Discrete solitons in nonlinear Schrödinger lattices with a power-law nonlinearity

We study the discrete nonlinear Schrödinger lattice model with the onsite nonlinearity of the general form, |u|^2σu. We systematically verify the conditions for the existence and stability of discrete solitons in the one-dimensional version of the model predicted by means of the variational approximation (VA), and demonstrate the following: monostability of fundamental solitons (FSs) in the case of the weak nonlinearity, 2σ+1<3.68; bistability, in a finite range of values of the soliton’s power, for 3.68<2σ+1<5; and the presence of a threshold (minimum norm of the FS), for 2σ+1≥5. We also perform systematic numerical simulations to study higher-order solitons in the same general model, i.e., bound states of the FSs. While all in-phase bound states are unstable, stability regions are identified for antisymmetric double solitons and their triple counterparts. These numerical findings are supplemented by an analytical treatment of the stability problem, which allows quantitively accurate predictions for the stability features of such multipulses. When these waveforms are found to be unstable, we show, by means of direct simulations, that they self-trap into a persistent lattice breather, or relax into a stable FS, or sometimes decay completely.     

Acoustic topology optimization of sound power using mapped acoustic radiation modes

An efficient approach for acoustic topology optimization to minimize the radiated sound power from a vibrating structure is described. The topology optimization is implemented by modifying the local stiffness at discrete locations on the surface of the structure. The radiated sound power level from the structure is directly chosen as the objective function to be minimized. A sensitivity analysis is then implemented to further optimize the layout of the locations of the modified local stiffness. To speed up the computational process, the radiated sound power is computed based on mapped acoustic radiation modes. To demonstrate the acoustic topology optimization using mapped acoustic radiation modes, the radiated sound power of a compressor housing is examined. Based on results from the numerical model, the local stiffness of a compressor housing was experimentally modified. Good agreement in sound power reduction obtained both numerically and experimentally was observed for the overall trend for the sound power levels as a function of one-third octave frequency bands.     

Coordination-Driven Selective Formation of D2 Symmetric Octanuclear Organometallic Cages

The coordination-driven self-assembly of organometallic half-sandwich iridium(III)- and rhodium(III)-based building blocks with asymmetric ambidentate pyridyl-carboxylate ligands is described. Despite the potential for obtaining a statistical mixture of multiple products, D₂ symmetric octanuclear cages were formed selectively by taking advantage of the electronic effects emanating from the two types of chelating sites – (O,O’) and (N,N’) – on the tetranuclear building blocks. The metal sources and the lengths of bridging ligands influence the selectivity of the self-assembly. Experimental observations, supported by computational studies, suggest that the D₂ symmetric cages are the thermodynamically favored products. Overall, the results underline the importance of electronic effects on the selectivity of coordination-driven self-assembly, and demonstrate that asymmetric ambidentate ligands can be used to control the design of discrete supramolecular coordination complexes.     

Two 2D Metal‐organic Networks Based on a Rigid Imidazolate/Sulfonate Functionalized Ligand – Effect of the Coordination Modes of the Ligand on Crystal Structures

A rigid imidazolate/sulfonate functionalized ligand, 6‐(4‐sulfonatopheny)imidazo[4, 5‐f]isoindole‐5, 7‐dione (SPID) was designed and used for assembling reactions with Mn²⁺ and Cu²⁺ ions. Two 2D frameworks compounds, [Mn(H_‐1SPID)₂(DMAC)₂] ( 1 ) and [Cu(H_‐2SPID)(H₂O)₂] · 0.7DMAC · 0.3H₂O ( 2 ) (DMAC = N,N‐dimethylacetamide) were obtained. Single crystal X‐ray analyses show that 1 has a 2D (4, 4)‐net based on 4‐connected Mn²⁺ nodes and μ₂‐coordinated H_‐1SPID spacers, whereas compound 2 has a 2D (6, 3)‐net built of 3‐connected Cu²⁺ nodes and μ₃‐coordinated H_‐2SPID spacers. Additionally, the thermal behavior of 1 and 2 is presented.     

Atom waveguide and 1D optical lattice using a two-color evanescent light field around an optical micro/nano-fiber

We propose a two-color scheme of atom waveguides and one-dimensional （1D） optical lattices using evanescent wave fields of different transverse modes around an optical micro/nano-fiber. The atom guide potential can be produced when the optical fiber carries a red-detuned light with TE01 mode and a blue-detuned light with HEll mode, and the 1D optical lattice potential can be produced when the red-detuned light is transformed to the superposition of the TE01 mode and HE11 mode. The two trapping potentials can be transformed to each other for accurately controlling mode transformation for the red-detuned light. This might provide a new approach to realize flexible transition between the guiding and trapping states of atoms.     

三维轴对称折叠腔CO2激光器的位相锁定

在一新型三维轴对称腔CO2激光器的基础上提出了一种对此激光器位相锁定的方法。通过在输出镜后放置一具有反射和整形作用的凹凸镜，让作为输出注入光束的谐振腔优先起振。此腔输出的光束到达凹凸镜时被其反射。利用重新定义光斑半径的方法，证明此光束能够覆盖其他放电管输出的光束，根据几何光学，此光束能反射进入各个放电管。然后利用光子简并度的概念证明了反射光束能够控制腔内的本征模式，并且数值分析了注入锁定后腔内模式匹配。在反射注入锁定的情况下，给出了数值计算的光强输出及其模拟，结果证明经位相锁定后，激光器输出光束的质量有了很大的提高。     

Propagation of light in(2+1)-dimensional nonlinear optical media with spatially inhomogeneous nonlinearities

The(2 1)-dimensional nonlinear Schr(o)dinger(NLS)equation with spatially inhomogeneous nonlinearities is investigated,which describes propagation of light in(2 1)-dimensional nonlinear optical media with inhomogeneous nonlinearities.New types of optical modes and nonlinear effects in optical media are presented numerically.The results reveal that the regular split of beam can be obtained in (2 1)-dimensional nonlinear optical media with inhomogeneous nonlinearities,by adjusting the guiding parameter.Furthermore,the stability of beam regular split is discussed numerically,and the results reveal that the beam regular split is stable to the finite initial perturbations.     

Study on Planar Whispering Gallery Dielectric Resonators. I. General Properties

Several basic properties of homogeneous planar Whispering Gallery dielectric resonators are investigated through a general approach. In particular the values for the minimum and maximum allowed radius, defined by irradiation and dielectric losses, respectively, are obtained in terms of the complex dielectric constant of the involved media. The same approach is employed in the analysis of the limit allowed frequencies of a fixed family of mode, leading to the definition of the ideal frequency band. The role of the transverse mode is then discussed, and the effective frequency band is introduced and determined both in simple disc and circular ring resonators. The extension of the effective band is limited at least by a factor 3, in terms of decades, in comparison to the extension of the ideal one; this limitation, due to the presence of transverse modes, can be overcome using suitable designed nonhomogeneous resonators, as discussed in a following companion paper.     

Entanglement of Resonantly Coupled Field Modes in Cavities with Vibrating Boundaries

We study time dependence of various measures of entanglement (covariance entanglement coefficient, purity entanglement coefficient, normalized distance coefficient, entropy coefficients) between resonantly coupled modes of the electromagnetic field in ideal cavities with oscillating boundaries. Two types of cavities are considered — a three-dimensional cavity possessing eigenfrequencies ₃ = 3₁, whose wall oscillates at the frequency _w = 2₁, and a one-dimensional (Fabry–Perot) cavity with an equidistant spectrum _n = n₁ where the distance between perfect mirrors oscillates at the frequencies ₁ and 2₁. The behavior of entanglement measures in these cases turns out to be completely different, although all three coefficients demonstrate qualitatively similar time dependences in each case (except some specific situations where the covariance entanglement coefficient based on traces of covariance submatrices seems to be essentially more sensitive to entanglement than other measures, which are based on determinants of covariance submatrices). Different initial states of the field, namely, vacuum, squeezed vacuum, thermal, Fock, and even/odd coherent states, are considered.     

Algebraic domain decomposition solver for linear elasticity

We generalize the overlapping Schwarz domain decomposition method to problems of linear elasticity. The convergence rate independent of the mesh size, coarse-space size, Korn's constant and essential boundary conditions is proved here. Abstract convergence bounds developed here can be used for an analysis of the method applied to singular perturbations of other elliptic problems.