Nonuniversal Effects in the Homogeneous Bose Gas

Effective field theory predicts that the leading nonuniversal effects in the homogeneous Bose gas arise from the effective range for S-wave scattering and from an effective three-body contact interaction. We calculate the leading nonuniversal contributions to the energy density and condensate fraction and compare the predictions with results from diffusion Monte Carlo calculations by Giorgini, Boronat, and Casulleras. We give a crude determination of the strength of the three-body contact interaction for various model potentials. Accurate determinations could be obtained from diffusion Monte Carlo calculations of the energy density with higher statistics.Comment: 24 pages, RevTex, 5 ps figures, included with epsf.te

On the dispersion management of fluorite whispering-gallery mode resonators for Kerr optical frequency comb generation in the telecom and mid-infrared range

Optical whispering gallery mode (WGM) resonators have been very attracting platforms for versatile Kerr frequency comb generations. We report a systematic study on the material dispersion of various optical materials that are capable of supporting quality factors above $10^9$. Using an analytical approximation of WGM resonant frequencies in disk resonators, we investigate the effect of the geometry and transverse mode order on the total group-velocity dispersion ($GVD$). We demonstrate that the major radii and the radial mode indices play an important role in tailoring the $GVD$ of WGM resonators. In particular, our study shows that in WGM disk-resonators, the polar families of modes have very similar $GVD$, while the radial families of modes feature dispersion values that can differ by up to several orders of magnitude. The effect of these giant dispersion shifts are experimentally evidenced in Kerr comb generation with magnesium fluoride. From a more general perspective, this critical feature enables to push the zero-dispersion wavelength of fluorite crystals towards the mid-infrared (mid-IR) range, thereby allowing for efficient Kerr comb generation in that spectral range. We show that barium fluoride is the most interesting crystal in this regard, due to its zero dispersion wavelength ($ZDW$) at $1.93 \rm{\mu m}$ and an optimal dispersion profile in the mid-IR regime. We expect our results to facilitate the design of different platforms for Kerr frequency comb generations in both telecommunication and mid-IR spectral ranges

Quantum Transport Calculations Using Periodic Boundary Conditions

An efficient new method is presented to calculate the quantum transports using periodic boundary conditions. This method allows the use of conventional ground state ab initio programs without big changes. The computational effort is only a few times of a normal ground state calculation, thus it makes accurate quantum transport calculations for large systems possible.Comment: 9 pages, 6 figure

Air Temperature Comparison between the MMTS and the USCRN Temperature Systems

A new U.S. Climate Reference Network (USCRN) was officially and nationally commissioned by the Department of Commerce and the National Oceanic and Atmospheric Administration in 2004. During a 1-yr side-by-side field comparison of USCRN temperatures and temperatures measured by a maximum-minimum temperature system (MMTS), analyses of hourly data show that the MMTS temperature performed with biases: 1) a systematic bias–ambient-temperature-dependent bias and 2) an ambient-solar-radiation- and ambient-wind- speed-dependent bias. Magnitudes of these two biases ranged from a few tenths of a degree to over 1C compared to the USCRN temperatures. The hourly average temperatures for the USCRN were the dependent variables in the development of two statistical models that remove the biases due to ambient temperature, ambient solar radiation, and ambient wind speed in the MMTS. The model performance was examined, and the results show that the adjusted MMTS data were substantially improved with respect to both systematic bias and the bias associated with ambient solar radiation and ambient wind speed. In addition, the results indicate that the historical temperature datasets prior to the MMTS era need to be further investigated to produce long-term homogenous times series of area-average temperature

An experimental study of a self-confined flow with ring-vorticity distribution

A new form of self-confined flow was investigated in which a recirculation zone forms away from any solid boundary. An inviscid flow analysis indicated that in a purely meridional axisymmetric flow a stationary, spherical, self-confined region should occur in the center of a streamlined divergent-convergent enlargement zone. The spherical confinement region would be at rest and at constant pressure. Experimental investigations were carried out in a specially built test apparatus to establish the desired confined flow. The streamlined divergent-convergent interior shape of the test section was fabricated according to the theoretical calculation for a particular streamline. The required inlet vorticity distribution was generated by producing a velocity profile with a shaped gauze screen in the straight pipe upstream of the test section. Fluid speed and turbulence intensity were measured with a constant-temperature hot-wire anemometer system. The measured results indicated a very orderly and stable flow field

Symmetrized importance samplers for stochastic differential equations

We study a class of importance sampling methods for stochastic differential equations (SDEs). A small-noise analysis is performed, and the results suggest that a simple symmetrization procedure can significantly improve the performance of our importance sampling schemes when the noise is not too large. We demonstrate that this is indeed the case for a number of linear and nonlinear examples. Potential applications, e.g., data assimilation, are discussed.Comment: Added brief discussion of Hamilton-Jacobi equation. Also made various minor corrections. To appear in Communciations in Applied Mathematics and Computational Scienc