Laminar boundary layer between two planes perpendicular to each other

In this paper, we obtain a third-order approximate solution for the laminar boundary layer between two planes perpendicular to each other.In boundary layer equations, the viscous and the inertial terms have the same quantity step. In this paper, at first, supposing that the inertial terms are bigger than the viscous terms, we solve the boundary layer equations, and then we suppose that the viscous terms are bigger than the inertial terms. At last, we take the mean value as the valid solution of the boundary layer equations.The first- and the second-order approximate solutions obtained in this paper coincide with the results in ref. [1], while the third-order solution obtained in this paper is better than that in ref. [1].     

一类二阶非线性常微分方程非线性边界条件的两点边值问题

本文讨论了一类二阶非线性常微分方程之具有线性边界条件的和具有非线性边界条件的两点边值问题解的存在性.     

Design and synthesis of interpenetrating polymer networks for second-order nonlinear optics

There has been a tremendous recent interest in the development of second-order nonlinear optical (NLO) polymeric materials for photonic applications. However, a major drawback of second-order NLO polymers that prevents them from being used in device applications is the instability of their electric field induced dipolar alignment. The randomization of the dipole orientation leads to the decay of second-order optical nonlinearities. Numerous efforts have been made to increase the stability of the second-order NLO properties of polymers. The search for new approaches to develop NLO polymers with optimal properties has been an active research area since the past decade. A novel approach, combining the hybrid properties of high glass transition temperatures, extensively extensively crosslinked networks and permanent entanglements, based on interpenetrating polymer networks (IPN) is introduced to develop stable second-order NLO materials. Two types of IPN systems are prepared and their properties are investigated. The designing criteria and the rationale for the selection of polymers are discussed. The IPN samples show excellent temporal stability at elevated temperatures. Long-term stability of the optical nonlinearity at 100°C has been observed in these materials. Temporal stability of the NLO properties of these IPNs is synergistically enhanced. Relaxation behavior of the optical nonlinearity of an IPN system has been studied and compared with that of a typical guest/host system. The improved temporal stability of the second-order NLO properties of this IPN system is a result of the combination of the high rigidity of the polymer backbones, crosslinked matrices and permanent entanglements of the polymer networks. A slight modification of the chemical structure resulted in an improvement of the optical quality of the sample.     

强激光场作用下部分离化等离子体的非线性极化

针对线偏振光场,提出一个原子极化模型。假设原子核为静止不动的正电背景,束缚电子不发生再电离,自由电子与离子也不发生复合,电子对电场的响应是瞬时的,并用旋转椭球来近似描述电子云的形状。通过此模型,可解析地计算出不同电离状态原子的第1阶线性和第3阶非线性极化率、相应的极化电流、以及极化介质（原子）的折射系数。在低场近似下,这些结果可自洽地过渡到传统的非简谐振子模型,并可得到对应的谐振子的固有频率和非线性系数。     

External Stimuli on Neural Networks: Analytical and Numerical Approaches

Based on the behavior of living beings, which react mostly to external stimuli, we introduce a neural-network model that uses external patterns as a fundamental tool for the process of recognition. In this proposal, external stimuli appear as an additional field, and basins of attraction, representing memories, arise in accordance with this new field. This is in contrast to the more-common attractor neural networks, where memories are attractors inside well-defined basins of attraction. We show that this procedure considerably increases the storage capabilities of the neural network; this property is illustrated by the standard Hopfield model, which reveals that the recognition capacity of our model may be enlarged, typically, by a factor 102. The primary challenge here consists in calibrating the influence of the external stimulus, in order to attenuate the noise generated by memories that are not correlated with the external pattern. The system is analyzed primarily through numerical simulations. However, since there is the possibility of performing analytical calculations for the Hopfield model, the agreement between these two approaches can be tested—matching results are indicated in some cases. We also show that the present proposal exhibits a crucial attribute of living beings, which concerns their ability to react promptly to changes in the external environment. Additionally, we illustrate that this new approach may significantly enlarge the recognition capacity of neural networks in various situations; with correlated and non-correlated memories, as well as diluted, symmetric, or asymmetric interactions (synapses). This demonstrates that it can be implemented easily on a wide diversity of models.     

Effects of axial magnetic field and nonextensivity on small amplitude dust acoustic solitary waves in dusty plasma

The nonlinear propagation of small amplitude dust‐acoustic (DA) solitary waves in magnetized dusty plasma consisting of negatively charged mobile dust fluid, and Boltzmann‐distributed electrons and ions with two distinct temperatures following a q‐nonextensive distribution are investigated. In this article, a number of nonlinear equations, namely, the Korteweg–de‐Vries (K‐dV) equations, have been derived by employing the reductive perturbation technique that is valid for a small but finite amplitude limit. The effects of nonextensivity of ions with two distinct temperatures and dust concentration on the amplitude and width of DA solitary waves are investigated theoretically. It is observed that both the nonextensive and low‐temperatures ions significantly modify the basic properties and polarities of DA solitary waves. It is shown that both positive and negative potential DA solitons occur in this case. The implications of these results to some astrophysical environments and space plasmas (e.g., stellar polytropes, peculiar velocity distributions of galaxies, and collisionless thermal plasma), and laboratory dusty plasma systems are briefly mentioned.     

APPLICATION OF WAVELET TRANSFORM TO BIFURCATION AND CHAOS STUDY

I.IntroductionThetypesofmotionforanonlinearvibrationsystemmaybeperiodic,quasiperiodicorchaotic.Foragivensetofparametersofthesystem,Poincarkmap,powerspectral,waveformandLyapunovexponentareusuallyutilizedtoseewhethertheresponseofthesystemischaoticornot,butitisdiftlculttodeterminepreciselytheexistingdomainsorattractingbasinsofdifferenttypesofmotionsinparametricspaceorinitialvaluespaceonlyfromgraphicsstudy,andcomputingLyapunovexponentistimeconsuming.Aswavelettransformcanreveallocalpropertyinboth…     

Nonlinear optical properties of strontium tartrato‐antimonate(III) dihydrate,Sr[Sb2{(+)‐C4H2O6}2]·2H2O

The tensor of nonlinear optical susceptibility for second harmonic generation [d^SHG _ijk ] of hexagonal (point group 6) strontium tartrato‐antimonate(III) dihydrate, Sr[Sb₂{(+)‐C₄H₂O₆}₂]·2H₂O, was determined using the Maker fringes method and a Nd:YAG laser with a wavelength of 1064 nm. The largest component of the tensor d^SHG ₃₃₃ amounts two times d^SHG ₁₁₁ of α‐quartz. Effective nonlinear optical susceptibility d^SHG _eff is given for phase matching type I for several wavelengths (for type II d^SHG _eff is nearly zero). The thermal stability of crystals of Sr[Sb₂{(+)‐C₄H₂O₆}₂]·2H₂O was determined in the temperature range from 153 K to 573 K by means of thermal expansion measurements and thermogravimetry. The temperature dependence of thermal expansion coefficients is given in the range from 153 K to 293 K. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

差分光学吸收光谱法在线监测烟气中SO2浓度的非线性补偿研究

差分光学吸收光谱法（DOAS）应用于固定污染源烟气排放监测时,烟气中污染气体SO₂浓度较高将产生非线性吸收问题。提出了一种非线性补偿方法,即将实际浓度所对应的气体分压与反演结果所对应的气体分压之比与反演结果之间的对应关系拟合成补偿函数,利用此补偿函数对反演结果进行非线性补偿。实验结果表明：该补偿方法能较好地减低高浓度气体非线性吸收产生的影响,可提高气体浓度反演精度。     

A theoretical and experimental study on all-normal-dispersion Yb-doped mode-locked fiber lasers

We report on a theoretical and experimental study of an all-normal-dispersion (ANDi) Yb-doped mode-locked fiber laser, in which nonlinear polarization rotation (NPR) is used to realize mode-locking without any dispersion compensation. Based on the coupled nonlinear Schrdinger (CNLS) equation, a model simulating the mode-locked process of an allnormal-dispersion ring fiber laser is developed, which shows that the achievement of stable mode-locking depends on the alignment of the polarization controller (PC) along the fast-polarization axis of the fiber, the birefringence intensity, and the net cavity dispersion. According to the theoretical analysis, stable mode-locked pulses with pulse duration 300 ps and average output power 33.9mW at repetition rate 36MHz are obtained.