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 $N$-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 $N$-body simulations including mutual gravitational forces between ring particles as well as direct (inelastic) collisions with identical (up to $N\sim40000$) 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 $G$, $\Sigma$, and $\kappa$ 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, $\epsilon$, 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 $\epsilon$ 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

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

X-ray Diffraction Results from Mars Science Laboratory: Mineralogy of Rocknest at Gale Crater

The Mars Science Laboratory rover Curiosity scooped samples of soil from the Rocknest aeolian bedform in Gale crater. Analysis of the soil with the Chemistry and Mineralogy (CheMin) x-ray diffraction (XRD) instrument revealed plagioclase (~An57), forsteritic olivine (~Fo62), augite, and pigeonite, with minor K-feldspar, magnetite, quartz, anhydrite, hematite, and ilmenite. The minor phases are present at, or near, detection limits. The soil also contains 27 ± 14 weight percent x-ray amorphous material, likely containing multiple Fe^(3+)- and volatile-bearing phases, including possibly a substance resembling hisingerite. The crystalline component is similar to the normative mineralogy of certain basaltic rocks from Gusev crater on Mars and of martian basaltic meteorites. The amorphous component is similar to that found on Earth in places such as soils on the Mauna Kea volcano, Hawaii

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

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

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