# [seqfan] Re: physics

RGWv rgwv at rgwv.com
Sun Nov 7 19:08:37 CET 2010

```?I hope that these comments can find their way into the sequence.

-----Original Message-----
From: Douglas McNeil
Sent: Sunday, November 07, 2010 8:01 AM
To: Sequence Fanatics Discussion list
Subject: [seqfan] physics

Several recent sequences (A181633-35) reference "unmatter".  Of course
sequences don't need to have any connection to the real world, only to
be well-defined, and if I understand them correctly these sequences
should be.  (I haven't actually checked the values.)  But as physics
they're, er, idiosyncratically speculative.

I'm not sure what the appropriate edit is to clarify the situation, or
even if one is needed.

On a happier note, I finally have an excuse to mention a gorgeous
physics-related sequence, my favourite sequence of the year:
http://oeis.org/classic/A180230

---
A180230   a(n) is the minimal number of additions needed to grow to
radius n, in the two-dimensional abelian sandpile growth model with
h=2.

2, 6, 10, 22, 26, 50, 66, 78, 122, 142, 154, 194, 254, 270, 342, 386,
418, 490, 518, 578, 654, 698, 766, 914, 942, 1074, 1150, 1178, 1310,
1366, 1410, 1570, 1646, 1794, 1894

COMMENT

The abelian sandpile growth model starts with height h on every site
of the square grid.  An addition increases the height of the origin by
1. After each addition, the model is stabilized by toppling unstable
sites.  A site is unstable if its height is at least 4; in a toppling,
its height decreases by 4 and the height of its neighbors increases by
1.

If h=2, then for any number of additions, the set of sites that
toppled at least once is a square. This was proved in Fey-Redig-2008.
For all n, a(n) <= (2n+3)^2. In Fey-Levine-Peres-2010, it was proved
that for n large enough, a(n) >= Pi/4 n^2.
---

This is the kind I like best of all.  A real physics problem;
references to published work; a simple code attached; a concise
description (although it could use a little clarification, you can
resolve the ambiguity from the examples); values I can reproduce; and
obviously a member of an interesting class of problem.  Also
apparently written by someone with no prior submissions.

Doug

--
Department of Earth Sciences
University of Hong Kong

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