DSpace Collection:
http://dspace.cityu.edu.hk:80/handle/2031/3772
Mon, 07 Apr 2014 01:15:24 GMT2014-04-07T01:15:24ZThe method of multiple scales and the perturbation-incremental method for autonomous non-linear oscillators
http://dspace.cityu.edu.hk:80/handle/2031/5348
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.Tue, 01 Jan 2008 00:00:00 GMThttp://dspace.cityu.edu.hk:80/handle/2031/53482008-01-01T00:00:00ZIT for school mathematics teaching projects
http://dspace.cityu.edu.hk:80/handle/2031/3783
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.Tue, 01 Jan 2002 00:00:00 GMThttp://dspace.cityu.edu.hk:80/handle/2031/37832002-01-01T00:00:00ZWaveguide mode-solving techniques using finite difference method with coordinate stretching
http://dspace.cityu.edu.hk:80/handle/2031/3782
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.Tue, 01 Jan 2002 00:00:00 GMThttp://dspace.cityu.edu.hk:80/handle/2031/37822002-01-01T00:00:00Z