Modeling film flows down inclined planes

A new model of film flow down an inclined plane is derived by a method combining results of the classical long wavelength expansion to a weighted-residuals technique. It can be expressed as a set of three coupled evolution equations for three slowly varying fields, the thickness h, the flow-rate q, and a new variable that measures the departure of the wall shear from the shear predicted by a parabolic velocity profile. Results of a preliminary study are in good agreement with theoretical asymptotic properties close to the instability threshold, laboratory experiments beyond threshold and numerical simulations of the full Navier-Stokes equations. Received: 16 April 1998 / Revised: 29 June 1998 / Accepted: 2 July 1998     

基于选择性填充的超高非线性纳米纤芯光纤特性

为了改善纳米纤芯光纤的非线性与色散特性,提出利用气孔填充非线性液体的新型纳米纤芯光纤结构来增强现有纳米纤芯光纤的非线性系数,利用选择性填充方法来改进现有纳米纤芯光纤的特性调控能力,实现改善光纤非线性和色散特性目的.分析结果表明采用选择性气孔填充方式和适当的光纤参量有助于实现光纤单模单偏振工作,可以大幅度地提升纳米纤芯光纤的非线性系数和改善光纤色散特性.     

光子晶体光纤非线性系数与其结构参量及光波长的关系

推导计算了全内反射型光子晶体光纤的非线性系数与其两个几何结构参量:包层空气孔半径和空气孔间距之间的关系,给出了输入光波长为1550 nm处,非线性系数与这两个结构参量之间的关系曲线并对其进行了分析.给出了全内反射型光子晶体光纤的非线性系数随输入光波长变化的曲线,分析了短波处高非线性系数产生的原因并指出这一特性的应用潜力.     

Singularities and spectral asymptotics of a random nonlinear wave in a nondispersive system

In this paper, we study the propagation of high-intensity acoustic noise in free space and in waveguide systems. A mathematical model generalizing the Burgers equation is used. It describes the nonlinear wave evolution inside tubes of variable cross-section, as well as in ray tubes, if the geometric approximation for heterogeneous media is used. The generalized equation transforms to the common Burgers equation with a dissipative parameter, known as the “Reynolds–Goldberg number”. In our model, this number depends on the distance travelled by the wave. With a zero “viscous” dissipative term, the model reduces to the Riemann (or Hopf) equation. Its solution presents the field by an implicit function. The spectral form of this solution makes it possible to derive explicit expressions for both dynamic and statistical characteristics of intense waves. The use of a spectral approach allowed us to describe the high-intensity noise in media with zero and finite viscosity. Applicability conditions of these solutions are defined. Since the phase matching is fulfilled for any triplet of interacting spectral components, there is an avalanche-like increase in the number of harmonics and the formation of shocks. The relationship between these discontinuities and other singularities and the high-frequency asymptotic of intense noise is studied. The possibility is shown to enhance nonlinear effects in waveguide systems during the evolution of noise.     

Low-dimensional nonlinearity of ENSO and its impact on predictability

Using a hybrid coupled model, we perform a bred vector (BV) analysis and retrospective ENSO (El Niño and the Southern Oscillation) forecast for the period from 1881 to 2000. The BV local dimension and BV-skewness inherent to the intensity of nonlinearity are analyzed. Emphasis is placed on exploring the nature of the low-dimensional nonlinearity of the ENSO system and the relationship between BV-skewness and model prediction skills. The results show that ENSO is a low-dimensional nonlinear system, and the BV-skewness is a good measure of its predictability at the decadal/interdecadal time scales. As the low-dimensional nonlinearity of ENSO is weakened, high predictability is attained, and vice versa. The low-dimensional nonlinearity of ENSO is also investigated and verified using observations.Another finding in this study is the relationship between the error growth rate (BV-rate) and actual prediction skill. While there is a good positive correlation between them in some decades, the BV-rate demonstrates a strong inverse correlation with the prediction skill in other decades. The BV-rate components contributed by the nonlinear process play a dominant role in quantifying ENSO predictability. The possible mechanism for the link between BV-rate, BV-skewness and ENSO predictability is discussed.     

A nondestructive method for estimation of the fracture toughness of CrMoV rotor steels based on ultrasonic nonlinearity

The objective of this paper is to develop a nondestructive method for estimating the fracture toughness (K(IC)) of CrMoV steels used as the rotor material of steam turbines in power plants. To achieve this objective, a number of CrMoV steel samples were heat-treated, and the fracture appearance transition temperature (FATT) was determined as a function of aging time. Nonlinear ultrasonics was employed as the theoretical basis to explain the harmonic generation in a damaged material, and the nonlinearity parameter of the second harmonic wave was the experimental measure used to be correlated to the fracture toughness of the rotor steel. The nondestructive procedure for estimating the K(IC) consists of two steps. First, the correlations between the nonlinearity parameter and the FATT are sought. The FATT values are then used to estimate K(IC) using the K(IC) versus excess temperature (i.e., T-FATT) correlation that is available in the literature for CrMoV rotor steel.     

Steady-state self-focusing of Gaussian electromagnetic beams in an inhomogeneous nonlinear medium: Effect of absorption and initial curvature of the beam

The authors have investigated the effect of linear absorption and initial curvature of an electromagnetic Gaussian beam on focusing/defocusing in an inhomogeneous nonlinear medium. Numerical computations have been made for linear inhomogeneity and saturating nonlinearity, characteristic of dielectrics and collisional plasmas. The maximum and minimum of the beam width keep decreasing with increase in distance of propagation (or absorption), till the beam becomes very weak and diverges steeply; penetration in an overdense medium also decreases with increasing absorption. Converging beams initially converge and then go in: (i) the oscillatory divergence (ii) self-focusing or (iii) steady divergence mode, depending upon the initial values of beam width and axial irradiance. The maximum penetration in an overdense medium has the highest values for −0.7<(df/dξ)_ξ=0<0.4 and falls sharply, outside these limits.     

Monetary policy rules in practice: Re-examining the case of Turkey

This paper investigates possible asymmetries in the monetary policy reaction function of the Central Bank of Republic of Turkey over the business cycles. It is found that the bank reacted more aggressively towards output stabilisation during recessions than expansions. The empirical evidence suggests that the inflation targeting policy of the Turkish Central Bank was accommodative rather than stabilising. Furthermore, it is found that although the Central Bank of Republic of Turkey responded to foreign reserves, real exchange rates and short-term capital inflows both in expansion and recession periods, the bank targeted money growth, budget deficits, and net foreign assets only in expansion periods.     

Nonlinearity in inverse and transverse piezoelectric properties of Pb(Zr0.52Ti0.48)O3 film actuators under AC and DC applied voltages

The motion of domain walls is a crucial factor in piezoelectric properties and is usually related to the irreversible and hysteretic behaviors. Herein, we report on the investigation of inverse and transverse piezoelectric coefficients of capacitor-based and microcantilever-based Pb(Zr_0.52Ti_0.48)O₃ films with a change in the DC bias and the AC applied voltage. A large inverse piezoelectric strain coefficient of about 350 p.m./V, and a low strain hysteresis of about 7.1%, are achieved in the film capacitors under a low applied voltage of 2 V (20 kV/cm) which can benefit the actuators for motion control in high-precision systems. The field-dependences of the transverse piezoelectric coefficients, obtained from four-point bending and microcantilever displacement, are in good agreement with each other. The results also reveal that the irreversible domain-wall motion is attributed to the nonlinearity in the field-dependent piezoelectric strain and cantilever displacement.     

How do mutative events modify moments evolution in thermostatted kinetic models?

This short communication aims at developing a thermostatted kinetic framework which includes conservative and nonconservative interactions. Specifically nonconservative interactions refer to proliferative/destructive and mutative events. The thermostatted kinetic framework is a set of autonomous partial integro-differential equations with quadratic nonlinearity. How the moments evolution is modified by mutative interactions is explored in the present communication. Applications refer to the cancer-immune system competition.