Hah, this was dead for quite a while. For those who care (at least one it seems!), I'm now in my second year of a joint experimental/theoretical PhD in systems biology. Lots of physics and lots of experiments. Very sunny here too, I would add.
I don't think there's much written on this idea. It's used in statistical physics when you want your argument to be independent of having a discrete collection of matter, so integrals can replace clumsy sums and stuff like that. You can only apply it when doing that is a physical reality. For...
I'm trying to derive fokker-planck equations using the Liouville operator for classical systems. part of it relies on a property I've seen in many places, that applying the Liouville operator e^{Lt} to a product of two functions A(\textbf{X})B(\textbf{X}) is the same as applying the Liouville...
right, i see what you are saying
if you pair each number with it's inverse
you can have every positive number a with 1/a and every negative number b with 1/b, so b and 1/b will cancel their minus signs in every pairing, the only unpairable number will be -1 so that the entire product...
it seems to satisfy the convergence conditions in each case
terms in the product are of the form (a*1/(2a)) = 1/2, each term in the infinite product is then 1/2 which obviously converges.
Multiplying every number
A long time ago I got asked the product of every real number except 0. The person was looking for -1 and the first mapping I tried was a -> 1/a so i got the answer. never really thought about it again. Just realized that you could map a -> 1/(2a) and the answer would...
Homework Statement
A long time ago I got asked the product of every real number except 0. The person was looking for -1 and the first mapping I tried was a -> 1/a so i got the answer. never really thought about it again. Just realized that you could map a -> 1/(2a) and the answer would seem...
yeah that is not what i'd want to do
i spent 4 years in high school researching in a RNA molecular biology lab at Rockefeller then a year at Cold Spring Harbor Labs doing bioinformatics and now I'm studing biological self assembly at my school and in denmark. I'm a class away from a biology...
i'm really interested in doing theoretical biology stuff about theoretical evolution, sequence spaces, autocatalytic sets, stuart kauffman kind of stuff...
this stuff is usually studied in physics programs rather than in biology despite the subject matter
i took a more than usual...
well in case anyone was wondering, the percolation threshold is the probability with which you need to fill in the nodes on a lattice so that in the limit of an infinite lattice, there is a non zero chance that you will have a spanning cluster going across it. for example, one could construct a...
i am having some trouble understanding the meaning of what a percolation threshold is p_{c}.
apparently on triangular lattices a threshold of 0.5 is the result on any sized lattice.
however i can definitely think of a way to fill in half the points on a triangle lattice and not have it span...
have you tried to use Stirling's approximation.
it says that N! roughly is equal to N^{N}\cdot e^{N}.
i've seen through a lot of confusion with that guy, also this is the first order version which it looks like you need. The second order mulitplies that whole thing by \sqrt{2\pi N}}
have you tried to use Stirling's approximation.
it says that N! roughly is equal to N^{N}\cdot e^{-N}.
i've seen through a lot of confusion in statistical mechanics books with that guy, also this is the first order version which it looks like you need. The second order mulitplies that whole...
hello, I'm trying to learn statistical mechanics with feynman's book
he seems to have a lot of times where he thinks something is very clear and then it will take me a few pages of working things out to get what he has jumped to.
i'm having one of those moments on page 15.
i was wondering if...