a recycling integrator current-to-frequency converter to achieve a required measurement capability for low current and a wide dynamic range. A novel scheme of using an FPGA-based time-to-digital converter (TDC) to measure time intervals between pulses output from the recycling integrator is employed to ensure a fast beam loss response along with a current measurement resolution better than 10-bit. This paper will describe the results obtained and highlight the processing techniques used.Comment: 7 pp. 2nd International Conference on Technology and Instrumentation in Particle Physics 2011: TIPP 2011. 9-14 Jun 2011. Chicago, Illinoi

Mechanism of Gravity Impulse

It is well-known that energy-momentum is the source of gravitational field. For a long time, it is generally believed that only stars with huge masses can generate strong gravitational field. Based on the unified theory of gravitational interactions and electromagnetic interactions, a new mechanism of the generation of gravitational field is studied. According to this mechanism, in some special conditions, electromagnetic energy can be directly converted into gravitational energy, and strong gravitational field can be generated without massive stars. Gravity impulse found in experiments is generated by this mechanism.Comment: 10 page

Competent genetic-evolutionary optimization of water distribution systems

A genetic algorithm has been applied to the optimal design and rehabilitation of a water distribution system. Many of the previous applications have been limited to small water distribution systems, where the computer time used for solving the problem has been relatively small. In order to apply genetic and evolutionary optimization technique to a large-scale water distribution system, this paper employs one of competent genetic-evolutionary algorithms - a messy genetic algorithm to enhance the efficiency of an optimization procedure. A maximum flexibility is ensured by the formulation of a string and solution representation scheme, a fitness definition, and the integration of a well-developed hydraulic network solver that facilitate the application of a genetic algorithm to the optimization of a water distribution system. Two benchmark problems of water pipeline design and a real water distribution system are presented to demonstrate the application of the improved technique. The results obtained show that the number of the design trials required by the messy genetic algorithm is consistently fewer than the other genetic algorithms

X-ray Polarization Signatures of Compton Scattering in Magnetic Cataclysmic Variables

Compton scattering within the accretion column of magnetic cataclysmic variables (mCVs) can induce a net polarization in the X-ray emission. We investigate this process using Monte Carlo simulations and find that significant polarization can arise as a result of the stratified flow structure in the shock-ionized column. We find that the degree of linear polarization can reach levels up to ~8% for systems with high accretion rates and low white-dwarf masses, when viewed at large inclination angles with respect to the accretion column axis. These levels are substantially higher than previously predicted estimates using an accretion column model with uniform density and temperature. We also find that for systems with a relatively low-mass white dwarf accreting at a high accretion rate, the polarization properties may be insensitive to the magnetic field, since most of the scattering occurs at the base of the accretion column where the density structure is determined mainly by bremsstrahlung cooling instead of cyclotron cooling.Comment: 7 pages, 8 figures, accepted by MNRA