Quasiperiodic spin-orbit motion and spin tunes in storage rings

We present an in-depth analysis of the concept of spin precession frequency for integrable orbital motion in storage rings. Spin motion on the periodic closed orbit of a storage ring can be analyzed in terms of the Floquet theorem for equations of motion with periodic parameters and a spin precession frequency emerges in a Floquet exponent as an additional frequency of the system. To define a spin precession frequency on nonperiodic synchro-betatron orbits we exploit the important concept of quasiperiodicity. This allows a generalization of the Floquet theorem so that a spin precession frequency can be defined in this case too. This frequency appears in a Floquet-like exponent as an additional frequency in the system in analogy with the case of motion on the closed orbit. These circumstances lead naturally to the definition of the uniform precession rate and a definition of spin tune. A spin tune is a uniform precession rate obtained when certain conditions are fulfilled. Having defined spin tune we define spin-orbit resonance on synchro--betatron orbits and examine its consequences. We give conditions for the existence of uniform precession rates and spin tunes (e.g. where small divisors are controlled by applying a Diophantine condition) and illustrate the various aspects of our description with several examples. The formalism also suggests the use of spectral analysis to ``measure'' spin tune during computer simulations of spin motion on synchro-betatron orbits.Comment: 62 pages, 1 figure. A slight extension of the published versio

Research and development of high-performance light-weight fuel cell electrodes final report, nov. 1, 1963 - oct. 31, 1964

High performance light weight fuel cell electrode developmen

A study to define meteorological uses and performance requirements for the Synchronous Earth Observatory Satellite

The potential meteorological uses of the Synchronous Earth Observatory Satellite (SEOS) were studied for detecting and predicting hazards to life, property, or the quality of the environment. Mesoscale meteorological phenonmena, and the observations requirements for SEOS are discussed along with the sensor parameters

Potts and percolation models on bowtie lattices

We give the exact critical frontier of the Potts model on bowtie lattices. For the case of $q=1$, the critical frontier yields the thresholds of bond percolation on these lattices, which are exactly consistent with the results given by Ziff et al [J. Phys. A 39, 15083 (2006)]. For the $q=2$ Potts model on the bowtie-A lattice, the critical point is in agreement with that of the Ising model on this lattice, which has been exactly solved. Furthermore, we do extensive Monte Carlo simulations of Potts model on the bowtie-A lattice with noninteger $q$. Our numerical results, which are accurate up to 7 significant digits, are consistent with the theoretical predictions. We also simulate the site percolation on the bowtie-A lattice, and the threshold is $s_c=0.5479148(7)$. In the simulations of bond percolation and site percolation, we find that the shape-dependent properties of the percolation model on the bowtie-A lattice are somewhat different from those of an isotropic lattice, which may be caused by the anisotropy of the lattice.Comment: 18 pages, 9 figures and 3 table

Modelling thermal flow in a transition regime using a lattice Boltzmann approach

Lattice Boltzmann models are already able to capture important rarefied flow phenomena, such as velocity-slip and temperature jump, provided the effects of the Knudsen layer are minimal. However, both conventional hydrodynamics, as exemplified by the Navier-Stokes-Fourier equations, and the lattice Boltzmann method fail to predict the nonlinear velocity and temperature variations in the Knudsen layer that have been observed in kinetic theory. In the present paper, we propose an extension to the lattice Boltzmann method that will enable the simulation of thermal flows in the transition regime where Knudsen layer effects are significant. A correction function is introduced that accounts for the reduction in the mean free path near a wall. This new approach is compared with direct simulation Monte Carlo data for Fourier flow and good qualitative agreement is obtained for Knudsen numbers up to 1.58

The Sound of Sonoluminescence

We consider an air bubble in water under conditions of single bubble sonoluminescence (SBSL) and evaluate the emitted sound field nonperturbatively for subsonic gas-liquid interface motion. Sound emission being the dominant damping mechanism, we also implement the nonperturbative sound damping in the Rayleigh-Plesset equation for the interface motion. We evaluate numerically the sound pulse emitted during bubble collapse and compare the nonperturbative and perturbative results, showing that the usual perturbative description leads to an overestimate of the maximal surface velocity and maximal sound pressure. The radius vs. time relation for a full SBSL cycle remains deceptively unaffected.Comment: 25 pages; LaTex and 6 attached ps figure files. Accepted for publication in Physical Review

Frequency evaluation of the doubly forbidden 1S0→3P0^1S_0\to ^3P_0 transition in bosonic 174^{174}Yb

We report an uncertainty evaluation of an optical lattice clock based on the $^1S_0\leftrightarrow^3P_0$ transition in the bosonic isotope $^{174}$Yb by use of magnetically induced spectroscopy. The absolute frequency of the $^1S_0\leftrightarrow^3P_0$ transition has been determined through comparisons with optical and microwave standards at NIST. The weighted mean of the evaluations is $\nu$($^{174}$Yb)=518 294 025 309 217.8(0.9) Hz. The uncertainty due to systematic effects has been reduced to less than 0.8 Hz, which represents $1.5\times10^{-15}$ in fractional frequency.Comment: 4 pages, 3 figure -Submitted to PRA Rapid Communication