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I have to give a 10 minute physics talk that have to involve a fair bit of mathematics -- i.e. not just qualitative/handwaving material to some undergrads. I have wasted the last 3 hours looking for appropriate topics and have pretty much lost the will to live. Any suggestions would be greatly appreciated.

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closed as not constructive by David Z Oct 7 '11 at 18:22

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What kind of mathematics? Any kind? Why not Kepler's laws? You probably should narrow down the question quite a bit by telling us what the expected background the audience is supposed to have, what sorts of physics (real classical stuff or more cutting edge stuff) and what sorts of mathematics you want to involve. –  Willie Wong Oct 7 '11 at 15:26
    
@WillieWong: You are quite right. The audience is a mixture of undergrads from 1st years to 3rd years. The first years are assumed to know a fair share of classical mechanics and have heard of the more exotic (e.g. quantum) ideas. The third years are familiar with fluid dynamics, quatum physics, etc. Any sort of mathematics will do. –  Markov Oct 7 '11 at 15:32
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@WillieWong: Worse comes to worst, I am happy to sacrifice the 1st years to benefit the higher years... –  Markov Oct 7 '11 at 15:36
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This strikes me as a "make a list" question that would be better suited for char then as a question. I'm not going to close it immediately as I note that Markov hasn't the requisite rep (20) for using chat. –  dmckee Oct 7 '11 at 17:01
    
The vast applicability of the harmonic oscillator model may be very interesting and tractable for your constraints. –  Jen Oct 7 '11 at 17:02

2 Answers 2

As a materials scientist I'm a bit biased, but I think that the Johnson-Mehl-Avrami-Kolmogorov kinetics of phase changes/crystal growth is one of the coolest mathematical physics talks that can be covered in 10 minutes. The wikipedia article is accurate, but not as enlightening as I'd like. My favorite introductory discussion appears in Kinetics of Materials by Baluffi, Allen, and Carter. I can't send that to you, but Craig Carter's lecture notes aren't a bad place to start. John Cahn's extension of this approach by the method of time cones has really nice parallels to special relatively (weird, right?) and could add some sparkle to a talk for undergrads. Let me know if this is something you'd be interested in pursuing and I can provide additional guidance/information.

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+1: a really nice piece of physics. And I'd say that everyone is biased in his own way :) –  Slaviks Oct 7 '11 at 17:30
    
Thanks, this is very intriguing. I would surely appreciate it if you could provide any extra interesting ref. material. :-) –  Markov Oct 7 '11 at 18:06
    
I must confess to not being too familiar with this piece of physics myself, so I'll be learning too! –  Markov Oct 7 '11 at 18:12

Just an idea that I have used once in a somewhat similar situation:

Explain the Casimir force and then "derive" it using analytic continuation of Riemann zeta function: $\sum_n n^3 \stackrel{!}{=} \zeta(-3) =1/120$. Depending on your audience, emphasis more physics or math. You probably should include an experimental graph confirming the pre-factor. This trick usually provokes quite a few questions.

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Thanks, this is a very interesting topic too. :-) –  Markov Oct 7 '11 at 18:09

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