Series expansions for the third incomplete elliptic integral via partial fraction decompositions

We find convergent double series expansions for Legendre's third incomplete elliptic integral valid in overlapping subdomains of the unit square. Truncated expansions provide asymptotic approximations in the neighbourhood of the logarithmic singularity $(1,1)$ if one of the variables approaches this point faster than the other. Each approximation is accompanied by an error bound. For a curve with an arbitrary slope at $(1,1)$ our expansions can be rearranged into asymptotic expansions depending on a point on the curve. For reader's convenience we give some numeric examples and explicit expressions for low-order approximations.Comment: The paper has been substantially updated (hopefully improved) and divided in two parts. This part is about third incomplete elliptic integral. 10 page

Analysis of Vesicular Basalts and Lava Emplacement Processes for Application as a Paleobarometer/Paleoaltimeter

We have developed a method for determining paleoelevations of highland areas on the basis of the vesicularity of lava flows. Vesicular lavas preserve a record of paleopressure at the time and place of emplacement because the difference in internal pressure in bubbles at the base and top of a lava flow depends on atmospheric pressure and lava flow thickness. At the top of the flow, the pressure is simply atmospheric pressure, while at the base, there is an additional contribution of hydrostatic lava overburden. Thus the modal size of the vesicle (bubble) population is larger at the top than at the bottom. This leads directly to paleoatmospheric pressure because the thickness of the flow can easily be measured in the field, and the vesicle sizes can now be accurately measured in the lab. Because our recently developed technique measures paleoatmospheric pressure, it is not subject to uncertainties stemming from the use of climate‐sensitive proxies, although like all measurements, it has its own sources of potential error. Because measurement of flow thickness presupposes no inflation or deflation of the flow after the size distribution at the top and bottom is “frozen in,” it is essential to identify preserved flows in the field that show clear signs of simple emplacement and solidification. This can be determined by the bulk vesicularity and size distribution as a function of stratigraphic position within the flow. By examining the stratigraphic variability of vesicularity, we can thus reconstruct emplacement processes. It is critical to be able to accurately measure the size distribution in collected samples from the tops and bottoms of flows because our method is based on the modal size of the vesicle population. Previous studies have used laborious and inefficient methods that did not allow for practical analysis of a large number of samples. Our recently developed analytical techniques involving high‐resolution x‐ray computed tomography (HRXCT) allow us to analyze the large number of samples required for reliable interpretations. Based on our ability to measure vesicle size to within 1.7% (by volume), a factor analysis of the sensitivity of the technique to atmospheric pressure provides an elevation to within about ±400 m. If we assume sea level pressure and lapse rate have not changed significantly in Cenozoic time, then the difference between the paleoelevation “preserved” in the lavas and their present elevation reflects the amount of uplift or subsidence. Lava can be well dated, and therefore a suite of samples of various ages will constrain the timing of epeirogenic activity independent of climate, erosion rates, or any other environmental factors. We have tested our technique on basalts emplaced at known elevations at the base, flanks, and summit of Mauna Loa. The results of the analysis accurately reconstruct actual elevations, demonstrating the applicability of the technique. The tool we have developed can subsequently be applied to problematic areas such as the Colorado and Tibetan Plateaus to determine the history of uplift

Primer for the Transportable Applications Executive

The Transportable Applications Executive (TAE), an interactive multipurpose executive that provides commonly required functions for scientific analysis systems, is discussed. The concept of an executive is discussed and the various components of TAE are presented. These include on-line help information, the use of menus or commands to access analysis programs, and TAE command procedures

Integrated technology rotor/flight research rotor concept definition study

As part of the Integrated Technology Rotor/Flight Research Rotor (ITR/FRR) Program a number of advanced rotor system designs were conceived and investigated. From these, several were chosen that best meet the started ITR goals with emphasis on stability, reduced weight and hub drag, simplicity, low head moment stiffness, and adequate strength and fatigue life. It was concluded that obtaining low hub moment stiffness was difficult when only the blade flexibility of bearingless rotor blades is considered, unacceptably low fatigue life being the primary problem. Achieving a moderate hub moment stiffness somewhat higher than state of the art articulated rotors in production today is possible within the fatigue life constraint. Alternatively, low stiffness is possible when additional rotor elements, besides the blades themselves, provide part of the rotor flexibility. Two primary designs evolved as best meeting the general ITR requirements that presently exist. An I shaped flexbeam with an external torque tube can satisfy the general goals but would have either higher stiffness or reduced fatigue life. The elastic gimbal rotor can achieve a better combination of low stiffness and high fatigue life but would be a somewhat heavier design and possibly exhibit a higher risk of aeromechanical instability

Experimental and Theoretical Determination of Forces and Moments on a Store and on a Store- Pylon Combination Mounted on a 45 Deg Swept- Wing-Fuselage Configuration at a Mach Number of 1.61

Forces and moments of store-pylon combination mounting on swept wing-fuselage configuration in supersonic pressure tunne

Scaling and Duality in Semi-exclusive Processes

We discuss extending scaling and duality studies to semi-exclusive processes. We show that semi-exclusive hard pion photoproduction should exhibit scaling behavior in kinematic regions where the photon and pion both interact directly with the same quark. We show that such kinematic regions exist. We also show that the constancy with changing momentum transfer of the resonance peak/scaling curve ratio, familiar for many resonances in deep inelastic scattering, is also expected in the semi-exclusive case.Comment: 8 pages, 4 figures, submitted to Phys.Rev.