Methods for the computation of detailed geoids and their accuracy

Two methods for the computation of geoid undulations using potential coefficients and 1 deg x 1 deg terrestrial anomaly data are examined. It was found that both methods give the same final result but that one method allows a more simplified error analysis. Specific equations were considered for the effect of the mass of the atmosphere and a cap dependent zero-order undulation term was derived. Although a correction to a gravity anomaly for the effect of the atmosphere is only about -0.87 mgal, this correction causes a fairly large undulation correction that was not considered previously. The accuracy of a geoid undulation computed by these techniques was estimated considering anomaly data errors, potential coefficient errors, and truncation (only a finite set of potential coefficients being used) errors. It was found that an optimum cap size of 20 deg should be used. The geoid and its accuracy were computed in the Geos 3 calibration area using the GEM 6 potential coefficients and 1 deg x 1 deg terrestrial anomaly data. The accuracy of the computed geoid is on the order of plus or minus 2 m with respect to an unknown set of best earth parameter constants

The determination of gravity anomalies from geoid heights using the inverse Stokes' formula, Fourier transforms, and least squares collocation

A numerical method for the determination of gravity anomalies from geoid heights is described using the inverse Stokes formula. This discrete form of the inverse Stokes formula applies a numerical integration over the azimuth and an integration over a cubic interpolatory spline function which approximates the step function obtained from the numerical integration. The main disadvantage of the procedure is the lack of a reliable error measure. The method was applied on geoid heights derived from GEOS-3 altimeter measurements in the calibration area of the GEOS-3 satellite

Comparisons of global topographic/isostatic models to the Earth's observed gravity field

The Earth's gravitational potential, as described by a spherical harmonic expansion to degree 180, was compared to the potential implied by the topography and its isostatic compensation using five different hypothesis. Initially, series expressions for the Airy/Heiskanen topographic isostatic model were developed to the third order in terms of (h/R), where h is equivalent rock topography and R is a mean Earth radius. Using actual topographic developments for the Earth, it was found that the second and third terms of the expansion contributed 30 and 3 percents, of the first of the expansion. With these new equations it is possible to compute depths (D) of compensation, by degree, using 3 different criteria. The results show that the average depth implied by criterion I is 60 km while it is about 33 km for criteria 2 and 3 with smaller compensation depths at the higher degrees. Another model examined was related to the Vening-Meinesz regional hypothesis implemented in the spectral domain. Finally, oceanic and continental response functions were derived for the global data sets and comparisons made to locally determined values

The detection of tightly closed flaws by nondestructive testing (NDT) methods

Liquid penetrant, ultrasonic, eddy current and X-radiographic techniques were optimized and applied to the evaluation of 2219-T87 aluminum alloy test specimens in integrally stiffened panel, and weld panel configurations. Fatigue cracks in integrally stiffened panels, lack-of-fusion in weld panels, and fatigue cracks in weld panels were the flaw types used for evaluation. A 2319 aluminum alloy weld filler rod was used for all welding to produce the test specimens. Forty seven integrally stiffened panels containing a total of 146 fatigue cracks, ninety three lack-of-penetration (LOP) specimens containing a total of 239 LOP flaws, and one-hundred seventeen welded specimens containing a total of 293 fatigue cracks were evaluated. Nondestructive test detection reliability enhancement was evaluated during separate inspection sequences in the specimens in the 'as-machined or as-welded', post etched and post proof loaded conditions. Results of the nondestructive test evaluations were compared to the actual flaw size obtained by measurement of the fracture specimens after completing all inspection sequences. Inspection data were then analyzed to provide a statistical basis for determining the flaw detection reliability

Detection of tightly closed flaws by nondestructive testing (NDT) methods in steel and titanium

X-radiographic, liquid penetrant, ultrasonic, eddy current and magnetic particle testing techniques were optimized and applied to the evaluation of 4340 steel (180 KSI-UTS) and 6Al-4V titanium (STA) alloy specimens. Sixty steel specimens containing a total of 176 fatigue cracks and 60 titanium specimens containing a total of 135 fatigue cracks were evaluated. The cracks ranged in length from .043 cm (0.017 inch) to 1.02 cm (.400 inch) and in depth from .005 cm (.002 inch) to .239 cm (.094 inch) for steel specimens. Lengths ranged from .048 cm (0.019 inch) to 1.03 cm (.407 inch) and depths from 0.010 cm (.004 inch) to .261 cm (0.103 inch) for titanium specimens. Specimen thicknesses were nominally .152 cm (0.060 inch) and 0.635 cm (0.250 inch) and surface finishes were nominally 125 rms. Specimens were evaluated in the "as machined" surface condition, after etch surface and after proof loading in a randomized inspection sequence

Microfluidic Delivery of Small Molecules into Mammalian Cells Based on Hydrodynamic Focusing

Microfluidics-based cell assays offer high levels of automation and integration, and allow multiple assays to be run in parallel, based on reduced sample volumes. These characteristics make them attractive for studies associated with drug discovery. Controlled delivery of drug molecules or other exogenous materials into cells is a critical issue that needs to be addressed before microfluidics can serve as a viable platform for drug screening and studies. In this study, we report the application of hydrodynamic focusing for controlled delivery of small molecules into cells immobilized on the substrate of a microfluidic device. We delivered calcein AM which was permeant to the cell membrane into cells, and monitored its enzymatic conversion into fluor- escent calcein during and after the delivery. Different ratios of the sample flow to the side flow were tested to determine how the conditions of hydrodynamic focusing affected the delivery. A 3D numerical model was developed to help understand the fluid flow, molecular diffusion due to hydrodynamic focusing in the microfluidic channel. The results from the simulation indicated that the calcein AM concentration on the outer surface of a cell was determined by the conditions of hydrodynamic focusing. By comparing the results from the simulation with those from the experi- ment, we found that the calcein AM concentration on the cell outer surface correlated very well with the amount of the molecules delivered into the cell. This suggests that hydro- dynamic focusing provides an effective way for potentially quantitative delivery of exogenous molecules into cells at the single cell or subcellular level. We expect that our technique will pave the way to high-throughput drug screening and delivery on a microfluidic platform

Report of the panel on geopotential fields: Gravity field, section 8

The objective of the Geopotential Panel was to develop a program of data acquisition and model development for the Earth's gravity and magnetic fields that meet the basic science requirements of the solid Earth and ocean studies. Presented here are the requirements for gravity information and models through the end of the century, the present status of our knowledge, data acquisition techniques, and an outline of a program to meet the requirements