63 research outputs found
Microscopic dynamics underlying the anomalous diffusion
The time dependent Tsallis statistical distribution describing anomalous
diffusion is usually obtained in the literature as the solution of a non-linear
Fokker-Planck (FP) equation [A.R. Plastino and A. Plastino, Physica A, 222, 347
(1995)]. The scope of the present paper is twofold. Firstly we show that this
distribution can be obtained also as solution of the non-linear porous media
equation. Secondly we prove that the time dependent Tsallis distribution can be
obtained also as solution of a linear FP equation [G. Kaniadakis and P.
Quarati, Physica A, 237, 229 (1997)] with coefficients depending on the
velocity, that describes a generalized Brownian motion. This linear FP equation
is shown to arise from a microscopic dynamics governed by a standard Langevin
equation in presence of multiplicative noise.Comment: 4 pag. - no figures. To appear on Phys. Rev. E 62, September 200
Effect of Density Inhomogeneity on YORP: The case of Itokawa
The effect of density inhomogeneity on the YORP effect for a given shape
model is investigated. A density inhomogeneity will cause an offset between the
center of figure and the center of mass and a re-orientation of the principal
axes away from those associated with the shape alone. Both of these effects can
alter the predicted YORP rate of change in angular velocity and obliquity. We
apply these corrections to the Itokawa shape model and find that its YORP
angular velocity rate is sensitive to offsets between its center of mass and
center of figure, with a shift on the order of 10 meters being able to change
the sign of the YORP effect for that asteroid. Given the non-detection of YORP
for Itokawa as of 2008, this can shed light on the density distribution within
that body. The theory supports a shift of the asteroid center of mass towards
Itokawa's neck region, where there is an accumulation of finer gravels.
Detection of the YORP effect for Itokawa should provide some strong constraints
on its density distribution. This theory could also be applied to asteroids
visited by future spacecraft to constrain density inhomogeneities.Comment: 23 pages, 3 figure
Minimum Energy Configurations in the -Body Problem and the Celestial Mechanics of Granular Systems
Minimum energy configurations in celestial mechanics are investigated. It is
shown that this is not a well defined problem for point-mass celestial
mechanics but well-posed for finite density distributions. This naturally leads
to a granular mechanics extension of usual celestial mechanics questions such
as relative equilibria and stability. This paper specifically studies and finds
all relative equilibria and minimum energy configurations for and
develops hypotheses on the relative equilibria and minimum energy
configurations for bodies.Comment: Accepted for publication in Celestial Mechanics and Dynamical
Astronom
Periodic orbits in the gravity field of a fixed homogeneous cube
In the current study, the existence of periodic orbits around a fixed
homogeneous cube is investigated, and the results have powerful implications
for examining periodic orbits around non-spherical celestial bodies. In the two
different types of symmetry planes of the fixed cube, periodic orbits are
obtained using the method of the Poincar\'e surface of section. While in
general positions, periodic orbits are found by the homotopy method. The
results show that periodic orbits exist extensively in symmetry planes of the
fixed cube, and also exist near asymmetry planes that contain the regular Hex
cross section. The stability of these periodic orbits is determined on the
basis of the eigenvalues of the monodromy matrix. This paper proves that the
homotopy method is effective to find periodic orbits in the gravity field of
the cube, which provides a new thought of searching for periodic orbits around
non-spherical celestial bodies. The investigation of orbits around the cube
could be considered as the first step of the complicated cases, and helps to
understand the dynamics of orbits around bodies with complicated shapes. The
work is an extension of the previous research work about the dynamics of orbits
around some simple shaped bodies, including a straight segment, a circular
ring, an annulus disk, and simple planar plates.Comment: 23 pages, 10 figures, accepted for publication in Astrophysics &
Space Scienc
Equilibria, periodic orbits around equilibria, and heteroclinic connections in the gravity field of a rotating homogeneous cube
This paper investigates the dynamics of a particle orbiting around a rotating
homogeneous cube, and shows fruitful results that have implications for
examining the dynamics of orbits around non-spherical celestial bodies. This
study can be considered as an extension of previous research work on the
dynamics of orbits around simple shaped bodies, including a straight segment, a
circular ring, an annulus disk, and simple planar plates with backgrounds in
celestial mechanics. In the synodic reference frame, the model of a rotating
cube is established, the equilibria are calculated, and their linear
stabilities are determined. Periodic orbits around the equilibria are computed
using the traditional differential correction method, and their stabilities are
determined by the eigenvalues of the monodromy matrix. The existence of
homoclinic and heteroclinic orbits connecting periodic orbits around the
equilibria is examined and proved numerically in order to understand the global
orbit structure of the system. This study contributes to the investigation of
irregular shaped celestial bodies that can be divided into a set of cubes.Comment: 29 pages, 16 figures, accepted for publication in Astrophysics &
Space Scienc
Tidal Evolution of Close Binary Asteroid Systems
We provide a generalized discussion of tidal evolution to arbitrary order in
the expansion of the gravitational potential between two spherical bodies of
any mass ratio. To accurately reproduce the tidal evolution of a system at
separations less than five times the radius of the larger primary component,
the tidal potential due to the presence of a smaller secondary component is
expanded in terms of Legendre polynomials to arbitrary order rather than
truncated at leading order as is typically done in studies of well-separated
system like the Earth and Moon. The equations of tidal evolution including
tidal torques, the changes in spin rates of the components, and the change in
semimajor axis (orbital separation) are then derived for binary asteroid
systems with circular and equatorial mutual orbits. Accounting for higher-order
terms in the tidal potential serves to speed up the tidal evolution of the
system leading to underestimates in the time rates of change of the spin rates,
semimajor axis, and mean motion in the mutual orbit if such corrections are
ignored. Special attention is given to the effect of close orbits on the
calculation of material properties of the components, in terms of the rigidity
and tidal dissipation function, based on the tidal evolution of the system. It
is found that accurate determinations of the physical parameters of the system,
e.g., densities, sizes, and current separation, are typically more important
than accounting for higher-order terms in the potential when calculating
material properties. In the scope of the long-term tidal evolution of the
semimajor axis and the component spin rates, correcting for close orbits is a
small effect, but for an instantaneous rate of change in spin rate, semimajor
axis, or mean motion, the close-orbit correction can be on the order of tens of
percent.Comment: 40 pages, 2 tables, 8 figure
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