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Re: This Week's Finds in Mathematical Physics (Week 296)
Posted:
May 10, 2010 3:21 AM


In article <83mci7F4suU3@mid.individual.net>, Dirk Bruere at NeoPax <dirk.bruere@gmail.com> wrote:
>Maybe you could do a bit on memristors?
Here's what I said about them in "week294":
Here's the last 1port I want to mention:
5. The "memristor". This is a 1port where the momentum p is a function of the displacement q:
p = f(q)
The function f is usually called the "memristance". It was invented and given this name by Leon Chua in 1971. The idea was that it completes a collection of four closely related 1ports. In "week290" I listed the other three, namely the resistor:
p' = f(q')
the capacitor:
q = f(p')
and the inductor:
p = f(q') The memristor came later because it's inherently nonlinear. Why? A *linear* memristor is just a linear resistor, since we can differentiate the linear relationship p = Mq and get p' = Mq'. But if p = f(q) for a nonlinear function f we get something new:
p' = f'(q) q'
So, we see that in general, a memristor acts like a resistor whose resistance is some function of q. But q is the time integral of the current q'. So a nonlinear memristor is like a resistor whose resistance depends on the time integral of the current that has flowed through it! Its resistance depends on its history. So, it has a "memory"  hence the name "memristance".
Memristors have recently been built in a number of ways, which are nicely listed here:
7) Wikipedia, Memristor, http://en.wikipedia.org/wiki/Memristor
Electrical engineering journals are notoriously resistant to the of open access, and I don't think there's a successful equivalent of the "arXiv" in this field. Shame on them! So, you have to nose around to find a freely accessible copy of Chua's original paper on memristors:
8) Leon Chua, Memristor, the missing circuit element, IEEE Transactions on Circuit Theory 18 (1971), 507519. Also available at http://www.lane.ufpa.br/rodrigo/chua/Memristor_chua_article.pdf To see what the mechnical or chemical analogue of a memristor is like, try this:
9) G. F. Oster and D. M. Auslander, The memristor: a new bond graph element, Trans. ASME, J. Dynamic Systems, Measurement and Control 94 (1972), 249252. Also available as http://nature.berkeley.edu/~goster/pdfs/Memristor.pdf
Memristors supposedly have a bunch of interesting applications, but I don't understand them yet. I also don't understand "memcapacitors" and "meminductors". The above PDF file also contains a New Scientist article on the wonders of these.



