Corrected confidence intervals for secondary parameters following sequential tests

Corrected confidence intervals are developed for the mean of the second component of a bivariate normal process when the first component is being monitored sequentially. This is accomplished by constructing a first approximation to a pivotal quantity, and then using very weak expansions to determine the correction terms. The asymptotic sampling distribution of the renormalised pivotal quantity is established in both the case where the covariance matrix is known and when it is unknown. The resulting approximations have a simple form and the results of a simulation study of two well-known sequential tests show that they are very accurate. The practical usefulness of the approach is illustrated by a real example of bivariate data. Detailed proofs of the main results are provided.Comment: Published at http://dx.doi.org/10.1214/074921706000000617 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

Synchronization framework for modeling transition to thermoacoustic instability in laminar combustors

We, herein, present a new model based on the framework of synchronization to describe a thermoacoustic system and capture the multiple bifurcations that such a system undergoes. Instead of applying flame describing function to depict the unsteady heat release rate as the flame's response to acoustic perturbation, the new model considers the acoustic field and the unsteady heat release rate as a pair of nonlinearly coupled damped oscillators. By varying the coupling strength, multiple dynamical behaviors, including limit cycle oscillation, quasi-periodic oscillation, strange nonchaos, and chaos can be captured. Furthermore, the model was able to qualitatively replicate the different behaviors of a laminar thermoacoustic system observed in experiments by Kabiraj et al.~[Chaos 22, 023129 (2012)]. By analyzing the temporal variation of the phase difference between heat release rate oscillations and pressure oscillations under different dynamical states, we show that the characteristics of the dynamical states depend on the nature of synchronization between the two signals, which is consistent with previous experimental findings.Comment: 18 pages, 7 figure

Investigative study on the development of a green UWB antenna

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Site Factors Influence on Herbaceous Understory Diversity in East Texas Pinus palustris savannas

Longleaf pine (Pinus palustris) savannas were once dominant across the southeastern U.S., including East Texas and parts of western and central Louisiana. The diverse understory associated with these historical savannas may occasionally be seen today, but not often in longleaf pine ecosystems. This project aimed to define east Texas site characteristics that are necessary to support these ecosystems with a dense and diverse herbaceous understory with little to no midstory cover. Fifty-nine plots across three study sites were established to evaluate the influence of overstory cover, basal area, aspect, elevation, and slope on the number of plant genera present. Forest structure and site characteristics had significant effects on the number of plant genera found. The number of genera increased with higher elevation and slope; as elevation increased, there was a decline in basal area and overstory cover, leading to a more diverse, understory layer. In order to re-establish and maintain a diverse, herbaceous understory in longleaf pine savannas, sites with more open canopies and on slopes with the most solar exposure should be given priority, particularly when planting desired understory species

Transverse instability of dunes

The simplest type of dune is the transverse one, which propagates with invariant profile orthogonally to a fixed wind direction. Here we show numerically and with a linear stability analysis that transverse dunes are unstable with respect to along-axis perturbations in their profile and decay on the bedrock into barchan dunes. Any forcing modulation amplifies exponentially with growth rate determined by the dune turnover time. We estimate the distance covered by a transverse dune before fully decaying into barchans and identify the patterns produced by different types of perturbation.Comment: 4 pages, 3 figures; To appear in Physical Review Letter

Casimir Force for Arbitrary Objects Using the Argument Principle and Boundary Element Methods

Recent progress in the simulation of Casimir forces between various objects has allowed traditional computational electromagnetic solvers to be used to find Casimir forces in arbitrary three-dimensional objects. The underlying theory to these approaches requires knowledge and manipulation of quantum field theory and statistical physics. We present a calculation of the Casimir force using the method of moments via the argument principle. This simplified derivation allows greater freedom in the moment matrix where the argument principle can be used to calculate Casimir forces for arbitrary geometries and materials with the use of various computational electromagnetic techniques.Comment: 6 pages, 2 figure

A New Site Index Model for Intensively Managed Loblolly Pine (Pinus taeda) Plantations in the West Gulf Coastal Plain

Site index (SI) estimation for loblolly pine (Pinus taeda L.) plantations is important for the successful management of this important commercial tree species in the West Gulf Coastal Plain of the United States. This study evaluated various SI models for intensively managed loblolly plantations in the West Gulf Coastal Plain using data collected from permanent plots installed in intensively managed loblolly pine plantations across east Texas and western Louisiana. Six commonly used SI models (Cieszewski GADA model, both Chapman-Richards ADA and GADA models, both Schumacher ADA and GADA models, and McDill-Amateis GADA model) were fit to the data and compared. The Chapman-Richards GADA model and the McDill-Amateis GADA model were similar and best in their fit statistics. These two models were further compared to the existing models (Diéguez-Aranda et al. 2006 (DA2006), Coble and Lee 2010 (CL2010)) commonly used in the region. Both the Chapman-Richards GADA and the McDill-Amateis GADA models consistently predicted greater heights up to age 25 than the models of DA2006 and CL2010, with larger height differences for the higher quality sites, but predicted shorter heights thereafter. Ultimately, the McDill-Amateis GADA model was chosen as the best model for its consistency in predicting reasonable heights extrapolated beyond the range of the data. Foresters can use this model to make more informed silvicultural prescriptions for intensively managed loblolly pine plantations in the West Gulf Coastal Plain