Calculation of effective material parameters by field averaging over lattices with non-negligible unit cell size

The Pendry et?al. field averaging method for calculation of effective material parameters is reviewed and its limits explored. The method is then extended so that it can accurately calculate the effective material parameters of lattices where the unit cell size is appreciable but still quasistatic (d??0.1?? ₀). The new algorithm is verified by calculating the effective material properties of periodically placed particles suspended in free space, as the unit cell size becomes appreciable. Results of our proposed formulation are then compared with the Pendry et?al. and conventional volumetric averaging algorithms.     

Optimization of the calculations of the electronic structure of carbon nanotubes

A method is proposed for calculating the electronic structure and physical properties (in particular, Young’s modulus) of nanotubes, including single-walled carbon nanotubes. This method explicitly accounts for the periodic boundary conditions for the geometric structure of nanotubes and makes it possible to decrease considerably (by a factor of 10–10³) the time needed to calculate the electronic structure with minimum error. In essence, the proposed method consists in changing the geometry of the structure by partitioning nanotubes into sectors with the introduction of the appropriate boundary conditions. As a result, it becomes possible to reduce substantially the size of the unit cell of the nanotube in two dimensions, so that the number of atoms in a new unit cell of the modified nanotube is smaller than the number of atoms in the initial unit cell by a factor equal to an integral number. A decrease in the unit cell size and the corresponding decrease in the number of atoms provide a means for drastically reducing the computational time, which, in turn, substantially decreases with an increase in the degree of partition, especially for nanotubes with large diameters. The results of the calculations performed for carbon and non-carbon (boron nitride) nanotubes demonstrate that the electronic structures, densities of states, and Young’s moduli determined within the proposed approach differ insignificantly from those obtained by conventional computational methods.     

Computation of Hele-Shaw flows with free boundaries

A novel method for calculation of Hele-Shaw flows with receding free boundaries is presented. The method is applied to flows with suction from a point sink and to flow in a channel with parallel walls. In each case the unknown fluid region is mapped conformally onto the unit disc, the free boundary being mapped onto the unit circle. This mapping, which is a function of position and time, is calculated numerically at points on the unit circle using a version of the boundary integral method. The free boundary is thus found without explicit calculation of the pressure at internal points, and the computation times are much less than those for other numerical methods for this problem. Numerical results are compared with explicit analytic solutions for several test problems.     

Improved Dirichlet-to-Neumann map method for modeling extended photonic crystal devices

A typical photonic crystal (PhC) device has only a small number of distinct unit cells. The Dirichlet-to-Neumann (DtN) map of a unit cell is an operator that maps the wave field to its normal derivative on the boundary of the cell. Based on the DtN maps of the unit cells, a PhC device can be efficiently analyzed by solving the wave field only on edges of the unit cells. In this paper, the DtN map method is further improved by an operator marching method assuming that a main propagation direction can be identified in at least part of the device. A Bloch mode expansion method is also developed for structures exhibiting partial periodicity. Both methods are formulated on a set of curves for maximum flexibility. Numerical examples are used to illustrate the efficiency of the improved DtN map method.     

含内部连接体的二维声子晶体弹性波宽频带隙特性

声子晶体的弹性波带隙特性使得它在开发用于减振降噪的新型功能材料方面具有广阔应用前景。为获得宽频大带隙,改进了一种含连接体的正方晶格声子晶体结构.利用有限元法计算并分析了不同结构配置下其能带特性和振动模态。数值结果表明,单胞中同时引入新的质量块以及连接体将对原连接体的自由振动模态产生抑制作用,可在原分离的两带隙频率范围内获得相对带宽超过100%的单一宽频带隙。此外,通过调整几何尺寸、连接体数目、结构对称性等参数可进一步调控结构带隙特性。      

Temperature-accelerated method for exploring polymorphism in molecular crystals based on free energy

The ability of certain organic molecules to form multiple crystal structures, known as polymorphism, has important ramifications for pharmaceuticals and high energy materials. Here, we introduce an efficient molecular dynamics method for rapidly identifying and thermodynamically ranking polymorphs. The new method employs high temperature and adiabatic decoupling to the simulation cell parameters in order to sample the Gibbs free energy of the polymorphs. Polymorphism in solid benzene is revisited, and a resolution to a long-standing controversy concerning the benzene II structure is proposed.     

Magnetotransport properties in magnetic nanotubes studied using Monte Carlo simulations

The dependences of the magnetoelectric transport properties of nanotubes on the temperature, diameter and anisotropy were simulated using the Monte Carlo method, the Heisenberg model and the Drude formula. The simulations included the effects of an external magnetic field, magnetocrystalline anisotropy and nearest neighbor interactions. Two types of nanotubes with different unit cells (square and hexagonal) were implemented. The influence of the nanotube geometry was also analyzed. A smaller dependence of the resistivity on the nanotube diameter and magnetocrystalline anisotropy was observed for the square unit cell nanotubes compared to the results obtained for the hexagonal unit cell nanotubes. Furthermore, lower fluctuations in the resistivity were observed in the former. In contrast, an external magnetic field had a greater influence on the resistivity of the square unit cell nanotubes than for the hexagonal unit cell nanotubes.     

Theoretical studies of hydrogen molecule adsorption on flat and stepped platinum surfaces

Theoretical calculations have been applied to the adsorption of hydrogen molecule on flat and stepped platinum surfaces. The method of large unit cell is modified to deal with the stepped surface as well as the flat one. This method is free from the boundary effect which is inevitable in the cluster method. The results calculated for the d-band width and the highest occupied level are in good agreement with the experiments. For the dissociative adsorption, the bottom of the step site is the most favorable, and the result is attributed to the extra orbital interactions at this site.     

A new integral representation for quasi-periodic fields and its application to two-dimensional band structure calculations

In this paper, we consider band structure calculations governed by the Helmholtz or Maxwell equations in piecewise homogeneous periodic materials. Methods based on boundary integral equations are natural in this context, since they discretize the interface alone and can achieve high order accuracy in complicated geometries. In order to handle the quasi-periodic conditions which are imposed on the unit cell, the free-space Green’s function is typically replaced by its quasi-periodic cousin. Unfortunately, the quasi-periodic Green’s function diverges for families of parameter values that correspond to resonances of the empty unit cell. Here, we bypass this problem by means of a new integral representation that relies on the free-space Green’s function alone, adding auxiliary layer potentials on the boundary of the unit cell itself. An important aspect of our method is that by carefully including a few neighboring images, the densities may be kept smooth and convergence rapid. This framework results in an integral equation of the second kind, avoids spurious resonances, and achieves spectral accuracy. Because of our image structure, inclusions which intersect the unit cell walls may be handled easily and automatically. Our approach is compatible with fast-multipole acceleration, generalizes easily to three dimensions, and avoids the complication of divergent lattice sums.     

大弹性常数差二维声子晶体带隙计算中的集中质量法

通过引入振动力学中的连续系统离散化的思想，将一维集中质量法延伸至二维，提出一种二维声子晶体带隙特性计算的集中质量法. 进而采用该算法对两种正方晶格的二维声子晶体的带结构进行了计算，计算结果与传统的平面波展开法相符合. 通过对计算结果以及两种算法收敛性的分析，发现集中质量法的收敛性对组成声子晶体的不同材料弹性参数差不敏感，这使得该算法在计算大弹性常数差二维声子晶体的带隙特性时较平面波展开法收敛速度更快. 此外，集中质量法对二维声子晶体单元形状没有特殊要求，这使得它更加适用于声子晶体带隙特性的计算. 关键词： 声子晶体 声子带隙 集中质量法     

基于超材料与电阻型频率选择表面的薄型宽频带吸波体的设计

设计了三种类型吸波体, 分别为基于正方形金属贴片(square metal patch, SMP) 结构超材料吸波体、 电阻型频率选择表面(Resistance Frequency Selective Surface, RFSS) 吸波体和SMP与RFSS的复合结构吸波体. 采用FDTD算法分别对这三种类型吸波体的电磁波吸收特性进行数值模拟分析. 模拟得到的结果表明: 在整个2-30 GHz频率范围内, SMP吸波体, 通过几何参数的设计可以实现多频窄带强吸收; RFSS吸波体, 通过方块电阻的设计可以实现高频宽带强吸收, 但强吸收的带宽有限; SMP与RFSS的复合结构吸波体, 在3-25 GHz之间吸收率大于90%以上, 且宽频范围内与自由空间具有较好的阻抗匹配特性.     

Obtaining effective metamaterial parameters through modal analysis

We develop a general method for analyzing the behavior of MTMs using modal decomposition. We replace the inclusions by equivalent lumped circuit elements and use transmission-line theory to solve the propagation problem in the longitudinal direction. This approach calculates physically observable quantities, such as the input impedance, reflection coefficient, dispersion relation, etc., directly without relying on homogenization first. Unlike previous methods, our method can handle complex configurations such as multiple graduated or random inclusion layers within an MTM unit cell. We calculate equivalent constitutive parameters that take into account the entire unit cell and any interactions among the shunt and series elements of the unit cell. We illustrate the utility of our model by evaluating the performance of a MTM composed of unit cells that consist of several layers of SRRs with graduated resonant frequency.     

Wave dispersion in periodic post-buckled structures

Wave propagation in pinned-supported, post-buckled beams can be described with the Korteweg de Vries (KdV) equation. Finite-element simulations however show that the KdV is applicable only to post-buckled beams with strong pre-compression. For weak and moderate pre-stress, a dispersive front is present and it is the aim of the current paper to analyze sources of dispersion beyond periodicity given three support types: guided, pinned, and free. Bloch theorem and a transfer-matrix method are employed to obtain numerical dispersion relations and characteristic wave modes, which are used to analyze the effects of pre-stress, initial curvature, and the influence of support types. Additionally, a new method is proposed to obtain a semi-analytical dispersion equation for the acoustic branch. Powers of frequency and the propagation constant are explicitly expressed and their coefficients are based on stiffness and mass-matrix components obtained from finite elements. This allows a physical interpretation of the dispersion sources, based on which, equivalent mass–spring models of post-buckled beam are proposed. It is found that mass and stiffness coupling are significant dispersion sources. In the present paper, a reduced form of Bloch theorem is presented exploiting glide-reflection symmetries, reducing the size of the unit cell and allowing an easier representation and interpretation of results.     

Cavity formation in split ring resonators

We report that it is possible to obtain a cavity structure by the deformation of a unit cell of an split ring resonator (SRR) structure. We presented the Q-factor of the cavity resonance as 192 for an SRR-based single cavity. Subsequently, we brought two and three cavities together with an intercavity distance of two metamaterial unit cells and investigated the transmission spectrum of SRR-based interacting 2-cavity and 3-cavity systems. The splitting of eigenmodes due to the interaction between the localized electromagnetic cavity modes was observed. Eventually, in taking full advantage of the effective medium theory, we modeled SRR-based cavities as 1D Fabry–Perot reflectors (FPRs) with a subwavelength cavity at the center. Finally, we observed that at the cavity resonance, the effective group velocity was reduced by a factor of 67 for an SRR-based single cavity compared to the electromagnetic waves propagating in free space.     

A New Method for the Measurement of Thickness in Single Crystals

A new method for thickness determination of single-crystal thin samples at exact zone axis orientation, based on pattern recognition in convergent beam electron diffraction (CBED), is presented. The method is especially well suited to materials with a large unit cell in zone axis directions where the reciprocal lattice is uniformly dense with diffraction points. The new method is based on comparison of a measured CBED zone axis pattern with a set of calculated ones. Its accuracy was estimated to be around 10% in the 5–100 nm thickness range as checked for garnets at the [111] zone orientation.     

Ordering in binary FCC alloys

A new method of approximation for studying the order-disorder transition in binary alloys is presented. The formulation is in terms of face-centered cubic alloys, although the method can also be applied to other structures. The technique is essentially a generalization of the constant-coupling approximation. We have applied the principles of that method to derive the free energy of the alloy using a tetrahedral cluster of nearest neighbouring sites as the basic unit of the calculation. We only consider the case of nearest neighbour pair interactions, but show how the method can be generalized to include many body and second neighbour interactions. Numerical results are presented and comparison of these results is made with results of cluster variation calculations on the same system and with experimental results on the copper-gold alloy system.     

两种新的SiC高层多型体——417R和453R

本文根据倒易点阵原理,详细分析了碳化硅劳埃照相中各种SiC三方多型体斑点和SiC基本类型6H斑点间的相互配置关系。这种关系共总结出不外乎十二种,本文提出利用这种关系,以及两6H类型斑点(hOl)间未知三方多型体的斑点数目,来计算未知多型体类型层数的方法。利用这一方法,对在实验室条件下以升华法制备的若干碳化硅单晶体进行了分析,发现了两种同时与6H类型连生的新的碳化硅高层多型体417R和453R,其空间群为R3m(C_3v⁵),点阵参数以六方晶胞表示时为 417R:α_H=3.0806?,c=1050.7?,z=417; 453R:α_H=3.0806?,c=1141.4?,z=453。以三方晶胞描述时则为 417R:α_R=350.4?,α=30.4′,z=139; 453R:α_R=380.6?,α=27.8′,z=151。     

FDTD analysis of 2D triangular-lattice photonic crystals with arbitrary-shape inclusions based on unit cell transformation

A finite-difference time-domain method based on Yee’s orthogonal cell is utilized to calculate the band structures of 2D triangular-lattice-based photonic crystals through a simple modification to properly shifting the boundaries of the original unit cell. A strategy is proposed for transforming the triangular unit cell into an orthogonal one, which can be used to calculate the band structures of 2D PhCs with various shapes of inclusions, such as triangular, quadrangular, and hexagonal shapes, to overcome the shortage of plane-wave expansion method for circular one. The band structures of 2D triangular-lattice-based PhCs with hexagonal air-holes are calculated and discussed for different values of its radius and rotation angle. The obtained results provide an insight to manipulate the band structures of PhCs.     

一种由自由电子能带模型计算费米能级的方法

对面心立方（fcc)、体心立方（bcc)和六角密堆积（hcp)三种不同结构的晶体,在假设它们的原胞中包含8个价电子并将价电子近似为自由电子的情况下,采用“自由电子气理论”和“自由电子能带模型”,研究其根据费米球确定的费米能级EF与根据自由电子能带模型计算的平均键能Em。研究结果表明,由自由电子能带模型计算所得3种不同结构晶体（因而电子密度也不一样）的平均键能Em等于各自自由电子系统的费米能级EF。平均键能Em是我们在异质结带阶理论计算中建议的一种参考能级,研究结果在深化对平均键能Em物理实质认识的同时,提供了一种借助于自由电子能带模型计算自由电子系统费米能级EF的新方法。