24 research outputs found
Dense Packings of Congruent Circles in Rectangles with a Variable Aspect Ratio
We use computational experiments to find the rectangles of minimum area into
which a given number n of non-overlapping congruent circles can be packed. No
assumption is made on the shape of the rectangles. Most of the packings found
have the usual regular square or hexagonal pattern. However, for 1495 values of
n in the tested range n =< 5000, specifically, for n = 49, 61, 79, 97, 107,...
4999, we prove that the optimum cannot possibly be achieved by such regular
arrangements. The evidence suggests that the limiting height-to-width ratio of
rectangles containing an optimal hexagonal packing of circles tends to
2-sqrt(3) as n tends to infinity, if the limit exists.Comment: 21 pages, 13 figure
Velocity Correlations in Driven Two-Dimensional Granular Media
Simulations of volumetrically forced granular media in two dimensions produce
s tates with nearly homogeneous density. In these states, long-range velocity
correlations with a characteristic vortex structure develop; given sufficient
time, the correlations fill the entire simulated area. These velocity
correlations reduce the rate and violence of collisions, so that pressure is
smaller for driven inelastic particles than for undriven elastic particles in
the same thermodynamic state. As the simulation box size increases, the effects
of veloc ity correlations on the pressure are enhanced rather than reduced.Comment: 12 pages, 6 figures, 21 reference