Saddlepoint approximation for moment generating functions of truncated random variables

We consider the problem of approximating the moment generating function (MGF) of a truncated random variable in terms of the MGF of the underlying (i.e., untruncated) random variable. The purpose of approximating the MGF is to enable the application of saddlepoint approximations to certain distributions determined by truncated random variables. Two important statistical applications are the following: the approximation of certain multivariate cumulative distribution functions; and the approximation of passage time distributions in ion channel models which incorporate time interval omission. We derive two types of representation for the MGF of a truncated random variable. One of these representations is obtained by exponential tilting. The second type of representation, which has two versions, is referred to as an exponential convolution representation. Each representation motivates a different approximation. It turns out that each of the three approximations is extremely accurate in those cases ``to which it is suited.'' Moreover, there is a simple rule of thumb for deciding which approximation to use in a given case, and if this rule is followed, then our numerical and theoretical results indicate that the resulting approximation will be extremely accurate.Comment: Published at http://dx.doi.org/10.1214/009053604000000689 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Effect of hydraulic fluid (MIL-H-83282) on selected commercial O-ring compounds

Acrylonitrile and fluorocarbon compounds were evaluated at various temperatures and time intervals in samples of the fluid obtained from three qualified suppliers. It was concluded that both polymers can function in hydraulic fluids within the conditions defined by this study. Hydraulic fluid from each manufacturer was similar in its effect upon each given O-ring material, with one exception. Similarly, there were no striking differences in the resistance of O-rings of the same generic rubber type when provided by the different manufacturers

Electromagnetic resonances of cylinders and aircraft model with resistive wires

The natural frequencies of the electromagnetic resonances of conducting bodies with attached wires were determined. The bodies included twp cylinders and an approximate scale model of the NASA F-106B aircraft. All were three feet in length. Time domain waveforms of B-dot and D-dot were obtained from a sampling oscilloscope, and Prony analysis was used to extract the natural frequencies. The first four natural frequencies of the cylinders (and wires) were determined, and a comparison with calculated results of other investigators shows reasonable agreement. Seven natural frequencies were determined for the F-106B model (with wires), and these were compared with results obtained by NASA in 1982 during direct lightning strikes to the aircraft. The agreement between the corresponding natural frequencies of the model and the aircraft is fairly good and is better than that obtained in the previous work using wires with less resistance. The frequencies lie between 6.5 MHz and 41 MHz, and all of the normalized damping rates are between 0.14 and 0.27

Electromagnetic resonances of cylinders and aircraft model with resistive wires

Laboratory experiments were done to determine the natural frequencies of the electromagnetic resonances of conducting bodies with attached wires. The bodies include two cylinders and an approximate scale model of the NASA F-106B aircraft. All are three feet in length. Time-domain waveforms of B-dot and D-dot were obtained from a sampling oscilloscope, and Prony analysis was used to extract the natural frequencies. This work is an extension of previous work, but smaller, more resistive wires have been used. The first four natural frequencies of the cylinders (and wires) were determined, and a comparison with calculated results of other investigators show reasonable agreement. Seven natural frequencies were determined for the F-106B model (wire wires), and these have been compared with results obtained by NASA in 1982 during direct lightning strikes to the aircraft. The agreement between the corresponding natural frequencies of the model and the aircraft is fairly good and is better than that obtained in the previous work using wires with less resistance. The frequencies lie between 6.5 MHz and 41 MHz, and all of the normalized damping rates are between 0.14 and 0.27

Current-eddy interaction in the Agulhas Return Current region from the seismic oceanography perspective

Interleaving in the Agulhas Return Current (ARC) frontal region is commonly manifested in the form of thermohaline intrusions, as sub-tropical and sub-polar water masses of similar density meet. In Jan/Feb 2012, the Naval Research Laboratory and collaborators carried out a field experiment in which seismic and traditional hydrographic observations were acquired to examine frontal zone mixing processes. The high lateral resolution (10 m) of the seismic observations allowed fine-scale lateral tracking of thermal intrusions, which were corroborated with simultaneous XBT casts. Between seismic deployments both salinity and temperature data were acquired via CTD, Underway-CTD and microstructure profiles. This study focuses on analyzing seismic reflection data in a particular E-W transect where the northward flowing ARC interacted with the southward flowing portion of a large anticyclonic eddy. Strong reflectors were most prominent at the edge of a hyperbolic zone formed between the eddy and ARC, where sub-polar waters interacted with waters of sub-tropical origin on either side. Reflectors were shallow within the hyperbolic zone and extended to 1200 m below the ARC. The nature of the observed reflectors will be determined from comparison of seismic reflection and derived ∂T/∂z fields, and XBT and TS profiles from the available hydrographic data

Optical and ROSAT X-ray observations of the dwarf nova OY Carinae in superoutburst and quiescence

We present ROSAT X-ray and optical light curves of the 1994 February superoutburst of the eclipsing SU UMa dwarf nova OY Carinae. There is no eclipse of the flux in the ROSAT HRI light curve. Contemporaneous `wide B' band optical light curves show extensive superhump activity and dips at superhump maximum. Eclipse mapping of these optical light curves reveals a disc with a considerable physical flare, even three days into the superoutburst decline. We include a later (1994 July) ROSAT PSPC observation of OY Car that allows us to put constraints on the quiescent X-ray spectrum. We find that while there is little to choose between OY Car and its fellow high inclination systems with regard to the temperature of the emitting gas and the emission measure, we have difficulties reconciling the column density found from our X-ray observation with the column found in HST UV observations by Horne et al. (1994). The obvious option is to invoke time variability.Comment: 16 pages, 14 figures, accepted for publication in MNRA

Fracture mechanics approach to design analysis of notches, steps and internal cut-outs in planar components

A new approach to the assessment and optimization of geometric stress-concentrating features is proposed on the basis of the correspondence between sharp crack or corner stressfield intensity factors and conventional elastic stress concentration factors (SCFs) for radiused transitions. This approach complements the application of finite element analysis (FEA) and the use of standard SCF data from the literature. The method makes it possible to develop closed-form solutions for SCFs in cases where corresponding solutions for the sharp crack geometries exist. This is helpful in the context of design optimization. The analytical basis of the correspondence is shown, together with the limits on applicability where stress-free boundaries near the stress concentrating feature are present or adjacent features interact. Examples are given which compare parametric results derived from FEA with closed-form solutions based on the proposed method. New information is given on the stress state at a 90° corner or width step, where the magnitude of the stress field intensity is related to that of the corresponding crack geometry. This correspondence enables the user to extend further the application of crack-tip stress-field intensity information to square-cornered steps, external U-grooves, and internal cut-outs

Seismic oceanography imaging of thermal intrusions in strong frontal regions

The Naval Research Laboratory and collaborating partners carried out two dedicated seismic oceanography field experiments in two very different strong frontal regions. ADRIASEISMIC took seismic oceanography measurements at the confluence of North Adriatic Dense Water advected along the Western Adriatic Current and Modified Levantine Intermediate Water advected around the topographic rim of the Southern Adriatic basin. ARC12 took seismic oceanography measurements in and around the Agulhas Return Current as it curved northwards past the Agulhas Plateau and interacted with a large anticyclone that had collided with the current. Despite one study focused on coastal boundary currents and the other focused on a major Western Boundary Current extension, the complex horizontal structures seen through seismic imaging are tied to the processes of thermal intrusions and interleaving in both systems. Seismic Oceanography provides a unique capability of tracking the fine-scale horizontal extent of these intrusions

On the equation of state of a dense columnar liquid crystal

An accurate description of a columnar liquid crystal of hard disks at high packing fractions is presented using an improved free-volume theory. It is shown that the orientational entropy of the disks in the one-dimensional fluid direction leads to a different high-density scaling pressure compared to the prediction from traditional cell theory. Excellent quantitative agreement is found with recent Monte-Carlo simulation results for various thermodynamic and structural properties of the columnar state.Comment: 4 pages, 2 figures, to appear in Phys. Rev. Let