Lower Half-spaces Research Articles

Characterization of Antenna Radiation Pattern and Penetration Depth in Ground Penetrating Radar Field Missions

This article discusses the methods and results of assessing the angular resolution and sounding depth of enhanced-power ground penetration radars obtained during archaeological and geographical expeditionary works in various natural areas. Elongated local objects were used as test objects to evaluate the horizontal radiation pattern of the Loza–V georadar in the upper- and lower-half spaces. The depth of operation of the Loza–N low-frequency radar was estimated during a geophysical study of a unique natural object in the Siberian taiga. The variability of the GPR antenna radiation patterns in different materials (air, dry, or wet soils) confirms the necessity of quantitative measurements with controlled electrophysical parameters.

Numerical integration of particle orbits in discontinuous fields using VENUS-LEVIS and SPEC

The orbit code VENUS-LEVIS is adapted to follow particles in plasma equilibria with discontinuous fields generated by the Stepped Pressure Equilibrium Code (SPEC). The latter is an implementation of the Multi-Region relaxed MHD model, which efficiently computes Taylor states in a series of nested toroidal volumes and supports the formation of magnetic islands and chaotic field regions. To adapt VENUS-LEVIS, an event location procedure is implemented in the existing numerical integrator, which ensures the particle sees the correct field along its trajectory, regardless of the discontinuities present in the Stepped Pressure Equilibrium model. The algorithm is tested in the case where the magnetic field is uniform in the upper and lower half-spaces but has a discontinuity in its direction (shear) on the plane z=0. Particle drifts due to the discontinuity are studied. The convergence properties of the numerical scheme are highlighted by the numerical accuracy, and conservation of the system's invariants, such as energy and momentum. Simulations and convergence studies using the SPEC-LEVIS interface in axisymmetric geometry are then presented. Finally, illustrative particle drifts due to the discontinuity are studied and explained: we examine drifts associated with the change in Larmor radius of passing particles with small excursion from flux surfaces.

An Overview of Probe-Based Millimeter-Wave/Terahertz Far-Field Antenna Measurement Setups [Measurements Corner

In recent years, there has been great interest in millimeter-wave (mmwave) and terahertz (THz) technologies due to an increasing demand for ultrahigh data transfer rate. Two novel solutions, i.e., antenna on chip (AoC) and antenna in package (AiP), have been proposed for the development of highly integrated radio and radar systems [1]-[5]. To measure the antenna characteristics of AoC and AiP, a reliable probe-based mm-wave/THz antenna measurement setup became essential. Over the last 20 years, the world has witnessed the prosperous development of various mmwave/THz antenna measurement setups, most of which can be divided into two types, i.e., probe-station and quasi-in-air based. The former type has a feature that allows the testing equipment to be compactly established on a large metal stage, which has been widely used for near-field based and as part of the farfield-based setups [6]-[10]. The antenna under test (AUT) is maintained on a wafer chuck placed on the stage and thus, only the radiation pattern in the upper half-space is measurable due to the metal stage obstruction. The latter type reduces the defect by using an extended supporting structure to hold the AUT in midair away from the stage so that the radiation patterns in both the upper and lower half-spaces are measurable. Many setups of this type measure antennas at far-field distances, and some of them are also compatible with near-field testing. Compared to probe-station based, quasi-inair based takes up much more space and is less compact.

Sound transmission through annular cylindrical apertures using rapidly converging expansion series.

The problem of sound transmission through an annular aperture with perfectly rigid walls and located in a hard infinite baffle was solved analytically. The three separated regions with suitable boundary conditions were considered. There are two regions for the upper and the lower half spaces and one for the aperture. The solutions to the Helmholtz equation in each region and the continuity conditions were satisfied. The rigorous formulations describing the acoustic pressure and the transmitted and scattered acoustic powers were obtained. The obtained solutions resulted in the derivation of the modal coupling coefficients in the form of infinite integrals. The spectral mapping technique based on the Zernike circle polynomials was adopted for the annular geometry. The modal coupling impedances were presented in the form of a rapidly convergent expansion series. Finally, high accuracy and time efficiency were achieved. The problem of sound scattering and transmission through a circular aperture could be generalized for the annular aperture.

Exact and approximate reflection/transmission responses from a layer containing vertical fractures

SUMMARYAnalyses of vertical fractures are of great interest in characterizing the fluid flow and minimum in situ stress direction in reservoirs. Long-wavelength equivalent orthorhombic (ORT) media typically characterize the anisotropy induced by a set of vertical parallel fractures or two sets of vertical and mutually orthogonal fractures embedded into a transversely isotropic medium with a vertical symmetry axis (VTI). Reflection and transmission (R/T) responses quantify wave amplitude variations in 1-D media and help to reveal the model property enclosing the heterogeneity. Conventionally, the R/T responses are analysed for an interface bounded by two half-spaces. However, for a plane wave travelling through a subsurface layer, the wave scattering effects at the top and bottom of the layer interact with each other. For a continuous infinite ORT space cut in two halves along the horizontal symmetry plane, we focus on the plane wave R/T responses from an ORT layer that is placed between the two halves, where the azimuths of the vertical symmetry plane in the layer and in the upper and lower half-spaces are identical. The R/T coefficient modelling method can be found in many publications for the ORT layer with an arbitrary finite thickness. We decompose the exact R/T coefficients into series expansions that correspond to different orders of intrabed multiples in the ORT layer. Under the weak-contrast assumption for the ORT half-spaces and the ORT layer, we use the anisotropic background medium to obtain the first-order R/T coefficient approximations and second-order reflectivity approximations. There is no constraint for the middle layer thickness in the obtained first-order reflectivity approximations. In the proposed first-order transmissivity approximations and second-order reflectivity approximations, the layer thickness is assumed to be thin to obtain appropriate approximations for a few wave modes. The isotropic background medium is also considered for weakly anisotropic models to obtain simpler approximations that facilitate parametric analyses. For the ORT layer with its thickness much smaller than the propagating wave's wavelength, the influences of the layer thickness on R/T coefficients can be inspected conveniently from the derived approximations. Particularly, the R/T coefficients are analysed for the model which would be a homogeneous VTI medium, if the vertical parallel fractures were absent from the middle layer. Numerical tests demonstrate that the proposed R/T coefficient approximations perform well for the thin ORT layer. The approximation accuracy decreases when the thin layer thickness increases.

Study of tunable and enhanced transition radiation from graphene in terahertz band

Terahertz (THz) radiation has many special properties, such as low quantum energy, high signal-to-noise ratio and wide frequency, so that it possesses important application prospects in various fields. With the development of THz technology and its application fields, it is an urgent need to develop all types of terahertz source. It is as well-known that the radiation generated by traditional electronics methods has high power with low frequency, while by traditional photonics method has relatively high frequency with low power. Fortunately, the method of generating radiation based on the combination of photonics and electronics can overcome the above disadvantages, so it can solve the problem encountered by the terahertz source. In this paper, the integrated method by using electron beam to excite surface plasmon waves and generate transition radiation is adopted to obtain terahertz waves. Although the output power by this method is not remarkably high, the method is flexible and easy to implement. Due to the merit of graphene plasmon in THz band, a physical model of a moving electron incidence on a monolayer graphene at arbitrary angle is established in this paper to generate transition radiation in THz band. The field of the transition radiation is fully deduced by Maxwell’s equations combined with the special boundary conditions due to graphene’s conductivity. Then the expression of spectral-angular distribution is also derived in order to show the radiation energy characteristic more intensively in three-dimensional space. The characteristic of the radiation is numerically calculated by MATLAB. We focus on the transition radiation generated by a charged particle with a moderate energy and explain some contributions to the radiation, such as the incident angle, the conductivity or the Fermi level in graphene and the substrate dielectric characteristic. The pattern and intensity of the radiation field are numerically analyzed in the upper and lower half-spaces. We plot the figures of field distribution and the spectral angular distribution related to these variables mentioned above to analyze their influences on the radiation. In the case of the normal incidence, the transition radiation exhibits strong symmetry and considerably more intensive than that at grazing and oblique incidence. The results of the spectral angular distribution display that the radiation intensity increases strongly with the incident angle, and that the radiation energy focuses in backward and forward directions in the case of normal incidence. This study summarizes that the parameter adjustment mechanism is favorable for the performance of terahertz source. Since the conductivity of graphene can be adjusted by applying a bias voltage and doping, the radiation frequency and intensity can be tuned by the conductivity of graphene. Meanwhile, the substrate, electron energy and incident angle are conveniently controlled, therefore a more flexible way is obtained to develop tunable terahertz radiation sources.

Realization of entire-space electromagnetic wave manipulation with multifunctional metasurface

In this paper, we present a multifunctional metasurface (MS) to manipulate electromagnetic wave in the entire-space. First, we propose a MS unit structure which consists of four elaborately designed metal patterns separated by three substrate layers. Through changing the structures of metal layer 2 and layer 4, two different 1-bit units for transmission and reflection modes are obtained. By combining these two working modes together, the proposed MS can adjust the transmitted and reflected phases respectively in the upper and lower half-spaces. Thus we demonstrate some intriguing electromagnetic modulation functions in the entire-space, such as beam forming, anomalous reflection and diffusion. The simulated and experimental results prove that our method offers a feasible strategy for multifunctional MS design and other related practical applications.

On a selection problem for small noise perturbation in the multidimensional case

The problem on identification of a limit of an ordinary differential equation with discontinuous drift that perturbed by a zero-noise is considered in multidimensional case. This problem is a classical subject of stochastic analysis, see, for example, [6, 29, 11, 20]. However the multidimensional case was poorly investigated. We assume that the drift coefficient has a jump discontinuity along a hyperplane and is Lipschitz continuous in the upper and lower half-spaces. It appears that the behavior of the limit process depends on signs of the normal component of the drift at the upper and lower half-spaces in a neighborhood of the hyperplane, all cases are considered.

Experimental demonstration of metamaterial-assisted antenna beam deflection through folded transformation optics

Based on the folded transformation optics, a methodical approach for manipulating the orientation and directivity of a planar antenna beam is propounded. Unlike the classical phased array antennas, the tilted emitting beam is achieved by a homogeneous metamaterial-based superstrate in a triangle shape configuration, rather than by utilizing complicated and bulky phase shifters. Such a simple coating layer is elaborately designed via folding the virtual space to physical one with an affine transformation. The competency of the proposed method is demonstrated through some examples, indicating the capability of the coating layer in tilting the radiated beam to any desired off-normal directions in both the upper and lower half spaces. To authenticate the concept, a tilted beam metamaterial-based antenna is fabricated and tested; it is observed that the experimental results are in a good agreement with the numerical simulations and theoretical predictions. The presented method paves the way towards steering the beam of a metamaterial-assisted antenna, which has been a topic of great interest in several fields of engineering, such as antenna technologies, satellite communication, and multiple-input multiple-output systems.

Dynamic stresses around an interface crack between a nonhomogeneous bonding layer and two dissimilar orthotropic half-spaces subject to an impact load

Two dissimilar orthotropic half-spaces are bonded by a nonhomogeneous orthotropic layer. An internal pressure is applied suddenly to the surfaces of an interface crack that is situated at the lower interface between the lower half-space and the layer. The material properties of the bonding layer are assumed to vary continuously from the lower half-space to the upper half-space. The boundary conditions are reduced to dual integral equations using the Fourier transform technique in the Laplace domain. In order to satisfy the boundary conditions outside the crack, the differences in displacements at the crack surfaces in the Laplace domain are expanded in a series of functions that vanish outside the crack. The unknown coefficients in each series are evaluated using the Schmidt method in the Laplace domain. The stress intensity factors are determined, and these are inverted using a numerical method. The stress intensity factors are calculated numerically for the case in which the lower and upper half-spaces are made of unidirectional glass-fiber-reinforced epoxy composites.

On the $\mathcal{R}$-boundedness of solution operator families for two-phase Stokes resolvent equations

The aim of this paper is to show the existence of $\mathcal{R}$-bounded solution operator families for two-phase Stokes resolvent equations in $\dot\Omega =\Omega _+\cup\Omega _-$, where $\Omega _\pm$ are uniform $W_r^{2-1/r}$ domains of $N$-dimensional Euclidean space ${\mathbf{R}^N}$ ($N\geq 2$, $N < r < \infty$). More precisely, given a uniform $W_r^{2-1/r}$ domain $\Omega $ with two boundaries $ \Gamma _\pm$ satisfying $ \Gamma _+\cap \Gamma _-=\emptyset$, we suppose that some hypersurface $ \Gamma $ divides $\Omega $ into two sub-domains, that is, there exist domains $\Omega _\pm\subset\Omega $ such that $ \Omega _+\cap\Omega _-=\emptyset$ and $\Omega \setminus \Gamma =\Omega _+\cup\Omega _-, $ where $ \Gamma \cap \Gamma _+=\emptyset$, $ \Gamma \cap \Gamma _-=\emptyset$, and the boundaries of $\Omega _\pm$ consist of two parts $ \Gamma $ and $ \Gamma _\pm$, respectively. The domains $\Omega _\pm$ are filled with viscous, incompressible, and immiscible fluids with density $\rho_\pm$ and viscosity $\mu_\pm$, respectively. Here, $\rho_\pm$ are positive constants, while $\mu_\pm=\mu_\pm(x)$ are functions of $x\in{\mathbf{R}^N}$. On the boundaries $ \Gamma $, $ \Gamma _+$, and $ \Gamma _-$, we consider an interface condition, a free boundary condition, and the Dirichlet boundary condition, respectively. We also show, by using the $\mathcal{R}$-bounded solution operator families, some maximal $L_p{\theta}xt{-}L_q$ regularity as well as generation of analytic semigroup for a time-dependent problem associated with the two-phase Stokes resolvent equations. This kind of problems arises in the mathematical study of the motion of two viscous, incompressible, and immiscible fluids with free surfaces. The essential assumption of this paper is the unique solvability of a weak elliptic transmission problem for $\mathbf{f}\in L_q(\Omega )^N$, that is, it is assumed that the unique existence of solutions ${\theta}\in\mathcal{W}_q^1(\Omega )$ to the variational problem: $ (\rho^{-1}\nabla{\theta},\nabla{\varphi})_{\dot\Omega }=(\mathbf{f},\nabla{\varphi})_{\Omega } $ for any ${\varphi}\in\mathcal{W}_{q'}^1(\Omega )$ with $1 < q < \infty$ and $q'=q/(q-1)$, where $\rho$ is defined by $\rho=\rho_+$ ($x\in\Omega _+$), $\rho=\rho_-$ ($x\in\Omega _-$) and $\mathcal{W}_q^1(\Omega )$ is a suitable Banach space endowed with norm $\|\cdot\|_{\mathcal{W}_q^1(\Omega )}:=\|\nabla\cdot\|_{L_q(\Omega )}$. Our assumption covers e.g. the following domains as $\Omega $: ${\mathbf{R}^N}$, $\mathbf{R}_\pm^N$, perturbed $\mathbf{R}_\pm^N$, layers, perturbed layers, and bounded domains, where $\mathbf{R}_+^N$ and $\mathbf{R}_-^N$ are the open upper and lower half spaces, respectively.

The multifunctional process of resonance scattering and generation of oscillations by nonlinear layered structures

AbstractThe paper focuses on the development of a mathematical model, an effective algorithm and a self-consistent numerical analysis of the multifunctional properties of resonant scattering and generation of oscillations by nonlinear, cubically polarizable layered structures. The multifunctionality of such layered media is caused by the nonlinear mechanism between interacting oscillations—the incident oscillations (exciting the nonlinear layer from the upper and lower half-spaces) as well as the scattered and generated oscillations at the frequencies of excitation/scattering and generation. The study of the resonance properties of scattering and generation of oscillations by a nonlinear structure with a controllable permittivity in dependence on the variation of the intensities of the components of the exciting wave package is of particular interest. In the present paper, we extend our former results, and furthermore we analyze the realizability of multifunctional properties of nonlinear electromagnetic ...

Dispersion of torsional surface wave in an intermediate vertical prestressed inhomogeneous layer lying between heterogeneous half spaces

The purpose of this study is to illustrate the propagation of the torsional surface waves in an intermediate inhomogeneous initially stressed vertical elastic layer sandwiched between two heterogeneous half-spaces. It is considered that the mass density and the rigidity of upper and lower half-spaces are space dependent. The proposed model is solved to obtain the different dispersion relations for the torsional surface wave in the elastic medium of different properties. The effects of compressive and tensile stresses along with the heterogeneity on the dispersion of torsional surface wave in the intermediate layer are shown numerically. The wave analysis further indicates that the inhomogeneity, the initial stress of the layer and the heterogeneity of both the half spaces affect the wave velocity remarkably. The results may be useful to understand the nature of seismic wave propagation in geophysical applications and in the field of earthquake engineering.

Potential field transformation on the basis of a continuous wavelet transform

The possibility of applying the continuous wavelet analysis on the basis of a Poissonian core for the processing and interpretation of gravity and magnetic survey data is considered. Based on the wavelet spectrum, W(x,h), reconstruction of the initial signal, g(x), is possible. Additionally, based on this wavelet spectrum, the equivalent distributions of mass and magnetization that produce the initial field, g(x), can be reconstructed. These possibilities allow the wavelet transform to be used for solving such classical problems as the filtering of initial signals, continuation of the field, calculation of higher field derivatives in the upper and lower half-spaces, and reduction of magnetic anomalies to the pole.

Representation of Distributions by Harmonic and Monogenic Potentials in Euclidean Space

In the framework of Clifford analysis, a chain of harmonic and monogenic potentials in the upper half of Euclidean space \({\mathbb{R}^{m+1}_+}\) was recently constructed, including a higher dimensional analogue of the logarithmic function in the complex plane, and their distributional boundary values were computed. In this paper we determine these potentials in lower half–space \({\mathbb{R}^{m+1}_-}\) and investigate whether they can be extended through the boundary \({\mathbb{R}^m}\) . This is a stepping stone to the representation of a doubly infinite sequence of distributions in \({\mathbb{R}^m}\) , consisting of positive and negative integer powers of the Dirac and the Hilbert–Dirac operator, as the jump across \({\mathbb{R}^m}\) of monogenic functions in the upper and lower half–spaces, in this way providing a sequence of interesting examples of Clifford hyperfunctions.

WIDE-ANGLE ABSORPTION BY THE USE OF A METAMATERIAL PLATE

The problem regarding top possible (hopefully, total) fleld suppression of a fll- amentary source placed above nonuniform impedance plane is discussed. New designs of the electromagnetic fleld absorbers and resonators are suggested which may be engineered with the use of metamaterials. 1. INTRODUCTION | ABSORPTION OF THE ENERGY OF A POINT SOURCE BY A HALF-SPACE Interest to the fleld propagation along the imperfect surface has about century-old history, the beginnings of which trace back to the Sommerfeld's solution of the classical problem for the dipole radiating above the plane with flnite conductivity. Later, as the radio broadcasting evolved, a lot of publications appeared which dealt with electromagnetic fleld propagation in the presence of an absorbing half-space with the aim to minimize the signal losses. Now certain practical needs (1) set questions about what value of impedance of a plane should be chosen to absorb the maximum portion of energy radiated by a point source (say, fllamentary current), how much the amount of the absorbed energy is and how to create such an impedance. Note, in view of the symmetry of the radiation pattern of the fllament, at the absence of the plate (in the free space) equal power ∞uxes are radiated into upper and lower half-spaces, and exactly one half of the radiated energy penetrates through the plane y = 0, see Fig. 1.

Reflection and refraction of waves at the interface of an isotropic medium over a highly anisotropic medium

In this paper, we have considered the reflection and refraction of a plane wave at an interface between two half-spaces. The lower half-spaces is composed of highly anisotropic triclinic crystalline material and the upper half-space is homogeneous and isotropic. It has been assumed that due to incidence of a plane quasi-P (qP) wave, three types of waves, namely, quasi-P (qP), quasi-SV (qSV) and quasi-SH (qSH), will be generated in the lower half space whereas P and S waves will be generated in the upper half space. The phase velocities of all the quasi waves have been calculated. It has been assumed that the direction of particle motion is neither parallel nor perpendicular to the direction of propagation. Some specific relations have been established between directions of motion and propagation, respectively. The expressions for reflection coefficients of qP, qSV, qSH and refracted coefficients of P and SV waves are obtained. Results of reflection and refraction coefficients are presented.

Appropriate formulation of the Characteristic equation for open nonreciprocal Layered waveguides with different upper and lower half-spaces

This paper will study the most convenient way of formulating the characteristic equation for shielded, parallel-plate, grounded, and open reciprocal/nonreciprocal planar layered waveguides, including the possibility of different upper and lower half-spaces. A detailed study of the suitable mapping for each kind of waveguide will lead to the formulation of analytic characteristic equations for shielded/parallel-plate/grounded reciprocal/nonreciprocal waveguides and also for open reciprocal ones. Although no mapping has been found to remove all the branch points of the characteristic equation for open nonreciprocal waveguides with different half-spaces, a robust approach will be proposed to overcome the main drawbacks caused by the multivalued nature of this problem. The combination of the suitable formulation of the characteristic equation with a systematic integral-nature root-searching strategy bears a reliable and efficient method. Some novel numerical results will be presented for open anisotropic reciprocal waveguides and for open magnetized ferrite slabs to illustrate the performance of the present proposal.

Reflection and transmission of SH-waves at a corrugated interface between two laterally and vertically heterogeneous anisotropic elastic solid half-spaces

This paper is concerned with the reflection and transmission coefficients of SH-waves at a corrugated interface between two anisotropic heterogeneous elastic solid half spaces. Both the half spaces are taken transversely isotropic and laterally and vertically heterogeneous. The Rayleigh’s method of approximation is adopted and expressions for reflection and transmission coefficients are obtained in closed form for the first-order approximation of the corrugation. In Rayleigh’s method, expressions in boundary conditions containing the function defining the corrugated boundary are expanded in Fourier series and unknown coefficients in the solutions are determined to any given order of approximation in terms of a small parameter characteristic of the boundary. The analytical expressions of these coefficients show that they depend upon corrugation of the interface and are strongly influenced by the anisotropy and heterogeneity of the half-spaces. Numerical computations are performed for the case of a particular corrugated interface: ζ =c cos k* x showing that the effect of heterogeneity on the reflection and transmission coefficients is minimum near the normal incidence and dominance of this effect increases with the angle of incidence. For incident wave striking at 45°, the effect of the corrugation is found significant on the reflection and transmission coefficients. The maximum effect of transverse isotropy on the reflection and transmission coefficients is observed at normal incidence when the values of the anisotropy parameters are 0.5 and 0.8 for the upper and lower half-spaces, respectively. The effect of frequency of the incident wave is observed on all reflected and refracted waves. The analytical expressions derived by Tomar and Saini (1997), Gupta (1987) and Asano (1960) are obtained as particular cases with our formulation.

The asymptotic stress field for a rigid circular inclusion at the interface of two bonded dissimilar elastic half-space materials

The paper considers three-dimensional interface inclusion problems. The axisymmetric elastostatics problem of a rigid circular inclusion at the interface between two perfectly bonded dissimilar elastic half spaces is analyzed. Based on the representations of displacements and stresses in terms of Love's strain potential and the Hankel transform technique, the mixed boundary value problem associated with a rigid circular inclusion at the interface reduces to a pair of simultaneous integral equations for the stress jumps across the inclusion, which are further transformed to a single singular integral equation. For the case of uniform axial and radial tensions at infinity, the asymptotic stresses near the inclusion front are obtained and they exhibit the oscillatory singularity. Meanwhile, the magnitude of the singularity for the interface inclusion depends on the material constants of the upper and lower half spaces, the dependence of singularity coefficients on material constants for interface inclusion problems, however, is different from that for interface crack problems.