The three-body recombination of a condensed Bose gas near a Feshbach resonance

In this paper, we study the three-body recombination rate of a homogeneous dilute Bose gas with a Feshbach resonance at zero temperature. The ground state and excitations of this system are obtained. The three-body recombination in the ground state is due to the break-up of an atom pair in the quantum depletion and the formation of a molecule by an atom from the broken pair and an atom from the condensate. The rate of this process is in good agreement with the experiment on $^{23}$Na in a wide range of magnetic fields.Comment: 10 pages, 2 figures, to be published in Phys. Rev.

ANOVA for diffusions and It\^{o} processes

It\^{o} processes are the most common form of continuous semimartingales, and include diffusion processes. This paper is concerned with the nonparametric regression relationship between two such It\^{o} processes. We are interested in the quadratic variation (integrated volatility) of the residual in this regression, over a unit of time (such as a day). A main conceptual finding is that this quadratic variation can be estimated almost as if the residual process were observed, the difference being that there is also a bias which is of the same asymptotic order as the mixed normal error term. The proposed methodology, ``ANOVA for diffusions and It\^{o} processes,'' can be used to measure the statistical quality of a parametric model and, nonparametrically, the appropriateness of a one-regressor model in general. On the other hand, it also helps quantify and characterize the trading (hedging) error in the case of financial applications.Comment: Published at http://dx.doi.org/10.1214/009053606000000452 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Frequency domain criteria for lp-robust stability of systems with fuzzy parameters

The paper deals with the problem of determining stability margin of linear continuous-time system with fuzzy parametric uncertainty. Non-symmetric multivariate membership functions with lp -constraints describing the uncertainty of characteristic polynomial parameters are considered. An elegant solution, graphical in nature, based on generation of Tsypkin-Polyak plot is presented

Multivariate hydrological frequency analysis and risk mapping

In hydrological frequency analysis, it is difficult to apply standard statistical methods to derive multivariate probability distributions of the characteristics of hydrologic or hydraulic variables except under the following restrictive assumptions: (1) variables are assumed independent, (2) variables are assumed to have the same marginal distributions, and (3) variables are assumed to follow or are transformed to normal distribution. Relaxing these assumptions when deriving multivariate distributions of the characteristics of correlated hydrologic and hydraulic variables. The copula methodology is applied to perform multivariate frequency analysis of rainfall, flood, low-flow, water quality, and channel flow, using data from the Amite river basin in Louisiana. And finally, the risk methodology is applied to analyze flood risks. Through the study, it was found that (1) copula method was found reasonably well to be applied to derive the multivariate hydrological frequency model compared with other conventional methods, i.e., multivariate normal approach, N-K model approach, independence transformation approach etc.; (2) nonstationarity was found more or less existed in the rainfall and streamflow time series, but according to the nonstationary test, in most cases, the stationarity assumption may be approximately valid; (3) the multivariate frequency analysis coupling nonstationarity indicated that the stationary assumption was valid for both bivariate and trivariate analysis; and (4) risk, defined by both flooding event and the damage caused by the scenario, showed the difference from that defined by T-year return period design event and the probability of total damage with the comparison indicating that only one character, i.e., T-year event or probability of total damage was not adequate to define the risk

Charge transport measurements of vertically aligned carbon nanofiber

Vertically aligned carbon nanofibers (VACNFs) have found a variety of electronic applications. To further realize these applications, a good understanding of the charge transport properties is essential. In this work, charge transport properties have been systematically measured for three types of VACNF forests with Ni as catalyst, namely VACNFs grown by direct current PECVD, and inductively coupled PECVD at both normal pressure (3.6 Torr) and low pressure (50 mTorr). The structure and composition of these nanofibers have also been investigated in detail prior to the charge transport measurements. It has been found that the dc VACNF body consists of three parts: a 10-15 nm thick graphitic outer layer, cross-struts, and a layer with darker contrast in between. Carbon, nitrogen, silicon, nickel and oxygen are all present in the dc VACNF body. Ni is distributed along the entire dc VACNF body, as first reported in this work. Auger electron spectroscopy results indicate that Ni is primarily located in fiber walls, not in the center catalytic part. Four-probe I-V measurements on individual nanofibers have been enabled by the fabrication of multiple metal ohmic contacts on individual fibers that exhibited resistance of only a few kΩ. An O2 plasma reactive ion etch method has been used to achieve ohmic contacts between the nanofibers and Ti/Au, Ag/Au, Cd/Au, and Cr/Au electrodes. Dc VACNFs exhibit linear I-V behavior at room temperature, with a resistivity of approximately 4.2x10-3 Ω×cm. Gate effect is not observed when the heavily doped Si substrate is used as a back gate. Our measurements are consistent with a dominant transport mechanism of electrons traveling through intergraphitic planes in the dc VACNFs. The resistivity of these fibers is almost independent of temperature, and the contact resistance decreases as temperature increases. Further studies reveal that the 10-15 nm thick graphitic outer layer dominates the charge transport properties of dc VACNFs. This is demonstrated by comparison of charge transport properties of as-grown VACNFs and VACNFs with the outer layer partially removed by oxygen plasma reactive ion etch. The linear I-V behavior of the fibers does not vary as this outer layer becomes thinner, but displays a drastic shift to a rectifying behavior when this layer is completely stripped away from some regions of the nanofiber. This shift may be related with the compositional differences in the outer layer and the inner core of the nanofibers. Our results imply that by varying the extent of graphitization and structure of the outer layer, it may be possible to achieve controllable charge transport properties for dc VACNFs. VACNFs grown by inductively coupled PECVD at normal and low pressure both have a defective outer layer and a more crystalline inner core. The composition of these fibers is predominately carbon, and Ni is not observed along the fiber body. Nitrogen is present possibly as a result of sample storage in air. Two-probe charge transport measurements indicate linear I-V behavior, and the resistivity of both types of inductively coupled PECVD grown VACNFs is on the order of 10-3 to 10-4Ω.cm