Mode competition in acousto-optically Q-switched planar waveguide lasers

Multi-mode rate equations have been developed to investigate mode competition in high-power acousto-optically Q-switched planar waveguide lasers. The mode competition arises from coupling effects and temporal losses in the transform between guided modes and free-space propagation. Pulse-to-pulse instability and temporal beam distortions are enlarged by mode competition when the laser works in the multi-mode regime. The influence of parasitic oscillation is also discussed. A Nd:YAG planar waveguide laser has been established with a folded hybrid/unstable resonator. A maximum average power of 83 W with a beam propagation factor is obtained. The theoretical simulation agrees well with the experimental observation.     

Improved method for loss measurements in planar waveguides

A method employing an isosceles prism and a right-angle one is developed for loss measurement in planar waveguides. During the measuring process, the isosceles prism is fixed and the right-angle prism fixed on the waveguide slides by following the waveguide. Only by adjusting the gap thickness we can realize the loss measurement in planar waveguides. The method is demonstrated with an Ag/Na ion-exchanged waveguide fabricated on BK7 glass from AgNO₃ melt diluted with NaNO₃ (mass ratio 1:9), with the condition of 4 h and . The experimental results show that the method has the advantages on convenient operation, accurate results and no required end polishing.     

Development of the large increment method for elastic perfectly plastic analysis of plane frame structures under monotonic loading

The displacement-based finite element method dominates current practice for material nonlinear analysis of structures. However, there are several characteristics that may limit the effectiveness of this approach. In particular, for elastoplastic analysis, the displacement method relies upon a step-by-step incremental approach stemming from flow theory and also requires significant mesh refinement to resolve behavior in plastic zones. This leads to computational inefficiencies that, in turn, encourage the reconsideration of force-based approaches for elastoplastic problems.One of these force algorithms that has been recently developed is the large increment method. The main advantage of the flexibility-based large increment method (LIM) over the displacement method is that it separates the global equilibrium and compatibility equations from the local constitutive relations. Consequently, LIM can reach the solution in one large increment or in a few large steps, thus, avoiding the development of cumulative errors. This paper discusses the extension of the large increment methodology for the nonlinear analysis of plane frame structures controlled by an elastic, perfectly plastic material model. The discussion focuses on the power of LIM to handle these nonlinear problems, especially when plastic hinges form in the frame and ultimately as the structure approaches the collapse stage. Illustrative planar frame examples are presented and the results are compared with those obtained from a standard displacement method.     

Variation of fiber orientation in turbulent flow inside a planar contraction with different shapes

In this study, we have investigated the influence of shape of planar contractions on the orientation distribution of stiff fibers suspended in turbulent flow. To do this, we have employed a model for the orientational diffusion coefficient based on the data obtained by high-speed imaging of suspension flow at the centerline of a contraction with flat walls. This orientational diffusion coefficient depends only on the contraction ratio and turbulence intensity. Our measurements show that the turbulence intensity decays exponentially independent of the contraction angle. This implies that the turbulence variation in the contraction is independent of the shape, consistent with the results by the rapid distortion theory and the experimental results of axisymmetric contractions. In order to determine the orientation anisotropy, we have solved a Fokker–Planck type equation governing the orientation distribution of fibers in turbulent flow. Although the turbulence variation and the orientational diffusion are independent of the contraction shape, the results show that the variation of the orientation anisotropy is dependent on shape. This can be explained by the variation of the rotational Péclet number, Pe_r, inside the contractions. This quantity is a measure of the importance of the mean rate of the strain relative to the orientational diffusion. We have shown that when Pe_r < 10 turbulence can significantly influence the evolution of the orientation anisotropy. Since in contractions with identical inlet conditions the streamwise position where Pe_r = 10 depends on the shape, the orientation anisotropy is dependent on the variation of rate of strain in a given contraction. We demonstrate the shape effect by considering contraction with flat walls as well as three contractions with different mean rate of strain variation.     

On solving the forward kinematics of 3RPR planar parallel manipulator using hybrid metaheuristics

Hybrid metaheuristics have been applied with success in solving many real-world problems. This work introduces hybrid metaheuristics to the field of kinematics problem, in particular, for solving the forward kinematics of the 3RPR parallel manipulator. It implements a combination of genetic algorithms and simulated annealing into two popular hybrid metaheuristic techniques. They are combined as teamwork and relay collaborative hybrid metaheuristics and compared to the performance of genetic algorithms and simulated annealing alone. The results show that the meta-heuristic approaches give robust and high quality solutions. Genetic algorithms and teamwork collaborative metaheuristics showed better performance than simulated annealing and relay collaborative metaheuristics. The given metaheuristic methods obtain all the unique solutions and comparisons with algebraic methods show promising results.     

The planar jet-plate oscillator

The aeroacoustic noise generated by a high speed, planar gas jet impinging on a flat plate is investigated experimentally. The jet used in this study is typical of those commonly found in industrial applications such as in various coating control and heat transfer processes. Normal jet impingement on the plate is found to generate strong acoustic tones over a wide range of impingement distances and jet velocities. The characteristics of these tones, as a function of the jet velocity and impingement distance, are quantified. Phase and amplitude measurements of the pressure fluctuations on the impingement plate indicate that the acoustic tones are generated by an antisymmetric instability mode of the jet oscillation. The effect of plate inclination in both the transverse and span-wise directions, with respect to the incident jet, is also studied. The jet-plate tone is found to be much more sensitive to changes in the span-wise plate inclination than to changes in the transverse inclination, but in both cases, a complete suppression of the tone is found to be possible.     

平面图的k-重(2k+2)-染色

G=(V,E)表示一个顶点集为V,边集为E的有限简单无向图.若存在映射φ:V(G)→Zk(n)(Zk(n)是由{1,2,…,n}的所有k-元子集构成的集合),满足:(A) uv∈E(G),有φ(u)∩φ(u)=θ,则称φ是G的一个k-重n-顶点染色.本文证明了奇围长至少为5k-7(k=4)或5k-9(k=6)的平面图G...     

平面图线性色数的一个上界

如果图G的一个正常染色满足染任意两种颜色的顶点集合导出的子图是一些点不交的路的并,则称这个正常染色为图G的线性染色．图G的线性色数用lc（G）表示,是指G的所有线性染色中所用的最少颜色的个数．证明了：若G是一个最大度△（G）≠5,6的平面图,则lc（G）≤2△（G）．     

Chaotic motions for a perturbed nonlinear Schrödinger equation with the power-law nonlinearity in a nano optical fiber

Perturbed nonlinear Schrödinger (NLS) equation with the power-law nonlinearity in a nano optical fiber is studied with the help of its equivalent two-dimensional planar dynamic system and Hamiltonian. Via the bifurcation theory and qualitative theory, equilibrium points for the two-dimensional planar dynamic system are obtained. With the external perturbation taken into consideration, chaotic motions for the perturbed NLS equation with the power-law nonlinearity are derived based on the equilibrium points.     

Exact boundary controllability of partial nodal profile for network of strings

Based on the theory of exact boundary controllability of nodal profile for hyperbolic systems, the authors propose the concept of exact boundary controllability of partial nodal profile to expand the scope of applications. With the new concept, we can shorten the controllability time, save the number of controls, and increase the number of charged nodes with given nodal profiles. Furthermore, we introduce the concept of in-situ controlled node to deal with a new situation that one node can be charged and controlled simultaneously. The minimum number of boundary controls on the entire tree-like network is determined by using the concept of ‘degree of freedom of charged nodes’ introduced. And the concept of ‘control path’ is introduced to appropriately divide the network, so that we can determine the infimum of controllability time. General frameworks of constructive proof are given on a single interval, a star-like network, a chain-like network and a planar tree-like network for linear wave equation(s) with Dirichlet, Neumann, Robin and dissipative boundary conditions to establish a complete theory on the exact boundary controllability of partial nodal profile.