DSpace Collection:

The method of multiple scales and the perturbation-incremental method for autonomous non-linear oscillators

2010-04-08T06:11:14Z

Title: The method of multiple scales and the perturbation-incremental method for autonomous non-linear oscillators Authors: Ng, Kwok Tim (伍國添) Abstract: In this report, a method of multiple scales is presented for the analysis of weakly non-linear oscillators in the form 2 2 2 0 , d u du u F u dt dt +ω =ε  , where , du F u dt is arbitrary non-linear function of its arguments and 0 <ε ≪1. Maple, a computer tool, is used for the analysis. Then a perturbation-incremental method is presented for the analysis of strongly non-linear oscillators in the form ɺxɺ+ g ( x) =λ f ( x, xɺ ) xɺ , where g ( x) and f ( x, xɺ ) are arbitrary non-linear functions of their arguments and λ > 0 . The perturbation-incremental method is an extension of the classical perturbation method to the case where λ is not necessarily small. The method incorporates salient features from both the perturbation method and the incremental method. Matlab is used for the perturbation-incremental method. Limit cycles of an oscillator can be calculated to any desired degree of accuracy. The stability of a limit cycle is also considered.

IT for school mathematics teaching projects

2007-05-15T00:58:29Z

Title: IT for school mathematics teaching projects Authors: Sam, Chi Ngai (岑智毅) Abstract: MathPages is a utility to view equations in your Internet browser by transforming mathematics language into equation. MathPages is run on Internet. You can insert any equation which will then be complied as visualized pictures. In the past, people could not discuss mathematics interactively on Internet, but MathPages completely changed this situation. Now, by the power of MathPages, people, both teachers and students, can discuss mathematics on message board with MathPages supported, type and check solutions for exercises on a web pages and build up a web site with mathematical equations in a short time. The concept of mathematical communication on Internet is new and it is introduced by this project. This project is a basic element of IT for School Mathematics Teaching. Teachers, students and developers can develop any mathematical materials by the Power of MathPages. We hope that we can see some message boards, discussion groups, ICQ plug-in, real-time multiple choose systems, online exercise books, artificial intelligence solution provider and any mathematical related materials integrated with MathPages in the future.

Waveguide mode-solving techniques using finite difference method with coordinate stretching

2007-05-14T03:31:07Z

Title: Waveguide mode-solving techniques using finite difference method with coordinate stretching Authors: Lin, Li Ming (林立鳴) Abstract: Dielectric waveguides are commonly used in photonic integrated circuits and their accurate modeling is essential for the development of new, higher performance optical components required by high-bandwidth communications system. Modal analysis is a critical part of the waveguide design process, providing information on the modes that may propagate, such as propagation constants and mode shapes. In brief, by reformulating the Maxwell equation, the problem is deducted to an eigenvalue equation and it can be discretized by a finite difference method. The full-vector waveguide equation is solved by the classic inverse iteration method and the alternating-direction-implicit (ADI). In addition, coordinate stretching technique is employed, which effectively removes the sensitivity of the calculated results to the size of the computational domain.