[Shootout-list] n-body anomalies

[Jon Harrop]

On Thursday 05 May 2005 03:44, Greg Buchholz wrote:
>     Just a few questions about the n-body test.  It looks like we're
> mostly computing the amount of round-off error in simulating our
> algorithm, correct?

Do you mean most of the code or most of the time is spent computing round-off 
error?

In molecular dynamics, the particles are artificially sped up or slowed down 
to maintain the energy (or, more often, the temperature). So round-off error 
doesn't cause the energy to deviate when it is supposed to remain constant.

> What does a negative energy imply (i.e. the answer is -0.169)?

Negative energy probably implies nothing at all. Energy is often taken from an 
arbitrary origin, such as the potential energy when all particles are 
infinitely separated.

> And why isn't energy simply computed as 1/2*m*v^2?

By "energy", you probably mean the total energy = kinetic + potential. So 
you've got that kinetic term:

  1/2 m v^2

but you also have to add terms like:

  - G M m / r

for each pair of particles, where "r" is their separation.

I haven't looked carefully but it looks like the code is missing "G" and a 
factor of "2" (as it only counts (i, j) pairs satisfying i > j). Also, the 
sun doesn't weigh 39kg. ;-)

-- 
Dr Jon D Harrop, Flying Frog Consultancy Ltd.
Objective CAML for Scientists
http://www.ffconsultancy.com/products/ocaml_for_scientists