In this paper, a model describing the process of transition to chaotic fluid motion in an acoustically driven fluid is presented. The nonlinear interaction between the Stokes boundary layer and linearly unstable three-dimensional vortical disturbances is examined. Special consideration is given to the amplitude range above which these disturbances bifurcate from linear stability. It is found that oscillatory modulation present in the basic-flow results in successive period-doubling bifurcations of the three-dimensional vortical disturbances. It is shown that these bifurcations result in the disturbance amplitude becoming chaotic.

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The nonlinear stability analysis of viscoelastic fibers is presented. The molten fiber is modeled as a Maxwellian viscoelastic fluid and the zeroth order equations governing its behavior given. Linear stability analysis is performed to determine the influence of winder speed and impedance as well as viscosity and elasticity. The results of numerical solution of the nonlinear equations are given.

In this paper, a simulation-based investigation of a strategy to control optical fiber diameter variations is reported. The proposed control scheme is based on the principles of modal control. A model of the fiber manufacture is presented and its sensitivity to the fiber draw speed is demonstrated. A control methodology, utilizing the basic concepts of modal control approach, is attempted on the linear isothermal optical fiber model, and this approach is shown to yield satisfactory results. The proposed approach can be modified and extended for nonlinear control of the fiber diameter.Optical fibers are currently used in diverse applications such as biomedical instrumentation, comunicationS, and space applications. These fibers are usually manufactured by the drawing process. In the single fiber drawing process, a glass preform, of acceptable physical and optical properties, is fed into a fumace, and heated until it becomes soft. The temperature at which the preform is soft enough for drawing fibers, ranges from 1500 to 2 5 W C, depending on the physical properties of the particular glass preform [ 11. The soft. glass is then pulled by means of a winder to form optical fiber. The performance of optical fibers and related optical components depends critically on the evenness of the fiber diameter [2]. Very precise control of the fiber diameter, therefore, is an important manufacturing consideration. Sufficiently large winder speeds have been shown to induce a hydrodynamic instability in the steady fiber flow, called draw resonance [3]. It is known that this instability causes periodic variations in the fiber diameter, which degrade product performance, and may even cause fiber breakage [4].Experimental work with polymers [5.6] has shown that the most significant parameter affecting the onset of draw resonance is the fiber draw ratio U, which is the ratio of the logarithms of the final and initial fiber velocities. This was confirmed theoretically through linearized perturbation analyses [7.8]. In addition, the fiber drawing process is also susceptible to small external disturbances, resulting from unsteady preform feed-in rates, heat sources and sinks. and noise induced vibrations. The effects of these disturbances are as important as the effect of winder speed variations [2]. The need to improve product quality and yield of the drawing process has motivated numerous investigations of modeling and stability analysis of the process [2-201, and several attempts to devise better diameter controllers [21-261.Imoto and coworkers [21,25] devised an optical fiber drawing process which features a gas flow controlling system, in addition to the drawing speed controlling system. Gas flow in the fumace is regulated such that faster fluctuations in fiber diameter are controlled, and the winder speed is varied such that slower fluctuations are reduced. It i s reported that the system works well, even in the presence of large changes in the preform feed-in velocity. Smithgd [23] applied optimization theory, based on a mean squar...