A mathematical approach to improving the representation of surface water–groundwater exchange in the hyporheic zone

It is well known that land surface topography governs surface–groundwater interactions under some circumstances and can be separated in a Fourier-series spectrum that provides an exact analytical solution of both the surface and the underlying three-dimensional groundwater flows. We evaluate the performance of the current Fourier fitting process by testing on different scenarios of synthetic surfaces. We identify a technical gap and propose a new version of the approach which incorporates the spectral analysis method to help identify the statistically significant frequencies of the surface to guide the refinement and mesh. Our results show that spectral analysis is the method that can help improve the accuracy of representing the surface, thus further improving the accuracy of predicting the bedform-driven hyporheic exchange flows.

Comprehensive Evaluation of Anterior Corneal Change in Asphericity Calculated by the Tangential Radius of Curvature after LASIK

To evaluate the change in the anterior corneal asphericity (ΔQ) comprehensively calculated using the tangential radius (rt) after LASIK. Forty-two right eyes were evaluated using the Orbscan II corneal topographer. The pre- and postoperativeQ-values of the flat principal semimeridians calculated by the sagittal radius were compared to those by the tangential radius. TheQ-value of each semimeridian in the horizontal region was calculated byrt. Fourier fitting was used to model the 360-semimeridional variation ofQ-values and to fit theQ-values in the vertical region before and after surgery. There were significant differences inQ-values between the two methods before (P<0.001) and after surgery (P=0.003). A significant increase in postoperativeQ-value was detected compared to preoperativeQ-value (P<0.001) calculated byrt. The 360-semimeridional variation of theQ-values was well fitted with a third- and fourth-degree Fourier function before and after surgery. The ΔQ-value distribution presented double valley variation, with the amount of ΔQbeing lowest in the near-vertical regions and highest in the near-horizontal regions. Calculating theQ-value withrtcombined with Fourier fitting, we evaluated 360 ΔQ-values’ variation of semimeridians of the entire anterior corneal surface and then displayed true and complete anterior corneal shape after LASIK.

The Masses and Pulsation Modes of Classical Cepheids

Recent general observations pertaining to the masses and pulsation modes of classical Cepheids are reviewed. Certain special ones of these variables that display unusual behavior such as long term amplitude variations, overtone pulsations, and double-mode behavior, including one Cepheid in the first and second overtones as well as those in the fundamental and first overtone, are discussed in some detail. I suggest that the amplitude varying supergiant Cepheid HR 7308, which seems to be pulsating in the second radial overtone, is alternating between states where there is enough helium to barely give kappa and gamma effect driving, and where the helium has settled too deep for this driving. Reestablishment of the helium may be due to rapid levitation of the CNONe elements which cause convection and which then dredge-up the helium again to suppress the convection and also to drive pulsations. The use of Fourier fitting to the light and velocity curves have revealed some features that are interesting and are discussed, such as the pulsation mode discrimination and the derivation of accurate Wesselink radii. The seven methods of determining the masses of these stars are presented with a short critique of each. Evolution and pulsation masses depend on uncertain observed luminosities, and these have been revised recently. Evolution masses also depend on the blue looping yellow giant evolution tracks that may need revision because of convective core overshooting and possible opacity, Z, or Y abundance increases. The most discrepant masses, however, are those that depend on period ratios – the “bump” and “beat” masses. The possibility that the Cepheid internal structure can be modified enough by doubling the material opacity seems unlikely. It is suggested, though, that perhaps the period ratio mass anomaly solution can be found in CNONe element enhancement by radiation absorption levitation that would give higher opacities by abundance effects instead of any revisions in the opacity calculations. Some details for this mass anomaly “solution” are presented.