Search Results (3)

We define a family of special functions (the CSI ones), which can be used to write any parameterized plane curve with polynomial curvature explicitly. These special functions generalize the Fresnel integrals, and may have an interest in their own right. We prove that any plane curve with polynomial curvature is asymptotically a pseudo-spiral. Using the CSI functions, we can approximate, locally, any plane curve; this approach provides a useful criterion for a (local) classification of plane curves. In addition, we present a new algorithm for finding an arc-length parametrization for any curve, within a prescribed degree of approximation. Full article

Background: To evaluate the corneal biomechanics of stable keratoconus suspects (Stable-KCS) at 1-year follow-up and compare them with those of subclinical keratoconus (SKC). Methods: This prospective case-control study included the eyes of 144 patients. Biomechanical and tomographic parameters were recorded (Corvis ST and Pentacam). Patients without clinical signs of keratoconus in both eyes but suspicious tomography findings were included in the Stable-KCS group (n = 72). Longitudinal follow-up was used to evaluate Stable-KCS changes. Unilateral keratoconus contralateral eyes with suspicious tomography were included in the SKC group (n = 72). T-tests and non-parametric tests were used for comparison. Multivariate general linear models were used to adjust for confounding factors for further analysis. Receiver operating characteristic (ROC) curves were used to analyze the distinguishability. Results: The biomechanical and tomographic parameters of Stable-KCS showed no progression during the follow-up time (13.19 ± 2.41 months, p > 0.05). Fifteen biomechanical parameters and the Stress–Strain Index (SSI) differed between the two groups (p < 0.016). The A1 dArc length showed the strongest distinguishing ability (area under the ROC = 0.888) between Stable-KCS and SKC, with 90.28% sensitivity and 77.78% specificity at the cut-off value of −0.0175. Conclusions: The A1 dArc length could distinguish between Stable-KCS and SKC, indicating the need to focus on changes in the A1 dArc length for keratoconus suspects during the follow-up period. Although both have abnormalities on tomography, the corneal biomechanics and SSI of Stable-KCS were stronger than those of SKC, which may explain the lack of progression of Stable-KCS. Full article

This study illustrates the impact of single discrete arc-shaped ribs (SDASR)-type artificial roughness on the performance of a jet impingement solar thermal collector (JISTC). The impact of parametric variations of SDASR on the Nusselt number $(N{u}_{sdr})$, friction factor $(f_{sdr})$, and thermohydraulic performance $({\eta }_{sdr})$ is examined. The spacer length ($S_{sdr}$) of the SDASR was changed from 0 mm to 300 mm in stages of 100 mm during the experiment. The fixed parameters of the SDASR were a relative discrete distance $\left(D_d/L_v\right)$ of 0.67, relative discrete width $\left(g_w/H_r\right)$ of 0.87, relative rib height $\left(H_r/H\right)$ of 0.047, relative rib pitch $\left(P_r/H\right)$ of 1.7, angle of an arc $\left({\alpha }_{sdr}\right)$ of 60°, jet diameter ratio $\left(D_j/D_{hy}\right)$ of 0.065, streamwise pitch ratio $\left(X/D_{hy}\right)$ of 1.72, and spanwise pitch ratio $\left(Y/D_{hy}\right)$ of 0.82. The Reynolds number $\left(Re\right)$ was altered from 3000 to 19,000. The $N{u}_{sdr}$ and $f_{sdr}$ of a JISTC with a roughened absorber plate was found to be enhanced by 5.25 and 5.98 times as compared to an STC without artificial roughness. The optimal findings of $N{u}_{sdr}$, $f_{sdr},$ and ${\eta }_{sdr}$ were achieved at $S_{sdr}$ = 0 mm. The maximum value of the ${\eta }_{sdr}$ obtained at $S_{sdr}$ = 0 mm was 2.9. Full article