Spectral element modeling for extended Timoshenko beams

Periodic lattice structures such as the large space lattice structures and carbon nanotubes may take the extension-transverse shear-bending coupled vibrations, which can be well represented by the extended Timoshenko beam theory. In this paper, the spectrally formulated finite element model (simply, spectral element model) has been developed for extended Timoshenko beams and applied to some typical periodic lattice structures such as the armchair carbon nanotube, the periodic plane truss, and the periodic space lattice beam.     

A general method for constructing vector integrable lattice systems

A method for generating vector-value integrable analogies of integrable lattice systems or integrable differential-difference equations is presented. The basic ingredient of the method is to insert permutation matrices. We formulate the zero-curvature representations and Hamiltonian structures of the resulting vector lattice systems. The effectiveness of the method is illustrated using some examples such as the Volterra lattice, the Belov–Chaltikian lattice, the Ablowitz–Ladik lattice and the Heisenberg ferromagnet lattice.     

A lattice Boltzmann method for nonlinear disturbances around an arbitrary base flow

In this paper we address the problem of the time evolution of a perturbation around a steady base flow with the use of the lattice Boltzmann method (LBM). This approach, named base flow lattice Boltzmann method, is of great interest in particular for aeroacoustic fields where the acoustic perturbation, on the one hand, is almost exclusively influenced by the large scale average structures of the underlying flow, and on the other hand, has a low effect on the large structures. The method is implemented for weakly compressible flows and the results of the base flow lattice Boltzmann are compared with the standard single relaxation time LBM. The boundary conditions for the base flow lattice Boltzmann method are discussed, as well as the implementation of outflow conditions for acoustic waves.     

Compass-anisotropy-modulated helical states and skyrmion crystals in chiral magnets

The compass-type anisotropy appears naturally in chiral magnets with strong spin-orbit coupling. In this work, we investigate the critical roles of compass anisotropy in modulating various spin textures of chiral magnets, by Monte Carlo simulations. The simulated results reveal a gradual helical reorientation and varying symmetry of skyrmion crystal structures as a function of compass anisotropy. Furthermore, an extended continuum spin model with the lattice discretization anisotropy is proposed to interpret the dependences of helical and skyrmion crystal structures on the compass anisotropy. It is demonstrated that specific helical propagating directions are favored by the high-order lattice anisotropy arising from spin interactions in discretized lattice. Besides that, some threshold values for the helical structures are identified by analytical approach.     

Fabrication of large-area 3D photonic crystals using a holographic optical element

A holographic technique for fabricating 3D photonic crystal is presented. The key element in the fabrication system is a holographic optical element (HOE) consisting of three gratings. Used in combination with a mask, the HOE can generate four beams under single illuminating beam, and 3D lattice structures can be formed by the interference of the four beams. Holographic approach is used to make HOE, so large area lattice structures can be fabricated. Numerical simulations indicate that beam intensity ratio of central beam to outer beam is one of the factors that affects the structures fabricated in photoresist, and high diffraction efficiency of the gratings in HOE is favorable when using cw laser with relatively low power as light source. Experimental results show clear 3D lattice structures fabricated using the HOE, verifying the effectiveness of the technique.     

Large forbidden angles for a two-dimensional photonic crystal of connected-honeycomb lattice

The off-plane band structures of a two-dimensional photonic crystals of connected-honeycomb lattice are calculated by the plane-wave expansion method. To investigate how the band gaps vary with the off-plane angle, an effective refractive-index model is employed to work out the corresponding angular gap map. We find that the connected-honeycomb lattice can provide forbidden angles taking up as much as 58.6% of the solid angle. The result will be helpful in the design of photonics devices incorporating two-dimensional photonic crystal structures.     

Rapid evaluation of oscillating lattice sums

We have generalized a method for the rapid evaluation of oscillating lattice sums for layered geometries, based on the Ewald's summation technique. Different types of long range interactions as well as different lattice symmetries can be considered, in particular modulated magnetic structures, periodic domain patterns, or periodic lattice distortions. As examples the demagnetizing energies for different thin films systems and magnetic excitations in a single atomic layer are calculated.     

Solitonic eigenstates of the chaotic Bose–Hubbard Hamiltonian

We study the evolving energy spectrum of interacting ultra-cold atoms in an optical lattice as a function of an external parameter, the tilt of the lattice. In a regime where the quantum mechanical model, the Bose–Hubbard Hamiltonian, shows predominantly chaotic behavior, we identify regular structures in the parametric level evolution and characterize the eigenstates associated with these structures. The mechanism generating these structures is found to be different from Stark localization or energetic isolation and is induced by an interplay of driving and interaction.     

Fe原子薄片的磁性:第一性原理计算

使用基于密度泛函理论的第一原理方法,对Fe单层原子薄片在二维正方、二维六角晶格下的电子结构和磁学性质进行了系统研究.结果表明,二维正方、二维六角以及bcc晶格在平衡晶格常数下都具有磁性,其单位原子磁矩分别为2.65,2.54和2.20μ_В.对二维晶格在被压缩和被拉伸时的磁性计算表明,随着晶格的被拉伸,当最近邻原子间距大于4.40时,铁原子间的键合被拉断,体系单位原子的磁矩趋于孤立Fe原子的磁矩4μ_В;随着原子键长的减小,各体系的磁矩 关键词： Fe 原子薄片 磁性 从头计算     

Physical content of preparation-question structures and Brouwer-Zadeh lattices

We give a criterion to compare the physical content of different mathematical structures derived from a preparation-question structure. Then this criterion is used in order to compare the physical content of the (Jauch-Piron's) property lattice with the physical content of the poset of testable properties. We prove that for complete preparation-question structures these two structures carry the same physical content; moreover the set of testable properties has the algebraic structure of the Brouwer-Zadeh lattice. For more general preparation-question structures the physical content of the poset of testable property can be larger than that of the property lattice. Physically relevant examples of the possible cases are given.     

格芯夹层结构散热性能的数值计算评估

为评估格芯夹层结构的传热性能以及代替传统的板式肋片结构应用于汽车散热系统中的可能性,文章对几种典型的格芯夹层结构（如kagome lattice,tetrahedral lattice和pyramidal lattice）和板式肋片（corrugated plate）结构实施了一系列的三维数值计算评估.通过对比相同Reynolds数下的传热系数和相同泵功率下的局部Nusselt数来评估各组结构的传热性能.结果显示,相同Reynolds数条件下,各组格芯夹层结构的传热系数较板式肋片结构均有提高,同时摩擦阻力也大幅度增大.在相同泵功率条件下,由于板式肋片结构所受形阻基本可以忽略,因此在较低泵功率范围内（< 1 500 W）,板式肋片的局部Nusselt数最大.随着泵功率的增长,当泵功率提高到3 000 W,tetrahedral的Nusselt数与板式肋片持平并进一步增大,显示出了格芯夹层结构的应用潜力.高传热性能而低摩擦阻力的格芯夹层结构完全有潜力代替传统的板式肋片结构应用于新型高效紧凑的散热系统中.      

Optimized interactions for targeted self-assembly: application to a honeycomb lattice

We devise an inverse statistical-mechanical methodology to find optimized interaction potentials that lead spontaneously to a target many-particle configuration. Target structures can possess varying degrees of disorder, thus extending the traditional idea of self-assembly to incorporate both amorphous and crystalline structures as well as quasicrystals. For illustration purposes, our computational technique is applied to yield an optimized isotropic (nondirectional) pair potential that spontaneously yields the three-coordinated honeycomb lattice as the ground state structure in two dimensions. This target choice is motivated by its three-dimensional analog, the diamond lattice, which is known to possess desirable photonic band gap properties.     

Three-dimensional structure of low-density nuclear matter

We numerically explore the pasta structures and properties of low-density nuclear matter without any assumption on the geometry. We observe conventional pasta structures, while a mixture of the pasta structures appears as a metastable state at some transient densities. We also discuss the lattice structure of droplets.     

Topology of the space of periodic ground states in the antiferromagnetic Ising and Potts models in selected spatial structures

Topology of the space of periodic ground states in the antiferromagnetic Ising and Potts (3-state) models is analysed in selected spatial structures. The states are treated as graph nodes, connected by one-spin-flip transitions. The spatial structures are the triangular lattice, the Archimedean (3,¹²²) lattice and the cubic Laves C15 lattice with the periodic boundary conditions. In most cases the ground states are isolated nodes, but for selected systems we obtain connected graphs. The latter means that the magnetisation can vary in time with zero energy cost. The ground states are classified according to their degree and type of neighbours.     

Optimization of Binary Hologram Degraded by Periodic Lattice Structure of Liquid-Crystal Device Panel in Real Optical Security Systems

A numerically generated encryption pattern in practical optical security systems is processed through real display devices such as electronically addressed spatial liquid-crystal devices (LCDs). The pattern to be encrypted must be therefore congenial with electronic interfaces. In usual fact, the quality of a decrypted image in a practical system is greatly degraded due to the mismatch between the desired encryption pattern and the generated pattern without consideration of the device structures, such as lattice structures of LCDs. We take into account lattice structures for the displays of encryption and key patterns in real optical security systems and apply a simulated-annealing like method for the optimization of an encrypted binary hologram. We successfully demonstrate the decryption of holograms by this method.     

通信波段硅基气孔光子晶体的带隙特性及其物理模型研究

用平面波展开法对硅背景下的通信波段不同晶格类型和气孔形状光子晶体的能带结构进行数值计算与分析,提出了相应的物理模型.结果表明:利用光子受限效应和晶格对称性效应可以有效地调控光子带隙.随光子晶体填充率的增加,其约束光子的能力增强,光子带隙在一定范围内展宽且其中心频率蓝移;带隙随晶格对称性增加而变宽.对基元形状和旋转角度的研究发现,光子带隙随基元旋转角度变化具有周期性和对称性,表现出各向异性,由此优化出对应的不同晶格的最佳谐振腔型结构.     

Design of Two 8-Channel Optical Demultiplexers Using 2D Photonic Crystal Homogeneous Ring Resonators

ABSTRACT

Ring resonators have always been referred to as a highly flexible structure for designing optical devices. In this paper, we have designed and evaluated two 8-channel optical demultiplexers using photonic crystal ring resonators. The purpose of this study is to investigate the flexibility of this type of resonator for designing and manufacturing optical devices based on photonic crystals. To the extent that we have investigated the literature, there is no report so far on such a study. For this purpose, two structures with the same structural parameters, but only with a difference in the type of lattice constant (square or triangular) are used. Both structures have a common photonic band gap within a proper range for telecommunication applications used in wavelength-division multiplexing (WDM) systems. Both designed structures have an average crosstalk of ?26 dB. For the demultiplexer structure with a square lattice constant, the quality factor and the transmission coefficient are 3,046 and 93.7% respectively, and its channel spacing is 1.97 nm. For the structure with a triangular lattice constant, the quality factor and the transmission coefficient are 1577.7 and 94.5%, respectively and its channel spacing is equal to 4 nm. To obtain the photonic band gap of the structures, the plane wave expansion (PWE) method is used and the output spectrum of the structures is obtained using the finite-difference time-domain (FDTD) method. The good results obtained in this study is through designing and simulating optical demultiplexer structures only by creating a change in the type of lattice constant used. This undoubtedly justifies the high flexibility of ring resonators, when used in the design of optical devices, as well as their suitability for the use in WDM systems     

A hierarchy of Hamiltonian lattice equations associated with the relativistic Toda type system

By considering a discrete iso-spectral problem, a hierarchy of bi-Hamiltonian relativistic Toda type lattice equations are revisited. After introducing a semi-direct sum Lie algebras of four by four matrices, integrable coupling system associated with the relativistic Toda type lattice are derived. It is shown that the resulting lattice soliton hierarchy possesses Hamiltonian structures and infinitely many common commuting symmetries as well infinitely many conserved functions. The Liouville integrability of the resulting system is then demonstrated.     

A lattice Maxwell system with discrete space–time symmetry and local energy–momentum conservation

A lattice Maxwell system is developed with gauge-symmetry, symplectic structure and discrete space–time symmetry. Noether's theorem for Lie group symmetries is generalized to discrete group symmetries for the lattice Maxwell system. As a result, the lattice Maxwell system is shown to admit a discrete local energy–momentum conservation law corresponding to the discrete space–time symmetry. A lattice model that respects all local conservation laws and geometric structures is as good as and probably more preferable than standard models on continuous space–time. It can also be viewed as an effective algorithm for the governing differential equations on continuous space–time.     

Ground state structures of a lattice model: honeycomb and tetrahedral lattices

The ground state structures of a lattice model with nearest-neighbor and next-nearest-neighbor interactions were examined by the method of “partitioning” the hamiltonian. This model is Widom's lattice model of microemulsions. Previous analysis had examined only cubic lattices, however the analysis is more general as this paper illustrates.