Lommel pulses: An analytic form for localized waves of the focus wave mode type with bandlimited spectrum

Chapter 4 analyses the transition from an attached flow to a flow with local recirculation region near a corner point of a body contour. It considers both subsonic and supersonic flow regimes, and shows that the flow near a corner can be studied in the framework of the triple-deck theory. It assumes that the body surface deflection angle is small, and formulates the linearized viscous-inviscid interaction problem. Its solution is found in an analytic form. It also presents the results of the numerical solution of the full nonlinear problem. It shows how, and when, the separation region forms in the boundary layer. In conclusion, it suggests that in the subsonic flow past a concave corner, the solution is not unique.

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Partial Energy Transfer Model of Lamb Waves Scattering in Materially Isotropic Waveguides

Applied Sciences ◽

10.3390/app11104508 ◽

2021 ◽

Vol 11 (10) ◽

pp. 4508

Author(s):

Pavel Šofer ◽

Michal Šofer ◽

Marek Raček ◽

Dawid Cekus ◽

Paweł Kwiatoń

Keyword(s):

Energy Transfer ◽

Lamb Waves ◽

Hybrid Approach ◽

Wave Mode ◽

Transfer Model ◽

Material Interface ◽

Modal Expansion ◽

Scattering Coefficients ◽

Expansion Technique ◽

Partial Energy

The scattering phenomena of the fundamental antisymmetric Lamb wave mode with a horizontal notch enabling the partial energy transfer (PET) option is addressed in this paper. The PET functionality for a given waveguide is realized using the material interface. The energy scattering coefficients are identified using two methods, namely, a hybrid approach, which utilizes the finite element method (FEM) and the general orthogonality relation, and the semi-analytical approach, which combines the modal expansion technique with the orthogonal property of Lamb waves. Using the stress and displacement continuity conditions on the present (sub)waveguide interfaces, one can explicitly derive the global scattering matrix, which allows detailed analysis of the scattering process across the considered interfaces. Both methods are then adopted on a simple representation of a surface breaking crack in the form of a vertical notch, of which a certain section enables not only the reflection of the incident energy, but also its nonzero transfer. The presented results show very good conformity between both utilized approaches, thus leading to further development of an alternative technique.

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Analysis of Flaw Detection Sensitivity of Phased Array Ultrasonics in Austenitic Steel Welds According to Inspection Conditions

Sensors ◽

10.3390/s21010242 ◽

2021 ◽

Vol 21 (1) ◽

pp. 242

Author(s):

YoungLae Kim ◽

Sungjong Cho ◽

Ik Keun Park

Keyword(s):

Austenitic Steel ◽

Simulation Modeling ◽

Power Plants ◽

Phased Array ◽

Flaw Detection ◽

Wave Mode ◽

Ultrasonic Waves ◽

Detection Sensitivity ◽

Flaw Sensitivity ◽

Steel Welds

The anisotropy and inhomogeneity exhibited by austenitic steel in welds poses a challenge to nondestructive testing employing ultrasonic waves, which is predominantly utilized for the inspection of welds in power plants. In this study, we assess the reliability of phased array ultrasonic testing (PAUT) by analyzing the flaw detection sensitivity of ultrasonic beams in anisotropic welds, based on the inspection conditions. First, we simulated the sectorial scan technique, frequently employed for the inspection of actual welds, while taking into account the ultrasonic wave mode, frequency, and shape and position of a flaw. Subsequently, we analyzed the flaw sensitivity by comparing A-scan signals and S-scan results. The sensitivity analysis results confirmed the detection of all flaws by considering at least two inspection methods based on the shape and position of the flaw. Furthermore, we verified our model by performing an experiment under the same conditions as the simulation and found that the results were in agreement. Hence, we find that the simulation modeling technique proposed in this study can be utilized to develop suitable inspection conditions, according to the flaw characteristics or inspection environment.

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Structure factors for generalized grey Browinian motion

Fractional Calculus and Applied Analysis ◽

10.1515/fca-2019-0024 ◽

2019 ◽

Vol 22 (2) ◽

pp. 396-411

Author(s):

José L. da Silva ◽

Ludwig Streit

Keyword(s):

Gaussian Processes ◽

Form Factors ◽

Analytic Form ◽

Debye Function ◽

Asymptotic Decay ◽

Structure Factors ◽

Closed Analytic Form ◽

Non Gaussian

Abstract In this paper we investigate the form factors of paths for a class of non Gaussian processes. These processes are characterized in terms of the Mittag-Leffler function. In particular, we obtain a closed analytic form for the form factors, the Debye function, and can study their asymptotic decay.

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Analysis of Dielectric Waveguide Grating and Fabry–Perot Modes in Elastic Grating in Optical Detection of Ultrasound

Sensors ◽

10.3390/s21124081 ◽

2021 ◽

Vol 21 (12) ◽

pp. 4081

Author(s):

Suejit Pechprasarn ◽

Chayanisa Sukkasem ◽

Phitsini Suvarnaphaet

Keyword(s):

Optical Properties ◽

Dielectric Waveguide ◽

Figure Of Merit ◽

Pressure Range ◽

Optical Filter ◽

Grating Period ◽

Wave Mode ◽

Waveguide Grating ◽

Fabry Perot ◽

Optical Grating

In our previous work, we have demonstrated that dielectric elastic grating can support Fabry–Perot modes and provide embedded optical interferometry to measure ultrasonic pressure. The Fabry–Perot modes inside the grating provide an enhancement in sensitivity and figure of merit compared to thin film-based Fabry–Perot structures. Here, in this paper, we propose a theoretical framework to explain that the elastic grating also supports dielectric waveguide grating mode, in which optical grating parameters control the excitation of the two modes. The optical properties of the two modes, including coupling conditions and loss mechanisms, are discussed. The proposed grating has the grating period in micron scale, which is shorter than the wavelength of the incident ultrasound leading to an ultrasonic scattering. The gap regions in the grating allow the elastic grating thickness to be compressed by the incident ultrasound and coupled to a surface acoustic wave mode. The thickness compression can be measured using an embedded interferometer through one of the optical guided modes. The dielectric waveguide grating is a narrow bandpass optical filter enabling an ultrasensitive mode to sense changes in optical displacement. This enhancement in mechanical and optical properties gives rise to a broader detectable pressure range and figure of merit in ultrasonic detection; the detectable pressure range and figure of merit can be enhanced by 2.7 times and 23 times, respectively, compared to conventional Fabry–Perot structures.

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A theory of giant vortices

Journal of High Energy Physics ◽

10.1007/jhep08(2021)056 ◽

2021 ◽

Vol 2021 (8) ◽

Author(s):

Alexander A. Penin ◽

Quinten Weller

Keyword(s):

Asymptotic Expansion ◽

Analytic Form ◽

Scalar Fields ◽

Winding Number ◽

Asymptotic Results ◽

Convergence Region ◽

Ginzburg Landau ◽

Landau Model ◽

Neutral Scalar ◽

Vortex Solutions

Abstract We elaborate a theory of giant vortices [1] based on an asymptotic expansion in inverse powers of their winding number n. The theory is applied to the analysis of vortex solutions in the abelian Higgs (Ginzburg-Landau) model. Specific properties of the giant vortices for charged and neutral scalar fields as well as different integrable limits of the scalar self-coupling are discussed. Asymptotic results and the finite-n corrections to the vortex solutions are derived in analytic form and the convergence region of the expansion is determined.

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