Search Results (4)

It is common knowledge that studying integral equations accompanied by and related to phase delay is significant, and that significance grows when considering the problem’s time factor. Through this study, one may predict the material’s state for a short time or infer its state before beginning the investigation. In this work, a phase-lag mixed integral equation (P-MIE) with a continuous kernel in time and a singular kernel in position is studied in (2 + 1) dimensions in the space $L_2\left(\right[a,b]\times [c,d\left]\right)\times C[0,T],T<1$. The properties of fractional integrals are used to generate the mixed integral equation (MIE). Certain assumptions are considered in order to examine convergence, uniqueness of solution, and estimation error. We achieve a class of two-dimensional Fredholm integral equations (FIEs) with time-dependent coefficients after applying the separation technique. After that, we will get a linear algebraic system (LAS) in 2Ds applying the product Nystrӧm method (PNM). The convergence of the LAS’s unique solution is covered. Two applications on the MIE with a logarithmic kernel and a Carleman function are discussed to illustrate the viability and efficiency of the applied techniques. At the end, a valuable conclusion is established. Full article

In this article, we investigate a couple of nonlinear time-fractional evolution equations, namely the cubic-quintic-septic-nonic equation and the Davey–Stewartson (DS) equation, both of which have significant applications in complex physical phenomena such as fiber optical communication, optical signal processing, and nonlinear optics. Using a powerful technique named the extended generalized Kudryashov approach, we extract different rich structured soliton solutions to these models, including bell-shaped, cuspon, parabolic soliton, singular soliton, and squeezed bell-shaped soliton. We also study the impact of fractional-order derivatives on these solutions, providing new insights into the dynamics of nonlinear models. The results are compared with the existing literature, revealing novel and distinct solutions that offer a deeper understanding of these fractional models. The results show that the implemented approach is useful, reliable, and compatible for examining fractional nonlinear evolution equations in applied science and engineering. Full article

Objective: To present a novel pipeline for rapid and precise computation of fractional flow reserve from an analysis of routine two-dimensional coronary angiograms based on fluid mechanics equations (FFR2D). Material and methods: This was a pilot analytical study that was designed to assess the diagnostic performance of FFR2D versus the gold standard of FFR (threshold ≤ 0.80) measured with a pressure wire for the physiological assessment of intermediate coronary artery stenoses. In a single academic center, consecutive patients referred for diagnostic coronary angiography and potential revascularization between 1 September 2020 and 1 September 2022 were screened for eligibility. Routine two-dimensional angiograms at optimal viewing angles with minimal overlap and/or foreshortening were segmented semi-automatically to derive the vascular geometry of intermediate coronary lesions, and nonlinear pressure–flow mathematical relationships were applied to compute FFR2D. Results: Some 88 consecutive patients with a single intermediate coronary artery lesion were analyzed (LAD n = 74, RCA n = 9 and LCX n = 5; percent diameter stenosis of 45.7 ± 11.0%). The computed FFR2D was on average 0.821 ± 0.048 and correlated well with invasive FFR (r = 0.68, p < 0.001). There was very good agreement between FFR2D and invasive-wire FFR with minimal measurement bias (mean difference: 0.000 ± 0.048). The overall accuracy of FFR2D for diagnosing a critical epicardial artery stenosis was 90.9% (80 cases classified correctly out of 88 in total). FFR2D identified 24 true positives, 56 true negatives, 4 false positives, and 4 false negatives and predicted FFR ≤ 0.80 with a sensitivity of 85.7%, specificity of 93.3%, positive likelihood ratio of 13.0, and negative likelihood ratio of 0.15. FFR2D had a significantly better discriminatory capacity (area under the ROC curve: 0.95 [95% CI: 0.91–0.99]) compared to 50%DS on 2D-QCA (area under the ROC curve: 0.70 [95% CI: 0.59–0.82]; p = 0.0001) in predicting wire FFR ≤ 0.80. The median time of image analysis was 2 min and the median time of computation of the FFR2D results was 0.1 s. Conclusion: FFR2D may rapidly derive a precise image-based metric of fractional flow reserve with high diagnostic accuracy based on a single two-dimensional coronary angiogram. Full article

This paper proposes an analytical subdomain model for predicting magnetic field distributions in a three-phase double-stator permanent magnet synchronous machine (DS-PMSM) during open-circuit and on-load conditions. The geometric structure of DS-PMSM is quite challenging since the stator cores are located in the outer and inner parts of the motor, while the rotor magnets are placed between these two stators. Parameters that influence the motor performance in DS-PMSM include stator outer radius, stator inner radius, magnet thickness, magnet arc, slot opening, outer and inner airgap thickness and the number of winding turns. The analytical subdomain model proposed in this paper, which can accurately predict the performances of DS-PMSM with less computational time, has an excellent advantage as a rapid design tool. The model is initially generated using the separation of variables technique in four subdomains, namely, outer airgap, outer magnet, inner magnet, and inner airgap, based on Laplace’s and Poisson’s equations in polar coordinates. The field solutions in each subdomain are derived by applying the appropriate boundary and interface conditions. Furthermore, finite element analysis (FEA) is used to validate the analytical results in fractional DS-PMSM with a different number of slots between outer and inner stators and a non-overlapping winding configuration. The electromagnetic performances that have been evaluated are the slotted airgap flux density, back-emf and output torque. The results demonstrate that the proposed analytical model is able to predict the magnetic field distributions accurately in DS-PMSM. Full article