Elliptic Hypergeometric Summations by Taylor Series Expansion and Interpolation

We use elliptic Taylor series expansions and interpolation to deduce a number of summations for elliptic hypergeometric series. We extend to the well-poised elliptic case results that in the $q$-case have previously been obtained by Cooper and by Ismail and Stanton. We also provide identities involving S. Bhargava's cubic theta functions

Elliptic rook and file numbers

Utilizing elliptic weights, we construct an elliptic analogue of rook numbers for Ferrers boards. Our elliptic rook numbers generalize Garsia and Remmel's q-rook numbers by two additional independent parameters a and b, and a nome p. These are shown to satisfy an elliptic extension of a factorization theorem which in the classical case was established by Goldman, Joichi and White and later was extended to the q-case by Garsia and Remmel. We obtain similar results for our elliptic analogues of Garsia and Remmel's q-file numbers for skyline boards. We also provide an elliptic extension of the j-attacking model introduced by Remmel and Wachs. Various applications of our results include elliptic analogues of (generalized) Stirling numbers of the first and second kind, Lah numbers, Abel numbers, and r-restricted versions thereof.Comment: 45 pages; 3rd version shortened (elliptic rook theory for matchings has been taken out to keep the length of this paper reasonable

A novel potential/viscous flow coupling technique for computing helicopter flow fields

Because of the complexity of helicopter flow field, a zonal method of analysis of computational aerodynamics is required. Here, a new procedure for coupling potential and viscous flow is proposed. An overlapping, velocity coupling technique is to be developed with the unique feature that the potential flow surface singularity strengths are obtained directly from the Navier-Stokes at a smoother inner fluid boundary. The closed-loop iteration method proceeds until the velocity field is converged. This coupling should provide the means of more accurate viscous computations of the near-body and rotor flow fields with resultant improved analysis of such important performance parameters as helicopter fuselage drag and rotor airloads

Mango Dermatitis After Urushiol Sensitization

Prior exposure to poison ivy and poison oak, which are plants in the Anacardiacea family and contain high levels of urushiol, appear to be a risk factor for delayed hypersensitivity reactions to mango fruits. Cross-sensitization between these plants and mangos is believed to be secondary to an overlap in the urushiol antigen and 5-resorcinol, found predominately in mango peels. This unique combination of sensitization and reaction constitutes a type IV hypersensitivity response, mediated and driven by T cells reacting to similar antigens. We present a case of an otherwise healthy man, with a remote history of poison ivy exposure, who presented with a delayed but significant reaction to mango fruit. Obtaining the patient’s history of prior plant exposures and reactions was key to isolating the likely underlying causation of his presentation

A novel potential/viscous flow coupling technique for computing helicopter flow fields

The primary objective of this work was to demonstrate the feasibility of a new potential/viscous flow coupling procedure for reducing computational effort while maintaining solution accuracy. This closed-loop, overlapped velocity-coupling concept has been developed in a new two-dimensional code, ZAP2D (Zonal Aerodynamics Program - 2D), a three-dimensional code for wing analysis, ZAP3D (Zonal Aerodynamics Program - 3D), and a three-dimensional code for isolated helicopter rotors in hover, ZAPR3D (Zonal Aerodynamics Program for Rotors - 3D). Comparisons with large domain ARC3D solutions and with experimental data for a NACA 0012 airfoil have shown that the required domain size can be reduced to a few tenths of a percent chord for the low Mach and low angle of attack cases and to less than 2-5 chords for the high Mach and high angle of attack cases while maintaining solution accuracies to within a few percent. This represents CPU time reductions by a factor of 2-4 compared with ARC2D. The current ZAP3D calculation for a rectangular plan-form wing of aspect ratio 5 with an outer domain radius of about 1.2 chords represents a speed-up in CPU time over the ARC3D large domain calculation by about a factor of 2.5 while maintaining solution accuracies to within a few percent. A ZAPR3D simulation for a two-bladed rotor in hover with a reduced grid domain of about two chord lengths was able to capture the wake effects and compared accurately with the experimental pressure data. Further development is required in order to substantiate the promise of computational improvements due to the ZAPR3D coupling concept

Virtualizing the Stampede2 Supercomputer with Applications to HPC in the Cloud

Methods developed at the Texas Advanced Computing Center (TACC) are described and demonstrated for automating the construction of an elastic, virtual cluster emulating the Stampede2 high performance computing (HPC) system. The cluster can be built and/or scaled in a matter of minutes on the Jetstream self-service cloud system and shares many properties of the original Stampede2, including: i) common identity management, ii) access to the same file systems, iii) equivalent software application stack and module system, iv) similar job scheduling interface via Slurm. We measure time-to-solution for a number of common scientific applications on our virtual cluster against equivalent runs on Stampede2 and develop an application profile where performance is similar or otherwise acceptable. For such applications, the virtual cluster provides an effective form of "cloud bursting" with the potential to significantly improve overall turnaround time, particularly when Stampede2 is experiencing long queue wait times. In addition, the virtual cluster can be used for test and debug without directly impacting Stampede2. We conclude with a discussion of how science gateways can leverage the TACC Jobs API web service to incorporate this cloud bursting technique transparently to the end user.Comment: 6 pages, 0 figures, PEARC '18: Practice and Experience in Advanced Research Computing, July 22--26, 2018, Pittsburgh, PA, US