@article{BrilliantovKrapivskyBodrovaetal.2015, author = {Brilliantov, Nikolai V. and Krapivsky, P. L. and Bodrova, Anna and Spahn, Frank and Hayakawa, Hisao and Stadnichuk, Vladimir and Schmidt, Jurgen}, title = {Size distribution of particles in Saturn's rings from aggregation and fragmentation}, series = {Proceedings of the National Academy of Sciences of the United States of America}, volume = {112}, journal = {Proceedings of the National Academy of Sciences of the United States of America}, number = {31}, publisher = {National Acad. of Sciences}, address = {Washington}, issn = {0027-8424}, doi = {10.1073/pnas.1503957112}, pages = {9536 -- 9541}, year = {2015}, abstract = {Saturn's rings consist of a huge number of water ice particles, with a tiny addition of rocky material. They form a flat disk, as the result of an interplay of angular momentum conservation and the steady loss of energy in dissipative interparticle collisions. For particles in the size range from a few centimeters to a few meters, a power-law distribution of radii, similar to r(-q) with q approximate to 3, has been inferred; for larger sizes, the distribution has a steep cutoff. It has been suggested that this size distribution may arise from a balance between aggregation and fragmentation of ring particles, yet neither the power-law dependence nor the upper size cutoff have been established on theoretical grounds. Here we propose a model for the particle size distribution that quantitatively explains the observations. In accordance with data, our model predicts the exponent q to be constrained to the interval 2.75 <= q <= 3.5. Also an exponential cutoff for larger particle sizes establishes naturally with the cutoff radius being set by the relative frequency of aggregating and disruptive collisions. This cutoff is much smaller than the typical scale of microstructures seen in Saturn's rings.}, language = {en} } @article{SeissSpahn2011, author = {Seiss, Martin and Spahn, Frank}, title = {Hydrodynamics of saturn's dense rings}, series = {Mathematical modelling of natural phenomena}, volume = {6}, journal = {Mathematical modelling of natural phenomena}, number = {4}, publisher = {EDP Sciences}, address = {Les Ulis}, issn = {0973-5348}, doi = {10.1051/mmnp/20116409}, pages = {191 -- 218}, year = {2011}, abstract = {The space missions Voyager and Cassini together with earthbound observations revealed a wealth of structures in Saturn's rings. There are, for example, waves being excited at ring positions which are in orbital resonance with Saturn's moons. Other structures can be assigned to embedded moons like empty gaps, moon induced wakes or S-shaped propeller features. Furthermore, irregular radial structures are observed in the range from 10 meters until kilometers. Here some of these structures will be discussed in the frame of hydrodynamical modeling of Saturn's dense rings. For this purpose we will characterize the physical properties of the ring particle ensemble by mean field quantities and point to the special behavior of the transport coefficients. We show that unperturbed rings can become unstable and how diffusion acts in the rings. Additionally, the alternative streamline formalism is introduced to describe perturbed regions of dense rings with applications to the wake damping and the dispersion relation of the density waves.}, language = {en} } @misc{SeissSpahn2011, author = {Seiß, Martin and Spahn, Frank}, title = {Hydrodynamics of Saturn's dense rings}, series = {Postprints der Universit{\"a}t Potsdam : Postprint Mathematisch Naturwissenschaftliche Reihe}, journal = {Postprints der Universit{\"a}t Potsdam : Postprint Mathematisch Naturwissenschaftliche Reihe}, doi = {10.25932/publishup-41313}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-413139}, pages = {191 -- 218}, year = {2011}, abstract = {The space missions Voyager and Cassini together with earthbound observations re-vealed a wealth of structures in Saturn's rings. There are, for example, waves being excited at ring positions which are in orbital resonance with Saturn's moons. Other structures can be assigned to embedded moons like empty gaps, moon induced wakes or S-shaped propeller features. Further-more, irregular radial structures are observed in the range from 10 meters until kilometers. Here some of these structures will be discussed in the frame of hydrodynamical modeling of Saturn's dense rings. For this purpose we will characterize the physical properties of the ring particle ensemble by mean field quantities and point to the special behavior of the transport coefficients. We show that unperturbed rings can become unstable and how diffusion acts in the rings. Additionally, the alternative streamline formalism is introduced to describe perturbed regions of dense rings with applications to the wake damping and the dispersion relation of the density waves.}, language = {en} } @phdthesis{Albers2006, author = {Albers, Nicole}, title = {On the relevance of adhesion : applications to Saturn's rings}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-10848}, school = {Universit{\"a}t Potsdam}, year = {2006}, abstract = {Since their discovery in 1610 by Galileo Galilei, Saturn's rings continue to fascinate both experts and amateurs. Countless numbers of icy grains in almost Keplerian orbits reveal a wealth of structures such as ringlets, voids and gaps, wakes and waves, and many more. Grains are found to increase in size with increasing radial distance to Saturn. Recently discovered "propeller" structures in the Cassini spacecraft data, provide evidence for the existence of embedded moonlets. In the wake of these findings, the discussion resumes about origin and evolution of planetary rings, and growth processes in tidal environments. In this thesis, a contact model for binary adhesive, viscoelastic collisions is developed that accounts for agglomeration as well as restitution. Collisional outcomes are crucially determined by the impact speed and masses of the collision partners and yield a maximal impact velocity at which agglomeration still occurs. Based on the latter, a self-consistent kinetic concept is proposed. The model considers all possible collisional outcomes as there are coagulation, restitution, and fragmentation. Emphasizing the evolution of the mass spectrum and furthermore concentrating on coagulation alone, a coagulation equation, including a restricted sticking probability is derived. The otherwise phenomenological Smoluchowski equation is reproduced from basic principles and denotes a limit case to the derived coagulation equation. Qualitative and quantitative analysis of the relevance of adhesion to force-free granular gases and to those under the influence of Keplerian shear is investigated. Capture probability, agglomerate stability, and the mass spectrum evolution are investigated in the context of adhesive interactions. A size dependent radial limit distance from the central planet is obtained refining the Roche criterion. Furthermore, capture probability in the presence of adhesion is generally different compared to the case of pure gravitational capture. In contrast to a Smoluchowski-type evolution of the mass spectrum, numerical simulations of the obtained coagulation equation revealed, that a transition from smaller grains to larger bodies cannot occur via a collisional cascade alone. For parameters used in this study, effective growth ceases at an average size of centimeters.}, subject = {Saturn}, language = {en} }