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The Lightning Launch Commit Criteria (LLCC) are a set of complex rules to avoid natural and rocket-triggered lightning strikes to in-flight space launch vehicles. The LLCC are the leading source of scrubs and delays to space launches from Cape Canaveral Air Force Station (CCAFS) and NASA Kennedy Space Center (KSC). An LLCC climatology would be useful for designing launch concept of operations, mission planning, long-range forecasting, training, and setting LLCC improvement priorities. Unfortunately, an LLCC climatology has not been available for CCAFS/KSC. Attempts have been made to develop such a climatology, but they have not been entirely successful. The main shortfall has been the lack of a long continuous record of LLCC evaluations. Even though CCAFS/KSC is the world's busiest spaceport, the record of LLCC evaluations is not detailed enough to create the climatology. As a potential solution, the research in this study developed a proxy climatology of LLCC violations by using the long continuous record of surface electric field mills at CCAFS/KSC., Comment: 27 pages, 10 figures, 1 table

Experimental studies often fail to appropriately account for the number of collected samples within a fixed time interval for functional responses. Data of this nature appropriately falls under an Infill Asymptotic domain that is constrained by time and not considered infinite. Therefore, the sample size should account for this infill asymptotic domain. This paper provides general guidance on selecting an appropriate size for an experimental study for various simple linear regression models and tuning parameter values of the covariance structure used under an asymptotic domain, an Ornstein-Uhlenbeck process. Selecting an appropriate sample size is determined based on the percent of total variation that is captured at any given sample size for each parameter. Additionally, guidance on the selection of the tuning parameter is given by linking this value to the signal-to-noise ratio utilized for power calculations under design of experiments., Comment: 20 pages, 12 figures, 5 tables

Functional data present as functions or curves possessing a spatial or temporal component. These components by nature have a fixed observational domain. Consequently, any asymptotic investigation requires modelling the increased correlation among observations as density increases due to this fixed domain constraint. One such appropriate stochastic process is the Ornstein-Uhlenbeck process. Utilizing this spatial autoregressive process, we demonstrate that parameter estimators for a simple linear regression model display inconsistency in an infill asymptotic domain. Such results are contrary to those expected under the customary increasing domain asymptotics. Although none of these estimator variances approach zero, they do display a pattern of diminishing return regarding decreasing estimator variance as sample size increases. This may prove invaluable to a practitioner as this indicates perhaps an optimal sample size to cease data collection. This in turn reduces time and data collection cost because little information is gained in sampling beyond a certain sample size., Comment: 35 pages, 11 tables, and 14 figures

Let $S_n$ be the symmetric group on the set $\{1,2,\ldots,n\}$. Given a permutation $\sigma=\sigma_1\sigma_2 \cdots \sigma_n \in S_n$, we say it has a peak at index $i$ if $\sigma_{i-1}<\sigma_i>\sigma_{i+1}$. Let $\text{Peak}(\sigma)$ be the set of all peaks of $\sigma$ and define $P(S;n)=\{\sigma\in S_n\, | \,\text{Peak}(\sigma)=S\}$. In this paper we study the Hamming metric, $\ell_\infty$-metric, and Kendall-Tau metric on the sets $P(S;n)$ for all possible $S$, and determine the minimum and maximum possible values that these metrics can attain in these subsets of $S_n$., Comment: 7 pages, 3 tables

In this article we investigate how to score a dichotomous scored question when co-mingled with a typically scored set of Likert scale questions. The goal is to find the upper value of the dichotomous response such that no single question is overly weighted when analyzing the summed values of the entire set of questions. Results demonstrate that setting the upper value of the dichotomous value to the max value of the Likert scale question scale is inappropriate. We provide a more appropriate value to use when considering Likert scale questions up to the max value of 10., Comment: 7 pages, 1 Table

Students taking statistical courses orientated for business or economics often find the standard presentation of Bayes' Rule challenging. This key concept involves understanding multiple conditional probabilities and how they constitute an unconditional sample space. Many textbooks try to aid the comprehension of Bayes' Rule by illustrating these probabilities with tree diagrams. In our opinion, these diagrams fall short in fully assisting the students to visualize Bayes' Rule. In this article, we demonstrate a graphical approach that we have successfully used in the classroom, but is neglected in introductory texts. This approach uses mosaic plots to show the weighting of the conditional probabilities and greatly aids the student in understanding the sample space and its associated probabilities., Comment: 11 pages, 5 figures, 2 tables

Liquid drops that are pinned to solid surfaces by contact-angle hysteresis can be dislodged by wind forcing. When this occurs at high Reynolds numbers, substantial drop-interface oscillations precede depinning. It has been hypothesized that coupling between drop interface oscillations and unsteady airflow vortices are important to the depinning process. This possibility is investigated using simultaneous high-speed side-view drop images and airflow fluctuation measurements. The results show no evidence of coupling across a range of drop volumes and wind speeds for water drops in air. When properly scaled by drop volume, drop interface fluctuation frequencies are not affected by wind speed. Airflow vortex shedding occurs as if the drop were a solid surface protuberance. For the air/water system in these experiments, vortex shedding frequencies are substantially higher than drop interface frequencies and the disparate frequencies may make the hypothesized coupling impossible., Comment: 15 pages, 9 figures

Boundary layer transition triggered by a discrete roughness element generates a turbulent wedge that spreads laterally as it proceeds downstream. Historical literature reports the spreading half angle is approximately 6$^{\circ}$ in zero-pressure gradient flows regardless of Reynolds number and roughness shape. Recent simulations and experiments have sought to explain the lateral-spreading mechanism and have observed high- and low-speed streaks along the flanks of the wedge that appear central to the spreading process. To better elucidate the roles of Reynolds number and of streaks, a naphthalene flow-visualization survey and hotwire measurements are conducted over a wider range of Reynolds numbers and longer streamwise domain than previous experiments. The naphthalene results show that, while the mean spreading angle is consistent with the historical literature, there may be a weak dependency on $x$-based Reynolds number, which emerges as a result of the large sample size of the survey. The distance between the roughness element and the wedge origin exhibits a clear trend with the roughness-height-based Reynolds number. The hotwire measurements explain that this difference originates from whether breakdown occurs first in the central lobe or flanking streaks of the turbulent wedge. This observation highlights different transition dynamics at play within the supercritical regime. In agreement with past experiments, the hotwire measurements reveal that breakdown occurs in the wall normal shear layer above low-speed streaks. Due to the elongated streamwise extent of this experiment, secondary streak dynamics are also uncovered. A high-speed streak is produced directly downstream of the initiating low-speed streak. Subsequently, a new low-speed streak is observed outboard of the previous high-speed streak. This self-sustaining process is the driving mechanism of turbulent wedge spreading.

Liquid drops adhere to solid surfaces due to surface tension but can depin and run back along the surface due to wind or gravity forcing. This work develops a simple mechanistic model for depinning by combined gravity and high-Reynolds-number wind forcing and tests that model using water drops on a roughened aluminum surface. On non-inclined surfaces, drops depin at a constant critical Weber number, $W\!e_{\mathrm{crit}}=7.9$, for the present wettability conditions. On inclined surfaces, $W\!e_{\mathrm{crit}}$ decreases linearly with the product of the Bond number and the width-to-height aspect ratio of the unforced drop. The linear slope is different in distinct wind- and gravity-dominated forcing regimes above and below $W\!e_{\mathrm{crit}}=4$. Contact line shapes and drop profile shapes are measured at depinning conditions but do not adequately explain the differences between the two forcing regimes., Comment: Submitted to Physical Review Fluids. 12 pages, 8 figures

After carefully studying the comment by Wang et al. (arXiv:1408.6420), we found it includes several mistakes and unjustified statements and Wang et al. lack very basic knowledge of dislocations. Moreover, there is clear evidence indicating that Wang et al. significantly misrepresented our method and claimed something that they actually did not implement., Comment: 2 pages, 9 references