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.

Roles of equatorial waves and western boundary reflection in the seasonal circulation of the equatorial Indian Ocean

An ocean general circulation model (OGCM) is used to study the roles of equatorial waves and western boundary reflection in the seasonal circulation of the equatorial Indian Ocean. The western boundary reflection is defined as the total Kelvin waves leaving the western boundary, which include the reflection of the equatorial Rossby waves as well as the effects of alongshore winds, off-equatorial Rossby waves, and nonlinear processes near the western boundary. The evaluation of the reflection is based on a wave decomposition of the OGCM results and experiments with linear models. It is found that the alongshore winds along the east coast of Africa and the Rossby waves in the off-equatorial areas contribute significantly to the annual harmonics of the equatorial Kelvin waves at the western boundary. The semiannual harmonics of the Kelvin waves, on the other hand, originate primarily from a linear reflection of the equatorial Rossby waves. The dynamics of a dominant annual oscillation of sea level coexisting with the dominant semiannual oscillations of surface zonal currents in the central equatorial Indian Ocean are investigated. These sea level and zonal current patterns are found to be closely related to the linear reflections of the semiannual harmonics at the meridional boundaries. Because of the reflections, the second baroclinic mode resonates with the semiannual wind forcing; that is, the semiannual zonal currents carried by the reflected waves enhance the wind-forced currents at the central basin. Because of the different behavior of the zonal current and sea level during the reflections, the semiannual sea levels of the directly forced and reflected waves cancel each other significantly at the central basin. In the meantime, the annual harmonic of the sea level remains large, producing a dominant annual oscillation of sea level in the central equatorial Indian Ocean. The linear reflection causes the semiannual harmonics of the incoming and reflected sea levels to enhance each other at the meridional boundaries. In addition, the weak annual harmonics of sea level in the western basin, resulting from a combined effect of the western boundary reflection and the equatorial zonal wind forcing, facilitate the dominance by the semiannual harmonics near the western boundary despite the strong local wind forcing at the annual period. The Rossby waves are found to have a much larger contribution to the observed equatorial semiannual oscillations of surface zonal currents than the Kelvin waves. The westward progressive reversal of seasonal surface zonal currents along the equator in the observations is primarily due to the Rossby wave propagation.

An Efficient Front-Tracking Method For Fully Nonlinear Interfacial Waves

A fully nonlinear and dispersive model within the framework of potential theory is developed for interfacial (2-layer) waves. To circumvent the difficulties arisen from the moving boundary problem a viable technique based on the mixed Eulerian and Lagrangian concept is proposed: the computing area is partitioned by a moving mesh system which adjusts its location vertically to conform to the shape of the moving boundaries but keeps frozen in the horizontal direction. Accordingly, a modified dynamic condition is required to properly compute the boundary potentials. To demonstrate the effectiveness of the current method, two important problems for the interfacial wave dynamics, the generation and evolution processes, are investigated. Firstly, analytical solutions for the interfacial wave generations by the interaction between the barotropic tide and topography are derived and compared favorably with the numerical results. Furthermore simulations are performed for the nonlinear interfacial wave evolutions at various water depth ratios and satisfactory agreement is achieved with the existing asymptotical theories. (c) 2008 Elsevier Inc. All rights reserved.

Nonlinear Mechanical Modeling Of Cell Adhesion

Cell adhesion, which is mediated by the receptor-ligand bonds, plays an essential role in various biological processes. Previous studies often described the force-extension relationship of receptor-ligand bond with linear assumption. However, the force-extension relationship of the bond is intrinsically nonlinear, which should have significant influence on the mechanical behavior of cell adhesion. In this work, a nonlinear mechanical model for cell adhesion is developed, and the adhesive strength was studied at various bond distributions. We find that the nonlinear mechanical behavior of the receptor-ligand bonds is crucial to the adhesive strength and stability. This nonlinear behavior allows more bonds to achieve large bond force simultaneously, and therefore the adhesive strength becomes less sensitive to the change of bond density at the outmost periphery of the adhesive area. In this way, the strength and stability of cell adhesion are soundly enhanced. The nonlinear model describes the cell detachment behavior better than the linear model. (C) 2007 Elsevier Ltd. All rights reserved.

Two bifurcation processes for onset of oscillatory thermocapillary convection in a floating half zone

An overview on the onset of thermocapillary oscillatory convection in a floating half zone is provided, and it is a typical subject in the microgravity sciences related to the space materials science, especially the floating zone processing, and also to the microgravity fluid physics. The main interests are focused around the process for onset of oscillatory thermocapillary convection, which is known also as the bifurcation transition from quasi-steady convection to oscillatory convection. The onset of oscillation depends on a set of critical parameters, such as the Marangoni number, Prandtl number, geometrical parameters, and heat transfer parameters. Recent studies show that, there exists the bifurcation transition from steady and axial symmetric convection to the steady and axial non-symmetric convection before the onset of oscillation in cases of small Prandtl number fluids and in cases of larger Prandtl number fluids of fat liquid bridge with small aspect ratio. The transition process is a strong non-linear process because the velocity deviation has the same order of magnitude as that of an average flow after the onset of oscillation, and unsteady 3-D numerical simulation is suitable to do in depth analysis on strong non-linear process, and leads generally to a better comparison with the experimental results.

Nonlinear propagation of fs laser pulses in liquids and evolution of supercontinuum generation

Nonlinear propagation of fs laser pulses in liquids and the dynamic processes of filamentation such as self-focusing, intensity clamping, and evolution of white light production have been analyzed by using one- and two-photon fluorescence. The energy losses of laser pulses caused by multiphoton absorption and conical emission have been measured respectively by z-scan technique. Numerical simulations of fs laser propagation in water have been made to explain the evolution of white light production as well as the small-scale filaments in liquids we have observed by a nonlinear fluorescence technique. (c) 2005 Optical Society of America.

TG-DTA properties of new nonlinear optical materials: K(2)Ln(NO3)(5)center dot 2H(2)O (Ln = La, Ce, Pr, Nd, Sm)

Single crystals of K(2)Ln(NO3)(5). 2H(2)O (KLnN) (Ln = La, Ce, Pr, Nd, Sm) were grown from aqueous solution. The thermogravimetric analysis and differential thermal analysis curves of KLnN demonstrate that the processes of dehydration, melting, irreversible phase transformation and decomposition of NO3- take place in sequence in the heating processes (except KCN). There are three stages in the decomposition of NO3- in KLnN (Ln = La, Nd, Sm) while two in KLnN (Ln = Ce, Pr). K(2)Ln(NO3)(5) is formed at about 225 degrees C by the reaction of KNO3 and Ln(NO3)(3). nH(2)O (Ln = La, Ce, Pr, Nd). (C) 2000 Elsevier Science Ltd. All rights reserved.

Evaluation of nonlinear chromatographic performance by frontal analysis using a simple multi-plate mathematical model

A multi-plate (NIP) mathematical model was proposed by frontal analysis to evaluate nonlinear chromatographic performance. One of its advantages is that the parameters may be easily calculated from experimental data. Moreover, there is a good correlation between it and the equilibrium-dispersive (E-D) or Thomas models. This shows that it can well accommodate both types of band broadening that is comprised of either diffusion-dominated processes or kinetic sorption processes. The MP model can well describe experimental breakthrough curves that were obtained from membrane affinity chromatography and column reversed-phase liquid chromatography. Furthermore, the coefficients of mass transfer may be calculated according to the relationship between the MP model and the E-D or Thomas models. (C) 2004 Elsevier B.V. All rights reserved.

Identification of nonlinear dynamic systems: Time-frequency filtering and skeleton curves

The nonlinear behavior varying with the instantaneous response was analyzed through the joint time-frequency analysis method for a class of S. D. O. F nonlinear system. A masking operator an definite regions is defined and two theorems are presented. Based on these, the nonlinear system is modeled with a special time-varying linear one, called the generalized skeleton linear system (GSLS). The frequency skeleton curve and the damping skeleton curve are defined to describe the main feature of the non-linearity as well. Moreover, an identification method is proposed through the skeleton curves and the time-frequency filtering technique.

Characteristic Dimensionless Numbers in Multi-Scale and Rate-Dependent Processes

For this sake, the macroscopic equations of mechanics and the kinetic equations of the microstructural transformations should form a unified set that be solved simultaneously. As a case study of coupling length and time scales, the trans-scale formulation

Effects of heat-treatment processes on the electroless Ni-B coating and its natural aging mechanism

A Ni-B coating was prepared with EN using potassium borohydride reducing agent. The as-plated micro-structure of the coating was confirmed from XRD to be a mixture of amorphous and supersaturated solid solution. Three kinds of phase transformation were observed from the DSC curve. Different from the previous works, the formation of Ni4B3 and Ni2B was found during some transformation processes. The key factors which influence the variation of micro-hardness and micro-structure in deposits are the formation, the size and amount of Ni3B, Ni4B3 and Ni2B. Aging of the deposits treated under some heat treatment conditions occurred at room temperature. Changes of the micro-hardness indicated aging phenomena evidently. the natural aging phenomena are concerned with various kinds of decomposition of borides, especially with Ni4B3 phase. The extent of natural aging depends on the formation and the quantity of Ni(4)B3 and Ni2B.

Nonlinear Analysis of Submarine Pipelines During Single Point Lifting

基于管道微单元体平衡建立了海管单点提升的非线性力学模型的控制微分方程组,使用变弧长的无量纲代换将动边界问题化为固定边界的两点边值问题,利用maple环境下编制的两点边值问题的打靶法程序得到了该问题在各个提升阶段的数值解答和在单点提升过程中管道的极限弯矩约为0.71q~{1/3}(EI)~{2/3}。

Identification of Nonlinear Systems Through Time-Frequency Filtering Technique

In the previous paper, a class of nonlinear system is mapped to a so-called skeleton linear model (SLM) based on the joint time-frequency analysis method. Behavior of the nonlinear system may be indicated quantitatively by the variance of the coefficients of SLM versus its response. Using this model we propose an identification method for nonlinear systems based on nonstationary vibration data in this paper. The key technique in the identification procedure is a time-frequency filtering method by which solution of the SLM is extracted from the response data of the corresponding nonlinear system. Two time-frequency filtering methods are discussed here. One is based on the quadratic time-frequency distribution and its inverse transform, the other is based on the quadratic time-frequency distribution and the wavelet transform. Both numerical examples and an experimental application are given to illustrate the validity of the technique.

Kramers Escape Rate in Nonlinear Diffusive Media

In this paper, we study nonlinear Kramers problem by investigating overdamped systems ruled by the one-dimensional nonlinear Fokker-Planck equation. We obtain an analytic expression for the Kramers escape rate under quasistationary conditions by employing

Partial-Dislocation-Mediated Processes in Nanocrystalline Ni with Nonequilibrium Grain Boundaries

The partial-dislocation-mediated processes have so far eluded high-resolution transmission electron microscopy studies in nanocrystalline nc Ni with nonequilibrium grain boundaries. It is revealed that the nc Ni deformed largely by twinning instead of extended partials. The underlying mechanisms including dissociated dislocations, high residual stresses, and stress concentrations near stacking faults are demonstrated and discussed.