We study the nonstationary flow of an incompressible fluid in a thin rectangle with an elastic plate as the upper part of the boundary. The flow is governed by a time-dependent pressure drop and an external force and it is modeled by Stokes equations. The dynamic of this fluid–structure interaction problem is studied in the limit when the thickness of the fluid domain tends to zero. Using the asymptotic techniques, we obtain for the effective plate displacement a sixth-order parabolic equation with a non standard boundary conditions. Results on existence, uniqueness and regularity of the solution are proved. The approximation is justified through a weak convergence theorem.

Enhanced single-patch NURBS (Non-uniform rational B-splines) parameterization is developed based on fitting parameter values, capable of handling dynamically changing shapes. With respect to NURBS and T-splines, the proposed single-patch parameteriza

In this paper, we study the interaction of an incompressible viscous fluid occupying two-dimensional channel with an elastic plate located on one part of fluid boundary. We assume that the deformation of the boundary is small enough and consider the fluid flow equations in the initial configuration. Non-steady Stokes equations are used to model the flow, and the pressure boundary conditions are prescribed on the channel’s ends. The results on existence, uniqueness, and regularity of solution are proved.

Standard fringe-based structured-light processing estimates wrapped phase from phase-shifted sinusoidal images and commonly relies on phase unwrapping to obtain a globally consistent phase representation. In practical measurements, this approach may become unstable on reflective objects and under low or non-uniform illumination, where the recorded fringe signal is distorted and the recovered phase becomes unreliable. To address these limitations, we propose a correspondence extraction method based on subpixel peak localization performed directly on phase-domain images. The wrapped phase is transformed into absolute value phase profiles, $\mathsf{\Phi }=\left|{\varphi }_w\right|$, whose local structure follows the projected fringe pattern and is less affected by object-dependent intensity variations. The proposed method reformulates correspondence extraction as a local signal-based estimation problem in the phase-domain, thereby reducing reliance on global phase-consistency constraints at the correspondence stage. A practical advantage observed in the evaluated examples is that the method remained usable in some regions where the phase became locally flat because of low modulation, saturation, or reflective surface effects. In such regions, conventional processing relies on sufficiently reliable phase gradients and subsequent unwrapping, whereas the proposed method uses local peak geometry in the transformed phase representation. In the implementation used here, Gray-code information is employed only for pixel-wise phase extension and reference indexing, not as a spatial phase-unwrapping mechanism. The method does not require machine learning models or training data and can be integrated as a correspondence analysis stage in practical structured-light systems.