Attractor Reconstruction of Lorenz Attractor

Attractor reconstruction of Lorenz attractor with Python.

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Breaking WIFI WEP

Just found that WEP can be decrypted within 30mins (depends on how fast the sniffer works). It seems like it is time to change to WPA encryption 😦

15-March-2011: If you WIFI card has been patched (by some means), you can break WEP WIFI within 10 seconds.

Search for the available base stations.
WEP key is decrypted.

Lorenz Attractor

My salutation to Edward Lorenz, the founder of Chaos Theory. These graphs are generated through Python and SciPy. Try dumping the following codes into the IPython and have fun changing the view of the Lorenz attactor.

Lorenz attractor.
Lorenz attractor.
Lorenz attractor.
Lorenz attractor – YZ view.
Lorenz attractor.
Lorenz attractor – side view.

The following is my Python source code.
Continue reading “Lorenz Attractor”

A Joke of Pi

Recently I read a joke from a book named It must be Beautiful: Great Equation of Modern Science (Farmelo, 2002).

The author wrote a joke:

A mathematician, a physicist, an engineer and a biologist are together and someone asks them what is the value of \pi .

The mathematician responds crisply that it is “equal to the circumference of a circle divided by its diameters”.

The physicist counters that is is “3.141593, give or take 0.000001”

The engineer says it is “about 3”.

And, the biologist asks back, “What is \pi ?”

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Someone was not happy with this joke and asked me what is the value of \pi .
I said, “I am just a tutor. Please ask your lecturer.”

IEEE 802.15.5 – Standard for both High-Rate and Low-Rate Wireless Personal Area Networks (WPAN)

WPAN mesh and 802.15 family standards
WPAN mesh and 802.15 family standards.

There are two famous IEEE standards for mesh technology – IEEE 802.15.3x for high-rate WPAN and IEEE 802.15.4x for low-rate WPAN. Question is always arisen on the interoperability between these two standards. To answer that question, IEEE has introduced a new standard, IEEE 802.15.5 that is built on  the mesh sublayer on top of both IEEE 802.15.3x and IEEE 802.15.4x (refer to the figure).

More discussion on such standard can be found in IEEE Communication magazine in [1].

Reference:
[1]  M. Lee, R. Zhang, C. Zhu, T. R. Park, C. S. Shin, Y.A. Jeon, S. H. Lee, S. S. Choi, Y. Liu, S. W. Park, “Meshing Wireless Personal Area Networks: Introducing IEEE 802.15.5”, IEEE Communication Magazine, January 2010, page 54 – 61.

Constructing a Variable Speed DC Driver System to Achieve Maximum Speed

Closed-Loop DC Motor Speed Control

Some students ask me how to construct a variable speed DC driver system to achieve maximum speed.

I think this link/pdf has given a good explanation on the rough design of the said system. And of cause, it is an incomplete version and perhaps it even contains wrong information.

So, good luck~.

Time Delay of An Underdamped Second Order System

Transient response for a second-order system.

A student asked me how to find the time delay, t_d  for a second-order system by applying mathematical equation.

Let c_{final} denote the final value of the waveform. Then, the rise time t_r will be the time duration between 0.1c_{final} to 0.9c_{final} .

Since the time delay t_d equals to the time for the waveform to reach 0.5c_{final}. My rough idea for the mathematical equation is:
t_d \approx 1.25 * t_r / 2 .

Just an approximation as the waveform between 0.1c_{final} to 0.9c_{final} is not a linear line.