ABSTRACTThis paper models maximum entropy configurations of idealized gravitational ring systems. Such configurations are of interest because systems generally evolve toward an ultimate state of maximum randomness. For simplicity, attention is confined to ultimate states for which interparticle interactions are no longer of first order importance. The planets, in their orbits about the sun, are one example of such a ring system. The extent to which the present approximation yields insight into ring systems such as Saturn's is explored briefly.
AbstractNegative refraction of acoustic waves is demonstrated through underwater experiments conducted at ultrasonic frequencies on a 3D locally resonant acoustic metafluid made of soft porous silicone-rubber micro-beads suspended in a yield-stress fluid. By measuring the refracted angle of the acoustic beam transmitted through this metafluid shaped as a prism, we determine the acoustic index to water according to Snell’s law. These experimental data are then compared with an excellent agreement to calculations performed in the framework of Multiple Scattering Theory showing that the emergence of negative refraction depends on the volume fraction $$\Phi$$
Φ
of the resonant micro-beads. For diluted metafluid ($$\Phi =3\%$$
Φ
=
3
%
), only positive refraction occurs whereas negative refraction is demonstrated over a broad frequency band with concentrated metafluid ($$\Phi =17\%$$
Φ
=
17
%
).
Experimental demonstration of negative refraction with 3D locally resonant acoustic metafluids