Flower Pollination Heuristics for Parameter Estimation of Electromagnetic Plane Waves

For the last few decades,the parameter estimation of electromagnetic plane waves i.e.,far field sources,impinging on antenna array geometries has attracted a lot of researchers due to their use in radar,sonar and under water acoustic environments.In this work,nature inspired heuristics based on the flower pollination algorithm(FPA)is designed for the estimation problem of amplitude and direction of arrival of far field sources impinging on uniform linear array(ULA).Using the approximation in mean squared error sense,a fitness function of the problem is developed and the strength of the FPA is utilized for optimization of the cost function representing scenarios for various number of sources non-coherent located in the far field.The worth of the proposed FPA based nature inspired computing heuristic is established through assessment studies on fitness,histograms,cumulative distribution function and box plots analysis.The other worthy perks of the proposed scheme include simplicity of concept,ease in the implementation,extendibility and wide range of applicability to solve complex optimization problems.These salient features make the proposed approach as an attractive alternative to be exploited for solving different parameter estimation problems arising in nonlinear systems,power signal modelling,image processing and fault diagnosis.

A novel method for simulating nuclear explosion with chemical explosion to form an approximate plane wave: Field test and numerical simulation

A nuclear explosion in the rock mass medium can produce strong shock waves,seismic shocks,and other destructive effects,which can cause extreme damage to the underground protection infrastructures.With the increase in nuclear explosion power,underground protection engineering enabled by explosion-proof impact theory and technology ushered in a new challenge.This paper proposes to simulate nuclear explosion tests with on-site chemical explosion tests in the form of multi-hole explosions.First,the mechanism of using multi-hole simultaneous blasting to simulate a nuclear explosion to generate approximate plane waves was analyzed.The plane pressure curve at the vault of the underground protective tunnel under the action of the multi-hole simultaneous blasting was then obtained using the impact test in the rock mass at the site.According to the peak pressure at the vault plane,it was divided into three regions:the stress superposition region,the superposition region after surface reflection,and the approximate plane stress wave zone.A numerical simulation approach was developed using PFC and FLAC to study the peak particle velocity in the surrounding rock of the underground protective cave under the action of multi-hole blasting.The time-history curves of pressure and peak pressure partition obtained by the on-site multi-hole simultaneous blasting test and numerical simulation were compared and analyzed,to verify the correctness and rationality of the formation of an approximate plane wave in the simulated nuclear explosion.This comparison and analysis also provided a theoretical foundation and some research ideas for the ensuing study on the impact of a nuclear explosion.

Reflection of plane waves from a micropolar thermoelastic solid half-space with impedance boundary conditions

In this paper,the governing equations of linear,isotropic,homogeneous and generalized micropolar thermoelasticity are specialized in a plane.The governing equations are solved for plane harmonic wave solutions.Two separate velocity equations are obtained which indicate the existence of four plane waves with distinct speeds.A problem on reflection of plane waves from a thermally insulated/isothermal surface is considered with impedance boundary conditions.Appropriate potentials for incident and reflected waves are formulated which satisfy the boundary conditions at a plane surface.Relations between reflection coefficients as well as the expressions of energy ratios for various reflected waves are obtained.For illustration,the reflection coefficients and energy ratios of reflected waves are computed for relevant material parameters of an aluminium-epoxy composite.Effect of impedance parameters on all reflected waves is shown graphically at each angle of incidence.

Propagation of elastic plane waves in homogeneous and transversely isotropic media

Solutions to the equation of waves motion are derived for homogeneous and transversely isotropic media such as fiber-reinforced composites, and three dimensional slowness surfaces are shown as well. A brief discussion on the propagation of plane waves is given.Elastic plane waves are characterized by slowness vectors, wave vectors, polarization vectors and group velocity vectors, etc. The results obtained are presented in a coordinate-free form due to the introduction of the crystal axis' orieniation vector which specifies the anisotropy of the media. Therefore, the results are the most general and convenient for further application

PLANE WAVES NUMERICAL STABILITY OF SOME EXPLICIT EXPONENTIAL METHODS FOR CUBIC SCHRODINGER EQUATION

Numerical stability when integrating plane waves of cubic SchrSdinger equation is thor- oughly analysed for some explicit exponential methods. We center on the following second- order methods： Strang splitting and Lawson method based on a one-parameter family of 2-stage 2nd-order explicit Runge-Kutta methods. Regions of stability are plotted and numerical results are shown which corroborate the theoretical results. Besides, a tech- nique is suggested to avoid the possible numerical instabilities which do not correspond to continuous ones.

ELECTRO-MAGNETO-THERMOELASTIC PLANE WAVES IN MICROPOLAR SOLID INVOLVING TWO TEMPERATURES

The model of equations of micropolar generalized magneto-thermoelasticity is introduced within the context of the theory of two temperatures generalized thermoelasticity and we consider a problem of an isotropic homogeneous micropolar medium taking into account the heat effects and allowing the magnetic field effects. A plane wave analysis is employed to obtain the exact formulas of the two temperatures （conductive and mechanical）, displacement components, micro-rotation components, stresses, couple stresses, induced electric current, electric field and magnetic field. Arbitrary application is chosen to enable us to get the complete solution. The considered variables are presented graphically and discussions are made for the results.

The Plane WavesMethod for Numerical Boundary Identification

We study the numerical identification of an unknown portion of the boundary on which either the Dirichlet or the Neumann condition is provided from the knowledge of Cauchy data on the remaining,accessible and known part of the boundary of a two-dimensional domain,for problems governed by Helmholtz-type equations.This inverse geometric problem is solved using the plane wavesmethod(PWM)in conjunction with the Tikhonov regularizationmethod.The value for the regularization parameter is chosen according toHansen’s L-curve criterion.The stability,convergence,accuracy and efficiency of the proposedmethod are investigated by considering several examples.

Anti-plane (SH) waves diffraction by an underground semi-circular cavity:analytical solution

Diffraction of a two-dimensional （2D） semi-circular cavity in a half-space under incident SH-waves is studied using the classic wave function expansion method with a new de-coupling technique. This so-called ＂improved cosine half- range expansion＂ algorithm exhibits an excellent performance in reducing displacement residual errors at two rim points of concern. The governing equations are developed in a manner that minimizes the residues of the boundary conditions. Detailed derivation and analysis procedures as well as truncation of infinite linear governing equations are presented. The semi-circular cavity model presented in this paper, due to its simple profile, is expected to be used in seismic wave propagation studies as a benchmark for examining the accuracies of various analytical or numerical methods for mixed-boundary wave propagation problems.

Diffraction of plane SV waves by a cavity in poroelastic half-space

This paper presents an indirect boundary integration equation method for diffraction of plane SV waves by a 2-D cavity in a poroelastic half-space.The Green＇s functions of compressive and shear wave sources are derived based on Biot＇s theory. The scattered waves are constructed using fictitious wave sources close to the boundary of the cavity, and their magnitudes are determined by the boundary conditions. Verification of the accuracy is performed by： （1） checking the satisfaction extent of the boundary conditions, （2） comparing the degenerated solutions of a single-phased case with well- known solutions, and （3） examining the numerical stability of the solutions. The nature of diffraction of plane SV waves around a cavity in a poroelastic half-space is investigated by numerical examples.

Scattering of plane SH waves by a circular-arc hill with a circular tunnel

No abstract available

2.5D scattering of incident plane SV waves by a canyon in layered half-space

This paper presents a 2.5D scattering of incident plane SV waves by a canyon in a layered half-space by using the indirect boundary element method （IBEM）. A free field response analysis is performed to provide the displacements and stresses on the boundary of the canyon where fictitious uniform moving loads are applied to calculate the Green＇s fi.mctions for the displacements and stresses. The amplitudes of the loads are determined by the boundary conditions. The free field displacements are added to the fictitious uniform moving loads induced displacements and the total response is obtained. Numerical calculations are performed for a canyon with homogenous and in one layer over bedrock. The effects of the thickness and stiffness of the layer on the amplification are studied and discussed.

Diffraction of plane P waves by a canyon of arbitrary shape in poroelastic half-space (Ⅰ): Formulation

This paper presents an indirect boundary integration equation method for diffraction of plane P waves by a two-dimensional canyon of arbitrary shape in poroelastic half-space. The Green＇s functions of compressional and shear wave sources in poroelastic half-space are derived based on Biot＇s theory. The scattered waves are constructed using the fictitious wave sources close to the boundary of the canyon, and magnitude of the fictitious wave sources are determined by the boundary conditions. The precision of the method is verified by the satisfaction extent of boundary conditions, the comparison between the degenerated solutions of single-phased half-space and the well-known solutions, and the numerical stability of the method.

Surface motion of a semi-elliptical hill for incident plane SH waves

A closed-form analytical solution of surface motion of a semi-elliptical cylindrical hill for incident plane SH waves is presented. Although some previous analytical work had already dealt with hill topography of semi-circular and shallow circular, our work aims at calculating surface motion of very prolate hill for high incident frequency, and explaining the special vibrating is checked by boundary conditions, numerical results for and some conclusions are obtained. properties of very prolate hill. Accuracy of the solution surface motion of oblate and prolate hills are calculated,

Diffraction of plane P waves by a canyon of arbitrary shape in poroelastic half-space (Ⅱ): Numerical results and discussion

This paper investigates in detail the nature of diffraction of plane P waves around a canyon in poroelastic half-space, and studies the effects of incident frequency, drainage condition, porosity, etc, on the diffraction of waves. It is shown that the surface displacement amplitudes of the drained case are close to those of the undrained case, however, the surface displacement amplitudes of the dry case are very different from those of the saturated （either drained or undrained） cases. There are large phase shift between the dry case and the saturated cases, as well as slightly longer resultant wavelengths for the undrained case than those for the drained case and longer resultant wavelengths for the drained case than those for the dry case. For small porosity the surface displacement amplitudes for the saturated cases are almost identical to those for the dry case; while for large porosity, the effect of drainage condition becomes significant, and the surface displacement amplitudes for the undrained case are larger than those for the drained case. As the incident frequency increases, the effect of porosity becomes significant, and more significant for the undrained case than that for the drained case. As the porosity increases, the pore pressures increase significantly but their oscillations become smoother. As the incident frequency increases, the pore pressures become more complicated.

Scattering of plane P waves by a semi-cylindrical hill: analytical solution

An analytical solution for scattering of plane P waves by a semi-cylindrical hill was derived by using the wave function expansion method, and convergence of the solution and accuracy of truncation were verified. The effect of incident frequency and incident angle on the surface motion of the hill was discussed, and it was shown that a hill greatly amplifies incident plane P waves, and maximum horizontal displacement amplitudes appear mostly at the inclined incidence of waves, which are located at the half-space; and maximum vertical displacement amplitudes emerge mostly at the vertical incidence of waves, which are situated at the hill.

Dynamic soil-tunnel interaction in layered half-space for incident plane SH waves

The dynamic soil-tunnel interaction is studied by indirect boundary element method （IBEM）, using the model of a rigid tunnel in layered half-space, which is simplified to a single soil layer on elastic bedrock, subjected to incident plane SH waves. The accuracy of the results is verified through comparison with the analytical solution. It is shown that soil-tunnel interaction in layered half-space is larger than that in homogeneous half-space and this interaction mechanism is essentially different from that of soil-foundation-superstructure interaction.

THE USE OF PLANE WAVES TO APPROXIMATE WAVE PROPAGATION IN ANISOTROPIC MEDIA

In this paper we extend the standard Ultra Weak Variational Formulation （UWVF） of Maxwell＇s equations in an isotropic medium to the case of an anisotropic medium. We verify that the underlying theoretical framework carries over to anisotropic media （however error estimates are not yet available） and completely describe the new scheme. We then consider TM mode scattering, show how this results in a Helmholtz equation in two dimensions with an anisotropic coefficient and demonstrate how to formulate the UWVF for it. In one special case, convergence can be proved. We then show some numerical results that suggest that the UWVF can successfully simulate wave propagation in anisotropic media.

Reflection of plane seismic waves at the surface of double-porosity dual-permeability materials

The present work deals with the reflection of plane seismic waves at the stress-free plane surface of double-porosity dualpermeability material. The incidence of two main waves（i.e., P1 and SV） is considered. As a result of the incident waves,four reflected（three longitudinal and one shear） waves are found in the medium. The expressions of reflection coefficients for a given incident wave are obtained as a non-singular system of linear equations. The energy shares of reflected waves are obtained in the form of an energy matrix. A numerical example is considered to calculate the partition of incident energy for fully closed as well as perfectly open pores. Effect of incident direction on the partition of the incident energy is analyzed with the change in wave frequency, wave-induced fluid-flow, pore-fluid viscosity and double-porosity structure. It has been confirmed from the numerical interpretation that during the reflection process, conservation of incident energy is obtained at each angle of incidence.

Diffraction of plane P waves around an alluvial valley in poroelastic half-space

Diffraction of plane P waves around an alluvial valley of arbitrary shape in poroelastic half-space is investigated by using an indirect boundary integral equation method. Based on the Green＇s fimctions of line source in poroelastic half-space, the scattered waves are constructed using the fictitious wave sources close to the interface of the valley and the density of ficti- tious wave sources are determined by boundary conditions. The precision of the method is verified by the satisfaction extent of boundary conditions, and the comparison between the degenerated solutions and available results in single-phase case. Finally, the nature of diffraction of plane P waves around an alluvial valley in poroelastic half-space is investigated in detail through nu- merical examples.

Surface motion of a semi-cylindrical hill for incident plane SV waves: Analytical solution

An analytical solution for surface motion of a semi-cylindrical hill for incident plane SV waves was derived by using the wave function expansion method and the auxiliary function technique, and convergence of the solution and accuracy of truncation were verified. The effect of incident frequency and angle as well as hill width on the surface motion of the hill was discussed by numerical examples. It was shown that, a hill greatly amplifies incident plane SV waves, and the maximal amplification may reach 4 times of that for free-field response; and for incident waves of low frequency, the maximal displacement amplitudes emerge mostly at the half-space, however, for incident waves of high frequency, the maximal displacement amplitudes appear mostly at the hill.