Investigation of a silicon-based one-dimensional phononic crystal plate via the super-cell plane wave expansion method

The super-cell plane wave expansion method is employed to calculate band structures for the design of a siliconbased one-dimensional phononic crystal plate with large absolute forbidden bands. In this method, a low impedance medium is introduced to replace the free stress boundary, which largely reduces the computational complexity. The dependence of band gaps on structural parameters is investigated in detail. To prove the validity of the super-cell plane wave expansion, the transmitted power spectra of the Lamb wave are calculated by using a finite element method. With the detailed computation, the band-gap of a one-dimensional plate can be designed as required with appropriate structural parameters, which provides a guide to the fabrication of a Lamb wave phononic crystal.

Band structures analysis of one-dimensional photonic crystals using plane wave expansion

A theoretical analysis is made, using plane wave expansion, on how the width of the first three band gaps is influenced by filling ratio, dielectric constant ratio, and periodic width in one-dimensional photonic crystals （PhCs）. From simulation and analysis, there are one, two, and three peak points on the first, second and third band gaps respectively with the changes of filling ratio un- der fixed dielectric constant ratio. When filling ratio is fixed, the bandwidth of the first band gap consistently increases with dielectric constant ratio. However, no similar trend is observed in the second and the third band gaps. Because of scaling properties, varying periodic width does not alter the relative bandwidth.

Equatorial Wave Expansion of Instantaneous Flows for Diagnosis of Equatorial Waves from Data:Formulation and Illustration

This paper presents a method for expanding horizontal flow variables in data using the free solutions to the shallow-water system as a basis set. This method for equatorial wave expansion of instantaneous flows（EWEIF） uses dynamic constraints in conjunction with projections of data onto parabolic cylinder functions to determine the amplitude of all equatorial waves.EWEIF allows us to decompose an instantaneous wave flow into individual equatorial waves with a presumed equivalent depth without using temporal or spatial filtering a priori.Three sets of EWEIF analyses are presented. The first set is to confirm that EWEIF is capable of recovering the individual waves constructed from theoretical equatorial wave solutions under various scenarios. The other two sets demonstrate the ability of the EWEIF method to derive time series of individual equatorial waves from instantaneous wave fields without knowing a priori exactly which waves exist in the data as well as their spatial and temporal scales using outputs of an equatorial β-channel shallow-water model and ERA-Interim data. The third set of demonstrations shows, for the first time, the continuous evolutions of individual equatorial waves in the stratosphere whose amplitude is synchronized with the background zonal wind as predicted by quasi-biennial oscillation theory.

Scattering of SH waves induced by a symmetrical V-shaped canyon: a unified analytical solution

This paper reports a series solution of wave functions for two-dimensional scattering and diffraction of plane SH waves induced by a symmetrical V-shaped canyon with different shape ratios. A half-space with a symmetrical V-shaped canyon is divided into two sub-regions by using a circular-arc auxiliary boundary. The two sub-regions are represented by global and local cylindrical coordinate systems, respectively. In each coordinate system, the wave field satisfying the Helmholtz equation is represented by the separation of variables method, in terms of the series of both Bessel functions and Hankel functions with unknown complex coefficients. Then, the two wave fields are described in the local coordinate system using the Graf addition theorem. Finally, the unknown coefficients are sought by satisfying the continuity conditions of the auxiliary boundary. To consider the phase characteristics of the wave scattering, a parametric analysis is carried out in the time domain by assuming an incident signal of the Ricker type. Surface and subsurface transient responses demonstrate the characteristics and mechanisms of wave propagating and scattering.

Diffraction of plane SH waves by a semi-circular cavity in half-space

This paper presents a closed-form solution for diffraction of plane SH waves by a semi-circular cavity in half-space by using wave function expansion method. Accuracy of the solution is checked by the displacement residual and stress residual along the boundaries. Numerical results show that there are notable differences for response amplitudes between a semi-circular cavity and a whole-circular cavity in a half-space.

Bandgap calculation for mixed in-plane waves in 2D phononic crystals based on Dirichlet-to-Neumann map

In this paper, a method based on the Dirichlet- to-Neumann map is developed for bandgap calculation of mixed in-plane waves propagating in 2D phononic crystals with square and triangular lattices. The method expresses the scattered fields in a unit cell as the cylindrical wave expansions and imposes the Bloch condition on the boundary of the unit cell. The Dirichlet-to-Neumann （DtN） map is applied to obtain a linear eigenvalue equation, from which the Bloch wave vectors along the irreducible Brillouin zone are calculated for a given frequency. Compared with other methods, the present method is memory-saving and time-saving. It can yield accurate results with fast convergence for various material combinations including those with large acoustic mismatch without extra computational cost. The method is also efficient for mixed fluid-solid systems because it considers the different wave modes in the fluid and solid as well as the proper fluid-solid interface condition.

Electro-mechanical coupling wave propagating in a locally resonant piezoelectric/elastic phononic crystal nanobeam with surface effects

The model of a "spring-mass" resonator periodically attached to a piezoelectric/elastic phononic crystal(PC) nanobeam with surface effects is proposed, and the corresponding calculation method of the band structures is formulized and displayed by introducing the Euler beam theory and the surface piezoelectricity theory to the plane wave expansion(PWE) method. In order to reveal the unique wave propagation characteristics of such a model, the band structures of locally resonant(LR) elastic PC Euler nanobeams with and without resonators, the band structures of LR piezoelectric PC Euler nanobeams with and without resonators, as well as the band structures of LR elastic/piezoelectric PC Euler nanobeams with resonators attached on PZT-4, with resonators attached on epoxy, and without resonators are compared. The results demonstrate that adding resonators indeed plays an active role in opening and widening band gaps. Moreover, the influence rules of different parameters on the band gaps of LR elastic/piezoelectric PC Euler nanobeams with resonators attached on epoxy are discussed, which will play an active role in the further realization of active control of wave propagations.

Nonlocal symmetries,consistent Riccati expansion integrability,and their applications of the (2+1)-dimensional Broer–Kaup–Kupershmidt system

For the （2＋1）-dimensional Broer–Kaup–Kupershmidt（BKK） system, the nonlocal symmetries related to the Schwarzian variable and the corresponding transformation group are found. Moreover, the integrability of the BKK system in the sense of having a consistent Riccati expansion（CRE） is investigated. The interaction solutions between soliton and cnoidal periodic wave are explicitly studied.

Effects of orientation and shape of holes on the band gaps in water waves over periodically drilled bottoms

The complete band gaps （CBGs） of shallow water waves propagating over bottoms with periodically drilled holes are investigated numerically by the plane wave expansion method. Four different patterns are considered, containing triangular, square, hexagonal and circular cross-sectioned holes arranged into triangular lattices. Results show that the width of CBGs can be changed by adjusting the orientation of noncircular holes and the effect of hole shape on the width of the maximal CBGs is discussed.

INFLUENCES OF ANISOTROPY ON BAND GAPS OF 2D PHONONIC CRYSTAL

Band gaps of 2D phononic crystal with orthotropic cylindrical fillers embedded in the isotropic host are studied in this paper. Two kinds of periodic structures, namely, the square lattice and the triangle lattice, are considered. For anisotropic phononic crystal, band gaps not only depend on the periodic lattice but also the angle between the symmetry axis of orthotropic material and that of the periodic structure. Rotating these cylindrical fillers makes the angle changing continuously; as a result, pass bands and forbidden bands of the phononic crystal are changed. The plane wave expansion method is used to reduce the band gap problem to an eigenvalue problem. The numerical example is given for YBCO/Epoxy composites. The location and the width of band gaps are estimated for different rotating angles. The influence of anisotropy on band gaps is discussed based on numerical results.

Main Factors for Affecting Photonic Bandgap of Photonic Crystals

The factors affecting one dimensional （1D） and two dimensional （2D） photonic crystals （PhCs） are systemically analyzed in this paper by numerical simulation. Transfer matrix method （TMM） is employed for 1D PCs, both finite difference time domain method （FDTD） and plane wave expansion method （PWE） are employed for 2D PCs. The result shows that the photonic bandgaps （PBG） are directly affected by crystal type, crystal lattice constant, modulation of refractive index and periodicity, and it is should be useful for design of different type photonic crystals with the required PBG and functional devices. Finally, as an example, a near-IR 1D PCs narrow filter was designed.

The Photonic Band Gaps in the Two-Dimensional Plasma Photonic Crystals with Rhombus Lattice

In this paper,under two different electromagnetic modes,the photonic band gaps（PBGs） in the two-dimensional plasma photonic crystals（PPCs） are theoretically investigated based on the plane wave expansion method.The proposed PPCs are arranged in rhombus lattices,in which the homogeneous unmagnetized plasma rods are immersed in the isotropic dielectric background.The computed results showed that PBGs can be easily tuned by the angle of rhombus lattices,and a cutoff frequency and a flatbands region can be observed under the TM and TE polarized waves,respectively.The relationships between the relative bandwidths of first PBGs and the parameters of PPCs in two such cases also are discussed.The numerical simulations showed that the PBGs can be manipulated obviously by the parameters as mentioned above.The proposed results can be used to design the waveguide and filter based on the PPCs.

The features of band structures for woodpile three-dimensional photonic crystals with plasma and function dielectric constituents

The features of the band structures of woodpile three-dimensional （3D） photonic crystals composed of plasma and function dielectric constituents, referred to as function plasma photonic crystals （FPPCs）, are theoretically studied by a modified plane wave expansion method, and the formulas for computing the band structures are derived. The arrangement for the proposed FPPCs is that the function dielectric columns are surrounded by plasma, and the embedded dielectric columns are stacked according to the woodpile lattices, which are arrayed with facecentered-tetragonal symmetry. The relative permittivity of function dielectric rods depends on the function coefficient and space coordinates. The relationships between the parameters for inserted function dielectric rods and plasma and the band structures are also investigated. The computed results illustrate that the obtained PBG can be tuned by those parameters as mentioned above. Compared to dielectric-air PCs, function dielectric PCs and plasma dielectric PCs with the same topology, a wider bandwidth of the photonic band gap can be observed in the proposed FPPCs. The calculated results also show us another alternative way to realize reconfigurable applications with 3D FPPCs.

NEW PERIODIC SOLUTIONS OF ITO'S 5th-ORDER mKdV EQUATION AND ITO'S 7th-ORDER mKdV EQUATION

Based on the modified Jocobi elliptic function expansion method and the modified extended tanh function method,a new algebraic method is presented to obtain mu ltiple travelling wave solutions for nonlinear wave equations.By using the metho d,Ito's 5th order and 7th order mKdV equations are studied in detail and more new exact Jocobi elliptic function periodic solutions are found.With modulus m→1 or m→0,these solutions degenerate into corresponding solitary wave s olutions,shock wave solutions and trigonometric function solutions.

Comment on “Band gaps structure and semi-Dirac point of two-dimensional function photonic crystals” by Si-Qi Zhang et al.

Recently, Zhang et al. （Chin. Phys. B 26 024208 （2017）） investigated the band gap structures and semi-Dirac point of two-dimensional function photonic crystals, and the equations for the plane wave expansion method were induced to obtain the band structures. That report shows the band diagrams with the effects of function coefficient k and medium column ra under TE and TM waves. The proposed results look correct at first glance, but the authors made some mistakes in their report. Thus, the calculated results in their paper are incorrect. According to our calculations, the errors in their report are corrected, and the correct band structures also are presented in this paper.

Simulation of Compressible Two-Phase Flows Using a Void Ratio Transport Equation

A compressible and multiphase flows solver has been developed for the study of liquid/gas flows involving shock waves and strong expansion waves leading to cavitation.This solver has a structure similar to those of the one-fluid Euler solvers,differing from them by the presence of a void ratio transport-equation.The model and the system of equations to be simulated are presented.Results are displayed for shock and expansion tube problems,shock-bubble interaction and underwater explosion.Close agreement with reference solutions,obtained from explicit finite volume approaches,is demonstrated.Different numerical methods are additionally displayed to provide comparable and improved computational efficiency to the model and the system of equations.The overall procedure is therefore very well suited for use in general two-phase fluid flow simulations.

PHONONIC BAND GAPS IN TWO-DIMENSIONAL HYBRID TRIANGULAR LATTICE

Absolute phononic band gaps can be substantially improved in two-dimensional lattices by using a symmetry reduction approach. In this paper, the propagation of elastic waves in a two-dirnensional hybrid triangular lattice structure consisting of stainless steel cylinders in air is investigated theoretically. The band structure is calculated with the plane wave expansion （PWE） method. The hybrid triangular Bravais lattice is formed by two kinds of triangular lattices. Different from ordinary triangular lattices, the band gap opens at low frequency （between the first and the second bands） regime because of lifting the bands degeneracy at high symmetry points of the Brillouin zone. The location and width of the band gaps can be tuned by the position of the additional rods.

Advances in Research on Atmospheric Energy Propagation and the Interactions between Different Latitudes

Early theoretical analyses indicated that the tropics and extratropics are relatively independent due to the existence of critical latitudes.However,considerable observational evidence has shown that a clear dynamical link exists between the tropics and midlatitudes.To better understand such atmospheric teleconnection,several theories of wave energy propagation are reviewed in this paper：（1） great circle theory,which reveals the characteristics of Rossby waves propagating in the spherical atmosphere;（2） westerly duct theory,which suggests a ＂corridor＂ through which the midlatitude disturbances in one hemisphere can propagate into the other hemisphere;（3） energy accumulation-wave emanation theory,which proposes processes through which tropical disturbances can affect the atmospheric motion in higher latitudes;（4） equatorial wave expansion theory,which further explains the physical mechanisms involved in the interaction between the tropics and extratropics;and（5） meridional basic flow theory,which argues that stationary waves can propagate across the tropical easterlies under certain conditions.In addition,the progress made in diagnosing wave-flow interaction,particularly for Rossby waves,inertial-gravity waves,and Kelvin waves,is also reviewed.The meridional propagation of atmospheric energy exhibits significant annual and interannual variations,closely related to ENSO and variation in the westerly jets and tropical upper-tropospheric troughs,amongst others.

Modelling overall transmitted efficiency at 1550 nm for polymer grating Silicon-on-insulator structure with defect

The overall transmitted efficiency at 1550 nm for Nylon-Teflon/Teflon-Nylon （N-T/T-N） grating Silicon- on-insulator （SOI） structure with defect in even and odd position was investigated in this paper. Different types of losses, such as absorption, reflection and diffraction, were considered to find out the overall transmitted efficiency. The absorption loss of both Nylon-Teflon （N-T） and Teflon-Nylon （T-N） structure is zero at the wavelength of 1550 nm. Reflectance of these structures was analyzed by using plane wave expansion （PWE） method. Simulation result showed that reflectance as well as transmittance was varied linearly with respect to defect at odd and even positions. Simulation is also done for the diffraction efficiency at 1550nm with respect to detuning from Bragg＇s angle, which was ranged from -0.4 rad to ＋ 0.4 rad. Finally, it was found that overall transmitted efficiency increased as even defect position varied from 2nd to 10th for both N-T/T-N grating SOI structure. Similarly, the overall transmitted efficiency decreased as odd defect position changed from 3rd to l lth for both N-T/T-N grating SOI structure.