Correlation between single-cylinder properties and bandgap formation in photonic structures

The origin of frequency gaps in the dispersion relation of periodic, quasi-periodic, and random photonic structures consisting of different arrangements of dielectric cylinders has been investigated. For TM polarization it was found that the formation and properties of gaps are strongly affected by Mie resonances of a single cylinder. Both the spectral position and size depend on the properties of this single scatterer. In contrast, for TE polarization no correlation between the scattering properties and bandgap formation was found, as Mie resonances are spectrally not well separated. For the inverted structure consisting of air cylinders in a dielectric material, the frequency gaps depend on the spatial arrangement of the cylinders because no pronounced Mie resonances exist in this case.     

六角形散射子光子晶体的界面态

研究采用平面波展开加超元胞方法计算了正方格子六角形空气散射子二维光子晶体镜面对称异质结的界面态.经过研究发现,这种异质结界面态可以通过相对于界面横向拉开或者纵向错开而产生,并且调节到绝对带隙中成为传导模.界面态的个数和变化规律在很大程度上依赖于光子晶体异质结构的几何和物理参量.通过对比我们发现：与圆柱形散射子相比,在六角形散射子异质结中更易于产生传导模,但是比四方柱形散射子的情况要困难.     

通道中串列旋转圆柱的格子Boltzmann-虚拟区域方法的模拟

通过结合格子Boltzmann方法(LBM)和虚拟区域(Fictitiou sDomain)思想,建立格子Boltzmann-虚拟区域(LB-DF/FD)方法.采用两套网格系统,欧拉网格用于流体,拉格朗日网格用于固体.原有的LBM在计算运动固体的受力方面存在数据振荡,LB-DF/FD方法改进了此缺陷.为验证该方法,模拟圆柱绕流、圆形颗粒在无限长通道中平动及在无限大流场中转动三种情况,结果与其他数值解及理论解符合得很好.利用该方法模拟低雷诺数下通道中串列旋转圆柱周围的流场,分析圆柱间距(g)及雷诺数(Re)对流场结构的影响.给出Re=0.001,0.1和10下,0.2≤g≤8.0的流线结构、圆柱升力、阻力以及力矩等数值结果.结果表明,g对流场的结构及圆柱的受力有显著影响,Re对圆柱阻力及Stokes单元数目的影响较大.     

Electrostatic resonance of clusters of dielectric cylinders: A finite element simulation

Based on the finite-element method, it is demonstrated that the electrostatic resonance features of a range of heterostructures made of clusters of dielectric cylinders depend sensitively on the shape and arrangement of the inclusions in the background matrix, and on the polarization of the applied electric field.     

Lattice Boltzmann simulations of a dumbbell moving in a Poiseuille flow

In this paper, the lattice Boltzmann method is applied to simulate a dumbbell moving in a pressure-driven flow in a planar channel with the stress-integration method for the evaluation of hydrodynamic force acting on the cylinders. The simulation results show that the dumbbell also has the important feature of the Segr\'e--Silberberg effect like a particle in a Poiseuille flow. The dumbbell trajectories, orientations, the cylinders vertical velocities and angular velocities all reach their equilibrium values separately independent of their initial positions. It is also found that the dumbbell equilibrium positions depend on the flow Reynolds number, blockage ratio and elastic coefficient. This study is expected to be helpful to understand the dynamics of polymer solutions, polymer synthesis and reaction, etc.     

Vibrational characteristics of rotating soft cylinders

Rotating structural components are omnipresent in engineering structures and natural world. This work investigates the effects of the centrifugal and Coriolis forces on the free vibrational characteristics of soft cylinders rotating with respect to the axis of symmetry based on the nonlinear elasticity and linear incremental theories. The formulations indicate that the biasing deformation, instantaneous elastic moduli, and incremental equations of motion strongly depend on the rotating speed. The characteristic equation for the natural frequency is derived using the state-space method and approximate laminate technique.The numerical examples included in this work demonstrate that the centrifugal and Coriolis forces might have significant effects on the vibrational characteristics of the cylinder. Results of this work will benefit the design and control of novel engineering systems with rotating soft cylinders or shafts.     

Half-cylinders and branch-cut response functions

We consider the polarizability of half cylinders (explicitly, circular cylinders cut in half along a diameter), and the permittivity or permeability of dilute arrays of half cylinders, extending the work of of M. Pitkonen. We show that Pitkonen's results for the polarizability of half cylinders may be greatly simplified using a property of the dilogarithm function, and we comment on the correct choice of branches of the resulting simplified expression for complex cylinder permittivities. We discuss the relationship between response functions for systems having discrete resonances, as compared with those having branch-cut spectra, and highlight some of the advantages the latter may have in applications such as energy harvesting and design of metamaterials.     

Scattering characteristics of structures of lossy metamaterial–semiconductor cylinders

Here, we present for the first time the rigorous boundary problem solution of the Maxwell’s equations for the determination of scattering characteristics of a structure. The structure consists of a finite set of infinite parallel circular cylinders that can be made of different lossy isotropic materials. We numerically analyzed two structures that differ only in the symmetrical arrangement of semiconductor cylinders in relation to a central metamaterial cylinder. The electrical radii of cylinders can be arbitrary. Both polarizations of the incident microwave are considered in this work. The Poynting vector of the plane microwave that reflected from and transmitted through the structures analyzed here. We investigated dependency on the radius of an arc where are placed the semiconductor cylinders, the semiconductor-specific resistivity, the operating frequency at two radii of the metamaterial cylinder. We discovered that the structure can have features of a band gap photonic crystal dependent on the topology and the polarization of the incident microwave. We have found that the structure can operate as a microwave reflector at the certain radius of the arc on which are located thirteen n-Si cylinders. The Poynting vector is very sensitive to the change of semiconductor-specific resistivity when the incident microwave has the parallel polarization.     

Transverse, tilting and cross-coupling stiffness of cylindrical rubber isolators in the audible frequency range—The wave-guide solution

Audio-frequency wave-guide models for antisymmetric dynamic stiffness of arbitrary long elastomer cylinders are presented. The locally non-mixed boundary conditions at the lateral and radial surfaces are simultaneously satisfied by using the modes corresponding to the dispersion relation for axial waves in cylinders satisfying the stress free boundary conditions at the curved radial boundaries, while the displacement conditions on the flat cylinder ends are satisfied by mode matching. The elastomer is modelled as nearly incompressible with deviatoric visco-elasticity based on a fractional derivative, standard linear solid embodying a Mittag-Leffler relaxation kernel, the main advantage being the minimum parameter number required to successfully model the material properties over a broad frequency band. The stiffness is found to depend strongly on frequency; displaying resonances and anti-resonances. The method is compared with and verified against finite element models. In addition, comparison to thin beam theories, i.e. Euler and Timoschenko theory and a simple shear model, is presented, illustrating the limitations of these models.     

Acoustic breathing mode frequencies in cylinders,cylindrical shells and composite cylinders of general anisotropic crystals: Application to nanowires

We present here a study of the acoustic breathing modes for infinitely long cylinders, cylindrical shells and composite cylinders of general anisotropic crystals. We assume cylindrical anisotropy for the systems studied. We obtain expressions in closed form for their frequencies in the case of cylinders and cylindrical shells, valid for any anisotropic material, thus including up to 21 independent elastic constants. In the case of the lowest breathing mode of a thin cylindrical shell we obtain a simple analytical formula. This can be used to obtain a first estimate of the breathing mode frequency in nanotubes for any material. In the case of core–shell and composite cylinders we obtain the expressions for the secular determinant. We calculate the frequencies of the lowest acoustic breathing mode of Au, CdSe, InAs, GaAs, Ag and Bi nanowires obtained recently by different experimental groups. We also present results for the acoustic breathing modes of Au/Ag and ZnS/SiO₂ core–shell nanowires produced recently.     

Bi-layer steady state current cloak

We report that bi-layer copper and polystyrene cylinders can cloak steady current. We fabricated two hollow cylinders, the one made of copper, and the other made of polystyrene. Two hollow copper and polystyrene cylinders nested concentric bi-layer hollow copper and polystyrene cylinders. The background media are made of aluminum. Theory and experiment demonstrated that the electric potential gradients are parallel and equal outside the outer circle, the iso-potential lines are parallel outside the outer circle, and the electric potential is zero in the inner circle.     

Multipole analysis of a generic system of dielectric cylinders and application to fibrous materials

A multipole theory describing the interactions between dielectric cylinders in a uniform field is developed. We treat the most general case of $N$ parallel cylinders placed in arbitrary positions. The exact theory is obtained by developing the polarisation charge surface density on each cylinder in a Fourier series. The related coefficients, the so-called multipoles, may be obtained from a linear set of equations which is derived and analysed in the paper. For systems of closely spaced cylinders, with high ratio of the dielectric constant of the cylinders compared to that of the homogeneous medium (in the worst case, conductive cylinders in contact with each other) a very large number of multipole terms is required to achieve convergence. In spite of the large number of required terms, the general multipole expansion is rapidly convergent in all other cases and is important from a theoretical point of view. Numerical results are presented for canonical dispositions of cylinders and for more complicated arrangements. Finally, such a multipole expansion has been applied to the dielectric characterisation of composite materials formed by a regular array of parallel cylinders, thereby obtaining the equivalent permittivity using a numerically efficient technique.     

Analysis of tunable bandgaps in liquid crystal-infiltrated 2D silicon photonic crystals

We present a theoretical study on two-dimensional photonic crystals composed of silicon and the E7 liquid crystal. We analyze how the optical axis orientation of the liquid crystal influences the photonic bands and bandgaps, for the case when the Maxwell equations can be decoupled into the TE and TM modes. We consider two different structures, a triangular lattice of E7 liquid crystal cylinders in a silicon background and a triangular lattice of silicon cylinders in an E7 liquid crystal background. The effect of the liquid crystal anisotropy on the geometry of the irreducible Brillouin zone allows us to propose a simplified way to calculate the photonic bandgaps. Results show that the bandgap width and center frequency have a 60° periodicity for both structures. Using the plane-wave expansion method, we determined the maximum bandgap and the optimal radius of the cylinders for each structure. Finally, for the second structure, we propose an optical switch with a 50% duty cycle. These structures can be applied to design tunable photonic devices.     

Relative local density of states and cloaking in finite clusters of coated cylinders

We describe a method for accurate calculation of the Relative Local Density of States (RLDOS) as a function of frequency and position in finite sets of coated cylinders. The RLDOS is important, since it describes the interaction between sources and their environment, which controls their ability to radiate electromagnetic waves. We give numerical examples of distributions of RLDOS for clusters of cylinders with lossy coatings whose optical properties are in the range typical of metamaterials, and use these to show the tendency of RLDOS to concentrate on the coating boundaries when plasmonic cloaking is occurring.     

Closed-form solution for a pair of touching cylindrical conductors in an external electric field

We give expressions for the electric potential and field around two conducting cylinders in contact, in closed form and in terms of elementary functions. The polarizability tensor, and hence the torque acting on the cylinder pair, follow from these results. The surface charge density, and the total charge per unit length on each cylinder, can also be evaluated in closed form. The equal and opposite forces on the two cylinders are found in the case of equal cylinder radii.     

不同晶格光子晶体异质结的界面传导模

利用平面波展开方法与超原胞方法研究了两种不同晶格的光子晶体异质结的界面态. 这两种异质结都是在纯电介质背景上放置空气散射子. 一种异质结由正方形格子上放置正方形散射子和三角形格子上放置六角形散射子组成（SSTH异质结）. 另一种由长方格子上放置长方形散射子和三角形格子上放置圆形散射子组成（RRTC异质结）. 对于SSTH异质结，当沿着界面作晶格的横向拉开或者侧向滑移，都可产生界面态. 而对于RRTC异质结，无需从界面做晶格拉开或者侧向滑移就可产生界面传导模，这个结果有别于其他纯电介质光子晶体异质结的性质. 关键词： 光子晶体 异质结 传导模 超原胞     

无序对二维声子晶体平板负折射成像的影响

利用多重散射理论分析了位置无序对钢/水声子晶体负折射成像的影响.发现声子晶体负折射成像与周期结构中的方向性通路有关;该方向性通路不同于一般意义上的位置波导,它是声子晶体周期散射的结果;通路中的障碍对成像有较大影响;随着散射体位置无序程度的增加,周期性散射减弱,方向性通路被破坏,成像也随之减弱,甚至消失.     

二维声子晶体平板成像中的通道特征

利用多重散射理论分析了钢/水声子晶体平板成像过程.发现平板成像中的散射波会聚具有散射通道特征.对于确定的声源位置,不同入射角信号对应不同的通道;耦合进入通道的信号强度也不相同.小角度入射波能较强地耦合进入通道;大角度入射波在入射表面受到强烈散射,较弱地耦合进入通道.非理想成像情况下,不同入射角信号通过平板成像的位置不同,因而形成像差.声源位置改变,对应的通道亦随之改变.散射通道与声子晶体的各向异性能带结构和多重散射密切相关.     

Electronic structure, magnetism and superconductivity of layered iron compounds

The layered iron superconductors are discussed using electronic structure calculations. The four families of compounds discovered so far, including Fe (Se, Te) have closely related electronic structures. The Fermi surface consists of disconnected hole and electron cylinders and additional hole sections that depend on the specific material. This places the materials in proximity to itinerant magnetism, both due to the high density of states and due to nesting. Comparison of density functional results and experiment provides strong evidence for itinerant spin fluctuations, which are discussed in relation to superconductivity. It is proposed that the intermediate phase between the structural transition and the SDW transition in the oxy-pnictides is a nematic phase.     

Shedding patterns in flow-structure interactions

We use direct numerical simulation (DNS) based on spectral methods and the parallel codeNekTar to simulate incompressible and compressible flow past flexible structures. Specifically, we consider incompressible turbulent flow past flexible cylinders subject to vortex-induced vibrations (VIV), and compressible flow past a three-dimensional flexible wing subject to insect-like motion. We present several shedding patterns that reveal new oblique shedding modes resembling modulated traveling and standing wave response waves for flexible cylinders as well as strong three-dimensional interactions for flexible wings.