28 research outputs found
Coefficient of normal restitution of viscous particles and cooling rate of granular gases
We investigate the cooling rate of a gas of inelastically interacting
particles. When we assume velocity dependent coefficients of restitution the
material cools down slower than with constant restitution. This behavior might
have large influence to clustering and structure formation processes.Comment: 3 figures, Phys. Rev. E (in press
Cooling dynamics of a dilute gas of inelastic rods: a many particle simulation
We present results of simulations for a dilute gas of inelastically colliding
particles. Collisions are modelled as a stochastic process, which on average
decreases the translational energy (cooling), but allows for fluctuations in
the transfer of energy to internal vibrations. We show that these fluctuations
are strong enough to suppress inelastic collapse. This allows us to study large
systems for long times in the truely inelastic regime. During the cooling stage
we observe complex cluster dynamics, as large clusters of particles form,
collide and merge or dissolve. Typical clusters are found to survive long
enough to establish local equilibrium within a cluster, but not among different
clusters. We extend the model to include net dissipation of energy by damping
of the internal vibrations. Inelatic collapse is avoided also in this case but
in contrast to the conservative system the translational energy decays
according to the mean field scaling law, E(t)\propto t^{-2}, for asymptotically
long times.Comment: 10 pages, 12 figures, Latex; extended discussion, accepted for
publication in Phys. Rev.
Spatial Structure and Coherent Motion in Dense Planetary Rings Induced by Self-Gravitational Instability
We investigate the formation of spatial structure in dense, self-gravitating
particle systems such as Saturn's B-ring through local -body simulations to
clarify the intrinsic physics based on individual particle motion. In such a
system, Salo (1995) showed that the formation of spatial structure such as
wake-like structure and particle grouping (clump) arises spontaneously due to
gravitational instability and the radial velocity dispersion increases as the
formation of the wake structure. However, intrinsic physics of the phenomena
has not been clarified. We performed local -body simulations including
mutual gravitational forces between ring particles as well as direct
(inelastic) collisions with identical (up to ) particles. In the
wake structure particles no longer move randomly but coherently. We found that
particle motion was similar to Keplerian motion even in the wake structure and
that the coherent motion was produced since the particles in a clump had
similar eccentricity and longitude of perihelion. This coherent motion causes
the increase and oscillation in the radial velocity dispersion. The mean
velocity dispersion is rather larger in a more dissipative case with a smaller
restitution coefficient and/or a larger surface density since the coherence is
stronger in the more dissipative case. Our simulations showed that the
wavelength of the wake structure was approximately given by the longest
wavelength \hs{\lambda}{cr} = 4\pi^2 G\Sigma/\kappa^2 in the linear theory of
axisymmetric gravitational instability in a thin disk, where , , and
are the gravitational constant, surface density, and a epicyclic
frequency.Comment: Accepted by Earth, Planets, and Space. 39 pages, 20 figures.
PostScript files also available from
http://www.geo.titech.ac.jp/nakazawalab/hdaisaka/works
Coefficient of restitution for elastic disks
We calculate the coefficient of restitution, , starting from a
microscopic model of elastic disks. The theory is shown to agree with the
approach of Hertz in the quasistatic limit, but predicts inelastic collisions
for finite relative velocities of two approaching disks. The velocity
dependence of is calculated numerically for a wide range of
velocities. The coefficient of restitution furthermore depends on the elastic
constants of the material via Poisson's number. The elastic vibrations absorb
kinetic energy more effectively for materials with low values of the shear
modulus.Comment: 25 pages, 12 Postscript figures, LaTex2
Simulation for the oblique impact of a lattice system
The oblique collision between an elastic disk and an elastic wall is
numerically studied.
We investigate the dependency of the tangential coefficient of restitution on
the incident angle of impact.
From the results of simulation, our model reproduces experimental results and
can be explained by a phenomenological theory of the oblique impact.Comment: 30 pages, 9 figures, submitted to J. Phys. Soc. Japa
Accelerated planetesimal growth in self-gravitating protoplanetary discs
In this paper we consider the evolution of small planetesimals in marginally
stable, self-gravitating protoplanetary discs. The drag force between the disc
gas and the embedded planetesimals generally causes the planetesimals to drift
inwards through the disc at a rate that depends on the particle size. In a
marginally stable, self-gravitating disc, however, the planetesimals are
significantly influenced by the non-axisymmetric spiral structures resulting
from the growth of the gravitational instability. For small particles, that are
strongly coupled to the disc gas, and for large particles, that have
essentially decoupled from the disc gas, the effect is not particularly
significant. Intermediate sized particles, which would generally have the
largest radial drift rates, do, however, become significantly concentrated at
the peaks of the spiral arms. These high density regions may persist for, of
order, an orbital period and may attain densities comparable to that of the
disc gas. Although at the end of the simulation only ~ 25 % of the planetesimal
particles lie in regions of enhanced density, during the course of the
simulation at least 75 % of the planetesimal particles have at some stage been
in a such a region. We find that the concentration of particles in the spiral
arms results in an increased collision rate, an effect that could significantly
accelerate planetesimal growth. The density enhancements may also be sufficient
for the growth of planetesimals through direct gravitational collapse. The
interaction between small planetesimals and self-gravitating spiral structures
may therefore play an important role in the formation of large planetesimals
that will ultimately coagulate to form terrestrial planets or the cores of
gas/ice giant planets.Comment: 11 pages, 9 figures, Accepted for publication in MNRA
Planetary Rings
Planetary rings are the only nearby astrophysical disks, and the only disks
that have been investigated by spacecraft. Although there are significant
differences between rings and other disks, chiefly the large planet/ring mass
ratio that greatly enhances the flatness of rings (aspect ratios as small as
1e-7), understanding of disks in general can be enhanced by understanding the
dynamical processes observed at close-range and in real-time in planetary
rings. We review the known ring systems of the four giant planets, as well as
the prospects for ring systems yet to be discovered. We then review planetary
rings by type. The main rings of Saturn comprise our system's only dense broad
disk and host many phenomena of general application to disks including spiral
waves, gap formation, self-gravity wakes, viscous overstability and normal
modes, impact clouds, and orbital evolution of embedded moons. Dense narrow
rings are the primary natural laboratory for understanding shepherding and
self-stability. Narrow dusty rings, likely generated by embedded source bodies,
are surprisingly found to sport azimuthally-confined arcs. Finally, every known
ring system includes a substantial component of diffuse dusty rings. Planetary
rings have shown themselves to be useful as detectors of planetary processes
around them, including the planetary magnetic field and interplanetary
impactors as well as the gravity of nearby perturbing moons. Experimental rings
science has made great progress in recent decades, especially numerical
simulations of self-gravity wakes and other processes but also laboratory
investigations of coefficient of restitution and spectroscopic ground truth.
The age of self-sustained ring systems is a matter of debate; formation
scenarios are most plausible in the context of the early solar system, while
signs of youthfulness indicate at least that rings have never been static
phenomena.Comment: 82 pages, 34 figures. Final revision of general review to be
published in "Planets, Stars and Stellar Systems", P. Kalas and L. French
(eds.), Springer (http://refworks.springer.com/sss
Volatile and Organic Compositions of Sedimentary Rocks in Yellowknife Bay, Gale crater, Mars
H₂O, CO₂, SO₂, O₂, H₂, H₂S, HCl, chlorinated hydrocarbons, NO and other trace gases were evolved during pyrolysis of two mudstone samples acquired by the Curiosity rover at Yellowknife Bay within Gale crater, Mars. H₂O/OH-bearing phases included 2:1 phyllosilicate(s), bassanite, akaganeite, and amorphous materials. Thermal decomposition of carbonates and combustion of organic materials are candidate sources for the CO₂. Concurrent evolution of O₂ and chlorinated hydrocarbons suggest the presence of oxychlorine phase(s). Sulfides are likely sources for S-bearing species. Higher abundances of chlorinated hydrocarbons in the mudstone compared with Rocknest windblown materials previously analyzed by Curiosity suggest that indigenous martian or meteoritic organic C sources may be preserved in the mudstone; however, the C source for the chlorinated hydrocarbons is not definitively of martian origin
Mineralogy of a Mudstone at Yellowknife Bay, Gale Crater, Mars
Sedimentary rocks at Yellowknife Bay (Gale Crater) on Mars include mudstone sampled by the Curiosity rover. The samples, John Klein and Cumberland, contain detrital basaltic minerals, Ca-sulfates, Fe oxide/hydroxides, Fe-sulfides, amorphous material, and trioctahedral smectites. The John Klein smectite has basal spacing of ~10 Å indicating little interlayer hydration. The Cumberland smectite has basal spacing at ~13.2 Å as well as ~10 Å. The ~13.2 Å spacing suggests a partially chloritized interlayer or interlayer Mg or Ca facilitating H_2O retention. Basaltic minerals in the mudstone are similar to those in nearby eolian deposits. However, the mudstone has far less Fe-forsterite, possibly lost with formation of smectite plus magnetite. Late Noachian/Early Hesperian or younger age indicates that clay mineral formation on Mars extended beyond Noachian time
A Habitable Fluvio-Lacustrine Environment at Yellowknife Bay, Gale Crater, Mars
The Curiosity rover discovered fine-grained sedimentary rocks, inferred to represent an ancient lake, preserve evidence of an environment that would have been suited to support a Martian biosphere founded on chemolithoautotrophy. This aqueous environment was characterized by neutral pH, low salinity, and variable redox states of both iron and sulfur species. C, H, O, S, N, and P were measured directly as key biogenic elements, and by inference N and P are assumed to have been available. The environment likely had a minimum duration of hundreds to tens of thousands of years. These results highlight the biological viability of fluvial-lacustrine environments in the post-Noachian history of Mars