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Topic: This Week's Finds in Mathematical Physics (Week 296)
Replies: 3   Last Post: May 13, 2010 9:00 PM

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john baez

Posts: 460
Registered: 12/6/04
Re: This Week's Finds in Mathematical Physics (Week 296)
Posted: May 10, 2010 3:21 AM
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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 1-port I want to mention:

5. The "memristor". This is a 1-port 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 1-ports.
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), 507-519. 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), 249-252.
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.




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