Problem Of Diffraction Research Articles

Complex TE-modes in Slotted Waveguides of Arbitrary Cross Section

Implementation of the rigorous Analytical Regularization Method is presented for plane wave scattering by arbitrary two-dimensional cavities with longitudinal slit. The general solution of the Neumann boundary value problem for Helmholtz equation is obtained in a form of two coupled infinite systems of linear algebraic equations of the second kind. Compactness of the matrix operator provides efficient numerical solution of the joint system by truncation method. Fast convergence of the truncated system of linear algebraic equations makes this method an effective instrument for accurate analysis of spectral and diffraction problems. Considering the homogeneous version of equations and finding the complex roots of their determinants, we calculate the complex eigenvalues of complex oscillations. Employing spline interpolation and mollifier function the problem geometry is generalized.

Diffraction and Radiation of Water Waves by a Heaving Absorber in Front of a Bottom-Mounted, V-shaped Breakwater of Infinite Length

In the present study, the problems of diffraction and radiation of water waves by a cylindrical heaving wave energy converter (WEC) placed in front of a reflecting V-shaped vertical breakwater are formulated. The idea conceived is based on the possible exploitation of amplified scattered and reflected wave potentials originating from the presence of V-shaped breakwater, towards increasing the WEC’s wave power absorption due to the wave reflections. An analytical solution based on the method of images is developed in the context of linear water wave theory, taking into account the hydrodynamic interaction phenomena between the converter and the vertical wall. Numerical results are presented and discussed concerning the hydrodynamic forces on the absorber and its wave power efficiency for various examined parameters, namely, the breakwaters’ forming angle, the distance between the converter and the vertical walls and the wave heading angle. The results show that the amount of the harvested wave power by the WEC in front of the walls is amplified compared to the wave power absorbed by the same WEC in the open sea.

Research on real-time elimination of ultra-wideband radar ranging abnormal value data

Abstract. For indoor positioning, ultra-wideband (UWB) radar comes to the forefront due to its strong penetration, anti-jamming, and high-precision ranging abilities. However, due to the complex indoor environment and disorder of obstacles, the problems of diffraction, penetration, and ranging instability caused by UWB radar signals also emerge, which make it difficult to predict the noise and leads to a great impact on the accuracy and stability of the measurement data in the short term. Therefore, the abnormal value migration of the positioning trajectory occurred in real-time positioning. To eliminate this phenomenon and provide more accurate results, the abnormal values need to be removed. It is not difficult to eliminate abnormal values accurately based on a large number of data, but it is still a difficult problem to ensure the stability of the positioning system by using a small number of measurement data in a short time to eliminate abnormal value in real-time ranging data. Thus, this paper focuses on the experimental analysis of a UWB-based indoor positioning system. By repeatedly measuring the range , a large number of measurement data can be obtained. Using the massive data to train linear regression models, we get the parameter of the linear model of range data measured with the UWB radar. Based on the Gaussian function outlier detection, abnormal values are eliminated, and putting the new range data into the regression model trained by us, the ranging error is reduced by nearly 50 % compared with the peak and mean ranging errors in general.

Heuristic solution to the problem of diffraction of a TE-polarized electromagnetic wave on a semitransparent half-plane

Using the method of fundamental components for the problem of diffraction of a TE-polarized wave on a half-plane with two-sided impedance boundary conditions a heuristic solution is obtained that approximately describes the scattered field. The verification and adjustment of heuristic formulas using a rigorous solution by the Wiener–Hopf method are carried out. A physical interpretation of the rigorous solution based on the obtained heuristic relations is proposed.

Alternative approaches of evaluating Diffraction Transfer Matrix and Radiation Characteristics using the hybrid source-dipole formulation

The interaction theory presented by Kagemoto and Yue (1986) significantly reduces the computational burden in the wave interaction problem of multiple surface-piercing bodies, particularly arrays of wave energy converters in recent years. Two essential operators of the theory are the so-called Diffraction Transfer Matrix and Radiation Characteristics. Many subsequent researchers (Goo and Yoshida, 1990; Flavià et al., 2018) have implemented the theory using the source distribution method in evaluating the two linear operators of a single unique geometry. However, nowadays, a great majority of boundary element method codes have been written by virtue of the hybrid source-dipole distribution method on account of its high accuracy. In this regard, the present work aims to introduce a full set of mathematical formulations, as well as a complete derivation process of evaluating the two operators based on the hybrid source-dipole distribution method. The proposed formulations are then applied to two benchmark geometries, as given by McNatt et al. (2015) and Flavià et al. (2018). Good agreement is found between the present results and those from the literature. Moreover, two alternative approaches to solve the diffraction problem have been compared to assess both their accuracy and efficiency. It is found that the two methods present similar levels of accuracy but very different computational burden.

Diffraction waves on general two-legged rectangular floating breakwaters

In this paper, hydrodynamic characteristics of general two-dimensional rectangular floating breakwaters (FBs) with two legs in water of finite depth and infinite domain subjected to sinusoidal waves are studied using a numerical panel method. A parametric study is carried out in order to quantify the effect of the leg size and the leg angle on diffraction problem, especially on the transmission and reflection coefficients. Results show that legs play an effective role in breakwater’s response to incident waves and two-legged FBs could be used for achieving higher efficiencies compared to conventional rectangular FBs. The angle parameter shows that the inverse T-type FB is the best and the Π type FB is the least good in terms of transmission coefficients. However, practical considerations might also be considered when choosing the best FB configuration for different applications.

Calculation method of the radar cross section of the complex shape object located on the surface with an arbitrary reflection coefficient

Relevance. Currently, an important problem is the electromagnetic wave scattering modeling on the complex shape objects located on some underlying surface (this may be military equipment on bitumen/ grass, surface objects directly on the water). Such tasks are important when designing new inconspicuous equipment. The purpose of the work. Consider the existing and suggest improvements in the method solving of the problem of electromagnetic wave diffraction on the complex shape object, which is located on some underlying surface. In this case, the change in the electromagnetic parameters of the underlying surface should not lead to the need to re-calculate the field scattered from the object. Materials and methods. The diffraction problem is solved for the complex shape object, which is located on the underlying surface. The surface can be characterized by dielectric (and magnetic) permeability, complex reflection coefficient or surface impedance. In order to determine the resulting field for an object located on an arbitrary surface, the scattering problem is solved for cases when the object is located above an ideally conducting surface and above an ideal magnetic. Results. A modeling technique for the scattering of the electromagnetic waves by the complex shape objects located above an underlying surface is proposed. Numerical experiments have been caried out in order to demonstrate the effectiveness of this technique. Conclusion. It is shown that the method proposed in the article allows to effectively calculate the contribution of different underlying surfaces in the resulting scattered field of the complex shape objects that are located on it. You do not need to simulate directly for an object over a specific surface each time. It is enough to carry out only three simulations: for an object in free space, and also when ideal conductor and ideal magnetic are used as the underlying surface. Formulas that allow to calculate the field scattered by this object for an arbitrary underlying surface are obtained.

An Iterative Method for Solving the Problem of Diffraction of Longitudinal Shear Waves on A System of Thin Rigid Inclusions

An Iterative Method for Solving the Problem of Diffraction of Longitudinal Shear Waves on A System of Thin Rigid Inclusions

МЕТОД КЛАСИФІКАЦІЇ ЗАДАЧ ОПТИКИ ТА ЛАЗЕРНОЇ ФІЗИКИ

In recent decades, due to the use of computer technology, the results of research in a particular area of science and technique are accumulated very quickly. In the process of creating a database of optical images and knowledge base is appeared the task of classification method absence. Without such a method the creating the structure of data warehouse is difficult to solve. The classification of the tasks and the obtained results requires considerable attention in order to ensure their rapid and accurate search and further use. Classification is one of the most important tasks of large database analysis used in Data Mining. Assessment of classification accuracy can be performed using cross-checking or a test set. The proposed method is suitable for use when the accuracy of the test set classification meets the established requirements. In the field of optics and laser physics dealt with the problem, which usually is grouped by the next attributes: the initial field pattern, the type of the optical system, the characteristics of the obtained spatial distribution of light as the number of maxima, minima, zeros of intensity and other significant objects. The question of classification of the tasks themselves was considered in the paper for the first time. The method of classification of problems in optics and laser physics is developed. It is applied to the problems of diffraction, interference and observation of microobjects. The classification is carried out with the help of mathematical methods, a formal description of the objects and the decision trees method. The 5 classes was chosen: "meaning the task", "solution method", "appointment", "complexity", "way of expression." The attributes of the problem classification are "visual-optical", "optical", "computational", "experimental", "qualitative", "fundamental", "applied", "simple", "complex", "textual", "numerical", "graphical". The scheme of problems in optics and laser physics classification is shown. Decision-making to determine the attributes of the problem is carried out using the decision trees method. Application of the results in search engines of big databases and pattern recognition problems is discussed.

Effect of Internal Fluid Resonance on the Performance of a Floating OWC Device

In the present study, the performance of a floating oscillating water column (OWC) device has been studied in regular waves. The OWC model has the shape of a hollow cylinder. The linear potential theory is assumed, and a matched eigenfunction expansion method(MEEM) is applied for solving the diffraction and radiation problems. The radiation problem involves the radiation of waves by the heaving motion of a floating OWC device and the oscillating pressure in the air chamber. The characteristics of the exciting forces, hydrodynamic forces, flow rate, air pressure in the chamber, and heave motion response are investigated with various system parameters, such as the inner radius, draft of an OWC, and turbine constant. The efficiency of a floating OWC device is estimated in connection with the extracted wave power and capture width. Specifically, the piston-mode resonance in an internal fluid region plays an important role in the performance of a floating OWC device, along with the heave motion resonance. The developed prediction tool will help determine the various design parameters affecting the performance of a floating OWC device in waves.

Solving the Problem of Electromagnetic Wave Diffraction by a Flat Screen Using CUDA

Solving the Problem of Electromagnetic Wave Diffraction by a Flat Screen Using CUDA

On Generalized Solutions of the Problems of Electromagnetic Wave Diffraction in the Open Space

On Generalized Solutions of the Problems of Electromagnetic Wave Diffraction in the Open Space

Application of the Collocation Method for Solving the Problem of Diffraction of an Electromagnetic Wave by a Rectangular Metal Plate

Application of the Collocation Method for Solving the Problem of Diffraction of an Electromagnetic Wave by a Rectangular Metal Plate

Shock Diffraction Problem by Convex Cornered Wedges for Isothermal Gas

Shock Diffraction Problem by Convex Cornered Wedges for Isothermal Gas

Hull form optimization for reduced calm-water resistance and improved vertical motion performance in irregular head waves

A high-efficiency potential-flow based ship hydrodynamic optimization tool is presented in this paper to optimize hull forms for reduced calm-water resistance and improved vertical motion performance in irregular head waves. Besides calm-water ship resistance, the significant amplitudes of heave and pitch motion response spectra in irregular head waves are determined as objective functions. To obtain a more reliable result of ship motion in waves, the three-dimensional potential flow solver by using translating and pulsating line segment source Green's function is employed to solve ship radiation and diffraction problems and further to evaluate ship vertical motion. Several deformation methods are utilized to move the control points of NURBS hull surfaces to achieve the hull form deformation.For the purpose of illustration, this optimization tool is applied to the optimization design of the prototype of DTMB 5512. The resistance and vertical motion performance of four optimal hulls in Case 2 are investigated and further verified by the RANS CFD simulations. The optimization results in two cases indicate that this optimization tool can yield optimal ships with reduced calm-water resistance and improved vertical motion performance, and a reasonable determination of feasible region can increase the possibility of obtaining such target ship.

Hydroelastic behaviour of a submerged horizontal flexible porous structure in three-dimensions

A hydroelastic model is developed for the problem of linear wave interaction with a submerged horizontal flexible porous structure in three-dimensions. The generalized expansion formulae with orthogonal mode-coupling relations are derived by expanding Fourier cosine series in a channel width. Using eigensolutions, various aspects of hydroelastic wave behaviour in a channel with a porous plate submerged in finite water depth is investigated. Further, the usefulness of the expansion is analysed through a real physical problem of wave diffraction by a submerged flexible porous plate connected with mooting lines in three-dimensions. The accurateness of the three-dimensional solution is inspected and the hydroelastic behaviour of the submerged porous structure is analysed for oscillation modes, mooring stiffness, and porous-effect parameters on numerical assessment of reflection, dissipation coefficients, and plate displacements in different cases. The analysis of current hydroelastic behaviour will be beneficial for future design of a device for wave energy absorption in three-dimensions.

Influence of a new‐bored neighbouring cavity on the seismic response of an existing tunnel under incident P‐ and SV‐waves

AbstractOne of the important problems regarding the tunnel design in seismically active areas is the assessment of the mutual effect of two closely running tunnels. With the propagation of seismic waves, the stresses in certain sections of a tunnel, owing to the presence of an adjacent tunnel, can exceed those occurring when considering the single‐tunnel case. In the focus of this study is the hitherto unexplored elastic wave diffraction problem, which considers the influence of the presence of a new‐bored neighbouring cavity on the seismic response of an existing tunnel, under incident P‐waves/SV‐waves. The wave function expansion method, the corresponding boundary conditions along the tunnel and cavity contours, and the translational addition theorem for bi‐cylindrical wave functions are jointly employed to develop an exact mathematical solution of the given problem in the form of infinite FourierBessel series, under the plane‐strain conditions. The dynamic effects of structures are presented in the form of a newly introduced dynamic stress alteration factor as a measure of the variation of dynamic hoop stress amplitudes in the lining and the surrounding medium of an existing tunnel affected by the presence of a closely running newly‐constructed tunnel opening. The results of this study are believed to be useful for interpretation of design rules, particularly considering that seismic standards for tunnels are still in the preliminary stage, where the aspect of the minimum seismically safe distance of a newly‐constructed tunnel opening in the vicinity of an existing tunnel should be of particular concern.

Vertex Green’s Functions of a Quarter-Plane: Links Between the Functional Equation, Additive Crossing and Lamé Functions

Summary In our previous work (R. C. Assier and A. V. Shanin, Q. J. Mech. Appl. Math., 72, 2019), we gave a new spectral formulation in two complex variables associated with the problem of plane-wave diffraction by a quarter-plane. In particular, we showed that the unknown spectral function satisfies a condition of additive crossing about its branch set. In this article, we study a very similar class of spectral problem and show how the additive crossing can be exploited in order to express its solution in terms of Lamé functions. The solutions obtained can be thought of as tailored vertex Green’s functions whose behaviours in the near-field are directly related to the eigenvalues of the Laplace–Beltrami operator. This is important since the correct near-field behaviour at the tip of the quarter-plane had so far never been obtained via a multivariable complex analysis approach.

Chirped pulse propagation in a quasi-PT-symmetric medium with a broadband exceptional-point condition.

The boundary problem of dynamical Bragg diffraction of a chirped optical pulse in a dispersive quasi-PT-symmetric photonic crystal (PhC) in the Laue geometry ("on transmission") is solved by the analytical spectral method. It is shown that, in a quasi-PT-symmetric medium, in which an inhomogeneous spectral line width is much larger than the spectrum of investigated field, the exceptional-point (EP) condition is realized in a wide continuous frequency range, i.e., so-called broadband exceptional-point (BEP) condition takes place. If the Bragg condition is satisfied in a much narrower spectral range than the pulse spectrum, it leads to dramatic changes in the propagation dynamics and parameters of broadband chirped pulses in a quasi-PT-symmetric PhC. Indeed, for a positive Bragg angle of incidence in the case of diffraction in the Laue geometry, the entire spectrum of a broadband chirped pulse fulfills the BEP condition. The diffractionally reflected wave is absent in the BEP regardless of whether the Bragg condition is satisfied, and the pulse propagates as in a homogeneous conservative medium, i.e., without diffraction, gain and loss - unidirectional invisibility. When the sign of the angle of incidence changes, a unidirectional enhancement of the chirped diffracted pulse is observed in that part of it whose frequency simultaneously satisfies both the BEP condition and the Bragg condition. The rest part of the pulse, for which the Bragg condition is not satisfied, propagates as in the case of a positive angle of incidence - there is no diffracted wave. With a smooth change in the angle of incidence of the chirped pulse, a change in frequency that satisfies the Bragg condition occurs and, as a consequence, a smooth change appears in the frequency of the amplified output pulse, as well as in its duration and transverse size. It is also shown that the dispersion of the group velocity of the pulse is suppressed in the frequency range of the BEP condition. Therefore, all its frequency components propagate at a speed close to the speed of light in a conservative homogeneous medium.

Interactions of waves with a body floating in an open water channel confined by two semi-infinite ice sheets

Abstract