Jin-Yuan Hsieh

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.

Theoretical variations in the Young's modulus of single-walled carbon nanotubes with tube radius and temperature: a molecular dynamics study

This study uses molecular dynamics simulations to investigate the intrinsic thermal vibrations of a single-walled carbon nanotube (SWNT) modelled as a clamped cantilever. Using an elastic model defined in terms of the tube length, the tube radius and the tube temperature, the standard deviation of the vibrational amplitude of the tubes free end is calculated and the Youngs modulus of the SWNT evaluated. The numerical results reveal that the value of the Youngs modulus is independent of the tube length, but decreases with increasing tube radius. At large tube radii, the Youngs modulus value approaches the in-plane modulus of graphene, which can be regarded as an SWNT of infinitely large radius. The results also indicate that the Youngs modulus is insensitive to changes in the tube temperature at temperatures of less than approximately 1100 K, but decreases significantly at higher temperatures.

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.

General phase-matching condition for a quantum searching algorithm

A general consideration of the phase rotations in a quantum searching algorithm is undertaken in this work. As four phase rotations on the initial state, the marked state, and the states orthogonal to them are taken into account, we deduce a phase-matching condition for a successful search. The optimal options for these phases are then obtained.

Observation of the amorphous zinc oxide recrystalline process by molecular dynamics simulation

The detailed structural variations of amorphous zinc oxide (ZnO) as well as wurtzite (B4) and zinc blende (B3) crystal structures during the temperature elevation process were observed by molecular dynamics simulation. The amorphous ZnO structure was first predicted through the simulated-annealing basin-hopping algorithm with the criterion to search for the least stable structure. The density and X-ray diffraction profiles of amorphous ZnO of the structure were in agreement with previous reports. The local structural transformation among different local structures and the recrystalline process of amorphous ZnO at higher temperatures are observed and can explain the structural transformation and recrystalline mechanism in a corresponding experiment [Bruncko et al., Thin Solid Films 520, 866-870 (2011)].

The nanoindentation of a copper substrate by single-walled carbon nanocone tips: a molecular dynamics study.

This study dealt with deep nanoindentation of a copper substrate with single-walled carbon nanocones (SWCNCs) as the proximal probe tip, using molecular dynamics (MD) simulations. As an important feature, during the indentation the end part of the SWCNC tip will suffer a narrowing effect due to the radial component of resistant compression from the substrate and then forms into a somewhat flat arrowhead-like shape. The effective cross-sectional area of the SWCNC tip inside the substrate that the resistant force is acting on therefore is reduced to lower the normal resistant force on the tip. The narrowing effect is more significant for longer SWCNC tips. Two categories of SWCNCs are therefore classified according to whether the SWCNC tip buckles at its part inside or outside the substrate. SWCNCs of the first category defined in this paper are found able to indent into the substrate up to a desired depth. Further analyses demonstrate that a longer SWCNC tip of the first category will encounter smaller repulsive force during the indentation and thus require less net work to accomplish the indentation process. Raising temperatures will weaken the narrowing effect, so an SWCNC tip of the first category also encounters greater repulsive force and larger net work in the indentation process performed at a higher temperature. Notably, a permanent hollow hole with high aspect ratio will be produced on the copper substrate, while copper atoms in close proximity to the hole are only slightly disordered, especially when the indentation is manipulated at a lower temperature by using a longer SWCNC tip.

Localized electrochemical oxidation of p-GaAs(100) using atomic force microscopy with a carbon nanotube probe

Th en anometre-scale oxidation characteristics of a p-GaAs(100) surface are investigated by atomic force microscope (AFM) electrochemical nanolithography with a multiwalled carbon nanotube (MWCNT) probe. The electrochemical parameters, such as anodizing voltages, scanning rate and modulated voltages, and how they affect the creation and growth of the oxide nanostructures are explored. The present results reveal that the initial growth rate (∼600 nm s −1 for 10 V) decreases rapidly as the electric field strength is decreased. The oxide practically ceases to grow as the electric field is reduced to the order of ∼1.2 × 10 7 Vc m −1 .A lso,the oxide growth rate depends not only on the electric field strength but also on the applied anodizing voltage. The present results show that the height of the oxide structures can be significantly improved at an applied anodizing voltage of 10 V by using a CNT probe. In addition, Auger electron spectroscopy (AES) measurements performed in the present work confirm that modified structures replace the form of anodizing p-GaAs(100). (Some figures in this article are in colour only in the electronic version)

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.