I attended a colloquium talk on Thursday at the Institute I’m visiting for a couple of days. It was a colloquium on interesting magnetic orderings. There I learned that there are many species of bacteria that produce single domain magnetic crystals of high purity.
Here is a link with some of that information. It seems that this helps the bacteria determine the up and down direction: a really difficult problem in aquatic media. Sometimes it would be really cool to be equipped with such an extra magnetic sense (especially if I get turned around in a city I don’t know). We people fake it by GPS devices or by having a compass, but who walks with a compass nowadays anyway? Also, your favorite GPS device might run out of batteries…
In any case, I often get amazed by such facts
This Thursday we also had a colloquium about biophysics. A simple PDE du/dt = a x -b x^2 + c \nabla x admits a wave solution, which can model the spread of Ecoli and the human being from the African to other parts of the world! Most of the audience were very interested in that talk.
I think biophysics is one of the area full of simple yet interesting problems.
Sorry it should be \nabla^2 x rather than \nabla x
The famous claim that there is evidence for bacterial life in a Martian meteorite (which has, however, been widely disputed) is largely based on the presence of chains of perfect magnetite crystals in the meteorite. On earth, such crystals are produced by bacteria, as you describe.
However, the crystals are apparently different in some ways from those produced by earthly bacteria–but I forget exactly how. Their size, maybe?
Keith
Is n’t that minus sign in front of b term a bit scary?
Cheers
Dmitry
In fact, the equation was first proposed with only $ax$ on the right to model growth of some organism, say E coli. A guy, called Verhulst added the term $-bx^2$, which represents competition for food, etc so that the growth can’t be forever. It is quadratic in x since competition requires two party to occur. Since it models the effects which reduce the growth rate, it is negative. Suppose we neglect the diffusion term, and setting $du/dt$ to zero, we have the steady state solution x = 0 (extinction of the species) or $a/b$, a constant population. So the minus sign makes sense, right?
No, you are right, its the plus sign that would not make sense. I was thinking exactly this way – suppose we neglect the diffusion term, than the eq. is
du/dt = ax-bxˆ2 or
du/dt + bxˆ2 – ax = 0
i.e., oscillator with moved origin. Mistakingly, I thought that the energy (the int. of motion for this eq.) is unbounded from below for the b with minus sign.
Cheers
Oh, Jesus, sorry for being such a muppet
Of course, this is an_unharmonic_ oscillator, not an oscillator with displaced origin. In this case you probably want to consider only positive x’s (like population density), otherwise the energy is unbounded from below.
Cheers
David,
This may be yet another example where
biology is ahead of nanoscience. The quest
for single dot or magnetic domain high density
data storage greater than 10^12 bits/in^2
which is thermally stable is ongoing in the lab.
For example:
M. Haast, ”Pattern magnetic thin films for ultra high density recording”,
Thesis, ISBN-90-3613456 (1999).
Cheers