Thermocapillary Convection in Floating Zones

This paper provides an overview of ongoing studies in the area of thermocapillary convection driven by a surface tension gradient parallel to the free surface in a floating zone. Here, research interests are focused around the onset of oscillatory thermocapillary convection, also known as the transition from quasisteady convection to oscillatory convection. The onset of oscillation depends on a set of critical parameters, and the margin relationship can be represented by a complex function of the critical parameters. The experimental results indicate that the velocity deviation of an oscillatory flow has the same order of magnitude as that of an average flow, and the deviations of other quantities, such as temperature and free surface radii fluctuations, are much smaller when compared with their normal counterparts. Therefore, the onset of oscillation should be a result of the dynamic process in a fluid, and the problem is a strongly nonlinear one. In the past few decades, several theoretical models have been introduced to tackle the problem using analytical methods, linear instability analysis methods, energy instability methods, and unsteady 3D numerical methods. The last of the above mentioned methods is known to be the most suitable for a thorough analysis of strong nonlinear processes, which generally leads to a better comparison with the experimental results. The transition from oscillatory thermocapillary convection to turbulence falls under the studies of chaotic behavior in a new system, which opens a fascinating new frontier in nonlinear science, a hot research area drawing many recent works. This paper reviews theoretical models and analysis, and also experimental research, on thermocapillary connection in floating zones. It cites 93 references.

Nonlinear Analysis of Oscillatory Indentation in Elastic and Viscoelastic Solids

Determining the mechanical properties at micro- and nanometer length scales using nanoindentation or atomic force microscopy is important to many areas of science and engineering. Here we establish equations for obtaining storage and loss modulus from oscillatory indentations by performing a nonlinear analysis of conical and spherical indentation in elastic and viscoelastic solids. We show that, when the conical indenter is driven by a sinusoidal force, the square of displacement is a sinusoidal function of time, not the displacement itself, which is commonly assumed. Similar conclusions hold for spherical indentations. Well-known difficulties associated with measuring contact area and correcting thermal drift may be circumvented using the newly derived equations. These results may help improve methods of using oscillatory indentation for determining elastic and viscoelastic properties of solids.

Nonlinear Constitutive Behavior Of Ferroelectric Materials

The ferroelectric specimen is considered as an aggregation of many randomly oriented domains. According to this mechanism, a multi-domain mechanical model is developed in this paper. Each domain is represented by one element. The applied stress and electric field are taken to be the stress and electric field in the formula of the driving force of domain switching for each element in the specimen. It means that the macroscopic switching criterion is used for calculating the volume fraction of domain switching for each element. By using the hardening relation between the driving force of domain switching and the volume fraction of domain switching calibrated, the volume fraction of domain switching for each element is calculated. Substituting the stress and electric field and the volume fraction of domain switching into the constitutive equation of ferroelectric material, one can easily get the strain and electric displacement for each element. The macroscopic behavior of the ferroelectric specimen is then directly calculated by volume averaging. Meanwhile, the nonlinear finite element analysis for the ferroelectric specimen is carried out. In the finite element simulation, the volume fraction of domain switching for each element is calculated by using the same method mentioned above. The interaction between different elements is taken into account in the finite element simulation and the local stress and electric field for each element is obtained. The macroscopic behavior of the specimen is then calculated by volume averaging. The computation results involve the electric butterfly shaped curves of axial strain versus the axial electric field and the hysteresis loops of electric displacement versus the electric field for ferroelectric specimens under the uniaxial coupled stress and electric field loading. The present theoretical prediction agrees reasonably with the experimental results.

Threshold diversity and trans-scales sensitivity in a finite nonlinear evolution model of materials failure

We present a slice-sampling method and study the ensemble evolution of a large finite nonlinear system in order to model materials failure. There is a transitional region of failure probability. Its size effect is expressed by a slowly decaying scaling law. In a meso-macroscopic range (similar to 10(5)) in realistic failure, the diversity cannot be ignored. Sensitivity to mesoscopic details governs the phenomena. (C) 1997 Published by Elsevier Science B.V.

Preliminary report on the energy balance for nonlinear oscillations

In this paper, a reliable technique for calculating angular frequencies of nonlinear oscillators is developed. The new algorithm offers a promising approach by constructing a Hamiltonian for the nonlinear oscillator. Some illustrative examples are given. (C) 2002 Published by Elsevier Science Ltd.

Transition waves and nonlinear interactions in the near wake of a circular cylinder

Transition waves and interactions between two kinds of instability-vortex shedding and transition wave in the near wake of a circular cylinder in the Reynolds number range 3 000-10 000 are studied by a domain decomposition hybrid numerical method. Based on high resolution power spectral analyses for velocity new results on the Reynolds-number dependence of the transition wave frequency, i.e. f(t)/f(s) similar to Re-0.87 are obtained. The new predictions are in good agreement with the experimental results of Wei and Smith but different from Braza's prediction and some early experimental results f(t)/f(s) similar to Re-0.5 given by Bloor et nl. The multi-interactions between two kinds of vortex are clearly visualized numerically. The strong nonlinear interactions between the two independent frequencies (f(t), f(s)) leading to spectra broadening to form the coupling mf(s) +/- nf(t) are predicted and analyzed numerically, and the characteristics of the transition are described. Longitudinal variations of the transition wave and its coupling are reported. Detailed mechanism of the flow transition in the near wake before occurrence of the three-dimensional evolution is provided.

Effect of nonlinear wave-current interaction on flow fields and hydrodynamic forces

A fifth-order theory for solving the problem of interaction between Stokes waves and exponential profile currents is proposed. The calculated flow fields are compared with measurements. Then the errors caused by the linear superposition method and approximate theory are discussed. It is found that the total wave-current field consists of pure wave, pure current and interaction components. The shear current not only directly changes the flow field, but also indirectly does sx, by changing the wave parameters due to wave-current interaction. The present theory can predict the wave kinematics on shear currents satisfactorily. The linear superposition method may give rise to more than 40% loading error in extreme conditions. When the apparent wave period is used and the Wheeler stretching method is adopted to extrapolate the current, application of the approximate theory is the best.

Nonlinear laser focusing using a conical guide and generation of energetic ions

Using conventional methods, a laser pulse can be focused down to around 6-8 mu m, but further reduction of the spot size has proven to be difficult. Here it is shown by particle-in-cell simulation that with a hollow cone an intense laser pulse can be reduced to a tiny, highly localized, spot of around 1 mu m radius, accompanied by much enhanced light intensity. The pulse shaping and focusing effect is due to a nonlinear laser-plasma interaction on the inner surface of the cone. When a thin foil is attached to the tip of the cone, the cone-focused light pulse compresses and accelerates the ions in its path and can punch through the thin target, creating highly localized energetic ion bunches of high density.

Relativistic channel-coupling focusing enhanced nonlinear guiding of an intense laser beam in a plasma channel

We employ the variational method to study the optical guiding of an intense laser beam in a preformed plasma channel without using the weakly relativistic approximation. Apart from the dependence on the laser power and the nonlinear channel strength parameter, the beam focusing properties is shown also to be governed by the laser intensity. Relativistic channel-coupling focusing, arising from the coupling between relativistic self-focusing and linear channel focusing, can enhance relativistic self-focusing but its strength is weaker than that of linear channel focusing. (C) 2008 Elsevier B.V. All rights reserved.

Nonlinear spectroscopy of cold atoms in diffuse laser light

The nonlinear spectroscopy of cold atoms in the diffuse laser cooling system is studied in this paper. We present the theoretical models of the recoil-induced resonances (RIR) and the electromagnetically-induced absorption (EIA) of cold atoms in diffuse laser light, and show their signals in an experiment of cooling Rb-87 atomic vapor in an integrating sphere. The theoretical results are in good agreement with the experimental ones when the light intensity distribution in the integrating sphere is considered. The differences between nonlinear spectra of cold atoms in the diffuse laser light and in the optical molasses are also discussed. (c) 2009 Optical Society of America

A Z-scan model for optical nonlinear nanometric films

The Z-scan technique is useful for measuring the nonlinear refractive index of thin films. In conventional Z-scan theories, two effects are often ignored, namely the losses due to the internal multi-interference and the nonlinear absorption inside the sample. Therefore, the theories are restricted to relatively thick films. For films thinner than about 100 nm, the two effects become significant, and thus cannot be ignored. In the present work, we present a Z-scan theory that takes both effects into account. The proposed model calculation is suitable for optical nonlinear films of nanometric thickness. With numerical simulations, we demonstrate dramatic deviations from the conventional Z-scan calculations.

Laser tunable Toraldo superresolution with a uniform nonlinear pupil filter

We demonstrate that it is possible to reduce the focal spot size by inserting a uniform nonlinear thin film at the aperture of a focusing lens. The reduction of spot size is tunable by adjusting the incoming laser power. In comparison with the original diffraction spot, the transverse spot size can be reduced 0.65 times. The nonlinear thin film acts effectively as a Toraldo filter, and the phase and amplitude modulation stems from the laser-induced variances in the transmission of the thin film. The proposed technique removes the need of fabricating annular pupil filters. (C) 2008 Optical Society of America.

The effect of an electric field on the nonlinear response of InAs/GaAs quantum dots

The refractive nonlinearities of InAs/GaAs quantum dots under a dc electric field at photon energies above its band gap energy have been studied using the reflection Z-scan technique. The effect of the dc electric field on the nonlinear response of InAs/GaAs quantum dots showed similar linear and quadratic electro-optic effects as in the linear response regime at low fields. This implies that the electro-optic effect in the nonlinear regime is analogous to the response in the linear regime for semiconductor quantum dots. Our experimental results show the potential for voltage tunability in InAs quantum dot-based nonlinear electro-optic devices.

Nonlinear optical properties and thermal stability of the poled polymer NTAB/PEK-c

Films of high glass' transition temperature polymer polyetherketone doped with chromophore 2,2'[4-[(5-nitro-2-thiazolyl)azophenyl]-amino]-bisethanol NTAB) were prepared, poled by the corona-onset poling setup which includes a grid voltage making the surface-charge distribution uniform at elevated temperature. The thickness of the films was measured by the Model 2010 Prism Coupler system. Second harmonic generation d(33) was measured by the second harmonic generation method, and the d33 is 38.12 pm/V at 1064 nm under the absorption correction. The nonlinear optical activity maintains is 80% of its initial value. (C) 2002 Elsevier Science B.V. All rights reserved.