Incident Wave Number Research Articles

In situ reduction of copper nanoparticles in porous carbonized wood for efficiently enhancing electromagnetic interference shielding performance

In this study, porous carbonized wood was used as the substrate, and a multi-layer composite of copper/carbonized wood/copper (Cu/CW/Cu) layer with light weight, flame retardancy, and efficient electromagnetic shielding effectiveness was prepared by electroless copper method. The results showed that the copper particles can be filled in the layered porous structure of the carbonized wood. The metal Cu layer was evenly covered on the surface of the whole carbonized wood, and the average surface roughness was 7.62 µm. The absorption peak at 2340 cm−1 was significantly enhanced, which proved that the increase of the number of electroless Cu on the carbonized wood surface promoted the improvement of Cu autocatalytic ability. After three depositions of Cu, the conductivity of the composite material reached 1154 S/cm, showing good electrical properties. The shielding effectiveness in the X-band from 8.2 to 12.4 GHz was up to 55.97 dB at low density (0.27 g/cm3). Specific shielding effectiveness SSE/t was as high as 581.69 dB cm2 g−1. Through the “absorption–reflection–absorption” path, high absorption and low reflection are achieved, shielding a large number of incident electromagnetic waves.

Dynamic response of semi-cylindrical depression, cylindrical cavity and type-III crack to SH wave in half-space anisotropic media

In this study, the anti-plane dynamic response of an elastic half-space anisotropic medium containing surface semi-cylindrical depressions and internal cylindrical cavity and type-III crack is solved analytically. The wave function expansion method, the complex function method and the Green's function method can be used to effectively construct the free wave field equation and the scattered wave field equation in the case of SH wave incidence, in which the scattered wave field generated by the crack is constructed by the Green's function method and the "crack cut" method. For the scattered wave field generated by a circular cavity is constructed using the mirror method, where the positional offset coefficient in the mirror method of a half-space anisotropic medium is introduced, which well solves the problem of the asymmetry of the scattered wave field. Finally, the effects of anisotropic strength of the medium, SH wave incidence angle and dimensionless incident wave number on the surface displacement amplitude (|W|), dynamic stress concentration factor (DSCF) at the boundary of the circular cavity and dynamic stress intensity factor (DSIF) at the crack tip are investigated in both frequency and time domains under different working conditions, and conclusions different from those of isotropic medium are obtained, which provide some theoretical references for the earthquake-resistant design of the underground structure with canyon topography and the surface building.

Exactness of the First Born Approximation in Electromagnetic Scattering

Abstract For the scattering of plane electromagnetic waves by a general possibly anisotropic stationary linear medium in three dimensions, we give a condition on the permittivity and permeability tensors of the medium under which the first Born approximation yields the exact expression for the scattered wave whenever the incident wavenumber k does not exceed a preassigned value α. We also show that under this condition the medium is omnidirectionally invisible for k ≤ α/2, i.e. it displays broadband invisibility regardless of the polarization of the incident wave.

A generalized isogeometric boundary element method for the uncertain analysis of infinite domain two-dimensional acoustic problems

The key aim of this paper is to provide a new nth generalized order perturbed isogeometric fast multistage technique of boundary elements to compute the propagation of time harmonics in an infinite region. Structural geometry and boundary integral equations are constructed by using non-uniform rational B-splines. The source of system uncertainty is believed to be the incident plane wave number’s unpredictability. The actual field, depending on the input random variables, is simulated using the extended nth-order perturbation method. The field and kernel values for boundary integral formulas are generated via the nth-order generalized series of Taylor expansions using perturbation parameters. The fast multipole method (FMM) is utilized to speed up the process. The effectiveness and correctness of the proposed algorithm are verified by Monte Carlo simulations (MCs) with numerical examples.

Broadband directional invisibility

The discovery of unidirectional invisibility and its broadband realization in optical media satisfying spatial Kramers–Kronig relations are important landmarks of non-Hermitian photonics. We offer a precise characterization of a higher-dimensional generalization of this effect and find sufficient conditions for its realization in the scattering of scalar waves in two and three dimensions and electromagnetic waves in three dimensions. More specifically, given a positive real number α and a continuum of unit vectors Ω, we provide explicit conditions on the interaction potential (or the permittivity and permeability tensors of the scattering medium in the case of electromagnetic scattering) under which it displays perfect (non-approximate) invisibility whenever the incident wavenumber k does not exceed α (i.e., k∈(0,α]) and the direction of the incident wave vector ranges over Ω. A distinctive feature of our approach is that it allows for the construction of potentials and linear dielectric media that display perfect directional invisibility in a finite frequency domain.

Eigenfunction expansion solution for wave diffraction from a uniform cylinder in front of a partially reflective wall

In this work, wave diffraction from a uniform circular cylinder in front of a partially reflective wall is solved with the aid of its mirror image cylinder arranged symmetrically about the wall. The mirror image cylinder generates a scattering potential with its value being decreased by the wave reflection from the partially reflective wall. The eigenfunction expansion method is applied to solve this wave diffraction problem, and the Graf's addition theorem is applied to transform the scattering potential back from the imaginary to the original cylindrical coordinate system. Numerical simulations were carried out to examine the effects of the wave reflection of the partially reflective wall, the wave incidence direction, and the distance between the cylinder and the wall. It shows that the non-dimensional wave forces oscillate with the incident wave number, and the oscillation amplitude increases with the increasing reflection coefficient of the wall. In addition, the wave numbers at which the force peaks/troughs occur change significantly with the wave incidence angle and the distance between the cylinder and the wall.

Stability of grating diffraction problems for plane wave incidence: Explicit dependence on wavenumbers and incident angles

Suppose a time-harmonic plane wave is incident onto an impenetrable grating profile of Dirichlet or Impedance kind in two dimensions. The grating profile is assumed to be given by a Lipschitz function. We derive a stability estimate of this grating diffraction problem using the variational method with a transparent boundary condition. An explicit dependence of solutions on the incident wavenumber and the incident angle is obtained, which carries over to transmission problems for penetrable gratings. Our approach relies heavily on using Rellich's identities in periodic structures.

Deflagration and detonation induced by shock wave focusing at different Mach numbers

Shock wave focusing is an effective way to create a hot spot or a high-pressure and high-temperature region at a certain place, showing its unique usage in detonation initiation, which is beneficial for the development of detonation-based engines. The flame propagation behavior after the autoignition induced by shock wave focusing is crucial to the formation and self-sustaining of the detonation wave. In this study, wedge reflectors with two different angles (60° and 90°) and a planar reflector are employed, and the Mach number of incident shock waves ranging from 2.0 to 2.8 is utilized to trigger different flame propagation modes. Dynamic pressure transducers and the high-speed schlieren imaging system are both employed to investigate the shock-shock collision and ignition procedure. The results reveal a total of four flame propagation modes: deflagration, DDT (Deflagration-to-Detonation Transition), unsteady detonation, and direct detonation. The detonation wave formed in the DDT and unsteady detonation mode is only approximately 75%−85% of the Chapman-Jouguet (C-J) speed; meanwhile, the directly induced detonation wave speed is close to the C-J speed. Transverse waves, which are strong evidence for the existence of detonation waves, are discovered in experiments. The usage of wedge reflectors significantly reduces the initial pressure difference ratio needed for direct detonation ignition. We also provide a practical method for differentiating between detonation and deflagration modes, which involves contrasting the speed of the reflected shock wave with the speed of the theoretically nonreactive reflected shock wave. These findings should serve as a reference for the detonation initiation technique in advanced detonation propulsion engines.

Efficient electromagnetic interference shielding of three-dimensional hydrophobic Cu/wood/Cu porous composites

Three-dimensional hydrophobic and efficient electromagnetic shielding Cu/wood/Cu laminated composites were prepared by a simple one-step electroless Cu process. The number of electroless Cu on wood surface and the treatment time of electroless Cu were used as variables. The effects of independent variables in the range from 0.3 ×10−3 to 3.0 GHz (L-band) on the conductivity, water contact angle and electromagnetic shielding effectiveness of the composite were analyzed. The Cu particles are fully filled in the wood hierarchical porous structure, and the metal coating uniformly covers the entire wood surface. After three times of electroless Cu, the conductivity of the composite can reach 7255 S/cm, the contact angle is 130.8° when the time is 12 min, showing good hydrophobic properties, and the average electromagnetic shielding effectiveness is as high as 96 dB. Compared with the L-band (94 dB), the twice electroless sample has a maximum shielding effectiveness of 85.6 dB in the X-band (8.2-12.4 GHz), which can shield a large number of incident electromagnetic waves to achieve high absorption and low reflection. The anisotropic internal porous structure of wood matrix and the multi-interface polarization between wood and Cu are the main reasons for the effective electromagnetic interference shielding performance of Cu/wood/Cu laminated composites.

Reliability Analysis on Stability of Armor Units for Foundation Mound of Composite Breakwaters

Probabilistic and deterministic analyses are implemented for the armor units of rubble foundation mound of composite breakwaters which is needed to protect the upright section against the scour of foundation mounds. By a little modification and incorporation of the previous empirical formulas that has commonly been applied to design the armor units of foundation mound, a new type formula of stability number has been suggested which is capable of taking into account slopes of foundation mounds, damage ratios of armor units, and incident wave numbers. The new proposed formula becomes mathematically identical with the previous empirical formula under the same conditions used in the developing process. Deterministic design have first been carried out to evaluate the minimum weights of armor units for several conditions associated with a typical section of composite breakwater. When the slopes of foundation mound become steepening and the incident wave numbers are increasing, the bigger armor units more than those from the previous empirical formula should be required. The opposite trends however are shown if the damage ratios is much more allowed. Meanwhile, the reliability analysis, which is one of probabilistic models, has been performed in order to quantitatively verify how the armor unit resulted from the deterministic design is stable. It has been confirmed that 1.2% of annual encounter probability of failure has been evaluated under the condition of 1% damage ratio of armor units for the design wave of 50 years return period. By additionally calculating the influence factors of the related random variables on the failure probability due to those uncertainties, it has been found that Hudson’s stability coefficient, significant wave height, and water depth above foundation mound have sequentially been given the impacts on failure regardless of the incident wave angles. Finally, sensitivity analysis has been interpreted with respect to the variations of random variables which are implicitly involved in the formula of stability number for armor units of foundation mound. Then, the probability of failure have been rapidly decreased as the water depth above foundation mound are deepening. However, it has been shown that the probability of failure have been increased according as the berm width of foundation mound are widening and wave periods become shortening.

Quantum refractive index for two- and three-dimensional systems

We study the scattering of a plane-wave by two- and three-dimensional potentials — circular and elliptical disks and spherical and spheroidal regions. These regions are filled with Dirac delta functions, and we name these theoretical materials Dirac medium. By solving the Lippmann–Schwinger equation in the position-representation, we calculate the wavefunctions, differential, and total cross-sections as well as the quantum refractive index which characterizes these materials. The quantum refractive index is a complex function of the incident wavenumber k as well as of the coupling strength γ0. For certain special values of k and γ0, its real part can be negative, and its imaginary part can be positive, negative, and even zero, revealing that Dirac medium are the quantum mechanical analogues of certain materials that have electromagnetic properties such as negative extinction coefficient and refractive index.

Scattering of SH Waves by a Semi-cylindrical Bump in an Inhomogeneous Half-space

The wave propagation in an inhomogeneous half space with a semi-cylindrical surface bump is investigated by the means of complex function method. With the origin of the coordinate system as the center, the density of the medium changes radially. To solve the Helmholtz equation with variable coefficients caused by the inhomogeneous of the medium, a conformal transformation technique based on the theory of complex variable functions is adopted. Then, by adjusting the inhomogeneous parameters and comparing with the published analytical results, the correctness of the method in this paper is verified. Finally, the displacement amplitudes of typical observation points on the surface and inside are given, and the effects of incident wave angle, wave number and inhomogeneous parameters on wave energy distribution are analyzed.

Influence of Circular through Hole in Pt-Rh Bushing on Temperature Propagation at High Temperature.

In the fiberglass industry, Pt-Rh bushings made of platinum and rhodium have very good characteristics, such as high temperature resistance, corrosion resistance, oxidation resistance, and creep resistance. In this paper, a semi-infinite lath structure model is constructed, and the expression of the surface temperature distribution of a Pt-Rh alloy plate with a circular through hole is obtained based on the non-Fourier heat conduction equation, complex function method and conformal mapping method. At the same time, the influence of the position of the circular through hole in the Pt-Rh bushing and the parameters of the incident light source (Non-diffusion incident wave number and relative thermal diffusion length) on the surface temperature distribution of the Pt-Rh bushing is studied by using this formula. It is found that: 1. heat concentration and fracture are occur easily at the through hole; 2. when the through hole is in the asymmetric center, the greater the asymmetry, the smaller the maximum temperature amplitude; 3. when the buried depth of the through hole increases, the maximum temperature amplitude decreases; 4. when the incident wave number and the relative thermal diffusion length of the incident light source are larger, the maximum temperature amplitude is smaller. The numerical results are almost consistent with those of ANSYS thermal simulation. The expression of the surface temperature distribution of the semi-infinite lath structure proposed in this paper can effectively reduce the loss of precious metal materials and the time of thermal simulation in the experimental process, as well as provide important significance for structural design, quality inspection, process optimization, and service life improvement of Pt-Rh bushings.

Tunneling Phase Diagrams in Anisotropic Multi‐Weyl Semimetals

AbstractMotivated by the exciting prediction of multi‐Weyl topological semimetals stabilized by point group symmetries, tunneling in anisotropic multi‐Weyl semimetals is studied. It is found that distant detectors for different ranges of an anisotropy parameter λ and incident angle θ will measure different numbers of propagating transmitted modes. These findings are presented as phase diagrams that are valid for incoming waves with fixed wavenumber k. Energy is not held fixed for incoming waves but allowed to vary with choice of incident angle and wavenumber k. To gain a deeper understanding of this phenomenon they focus on the simplest case of anisotropic quadratic Weyl‐semimetals and tunneling coefficients are analyzed analytically and numerically to confirm observations extracted from phase diagrams. Results show nonanalytical behavior, which is the hallmark of phase transitions. This serves as motivation to make a formal analogy with phase transitions known from statistical mechanics. Specifically, they argued that the long distance limit in the tunneling problem mimics the thermodynamic limit in statistical mechanics. A direct formal connection is found to the recently developed formalism of dynamical phase transitions. They propose that usage of this analogy with dynamical phase transitions can be fruitful in classifying transport properties of exotic semimetals.

Electroelastic Coupled-Wave Scattering and Dynamic Stress Concentration of Piezoceramics Containing Regular N-Sided Holes

In this paper, the calculation method of dynamic stress concentration around piezoelectric ceramics containing regular n-sided holes under the action of electroelastic coupling wave was studied, and it was applied to promising barium calcium zirconate titanate material. First, electroelastic governing equations were decomposed by using the auxiliary function method, and the solution forms of the elastic wave field and electric field were obtained by using the wave function expansion method. Then, the triangular boundary was simplified to a circular boundary using the mapping function, and the corresponding modal coefficients were determined according to simplified boundary conditions. Finally, the dynamic stress-concentration factor was calculated to characterize the dynamic stress concentration. We performed numerical simulations with a correlation coefficient of (1 − x)[(Ba0.94Ca0.06) (Ti0.92Sn0.08)]-xSm2O3-0.06 mol% GeO2 (abbreviated as (1 − x)BCTS-xSm-0.06G). The numerical calculation results show that the incident wave number, piezoelectric properties, shape parameters of the hole, and deflection angle have a great influence on the dynamic stress around the defect, and some significant laws are summarized through analysis.

Magnetoacoustic Wave Scattering and Dynamic Stress Concentration around the Elliptical Opening in Exponential-Gradient Piezomagnetic Materials

Based on the theory of magnetoacoustic coupled dynamics, the purpose of this paper is to evaluate the dynamic stress concentration near an elliptical opening in exponential-gradient piezomagnetic materials under the action of antiplane shear waves. By the wave function expansion, the solutions for the acoustic wave fields and magnetic fields can be obtained. Stress analysis is performed by the complex function method and the conformal mapping method, which are used to solve the boundary conditions problem, and is used to express the dynamic stress concentration coefficient (DSCC) theoretically. As cases, numerical results of DSCCs are plotted and discussed with different incident wave numbers and material parameters by numerical simulation. Compared with circular openings, elliptical openings are widely used in material processing techniques and are more difficult to solve. Numerical results show that the dynamic stress concentration coefficient at the elliptical opening is strongly dependent on various parameters, which indicates that the elliptical opening is more likely to cause crack and damage to exponential-gradient piezomagnetic materials.

Reflection and Transmission in Non-Local Couple Stress Micropolar Thermoelastic Media

We have studied the problem of homogenous, isotropic non-local couple stress micropolar thermoelastic solid in the absence of body forces, couple density and heat resources. The reflection and transmission of waves at the interface of two distinct media have been investigated. It is observed that amplitude ratios of various reflected and transmitted waves are functions of wave number of incident waves and are affected by the non-local parameter of thermoelastic solid.

Electroelastic Coupled-Wave Scattering and Dynamic Stress Concentration of Triangular Defect Piezoceramics

In this paper, a method to calculate the dynamic stress concentration around the triangular defect of piezoelectric material under electroelastic coupling is studied and applied to the promising barium calcium zirconate titanate. Firstly, the electroelastic governing equation is decomposed by decoupling technique, and the analytical solutions of elastic wave field and electric field are obtained by wave function expansion method. Then, the conformal transformation is used to simplify the triangle boundary into a circular boundary, and the corresponding modal coefficients are determined according to the simplified boundary conditions. Finally, the analytical solution of the dynamic stress concentration factor can be obtained according to the constitutive equation. Substitute the relevant material parameters of (Ba0.85Ca0.15)(Zr0.1Ti0.9)O3 and set different temperatures, Ce doping amount, and incident wave number for numerical simulation. The numerical results show that the incident wave number, piezoelectric properties, and the shape parameters and deflection angle of the triangular defect have a great influence on the dynamic stress around the defect, and some meaningful laws are summarized through analysis.

Generate high data rate of optical carries by using nanomaterial graphene in slab waveguide

Abstract Single mode is one of the most practical applications in microwave propagations because of its high mode resolution and low transmission loss. In this paper, the single mode graphene material was implemented in slab waveguide to study the performance and optical properties of graphene material; the parameters that affect these models were found to be the cut-off frequency, attenuation wavenumbers, modes numbers, skin depth, angles incident, and propagation wave numbers. The effectiveness of these factors was simulated and analyzed using MATLAB software program. In this paper, the carriers were generated using nano-graphene; the optical carrier source provided seven carriers with the frequency spacing of 4.9682 GHz. After splitting the carriers using optical demultiplexer, these carriers were modulated independently using optical Quadrature phase shift keying (QPSK) modulators at symbol rate equal to 4.9682 Gsymbol/s; this matches the frequency spacing of the carriers. Under this argument, the total data rate was equal to 2*7*4.9682 Gsymbol/s = 69.5548 Gbit/s, and the total bandwidth was 34.774 GHz. These carriers were found to work in optical communication with high data rate.

Recovery of coherent reflection from rough-surface scattered acoustic fields via the frequency-difference autoproduct.

The acoustic field reflected from a random rough surface loses coherence with the incident field in the Kirchhoff approximation as kh cos θ increases, where k is the incident field wavenumber, h is the root mean square roughness height, and θ is the incidence angle. Thus, for fixed rough-surface properties and incidence angle, a reflected field at lower wavenumber should retain more coherence. Recent results suggest that the frequency-difference autoproduct formed from complex acoustic field amplitudes at two nearby frequencies can recover acoustic information at the difference of those frequencies even when the difference frequency is below the recorded field's bandwidth. Herein analytical, computational, and experimental results are presented for the extent to which the frequency-difference autoproduct recovers coherence from randomly rough-surface-scattered constituent fields that have lost coherence. The analytical results, developed from the Kirchhoff approximation and formal ensemble averaging over randomly rough surfaces with Gaussian height distributions and Gaussian correlation functions, indicate that the coherence of the rough-surface-reflected frequency-difference autoproduct depends on the surface correlation length and Δkh cos θ, where Δk is the difference of the autoproduct's constituent field wavenumbers. These results compare favorably with Monte Carlo simulations of rough surface scattering, and with laboratory experiments involving long surface correlation lengths where 1 ≤kh cos θ≤ 3.