Half Space Research Articles

Multibeam Metasurface Antenna Enabled by Orbital Angular Momentum Demultiplexing Feeding for IoT Communication

Multibeam antenna radiations provide linkages to multiple nodes and can bring enhanced communication quality with reduced power consumption for Internet of Things (IoT) applications. In this paper, a novel method providing a low-cost and flexible multibeam antenna solution is proposed. Multiple orbital angular momentum (OAM) modes are used as internal excitations of the antenna, and the generated multiple beams are pencil beams with no OAM mode, which is convenient for IoT nodes connection. First, aperture phase distributions that convert incident vortex beams with different and orthogonal topological orders into designated directional pencil beams are acquired and superimposed to form a metasurface aperture that, under excitations of vortex beams with multiple orders, produces multibeam each with a predefined direction. The proposed multibeam method is then illustrated with a transmissive metasurface design, with four beams pointing at arbitrary half space directions. Techniques such as OAM modes spacing and aperture partitioning are utilized for reducing sidelobe levels (SLLs). Furthermore, a similar multibeam metasurface antenna with additional linear-to-circular polarization conversion function is demonstrated, which opens the possibility of utilizing different polarizations on top of the OAM based multibeam. This paper successfully explores and achieves a novel antenna system with multiple radiations suited for multiple IoT nodes accessing with low cost and low energy consumption, and also provides a new degree-of-freedom for OAM applications.

Energy transfer at the interface of monoclinic piezothermoelastic and thermoelastic half spaces with MDD

This research article presents an analysis of the behavior of an initially stressed monoclinic piezothermoelastic half-space based on memory-dependent three-phase lags heat transfer law (MPS) underlying a thermoelastic half-space (TS) with subject to the hyperbolic two-temperature (H2T), classical two-temperature (C2T), and without two-temperature (W2T) models. By applying the normal mode approach, calculate the amplitude ratios and further utilize them to obtain the waves’ energy ratios and interaction energy. The effect of memory-dependent derivatives (MDD), initial stresses, various kernel functions, and two temperature factors on the variation of energy ratios with incidence angle are graphically shown. The findings of this study have the potential to optimize material design, enhance seismic imaging techniques, improve thermal management in machinery, develop renewable energy systems, and facilitate materials characterization across diverse industries.

Analysis of wavenumber resonances for the Rayleigh system in a half space

We present a comprehensive analysis of wavenumber resonances or leaking modes associated with the Rayleigh operator in a half space containing a heterogeneous slab, being motivated by seismology. To this end, we introduce Jost solutions on an appropriate Riemann surface, a boundary matrix and a reflection matrix in analogy to the studies of scattering resonances associated with the Schrödinger operator. We analyse their analytic properties and characterize the distribution of these wavenumber resonances. Furthermore, we show that the resonances appear as poles of the meromorphic continuation of the resolvent to the nonphysical sheets of the Riemann surface as expected.

Dual-Band Metasurface With Extreme Angular-Asymmetric Transmission and Frequency Selection Based on Resonant Coupling Effect

Asymmetric transmission plays an important role in many electromagnetic systems. Different to the asymmetric transmissions in full space, angular-asymmetric transmissions in half space support different characteristics for symmetrical oblique incidences, which has great potentials for antenna designs and wireless systems. By introducing guided wave modes and resonant coupling effect into metasurface design, this paper designs and demonstrates a dual band multi-functional metasurface with angular-asymmetric transmission and frequency selection under oblique incidences. At 8.7 GHz, the electromagnetic wave under 30° TM oblique incidence is absorbed, and the wave under -30° TM oblique incidence transmits, which presents an angular-asymmetric transmission. At 10.4GHz, both ±30° TM oblique incident waves can be transmitted, which presents a frequency selection function. The metasurface sample with optimized geometry parameters has been fabricated and measured, and the measurement agree well with the simulation results.

Dynamic Response of Lined Tunnel in Inhomogeneous Half Space with Variable Rigidity Under SH Waves

This work investigates the scattering of antiplane shear waves by tunnel in inhomogeneous half-space. The inhomogeneity of the medium is reflected in that the shear modulus is a two-dimensional function. Based on the complex function method, the analytical expressions of wave fields are obtained. The unknown coefficients can be obtained by boundary conditions. In the numerical example, the displacement amplitude of the horizontal surface and the dynamic response of lining structure are discussed. The results show that the inhomogeneous parameters, the reference wave numbers and the positions have obvious effects on the displacement amplitude and the dynamic response.

Effect of Inclined Mechanical Load on a Rotating Microelongated Two Temperature Thermoelastic Half Space with Temperature Dependent Properties

Effect of Inclined Mechanical Load on a Rotating Microelongated Two Temperature Thermoelastic Half Space with Temperature Dependent Properties

Qualitative properties of solutions for dual fractional nonlinear parabolic equations

In this paper, we consider the dual fractional parabolic problem{∂tαu(x,t)+(−Δ)su(x,t)=f(u(x,t)),inR+n×R,u(x,t)=0,in(Rn﹨R+n)×R, where R+n:={x∈Rn|x1>0} is the right half space. We prove that the positive solutions are strictly increasing in x1 direction without assuming the solutions be bounded.So far as we know, this is the first paper to explore the monotonicity of possibly unbounded solutions for the nonlocal parabolic problem involving both the fractional time derivative ∂tα and the fractional Laplacian (−Δ)s. To overcome the difficulties caused by the dual nonlocality in space-time and by the remarkably weak assumptions on solutions, we introduced several new ideas and our approaches are quite different from those in the previous literature. We first establish an unbounded narrow region principle without imposing any decay and boundedness assumptions on the antisymmetric functions at infinity by estimating the nonlocal operator ∂tα+(−Δ)s along a sequence of suitable auxiliary functions at their minimum points, which is an essential ingredient to carry out the method of moving planes at the starting point. Then in order to remove the decay or boundedness assumption on the solutions, we develop a new novel approach lies in establishing the averaging effects for such nonlocal operator and apply these averaging effects twice to guarantee that the plane can be moved all the way to infinity to derive the monotonicity of solutions.We believe that the new ideas and techniques developed here will become very useful tools in studying the qualitative properties of solutions, in particular of those unbounded solutions, for a wide range of fractional elliptic and parabolic problems.

Freezing limits for Calogero–Moser–Sutherland particle models

AbstractOne‐dimensional interacting particle models of Calogero–Moser–Sutherland type with N particles can be regarded as diffusion processes on suitable subsets of like Weyl chambers and alcoves with second‐order differential operators as generators of the transition semigroups, where these operators are singular on the boundaries of the state spaces. The most relevant examples are multivariate Bessel processes and Heckman–Opdam processes in a compact and noncompact setting where in all cases, these processes are related to special functions associated with root systems. More precisely, the transition probabilities can be described with the aid of multivariate Bessel functions, Jack and Heckman–Opdam Jacobi polynomials, and Heckman–Opdam hypergeometric functions, respectively. These models, in particular, form dynamic eigenvalue evolutions of the classical random matrix models like β‐Hermite, β‐ Laguerre, and β‐Jacobi, that is, MANOVA, ensembles. In particular, Dyson's Brownian motions and multivariate Jacobi processes are included. In all cases, the processes depend on so‐called coupling parameters. We review several freezing limit theorems for these diffusions where, for fixed N, one or several of the coupling parameters tend to ∞. In many cases, the limits will be N‐dimensional normal distributions and, in the process case, Gauss processes. However, in some cases, normal distributions on half spaces and distributions related to some other ensembles appear as limits. In all cases, the limits are connected with the zeros of the classical one‐dimensional orthogonal polynomials of order N.

Impact of light polarization on angle-resolved light scattering from gloss scale

The gloss scale is a set of coated paper samples with different surface roughness allowing for appearance variation from high gloss to mat. Nowadays, the gloss scale is widely used as a reference on visual appearance of glossy and mat surfaces. This work provides for angle resolved analysis of light scattering from gloss scales as well as the analysis of the surface topography parameters relevant for the analysis of light-scattering experiments: RMS-roughness σ, auto-correlation function and power spectrum density, correlation length ℓ c and surface slopes. The angle–resolved measurements of light scattered in reflection within the half–space are performed at 4 angles of incidence, while measurements within the incidence plane are made at 17 angles of incidence and under non–polarized, s–and p–polarized illumination. The polarization of incident light has a significant impact on both the specular and the diffused components of scattered light. Brewster scattering angle is especially well observed for black mat surfaces. Qualitative and quantitative analysis of measured scattered light is made with Rayleigh-Rice and Kirchhoff models applied to statistically representative analysis of surface topography.

Cluster solutions for the FitzHugh-Nagumo system with Neumann boundary conditions

We study cluster solution of the following FitzHugh-Nagumo system:{ε2Δu+f(u)−v=0in Ω,Δv−γv+βu=0in Ω,∂u∂n=∂v∂n=0on ∂Ω, where Ω is a smooth bounded domain in R2 and ε,γ,β are positive parameters. Under appropriate parameter regimes, given any integer k≥2, this system admits a cluster solution uε with k-boundary spikes that accumulate at Q0, a nondegenerate local maximum point of boundary curvature, whenever the term βεγ is sufficiently large or sufficiently small. Moreover, we show that these k-boundary spikes are separated from each other at a distance of O(log⁡(βεγ)γ) as βεγ→∞ or O((βε)12) as βεγ→0, respectively. The latter case proposes a new concentration feature of the activator-inhibitor type reaction-diffusion system which is barely observed in Gierer-Meinhardt system. The mechanism behind the scene is driven by two competing forces: a short range gravitational force with mass positioned at a local maximum point of the curvature and a long range repelling force between spikes whose major part comes from the Green's function of screened Poisson operator on the half space.

Vanishing dissipation limit of solutions to initial boundary value problem for three dimensional incompressible magneto-hydrodynamic equations with transverse magnetic field

In this paper, we study the vanishing dissipation limit of solutions to the initial boundary value problem of three-dimensional incompressible viscous magnetohydrodynamic equations in the upper half space where the magnetic field is assumed to be transverse to the boundary. When the tangential component of the magnetic field is imposed the zero Neumann boundary condition, we can establish the uniform energy estimates of the solutions to the initial boundary value problem in the conormal Sobolev spaces even if the velocity field satisfies the no-slip boundary condition. Then the vanishing dissipation limit of solutions to the initial boundary value problem can be achieved in L∞ sense based on some compactness arguments. Compared with the previous results, our results show that the strong boundary layer can still be prevented by the transverse magnetic field even with the magnetic diffusion.

Convergence rates to the planar stationary solution to a 2D model of the radiating gas on half space

This paper is concerned with the asymptotic stability of a planar stationary solution to an initial-boundary value problem for a two-dimensional hyperbolic–elliptic coupled system of the radiating gas on half space. We show that the solution to the problem converges to the corresponding planar stationary solution as time tends to infinity under small initial perturbation. This result is proved by the standard L2-energy method and the div–curl decomposition. Moreover, we prove that the solution (u, q) converges to the corresponding planar stationary solution at the rate t−α/2−1/4 for the non-degenerate case and t−1/4 for the degenerate case. The proof is based on the time and space weighted energy method.

Synthesis of Large Ultrawideband Sparse Planar Arrays by Utilizing a Cooperative Coevolutionary Iterative Fourier Transform

This letter introduces a cooperative coevolutionary iterative Fourier transform (CCIFT) technique to extend the conventional IFT to large ultra-wideband (UWB) sparse planar array synthesis. In the proposed CCIFT, a dense initial element position grid such as a spacing of half a wavelength at the highest frequency is adopted to avoid the presence of grating lobes at high frequency band, and a probability-assisted element selection mechanism is presented to guarantee the obtained array layout to meet a preset minimum spacing constraint, enabling the placement of physical UWB antenna elements. In addition, a cooperative coevolutionary strategy is presented to avoid prematurity by establishing the information interaction between different excitation distributions from multiple parallel IFT procedures. Two examples are conducted and results show that the CCIFT can achieve a considerably lower peak sidelobe level (PSL) than some state-of-art algorithms within an acceptable CPU time, which demonstrates its effectiveness and superiority.

Influence of Concentrated Forces and Heat Sources on the Distribution of Stresses in the Interface of Two Different Transversely Isotropic Half Spaces

Influence of Concentrated Forces and Heat Sources on the Distribution of Stresses in the Interface of Two Different Transversely Isotropic Half Spaces

Asymptotic stability of a nonlinear wave for the compressible Navier–Stokes–Korteweg equations in the half space

Asymptotic stability of a nonlinear wave for the compressible Navier–Stokes–Korteweg equations in the half space

Analysis of integrated effect of irregularity and corrugated interfaces of doubly layered half space on torsional surface wave propagation

Present geophysical model analyzes the propagation characteristics of torsional wave in an inhomogeneous viscoelastic fiber‐reinforced layer sandwiched between superior porous layer and transversely isotropic piezoelectric subspace with imperfect interfaces. Porous layer and intermediate reinforced layer are endowed with initial stress and corrugated interfaces, whereas the lower piezoelectric half space possesses rectangular cavity at the welded contact. Earth's adjacent layers near mountainous region often endowed with initial stresses resemble the present geological setup. The material properties of intermediate layer are considered to be varying exponentially. Particular cases have been deduced for electrically open and short condition for validation with the standard Love wave expressions. Effects of the relevant parameters on resultant torsional velocity have been explored through numerical simulation and depicted for electrically short and open conditions. Findings of present model may be utilized in the field of signal testing, sensors design, seismic acoustic wave (SAW) devices, and geophysical application concerned with torsional wave based on non‐destructive evaluation.

Two-Dimensional Problem of Thermoelasticity for a Half Space with Free, Rigidly, Smoothly, or Flexibly Fastened Boundary Subjected to the Action of Heat Sources

Two-Dimensional Problem of Thermoelasticity for a Half Space with Free, Rigidly, Smoothly, or Flexibly Fastened Boundary Subjected to the Action of Heat Sources

Seismic analysis of underground tunnels subjected to 3D oblique incident P and SV waves by 2.5D approach

This paper presents, for the first time, the consideration of three-dimensional (3D) oblique incident P and SV waves in calculating the 3D seismic response of a lined tunnel embedded in a half-space by the 2.5D finite/infinite element method (FIEM). Firstly, the applicability of the 2.5D FIEM for 3D seismic analysis is summarized. With the exact solutions obtained for the free field in the Appendix, the equivalent seismic forces are rationally computed for the near-field boundary, considering the horizontal and vertical excitations of the Chi-Chi Earthquake. By performing seismic analysis of the half space embedded with a tunnel using the 2.5D FIEM, the time-domain responses of the tunnel are obtained. The accuracy of the present solutions is verified against those of de Barros and Luco. Conclusions drawn from the parametric study include: (1) Stress concentration for the principal stress under oblique incident seismic waves occurs at the polar angles of 0° (vault), 90°, 180° (inverted arch), and 270° of the lining wall. (2) The vault and inverted arch are the weakest parts of the tunnel during earthquakes. (3) The accelerations of the tunnel during earthquakes can be regarded as of the rigid body type. (4) The responses of the tunnel lining caused by SV waves of an earthquake are much more critical than those by P waves. (5) For arbitrary seismic waves, the maximum longitudinal acceleration azmax is of the same order of magnitude as the maximum horizontal acceleration axmax.

On torsional wave in void type porous layers between viscoelastic and piezoelectric media with parabolic irregularity

The viscoelastic earth model is increasingly utilized by seismologists for studying surface seismic wave propagation through Earth’s porous crustal regions such as granular materials, including rock, soils, and synthetic porous bodies. The present study characterizes torsional wave propagation in an irregular void-type porous layer sandwiched between an initially stressed inhomogeneous viscoelastic layer and a piezoelectric substratum. Displacement fields for the layer and half spaces are obtained separately using a variable separable technique, whereas volume fraction and electric potential field are derived for layer and substratum, respectively using the matrix calculus approach. Dispersion relations have been derived for both electrically open and short circuit conditions and agree with standard results. Particular cases have been deduced to validate the finding of the study with literature results. Effects of change in relevant parameters such as initial stress, heterogeneities, attenuation coefficient, void parameters, piezoelectricity and dissipation factor have been analyzed on the phase velocity of the torsional wave through various plots and summarized in a tabular form for ready reference to researchers. Analysis of the present geophysical problem may be useful in characterizing torsional velocity in porous silicate rocks which are abundantly found in the transition zone between oceanic and continental crust called Conrad discontinuity. Highlights Torsional propagation in a void-type porous layer crammed between an initially stressed inhomogeneous viscoelastic layer and piezoelectric half-space has been investigated. Variable separable technique, the matrix calculus approach is used for computing the displacement fields of respective media. A comparative study has been carried out for both electrically open and short conditions. The impact of pertinent parameters including initial stress, heterogeneities, attenuation coefficient, void parameters, piezoelectricity, and dissipation factor on the phase velocity of the torsional wave has been examined.

Green’s function for solving initial-boundary value problem of evolutionary partial differential equations

We propose a new method to solve the initial-boundary value problem for hyperbolic-dissipative partial differential equations (PDEs) based on the spirit of LY algorithm [T.-P. Liu and S.-H. Yu, Dirichlet–Neumann kernel for hyperbolic-dissipative system in half-space, Bull. Inst. Math. Acad. Sin. 7 (2012) 477–543]. The new method can handle more general domains than that of LYs’. We convert the evolutionary PDEs into the elliptic PDEs by the Laplace transformation. Using the Laplace transformation of the fundamental solutions of the evolutionary PDEs and the image method, we can construct Green’s functions for the corresponding elliptic PDEs. Finally, we obtain Green’s functions for the evolutionary PDEs by inverting the Laplace transformation. As a consequence, we establish Green’s functions for some basic PDEs such as the heat equation, the wave equation and the damped wave equation, in a half space and a quarter plane with various boundary conditions. On the other hand, the structure of hyperbolic-dissipative PDEs means its fundamental solution is non-symestric and hence the image method does not work. We utilize the idea of Laplace wave train introduced by Liu and Yu in [Navier–Stokes equations in gas dynamics: Greens function, singularity and well-posedness, Comm. Pure Appl. Math. 75(2) (2022) 223–348] to generalize the image method. Combining this with the notions of Rayleigh surface wave operators introduced in [S. J. Deng, W. K. Wang and S.-H. Yu, Green’s functions of wave equations in [Formula: see text], Arch. Ration. Mech. Anal. 216 (2015) 881–903], we are able to obtain the complete representations of Green’s functions for the convection-diffusion equation and the drifted wave equation in a half space with various boundary conditions.