Chi-Chuan Hwang

Controlling hyperchaos of the Rossler system

A feedback control is designed to regulate the hyperchaotic behaviour of the Rossler oscillator. Two inputs are added to the system for the control where each of the inputs contains two portions of feedback. One of the feedback parts is to construct an equilibrium manifold by modifying the dynamics of the system, while the other is the proportional feedback part which will control the hyperchaotic state to desired states on the manifold. In the design, the desired states include fixed points as well as limit cycles. Some numerical experiments are presented to perform the control. As expected, and also verified by the numerical results, the hyperchaotic system can be well tracked to the desired state by the present design. Furthermore, the settling times of the tracking can be improved by increasing the proportional gains of the control.

A nonlinear feedback control of the Lorenz equation

This article proposes a nonlinear feedback controller to regulate the chaotic states of the Lorenz equation. This controller can control the chaotic state not only to fixed points but also to limit cycles. The benefit of this controller is that it can attain faster settling time than that by using previous controllers. Without any integral controller, the present design can eliminate the tracking errors easily.

A study of rupture process of thin liquid films by a molecular dynamics simulation

Three-dimensional ruptures in both thin films on plates and free thin films have been studied, using molecular dynamics simulations. The rupture process simulated in this work is divided into two stages. They are the stage from the initial equilibrium state to the occurrence of the rupture and the stage from this occurrence to the final state of the rupture. In this study, it is found that for the free film larger liquid–liquid potential induces quicker rupture speed, while for the film on a plate, smaller solid–liquid potential results in not only larger occurrence and spreading speeds of the rupture but also larger contact angle between solid and liquid. In the first rupture stage, the result obtained in this work is qualitatively similar to that predicted by the macroscopic rupture theory. In the second stage, the simulations of this work can help describe the evolutions of ruptures in detail, which the macroscopic theory is no longer able to do.

Nonlinear morphological instabilities in directional solidification—an integral approximation

In this article, we derive a strongly nonlinear evolution equation by using the integral method to study the instabilities in a directionally solidified binary mixture. This equation can not only describe the interfacial behaviors of all the long‐wave limits, but can also provide the possibility of strongly nonlinear instability analyses. Weakly nonlinear analyses proceeded from the critical conditions are undertaken to investigate the two‐dimensional bifurcation types and a transition curve separating subcritical and supercritical ranges is obtained.

Morphological instabilities in rapid directional solidifications under local nonequilibrium conditions

We perform the linear morphological instability analysis in rapid directional solidifications of dilute binary alloys considering the local nonequilibriums both in the bulk liquid and at the solid/liquid front. The generalized Ficks law for mass transport in the melt and the velocity dependence of the segregation coefficient modified by Sobolev and coworkers are employed for the analysis. The result shows that, compared to the situation where nonequilibrium effects at the interface only are considered, the effect of the local nonequilibrium in the bulk postpones the onset of the steady cellular instability but quickens the onset of the oscillatory cellular instability. Consequently, smaller surface-energy and larger attachment kinetics are expected for the absolute-stability boundaries of the steady and oscillatory cellular instabilities, respectively.

The effect of curved interface shape on thermal stress during Czochralski crystal growth

Abstract Analytical solutions of the quasi-steady-state thermal stresses in the crystal with finite length during Czochralski growth are obtained. In the temperature analysis, both the temperature distribution and the shape of the solid-liquid interface are simultaneously solved. It is found that the shape of the interface is parabolic-like and the Biot number is the dominating parameter. In the thermal stress analysis, we found that the results of the curved interface model are qualitatively similar to, but quantitatively different from those of the planar interface model. In addition, we also find that the effect of the crystal length should not be neglected, especially when the length is small.

Diffusion-induced stresses in a long bar under an electric field

Diffusion-induced stresses in a long bar with a square cross section under an electric field are calculated. We obtain in advance analytical solutions of the concentration, then with these results, the diffusion-induced stresses are also calculated analytically by introducing the displacement potential and Airy stress function. The results show that the electric field can depress the stresses and deviate the positions of local maximum stresses, and these effects are more apparent at short times than at long times.

Three-dimensional morphological instabilities in chemical vapor deposition films

Abstract In this article, an analysis of nonlinear three-dimensional (3-D) morphological instabilities in chemical vapor deposition (CVD) is presented. We establish a set of mathematically governing equation and boundary condition for the system of CVD and derive a weakly nonlinear evolution equation by considering a diffusion-limited growth condition to study the morphological instabilities in the CVD process. This evolution equation not only can predict the behaviors of interfacial growth of films, but can also be a basis of weakly nonlinear analysis. The analysis from critical condition is adopted to investigate the two-dimensional (2-D) band-like cells and the 3-D hexagonal structures.

Swelling Controlled Release of Drug from Polymetric Delivery Devices: A Local Similarity Solution

This paper presents a numerically integrated solution of moving boundary problems involving mass diffusion in polymer-penetrant system with a swelling controlled release of drug. Dividing the diffusion process into a finite number of fixed boundary problems, we have assumed the local similarity assumption to valid during the short period. Unlike the existing parameter expansion methods, the present solution is expected to be valid over a large range of control parameter representing the difference between solvent concentration at interface and the equilibrium value within the polymer. At small times, our numerical result shows that a larger values of the control parameter leads to a shorter interval for zero order drug release providing a higher release rate.

Nonlinear long-wave morphological instabilities in directional solidification system

Abstract Long-wave morphological instabilities in directional solidification of a dulite binary mixture are investigated. We present a new nonlinear evolution equation of the solid-liquid interface for lage surface energy. This evolution equation contains not only quadratic and cubic nonlinearity terms, but also terms whose nonlinearites are higher than cubic and terms which are nonlinear and with time derivatives. It is shown that, in the weakly nonlinear instability analysis, when surface energy is very large, the cubic nonlinearity terms can be neglected. However, as surface energy is only finite, these terms may become significant for instability effects. If the bifurcation is supercritical, the cubic terms tends to enlarge the steady-state amplitudes of disturbances. On the other hand, for subcritical bifurcation, the cubic terms will diminish the threshold amplitudes which should not be exceeded by the amplitudes of the initial disturbances in the linearly stable region if a stable solidification system is wanted.