384 research outputs found
Nonexistence of stable solutions to quasilinear elliptic equations on Riemannian manifolds
We prove nonexistence of nontrivial, possibly sign changing, stable solutions
to a class of quasilinear elliptic equations with a potential on Riemannian
manifolds, under suitable weighted volume growth conditions on geodesic balls
The secular evolution of the Kuiper belt after a close stellar encounter
We show the effects of the perturbation caused by a passing by star on the
Kuiper belt objects (KBOs) of our Solar System. The dynamics of the Kuiper belt
(KB) is followed by direct -body simulations. The sampling of the KB has
been done with up to , setting the KBOs on initially nearly
circular orbits distributed in a ring of surface density .
This modelization allowed us to investigate the secular evolution of the KB
upon the encounter with the perturbing star. Actually, the encounter itself
usually leads toward eccentricity and inclination distributions similar to
observed ones, but tends also to excite the low-eccentricity population ( around \, from the Sun), depleting this region of
low eccentricities. The following long-term evolution shows a "cooling" of the
eccentricities repopulating the low-eccentricity area. In dependence on the
assumed KBO mass spectrum and sampled number of bodies, this repopulation takes
place in a time that goes from 0.5 Myr to 100 Myr. Due to the unavoidable
limitation in the number of objects in our long-term simulations (), we could not consider a detailed KBO mass spectrum, accounting for low
mass objects, thus our present simulations are not reliable in constraining
correlations among inclination distribution of the KBOs and other properties,
such as their size distribution. However, our high precision long term
simulations are a starting point for future larger studies on massively
parallel computational platforms which will provide a deeper investigation of
the secular evolution (Myr) of the KB over its whole mass spectrum.Comment: 13 pages, 12 figures, 5 table
- …