Growth, optical and thermal studies on organic nonlinear optical crystal: 2-Furoic acid

2-Furoic acid (2FA), an organic third order nonlinear optical single crystal, has been synthesized and grown successfully by slow solvent evaporation technique. The space group and lattice parameters of the grown crystals were obtained by single crystal X-ray diffraction analysis. The presence of the functional groups was confirmed by Fourier Transform Infrared (FTIR) spectroscopy. Optical absorption studies reveal low absorption in the UV and visible regions and the UV cut-off wavelength is found to be at 240 nm. The thermal stability of the material examined by TGA analysis, reveals that the material is thermally stable up to 130 °C. The third order nonlinear optical parameters (nonlinear refractive index, nonlinear absorption coefficient and real and imaginary parts of the third order nonlinear optical susceptibility) were derived by Z-scan technique. This reveals that the crystal has a negative refractive index, which indicates the defocusing nature of the material.     

基于ANSYS提取单相单向换能器耦合模参数

基于有限元理论,给出了基于ANSYS提取单相单向换能器（Single Phase Unidirectional Transducers,SPUDT）耦合模参数的方法。首先,结合声表面波在压电介质中的传播原理,给出了压电有限元分析方程和对应的ANSYS分析步骤。然后针对SPUDT结构,给出了周期性近似分析的理论模型,利用耦合场分析对其进行模态分析和谐响应分析,最后结合两者的结果来计算SPUDT的耦合模参数。本文给出基底材料为压电晶体128°YX-LiNbO₃和YZ-LiNbO₃,电极材料为铝的三种不同SPUDT的计算结果,理论结果与Hashimoto和Hartmann文献报道的结果相吻合,并且和实验测试的结果基本一致。从而给出了提取SPUDT耦合模参数的一种通用、有效的方法。     

Application of near infrared spectroscopy and multivariate data analysis for the evaluation of glue lines of untreated and copper azole treated laminated timber before and after ageing

The necessity for inspection and assessment of glued laminated timber structures in service has raised interest in the evaluation of the glue lines. Glue line spectra were analysed and are discussed in detail with respect to spectral contributions from the adhesive, the hardener, the wood lamella below the adhesive, the curing temperature as well as ageing-related spectral changes. The combination of near infrared (NIR) spectroscopy and principal component analysis (PCA) allowed distinguishing between aged and non-aged samples and different copper azole preservative treatment levels of phenol-resorcinol-formaldehyde (PRF) glue lines. NIR-based partial least squares (PLS) regression modelling was performed for the glue line shear strength and for the curing temperature. These findings show that NIR spectroscopy is a fast and useful technique to evaluate the degradation on the PRF glue lines of untreated and copper azole treated laminated timber.     

Nonuniqueness of the traveling wave speed for harmonic heat flow

Given any wave speed c∈R, we construct a traveling wave solution of ut=Δu+²|∇u|u in an infinitely long cylinder, which connects two locally stable and axially symmetric steady states at x₃=±∞. Here u is a director field with values in S²⊂R³: |u|=1. The traveling wave has a singular point on the cylinder axis. In view of the bistable character of the potential, the result is surprising, and it is intimately related to the nonuniqueness of the harmonic map flow itself. We show that for only one wave speed the traveling wave behaves locally, near its singular point, as a symmetric harmonic map.     

Existence of non-trivial harmonic functions on Cartan–Hadamard manifolds of unbounded curvature

The Liouville property of a complete Riemannian manifold M (i.e., the question whether there exist non-trivial bounded harmonic functions on M) attracted a lot of attention. For Cartan–Hadamard manifolds the role of lower curvature bounds is still an open problem. We discuss examples of Cartan–Hadamard manifolds of unbounded curvature where the limiting angle of Brownian motion degenerates to a single point on the sphere at infinity, but where nevertheless the space of bounded harmonic functions is as rich as in the non-degenerate case. To see the full boundary the point at infinity has to be blown up in a non-trivial way. Such examples indicate that the situation concerning the famous conjecture of Greene and Wu about existence of non-trivial bounded harmonic functions on Cartan–Hadamard manifolds is much more complicated than one might have expected.      

Multiplier family of harmonic univalent functions

The aim of this paper is to study a multiplier family of harmonic univalent functions using the sequences {c_n} and {d_n} of positive real numbers. By specializing {c_n} and {d_n}, the generalized Bernardi–Libera–Livingston integral operator is modified for such functions and the closure of the multiplier family under the modified integral operator is determined. Also, convolution products, closure properties, distortion theorems, convex combinations and neighborhoods for such functions are given.     

Some methods for determination of the terahertz laser signal and the dynamics of its frequencies

The possibility of restoration of a terahertz signal transmitted through a substance and represented as a set of integral measurements is studied. Being related with substance identification, such problems are topical. In the study, two algorithms are proposed for spline-based signal restoration. Te algorithms enable one to reduce the presence of spurious frequencies. It is important that a spline with a number of nodes approximately equal to the number of measurements does not guarantee a high quality of signal restoration. The proposed algorithm, which involves the choice of the optimal number of measurements, is free from this drawback. Both a model signal and the real response of a medium are considered.     

Exact analysis of a two-workstation one-buffer flow line with parallel unreliable machines

This paper examines a model of a serial flow line with two workstations and an intermediate buffer. Each workstation consists of multiple unreliable parallel machines which are not necessarily identical, viz., the processing times, failure times and repair times of the parallel machines at each workstation are assumed to be exponentially distributed with non-identical mean rates. The system under consideration is solved via exact Markovian analysis. More specifically, a recursive algorithm that generates the transition matrix for any value of the intermediate buffer capacity is developed and all possible transition equations are derived and solved analytically. Once the transition equations are solved the performance measures of the model under consideration can be easily evaluated. This model may be used as a decomposition block for solving larger flow lines with parallel unreliable machines at each workstation.     

A collocation method of lines for two‐sided space‐fractional advection‐diffusion equations with variable coefficients

We present the method of lines (MOL), which is based on the spectral collocation method, to solve space‐fractional advection‐diffusion equations (SFADEs) on a finite domain with variable coefficients. We focus on the cases in which the SFADEs consist of both left‐ and right‐sided fractional derivatives. To do so, we begin by introducing a new set of basis functions with some interesting features. The MOL, together with the spectral collocation method based on the new basis functions, are successfully applied to the SFADEs. Finally, four numerical examples, including benchmark problems and a problem with discontinuous advection and diffusion coefficients, are provided to illustrate the efficiency and exponentially accuracy of the proposed method.     

Collisional effects in the tokamap

Plasmas confined in tokamaks with non-symmetric perturbations are surrounded by a chaotic layer of magnetic field lines that guide charged particles to the tokamak wall. We use an analytical two-dimensional symplectic mapping to study the resulting fractal patterns of field line escape. However, particles may experience several collisions before escaping toward the tokamaks wall. We add a random collisional term to the field line mapping to investigate how the particle collisions modify their escape patterns.