Wavelet multiresolution interpolation Galerkin method for nonlinear boundary value problems with localized steep gradients

The wavelet multiresolution interpolation for continuous functions defined on a finite interval is developed in this study by using a simple alternative of transformation matrix. The wavelet multiresolution interpolation Galerkin method that applies this interpolation to represent the unknown function and nonlinear terms independently is proposed to solve the boundary value problems with the mixed Dirichlet-Robin boundary conditions and various nonlinearities, including transcendental ones, in which the discretization process is as simple as that in solving linear problems, and only common two-term connection coefficients are needed. All matrices are independent of unknown node values and lead to high efficiency in the calculation of the residual and Jacobian matrices needed in Newton’s method, which does not require numerical integration in the resulting nonlinear discrete system. The validity of the proposed method is examined through several nonlinear problems with interior or boundary layers. The results demonstrate that the proposed wavelet method shows excellent accuracy and stability against nonuniform grids, and high resolution of localized steep gradients can be achieved by using local refined multiresolution grids. In addition, Newton’s method converges rapidly in solving the nonlinear discrete system created by the proposed wavelet method, including the initial guess far from real solutions.

     

Properties of polymer blends and triblock copolymers obtained by neutron scattering

Static and dynamic scattering properties of polymer blends and block copolymers are examined within the random phase approximation (RPA). A self-consistent theoretical scheme for a simultaneous analysis of elastic and quasielastic scattering data is presented. The case of a triblock copolymer made of an ordinary central block and two deuterated lateral blocks in a matrix of deuterated homopolymers is considered in detail. The theoretical predictions of the RPA are compared with the experimental data obtained by elastic neutron scattering experiments using mixtures of deuterated poly(dimethylsiloxane) homopolymers and copolymers made of three blocks of approximately equal sizes. The lateral blocks are deuterated poly(dimethylsiloxane) and the central one is an ordinary poly(dimethylsiloxane). A good agreement is found in the whole range of wavevectors covered by the experiments. An extension of the RPA to the analysis of the dynamical scattering data for the same systems is put forward. It is shown how the time relaxations of the bare response functions obtained from the single chain dynamics are used to extract the intermediate scattering function characterizing the system of interacting chains. © 1996 John Wiley & Sons, Inc.     

基于单通道反射型电光调制器实现不同路光同时调制的方法

提出了一种利用单通道反射型聚合物电光调制器同时调制不同路光的方法。衰减全反射结构的电光调制器,其每一个衰减全反射(ATR)峰的位置分别对应于一个导波共振模式。实验系统中利用衰减全反射导膜峰作为调制通道,使其每一路光路的入射角分别对应于不同导波共振模式的工作角,就可以实现利用单通道的电光调制器同时调制不同路光。提出了三种实现两路光同时调制的模式,并给出了三种模式的调制结果。结果表明,作为调制通道的导模阶数越低,调制效率越高。在832 nm光波波长下,采用最低阶导模进行调制时可以获得42.9%的调制效率。     

Nonlinear edge modes in a honeycomb electrical lattice near the Dirac points

We examine - both experimentally and numerically - a two-dimensional nonlinear driven electrical lattice with honeycomb structure. Drives are considered over a range of frequencies both outside (below and above) and inside the band of linear modes. We identify a number of discrete breathers both existing in the bulk and also (predominantly) ones arising at the domain boundaries, localized either along the arm-chair or along the zig-zag edges. The types of edge-localized breathers observed and computed emerge in distinct frequency bands near the Dirac-point frequency of the dispersion surface while driving the lattice subharmonically (in a spatially homogeneous manner). These observations/computations can represent a starting point towards the exploration of the interplay of nonlinearity and topology in an experimentally tractable system such as the honeycomb electrical lattice.     

Lossy mode resonance-based uniform core tapered fiber optic sensor for sensitivity enhancement

A lossy mode resonance (LMR)-supported fiber optic sensor in which a uniform fiber core is placed among two identical tapered regions, is investigated numerically. Indium tin oxide (ITO) and aluminum-doped zinc oxide (AZO) are considered as LMR active materials used to excite several lossy modes and gold and silver are used as surface plasmon resonance (SPR) active materials. In this probe design, a central uniform core coated with ITO/AZO is the active sensing region, whereas tapered regions are meant for bringing the incident angle close to the critical angle. The sensitivity of the present fiber optic bio-sensor is evaluated for first two LMRs utilizing both ITO and AZO separately, along with its variation with the taper ratio (TR). For ITO, the maximum sensitivity values are observed to be 18.425 μm RIU⁻¹ (refractive index unit) and 0.825 μm RIU⁻¹, corresponding to the first and second LMRs, respectively, at a TR of 1.6 and for AZO, equivalent values are 0.79 μm RIU⁻¹ and 0.35 μm RIU⁻¹, respectively, at a TR of 2.0. The results illustrate that the first LMR is more sensitive than the second LMR and the ITO-coated probe possesses greater sensitivity than the AZO-coated probe for both LMRs. Similarly, for the fiber optic SPR sensor, the maximum value of sensitivity is 5.6425 μm RIU⁻¹, in the case of gold and 5.0615 μm RIU⁻¹ in the case of silver, at a TR of 1.6. Hence, the result shows that the sensor with the present fiber optic probe design has around a 3-fold enhancement in sensitivity compared with conventional SPR sensors. This study will have applications in many sensing schemes where the requirement of large sensitivity is vital.     

Non-Abelian gauge potentials driven localization transition in quasiperiodic optical lattices

Derived from quantum waves immersed in an Abelian gauge potential, the quasiperiodic Aubry-André-Harper (AAH) model is a simple yet powerful Hamiltonian to study the Anderson localization of ultracold atoms. Here, we investigate the localization properties of ultracold atoms in quasiperiodic optical lattices subject to a non-Abelian gauge potential, which are depicted by non-Abelian AAH models. We identify that the non-Abelian AAH models can bear the self-duality. We analyze the localization of such non-Abelian self-dual optical lattices, revealing a rich phase diagram driven by the non-Abelian gauge potential involved: a transition from a pure delocalization phase, then to coexistence phases, and finally to a pure localization phase. This is in stark contrast to the Abelian counterpart that does not support the coexistence phases. Our results establish the connection between localization and gauge symmetry, and thus comprise a new insight on the fundamental aspects of localization in quasiperiodic systems, from the perspective of non-Abelian gauge potential.     

Splitting of coupled bright solitons in two-component Bose-Einstein condensates under parametric perturbation

We analyze the dynamics of bright-bright solitons in two-component Bose-Einstein condensates (BECs) subject to parametric perturbations using the variational approach and direct numerical simulations. The system is described by a vector nonlinear Schrödinger equation (NLSE) appropriate to coupled multi-component BECs. A periodic variation of the inter-component coupling coefficient is used to explore nonlinear resonances and splitting of the coupled bright solitons. The analytical predictions are confirmed by direct numerical simulations of the vector NLSE.     

Strongly localized states in a single carbon nanotube with polymer molecules

A single-walled carbon nanotube (SWCNT) with conjugated polymer molecules is analyzed via optical spectroscopy. The presence of strongly localized excitonic states in the SWCNT is confirmed using time-integrated photoluminescence (PL). The PL spectrum exhibits extremely narrow width (~0.8 meV) which is attributed to the strong confinement of the states by polymer molecules. In addition, I observed that the excited states are gradually filled as a function of the excitation power, which supports the localized excitonic behavior. Only the ground excitonic state is observed at low excitation powers, but three additional PL peaks appear as the excitation power is increased. Especially, the power-dependent PL spectrum shows a blueshift and increased width, which can be elucidated in terms of quantum confined stark effect and the screening of induced electric fields. Overall, I demonstrate that the presence of polymer molecules induces several localized states in a single SWCNT.     

离轴抽运对Nd:YAG激光器振荡模式影响的研究

以激光二极管端面抽运固体激光器为研究对象,通过实验研究了离轴抽运条件下,离轴量的大小对Nd:YAG激光器的振荡光阈值、振荡模式、光束质量以及激光器的斜效率的影响,分析了在同一抽运位置改变LD电流时输出光位置及模式的变化情况.实验结果表明,当抽运光离轴量增大时,斜效率增大,但输出光依次出现从低阶模到高阶模的变化,激光器的振荡阈值升高,光束质量变差;在同一抽运位置增大LD电流时,输出光从高阶模向低阶模转化,光斑中心向此时的抽运中心轴靠拢.