\begin{thebibliography}{212}
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  \def\selectlanguage#1{\relax}\fi

\bibitem[\protect\citename{Albers and Spahn, }2006]{albers2006}
Albers, N., and Spahn, F. 2006.
\newblock {The influence of particle adhesion on the stability of agglomerates
  in Saturn's rings}.
\newblock {\em Icarus}, {\bf 181}, 292--301.

\bibitem[\protect\citename{{Albers} {et~al.}, }2015]{albers2015}
{Albers}, N., {Sremcevic}, M., and {Esposito}, L.~W. 2015.
\newblock {A new moon-induced structure}.
\newblock {Page  874 of:} {\em {European Planetary Science Congress 2015}},
  vol. 10.

\bibitem[\protect\citename{Altobelli {et~al.}, }2007]{altobelli2007}
Altobelli, N., Spilker, L., Pilorz, S., Brooks, S., Edgington, S., Wallis, B.,
  and Flasar, M. 2007.
\newblock {C ring fine structures revealed in thermal infrared}.
\newblock {\em Icarus}, {\bf 191}, 691--701.

\bibitem[\protect\citename{{Altobelli} {et~al.}, }2009]{altobelli2009}
{Altobelli}, N., {Spilker}, L., {Pilorz}, S., {Leyrat}, C., {Eddgington}, S.,
  {Wallis}, B., and {Flandes}, A. 2009.
\newblock {Thermal phase curves observed in Saturn's main rings by
  Cassini-CIRS: Detection of an opposition effect?}
\newblock {\em Geophys. Res. Lett.}, {\bf 36}, L10105.

\bibitem[\protect\citename{Araki, }1988]{araki1988}
Araki, S. 1988.
\newblock {The dynamics of particle disks. II. Effects of spin degrees of
  freedom}.
\newblock {\em Icarus}, {\bf 76}, 182--198.

\bibitem[\protect\citename{Araki, }1991]{araki1991}
Araki, S. 1991.
\newblock {The dynamics of particle disks III. Dense and spinning particle
  disks.}
\newblock {\em Icarus}, {\bf 90}, 139--171.

\bibitem[\protect\citename{{Araki} and {Tremaine}, }1986]{araki1986}
{Araki}, S., and {Tremaine}, S. 1986.
\newblock {The dynamics of dense particle disks.}
\newblock {\em Icarus}, {\bf 65}, 83--109.

\bibitem[\protect\citename{{Attree} {et~al.}, }2012]{attree2012}
{Attree}, N.~O., {Murray}, C.~D., {Cooper}, N.~J., and {Williams}, G.~A. 2012.
\newblock {Detection of Low-velocity Collisions in Saturn's F Ring}.
\newblock {\em Astrophys. J. Lett.}, {\bf 755}, L27.

\bibitem[\protect\citename{{Bailli{\'e}} {et~al.}, }2011]{baillie2011}
{Bailli{\'e}}, K., {Colwell}, J.~E., {Lissauer}, J.~J., {Esposito}, L.~W., and
  {Srem{\v c}evi{\'c}}, M. 2011.
\newblock {Waves in Cassini UVIS stellar occultations. 2. The C ring}.
\newblock {\em Icarus}, {\bf 216}, 292--308.

\bibitem[\protect\citename{{Barbara} and {Esposito}, }2002]{Barbara02}
{Barbara}, J.~M., and {Esposito}, L.~W. 2002.
\newblock {Moonlet collisions and the effects of tidally modified accretion in
  Saturn's F ring}.
\newblock {\em Icarus}, {\bf 160}, 161--171.

\bibitem[\protect\citename{{Barkstrom}, }1973]{barkstrom1973}
{Barkstrom}, B.~R. 1973.
\newblock {A comparison of the Minneart reflectance law and the reflectance
  from a nonconservative isotropic scattering atmosphere}.
\newblock {\em J. Geophys. Res.}, {\bf 78}, 6370--6372.

\bibitem[\protect\citename{{Barnes} and {Hut}, }1986]{barnes1986}
{Barnes}, J., and {Hut}, P. 1986.
\newblock {A hierarchical $O(N \log N)$ force-calculation algorithm}.
\newblock {\em Nature}, {\bf 324}, 446--449.

\bibitem[\protect\citename{Belleman {et~al.}, }2008]{Belleman2008103}
Belleman, Robert~G., Bédorf, Jeroen, and Zwart, Simon F.~Portegies. 2008.
\newblock High performance direct gravitational N-body simulations on graphics
  processing units II: An implementation in CUDA.
\newblock {\em New Astronomy}, {\bf 13}(2), 103 -- 112.

\bibitem[\protect\citename{{Borderies} {et~al.}, }1985]{borderies1985}
{Borderies}, N., {Goldreich}, P., and {Tremaine}, S. 1985.
\newblock {A granular flow model for dense planetary rings}.
\newblock {\em Icarus}, {\bf 63}, 406--420.

\bibitem[\protect\citename{{Borderies} {et~al.}, }1989]{Borderies89}
{Borderies}, N., {Goldreich}, P., and {Tremaine}, S. 1989.
\newblock {The formation of sharp edges in planetary rings by nearby
  satellites}.
\newblock {\em Icarus}, {\bf 80}, 344--360.

\bibitem[\protect\citename{{Brahic}, }1977]{brahic1977}
{Brahic}, A. 1977.
\newblock {Systems of colliding bodies in a gravitational field. I - Numerical
  simulation of the standard model}.
\newblock {\em Astron. \& Astrophys.}, {\bf 54}, 895--907.

\bibitem[\protect\citename{Bridges {et~al.}, }1984]{bridges1984}
Bridges, F.G., Hatzes, A.P., and Lin, D.N.C. 1984.
\newblock {Structure, stability and evolution of Saturn's rings}.
\newblock {\em Nature}, {\bf 309}, 333--338.

\bibitem[\protect\citename{Brilliantov {et~al.}, }2015]{brilliantov2015}
Brilliantov, N., Krapivsky, P.L., Bodrova, A, Spahn, F, Hayakawa, H.,
  Stadnichuk, V., and Schmidt, J. 2015.
\newblock {Size distribution of particles in Saturn's rings from aggretion and
  fragementation}.
\newblock {\em PNAS}, {\bf 112}, 9536--9541.

\bibitem[\protect\citename{{Brilliantov} {et~al.}, }2007]{brilliantov2007}
{Brilliantov}, N.~V., {Albers}, N., {Spahn}, F., and {P{\"o}schel}, T. 2007.
\newblock {Collision dynamics of granular particles with adhesion}.
\newblock {\em Phys. Rev. E}, {\bf 76}(5), 051302.

\bibitem[\protect\citename{Brilliantov {et~al.}, }1996]{brilliantov1996}
Brilliantov, N.V., Spahn, F., Hertzsch, J.-M., and P{\"o}schel, T. 1996.
\newblock Model for collisions in granular gases.
\newblock {\em Phys. Rev. E}, {\bf 53}, 5382--5392.

\bibitem[\protect\citename{Burns and Cuzzi, }2006]{burns2006}
Burns, J.A., and Cuzzi, J.~N. 2006.
\newblock {Our local astrophysical laboratory}.
\newblock {\em Science}, {\bf 312}, 1753--1755.

\bibitem[\protect\citename{{Camichel}, }1958]{camichel1958}
{Camichel}, H. 1958.
\newblock {Mesures photom{\'e}triques de Saturne et de son anneau}.
\newblock {\em Annales d'Astrophysique}, {\bf 21}, 231--242.

\bibitem[\protect\citename{{Canup}, }2010]{canup2010}
{Canup}, R.~M. 2010.
\newblock {Origin of Saturn's rings and inner moons by mass removal from a lost
  Titan-sized satellite}.
\newblock {\em Nature}, {\bf 468}, 943--946.

\bibitem[\protect\citename{{Chandrasekhar}, }1960]{chandrasekhar1960}
{Chandrasekhar}, S. 1960.
\newblock {\em {Radiative transfer}}.
\newblock New York: Dover.

\bibitem[\protect\citename{Chandrasekhar, }1969]{Chandrasekhar69}
Chandrasekhar, S. 1969.
\newblock {\em {Ellipsoidal Figures of Equilibrium}}.
\newblock Yale Univ. Press.

\bibitem[\protect\citename{{Charnoz} {et~al.}, }2009]{charnoz2009}
{Charnoz}, S., {Morbidelli}, A., {Dones}, L., and {Salmon}, J. 2009.
\newblock {Did Saturn's rings form during the Late Heavy Bombardment?}
\newblock {\em Icarus}, {\bf 199}, 413--428.

\bibitem[\protect\citename{{Charnoz} {et~al.}, }2010]{charnoz2010}
{Charnoz}, S., {Salmon}, J., and {Crida}, A. 2010.
\newblock {The recent formation of Saturn's moonlets from viscous spreading of
  the main rings}.
\newblock {\em Nature}, {\bf 465}, 752--754.

\bibitem[\protect\citename{{Charnoz} {et~al.}, }2011]{charnoz2011}
{Charnoz}, S., {Crida}, A., {Castillo-Rogez}, J.~C., {Lainey}, V., {Dones}, L.,
  {Karatekin}, {\"O}., {Tobie}, G., {Mathis}, S., {Le Poncin-Lafitte}, C., and
  {Salmon}, J. 2011.
\newblock {Accretion of Saturn's mid-sized moons during the viscous spreading
  of young massive rings: Solving the paradox of silicate-poor rings versus
  silicate-rich moons}.
\newblock {\em Icarus}, {\bf 216}, 535--550.

\bibitem[\protect\citename{{Ciarniello} {et~al.}, }2014]{ciarniello2014}
{Ciarniello}, M., {Capaccioni}, F., and {Filacchione}, G. 2014.
\newblock {A test of Hapke's model by means of Monte Carlo ray-tracing}.
\newblock {\em Icarus}, {\bf 237}, 293--305.

\bibitem[\protect\citename{{Colombo} {et~al.}, }1976]{colombo1976}
{Colombo}, G., {Goldreich}, P., and {Harris}, A.~W. 1976.
\newblock {Spiral structure as an explanation for the asymmetric brightness of
  Saturn's A ring}.
\newblock {\em Nature}, {\bf 264}, 344--345.

\bibitem[\protect\citename{{Colwell} {et~al.}, }2006]{colwell2006}
{Colwell}, J.~E., {Esposito}, L.~W., and {Srem{\v c}evi{\'c}}, M. 2006.
\newblock {Self-gravity wakes in Saturn's A ring measured by stellar
  occultations from Cassini}.
\newblock {\em Geophys. Res. Lett.}, {\bf 33}, L07201.1--L07201.4§.

\bibitem[\protect\citename{{Colwell} {et~al.}, }2007]{colwell2007}
{Colwell}, J.~E., {Esposito}, L.~W., {Srem{\v c}evi{\'c}}, M., {Stewart},
  G.~R., and {McClintock}, W.~E. 2007.
\newblock {Self-gravity wakes and radial structure of Saturn's B ring}.
\newblock {\em Icarus}, {\bf 190}, 127--144.

\bibitem[\protect\citename{{Crida} and {Charnoz}, }2012]{crida2012}
{Crida}, A., and {Charnoz}, S. 2012.
\newblock {Formation of Regular Satellites from Ancient Massive Rings in the
  Solar System}.
\newblock {\em Science}, {\bf 338}, 1196.

\bibitem[\protect\citename{Cundall and Strack, }1979]{cundall1979}
Cundall, P.~A., and Strack, O. D.~L. 1979.
\newblock {A discrete numerical model for granular assemblies}.
\newblock {\em Geotechnique}, {\bf 29}, 47--65.

\bibitem[\protect\citename{{Cuzzi} {et~al.}, }2009]{cuzzi2009}
{Cuzzi}, J., {Clark}, R., {Filacchione}, G., {French}, R., {Johnson}, R.,
  {Marouf}, E., and {Spilker}, L. 2009.
\newblock {Ring Particle Composition and Size Distribution}.
\newblock {Page  459 of:} {Dougherty}, M.~K., {Esposito}, L.~W., and
  {Krimigis}, S.~M. (eds), {\em Saturn from Cassini-Huygens}.

\bibitem[\protect\citename{{Cuzzi} {et~al.}, }1979]{cuzzi1979a}
{Cuzzi}, J.~N., {Durisen}, R.~H., {Burns}, J.~A., and {Hamill}, P. 1979.
\newblock {The vertical structure and thickness of Saturn's rings}.
\newblock {\em Icarus}, {\bf 38}, 54--68.

\bibitem[\protect\citename{{Cuzzi} {et~al.}, }2002]{cuzzi2002}
{Cuzzi}, J.~N., {French}, R.~G., and {Dones}, L. 2002.
\newblock {HST Multicolor (255-1042 nm) Photometry of Saturn's Main Rings. I:
  Radial Profiles, Phase and Opening Angle Variations, and Regional Spectra}.
\newblock {\em Icarus}, {\bf 158}, 199--223.

\bibitem[\protect\citename{{Cuzzi} {et~al.}, }2010]{cuzzi2010}
{Cuzzi}, J.~N., {Burns}, J.~A., {Charnoz}, S., {Clark}, R.~N., {Colwell},
  J.~E., {Dones}, L., {Esposito}, L.~W., {Filacchione}, G., {French}, R.~G.,
  {Hedman}, M.~M., {Kempf}, S., {Marouf}, E.~A., {Murray}, C.~D., {Nicholson},
  P.~D., {Porco}, C.~C., {Schmidt}, J., {Showalter}, M.~R., {Spilker}, L.~J.,
  {Spitale}, J.~N., {Srama}, R., {Srem{\v c}evi{\'c}}, M., {Tiscareno}, M.~S.,
  and {Weiss}, J. 2010.
\newblock {An Evolving View of Saturn's Dynamic Rings}.
\newblock {\em Science}, {\bf 327}, 1470--1475.

\bibitem[\protect\citename{{Daisaka} and {Ida}, }1999]{daisaka1999}
{Daisaka}, H., and {Ida}, S. 1999.
\newblock {Spatial structure and coherent motion in dense planetary rings
  induced by self-gravitational instability}.
\newblock {\em Earth, Planets, and Space}, {\bf 51}, 1195--1213.

\bibitem[\protect\citename{{Daisaka} {et~al.}, }2001]{daisaka2001}
{Daisaka}, H., {Tanaka}, H., and {Ida}, S. 2001.
\newblock {Viscosity in a dense planetary ring with self-gravitating
  particles}.
\newblock {\em Icarus}, {\bf 154}, 296--312.

\bibitem[\protect\citename{{D{\'e}au}, }2015]{deau2015}
{D{\'e}au}, E. 2015.
\newblock {The opposition effect in Saturn's main rings as seen by Cassini ISS:
  2. Constraints on the ring particles and their regolith with analytical
  radiative transfer models}.
\newblock {\em Icarus}, {\bf 253}, 311--345.

\bibitem[\protect\citename{{D{\'e}au} {et~al.}, }2013]{deau2013}
{D{\'e}au}, E., {Dones}, L., {Charnoz}, S., {West}, R.~A., {Brahic}, A.,
  {Decriem}, J., and {Porco}, C.~C. 2013.
\newblock {The opposition effect in Saturn's main rings as seen by Cassini ISS:
  1. Morphology of phase functions and dependence on the local optical depth}.
\newblock {\em Icarus}, {\bf 226}, 591--603.

\bibitem[\protect\citename{Dilley, }1993]{dilley1993}
Dilley, J.P. 1993.
\newblock {Energy loss in collisions of icy spheres: Loss mechanism and
  size-mass dependence}.
\newblock {\em Icarus}, {\bf 105}, 225--234.

\bibitem[\protect\citename{{Dones}, }1991]{dones1991}
{Dones}, L. 1991.
\newblock {A recent cometary origin for Saturn's rings?}
\newblock {\em Icarus}, {\bf 92}, 194--203.

\bibitem[\protect\citename{{Dones} and {Porco}, }1989]{dones1989}
{Dones}, L., and {Porco}, C.~C. 1989.
\newblock {Spiral density wakes in Saturn's A ring?}
\newblock {Page  929 of:} {\em Bull. American Astron. Soc.},  vol. 21.

\bibitem[\protect\citename{{Dones} {et~al.}, }1993]{dones1993}
{Dones}, L., {Cuzzi}, J.~N., and {Showalter}, M.~R. 1993.
\newblock {Voyager Photometry of Saturn's A Ring}.
\newblock {\em Icarus}, {\bf 105}, 184--215.

\bibitem[\protect\citename{{Dunn} {et~al.}, }2004]{dunn2004}
{Dunn}, D.~E., {Molnar}, L.~A., {Niehof}, J.~T., {de Pater}, I., and
  {Lissauer}, J.~J. 2004.
\newblock {Microwave observations of Saturn's rings: anisotropy in directly
  transmitted and scattered saturnian thermal emission}.
\newblock {\em Icarus}, {\bf 171}, 183--198.

\bibitem[\protect\citename{{Durisen} {et~al.}, }1989]{durisen1989}
{Durisen}, R.~H., {Cramer}, N.~L., {Murphy}, B.~W., {Cuzzi}, J.~N., {Mullikin},
  T.~L., and {Cederbloom}, S.~E. 1989.
\newblock {Ballistic transport in planetary ring systems due to particle
  erosion mechanisms. I - Theory, numerical methods, and illustrative
  examples}.
\newblock {\em Icarus}, {\bf 80}, 136--166.

\bibitem[\protect\citename{{Esposito}, }1979]{esposito1979}
{Esposito}, L.~W. 1979.
\newblock {Extensions to the classical calculation of the effect of mutual
  shadowing in diffuse reflection}.
\newblock {\em Icarus}, {\bf 39}, 69--80.

\bibitem[\protect\citename{{Esposito} and {Lumme}, }1977]{esposito1977}
{Esposito}, L.~W., and {Lumme}, K. 1977.
\newblock {The tilt effect for Saturn's rings}.
\newblock {\em Icarus}, {\bf 31}, 157--167.

\bibitem[\protect\citename{{Estrada} {et~al.}, }2015]{estrada2015}
{Estrada}, P.~R., {Durisen}, R.~H., {Cuzzi}, J.~N., and {Morgan}, D.~A. 2015.
\newblock {Combined structural and compositional evolution of planetary rings
  due to micrometeoroid impacts and ballistic transport}.
\newblock {\em Icarus}, {\bf 252}, 415--439.

\bibitem[\protect\citename{{Ferrari} {et~al.}, }2009]{ferrari2009}
{Ferrari}, C., {Brooks}, S., {Edgington}, S., {Leyrat}, C., {Pilorz}, S., and
  {Spilker}, L. 2009.
\newblock {Structure of self-gravity wakes in Saturn's A ring as measured by
  Cassini CIRS}.
\newblock {\em Icarus}, {\bf 199}, 145--153.

\bibitem[\protect\citename{{Ferrin}, }1975]{ferrin1975}
{Ferrin}, I. 1975.
\newblock {On the structure of Saturn's rings and the 'real' rotational period
  for the planet}.
\newblock {\em Astrophys. Space Sci.}, {\bf 33}, 453--457.

\bibitem[\protect\citename{{Franklin} {et~al.}, }1987]{franklin1987}
{Franklin}, F.~A., {Cook}, A.~F., {Barrey}, R.~T.~F., {Roff}, C.~A., {Hunt},
  G.~E., and {de Rueda}, H.~B. 1987.
\newblock {Voyager observations of the azimuthal brightness variations in
  Saturn's rings}.
\newblock {\em Icarus}, {\bf 69}, 280--296.

\bibitem[\protect\citename{{French} {et~al.}, }2007a]{french2007a}
{French}, R.~G., {Salo}, H., {McGhee}, C.~A., and {Dones}, L. 2007a.
\newblock {HST observations of azimuthal asymmetry in Saturn's rings}.
\newblock {\em Icarus}, {\bf 189}, 493--522.

\bibitem[\protect\citename{{French} {et~al.}, }2007b]{french2007b}
{French}, R.~G., {Verbiscer}, A., {Salo}, H., {McGhee}, C., and {Dones}, L.
  2007b.
\newblock {Saturn's Rings at True Opposition}.
\newblock {\em Publ. Astron. Soc. Pacific}, {\bf 119}, 623--642.

\bibitem[\protect\citename{{Goldreich} and {Lynden-Bell}, }1965]{goldreich1965}
{Goldreich}, P., and {Lynden-Bell}, D. 1965.
\newblock {II. Spiral arms as sheared gravitational instabilities}.
\newblock {\em Mon. Not. R. Astron. Soc.}, {\bf 130}, 125--158.

\bibitem[\protect\citename{{Goldreich} and {Tremaine}, }1978a]{goldreich1978a}
{Goldreich}, P., and {Tremaine}, S. 1978a.
\newblock {The excitation and evolution of density waves}.
\newblock {\em Astrophys. J.}, {\bf 222}, 850--858.

\bibitem[\protect\citename{{Goldreich} and {Tremaine}, }1978b]{goldreich1978b}
{Goldreich}, P., and {Tremaine}, S. 1978b.
\newblock {The velocity dispersion in Saturn's rings.}
\newblock {\em Icarus}, {\bf 34}, 227--239.

\bibitem[\protect\citename{{Goldreich} {et~al.}, }1995]{Goldreich95}
{Goldreich}, P., {Rappaport}, N., and {Sicardy}, B. 1995.
\newblock {Single sided shepherding.}
\newblock {\em Icarus}, {\bf 118}, 414--417.

\bibitem[\protect\citename{{Hahn} and {Spitale}, }2013]{hahn2013}
{Hahn}, J.~M., and {Spitale}, J.~N. 2013.
\newblock {An N-body Integrator for Gravitating Planetary Rings, and the Outer
  Edge of Saturn's B Ring}.
\newblock {\em Astrophys. J.}, {\bf 772}, 122.

\bibitem[\protect\citename{{H{\"a}meen-Anttila}, }1978]{hameen-anttila1978}
{H{\"a}meen-Anttila}, K.~A. 1978.
\newblock {An improved and generalized theory for the collisional evolution of
  Keplerian systems}.
\newblock {\em Astrophys. Space Sci.}, {\bf 58}, 477--519.

\bibitem[\protect\citename{{H{\"a}meen-Anttila}, }1982]{hameen-anttila1982}
{H{\"a}meen-Anttila}, K.~A. 1982.
\newblock {Saturn's rings and bimodality of Keplerian systems}.
\newblock {\em Earth, Moon \& Planets}, {\bf 26}, 171--196.

\bibitem[\protect\citename{{H\"ameen-Anttila}, }1984]{hameen-anttila1984}
{H\"ameen-Anttila}, K.~A. 1984.
\newblock {Collisional theory of non-identical particles in a gravitational
  field}.
\newblock {\em Earth, Moon \& Planets}, {\bf 31}, 271--299.

\bibitem[\protect\citename{{H{\"a}meen-Anttila} and {Lukkari},
  }1980]{hameen-anttila1980}
{H{\"a}meen-Anttila}, K.~A., and {Lukkari}, J. 1980.
\newblock {Numerical simulations of collisions in Keplerian systems}.
\newblock {\em Astrophys. Space Sci.}, {\bf 71}, 475--497.

\bibitem[\protect\citename{{H{\"a}meen-Anttila} and {Salo},
  }1993]{hameen-anttila1993}
{H{\"a}meen-Anttila}, K.~A., and {Salo}, H. 1993.
\newblock {Generalized Theory of Impacts in Particulate Systems}.
\newblock {\em Earth, Moon \& Planets}, {\bf 62}, 47--84.

\bibitem[\protect\citename{{H{\"a}nninen} and {Salo}, }1994]{hanninen1994}
{H{\"a}nninen}, J., and {Salo}, H. 1994.
\newblock {Collisional simulations of satellite Lindblad resonances. 2:
  Formation of narrow ringlets}.
\newblock {\em Icarus}, {\bf 108}, 325--346.

\bibitem[\protect\citename{{H{\"a}nninen} and {Salo}, }1995]{hanninen1995}
{H{\"a}nninen}, J., and {Salo}, H. 1995.
\newblock {Formation of isolated narrow ringlets by a single satellite.}
\newblock {\em Icarus}, {\bf 117}, 435--438.

\bibitem[\protect\citename{Hansen and Lewis, }2015]{hansen2015simulating}
Hansen, Alexander~K, and Lewis, Mark~C. 2015.
\newblock Simulating``Straw''in the Keeler Gap Region.
\newblock {In:} {\em AAS/Division for Planetary Sciences Meeting Abstracts},
  vol. 47.

\bibitem[\protect\citename{{Hapke}, }1986]{hapke1986}
{Hapke}, B. 1986.
\newblock {Bidirectional reflectance spectroscopy. IV - The extinction
  coefficient and the opposition effect}.
\newblock {\em Icarus}, {\bf 67}, 264--280.

\bibitem[\protect\citename{{Hapke}, }1990]{hapke1990}
{Hapke}, B. 1990.
\newblock {Coherent backscatter and the radar characteristics of outer planet
  satellites}.
\newblock {\em Icarus}, {\bf 88}, 407--417.

\bibitem[\protect\citename{{Hapke}, }2002]{hapke2002}
{Hapke}, B. 2002.
\newblock {Bidirectional Reflectance Spectroscopy. 5. The Coherent Backscatter
  Opposition Effect and Anisotropic Scattering}.
\newblock {\em Icarus}, {\bf 157}, 523--534.

\bibitem[\protect\citename{{Hapke}, }2008]{hapke2008}
{Hapke}, B. 2008.
\newblock {Bidirectional reflectance spectroscopy. 6. Effects of porosity}.
\newblock {\em Icarus}, {\bf 195}, 918--926.

\bibitem[\protect\citename{{Harris}, }1984]{harris1984}
{Harris}, A.~W. 1984.
\newblock {The origin and evolution of planetary rings}.
\newblock {Pages  641--659 of:} Greenberg, R., and Brahic, A. (eds), {\em
  Planetary Rings}.
\newblock Tucson Arizona: Univ. of Arizona Press.

\bibitem[\protect\citename{Hatzes {et~al.}, }1988]{hatzes1988}
Hatzes, A., Bridges, F.~G., and Lin, D. N.~C. 1988.
\newblock {Collisional properties of ice spheres at low impact velocities}.
\newblock {\em Mon. Not. R. Astron. Soc.}, {\bf 231}, 1091--1115.

\bibitem[\protect\citename{{Hedman} and {Nicholson},
  }2014]{hedman_nicholson2014}
{Hedman}, M.~M., and {Nicholson}, P.~D. 2014.
\newblock {More Kronoseismology with Saturn's rings}.
\newblock {\em Mon. Not. Royal Astron. Soc.}, {\bf 444}, 1369--1388.

\bibitem[\protect\citename{{Hedman} and {Nicholson}, }2016]{hedman2016}
{Hedman}, M.~M., and {Nicholson}, P.~D. 2016.
\newblock {The B-ring's surface mass density from hidden density waves: Less
  than meets the eye?}
\newblock {\em ArXiv e-prints 1601.07955}.

\bibitem[\protect\citename{{Hedman} {et~al.}, }2007]{hedman2007}
{Hedman}, M.~M., {Nicholson}, P.~D., {Salo}, H., {Wallis}, B.~D., {Buratti},
  B.~J., {Baines}, K.~H., {Brown}, R.~H., and {Clark}, R.~N. 2007.
\newblock {Self-gravity wake structures in Saturn's A ring revealed by Cassini
  VIMS}.
\newblock {\em Astron. J.}, {\bf 133}, 2624--2629.

\bibitem[\protect\citename{{Hedman} {et~al.}, }2011]{hedman2011}
{Hedman}, M.~M., {Burns}, J.~A., {Evans}, M.~W., {Tiscareno}, M.~S., and
  {Porco}, C.~C. 2011.
\newblock {Saturn's Curiously Corrugated C Ring}.
\newblock {\em Science}, {\bf 332}, 708--711.

\bibitem[\protect\citename{{Hedman} {et~al.}, }2014]{hedman2014}
{Hedman}, M.~M., {Nicholson}, P.~D., and {Salo}, H. 2014.
\newblock {Exploring Overstabilities in Saturn's A Ring Using Two Stellar
  Occultations}.
\newblock {\em Astron.J}, {\bf 148}, 1--9.

\bibitem[\protect\citename{{Hernquist} and {Katz}, }1989]{hernquist1989}
{Hernquist}, L., and {Katz}, N. 1989.
\newblock {TREESPH - A unification of SPH with the hierarchical tree method}.
\newblock {\em Astrophys. J., Supp.}, {\bf 70}, 419--446.

\bibitem[\protect\citename{{Hertz}, }1882]{hertz1882}
{Hertz}, H. 1882.
\newblock {\"U}ber die Ber{\"u}hrung fester elastischer K{\"o}rper.
\newblock {\em J. f. Reine Angew. Math.}, {\bf 92}, 156.

\bibitem[\protect\citename{{Hyodo} and {Ohtsuki}, }2014]{hyodo2014}
{Hyodo}, R., and {Ohtsuki}, K. 2014.
\newblock {Collisional Disruption of Gravitational Aggregates in the Tidal
  Environment}.
\newblock {\em Astrophys. J.}, {\bf 787}, 56.

\bibitem[\protect\citename{{Hyodo} and {Ohtsuki}, }2015]{hyodo2015}
{Hyodo}, R., and {Ohtsuki}, K. 2015.
\newblock {Saturn's F ring and shepherd satellites a natural outcome of
  satellite system formation}.
\newblock {\em Nature Geoscience}, {\bf 8}, 686--689.

\bibitem[\protect\citename{{Hyodo} {et~al.}, }2015a]{hyodoetal2015}
{Hyodo}, R., {Ohtsuki}, K., and {Takeda}, T. 2015a.
\newblock {Formation of Multiple-satellite Systems From Low-mass
  Circumplanetary Particle Disks}.
\newblock {\em Astron. J.}, {\bf 799}, 40.

\bibitem[\protect\citename{{Hyodo} {et~al.}, }2015b]{hyodoetal2015b}
{Hyodo}, R., {Charnoz}, S., {Ohtsuki}, K., and {Genda}, H. 2015b (Nov.).
\newblock {Physics of Tidal Disruption of Big Objects at the Close Encounter to
  Saturn}.
\newblock {Page  218.10 of:} {\em Bull. American Astron. Soc.}
\newblock AAS/Division for Planetary Sciences Meeting Abstracts, vol. 47.

\bibitem[\protect\citename{{Julian} and {Toomre}, }1966]{julian1966}
{Julian}, W.~H., and {Toomre}, A. 1966.
\newblock {Non-axisymmetric responses of differentially rotating disks of
  stars}.
\newblock {\em Astrophys. J.}, {\bf 146}, 810--827.

\bibitem[\protect\citename{Karjalainen, }2007]{Karjalainen07}
Karjalainen, R. 2007.
\newblock {Aggregate impacts in Saturn's rings}.
\newblock {\em Icarus}, {\bf 189}, 523--537.

\bibitem[\protect\citename{{Karjalainen} and {Salo}, }2004]{karjalainen2004}
{Karjalainen}, R., and {Salo}, H. 2004.
\newblock {Gravitational accretion of particles in Saturn's rings}.
\newblock {\em Icarus}, {\bf 172}, 328--348.

\bibitem[\protect\citename{{Kolvoord} {et~al.}, }1990]{Kolvoord90}
{Kolvoord}, R.~A., {Burns}, J.~A., and {Showalter}, M.~R. 1990.
\newblock {Periodic features in Saturn's F ring - Evidence for nearby
  moonlets}.
\newblock {\em Nature}, {\bf 345}, 695--697.

\bibitem[\protect\citename{Langbert and Lewis, }2014]{langbert2014processing}
Langbert, Zachary, and Lewis, Mark~C. 2014.
\newblock Processing Hard Sphere Collisions on a GPU Using OpenCL.
\newblock {Pages  35--41 of:} {\em PDPTA},  vol. 1.
\newblock CSREA Press.

\bibitem[\protect\citename{{Latter} and {Ogilvie}, }2006]{latter2006}
{Latter}, H.~N., and {Ogilvie}, G.~I. 2006.
\newblock {The linear stability of dilute particulate rings}.
\newblock {\em Icarus}, {\bf 184}, 498--516.

\bibitem[\protect\citename{{Latter} and {Ogilvie}, }2008]{latter2008}
{Latter}, H.~N., and {Ogilvie}, G.~I. 2008.
\newblock {Dense planetary rings and the viscous overstability}.
\newblock {\em Icarus}, {\bf 195}, 725--751.

\bibitem[\protect\citename{{Latter} and {Ogilvie}, }2009]{latter2009}
{Latter}, H.~N., and {Ogilvie}, G.~I. 2009.
\newblock {The viscous overstability, nonlinear wavetrains, and finescale
  structure in dense planetary rings}.
\newblock {\em Icarus}, {\bf 202}, 565--583.

\bibitem[\protect\citename{{Latter} and {Ogilvie}, }2010]{latter2010}
{Latter}, H.~N., and {Ogilvie}, G.~I. 2010.
\newblock {Hydrodynamical simulations of viscous overstability in Saturn's
  rings}.
\newblock {\em Icarus}, {\bf 210}, 318--329.

\bibitem[\protect\citename{{Leinhardt} {et~al.}, }2012]{leinhardt2012}
{Leinhardt}, Z.~M., {Ogilvie}, G.~I., {Latter}, H.~N., and {Kokubo}, E. 2012.
\newblock {Tidal disruption of satellites and formation of narrow rings}.
\newblock {\em Mon. Not. R. Astron. Soc.}, {\bf 424}, 1419--1431.

\bibitem[\protect\citename{{Lewis} and {Stewart}, }2000]{lewis2000}
{Lewis}, M.~C., and {Stewart}, G.~R. 2000.
\newblock {Collisional Dynamics of Perturbed Planetary Rings. I.}
\newblock {\em Astron. J.}, {\bf 120}, 3295--3310.

\bibitem[\protect\citename{{Lewis} and {Stewart}, }2002]{lewis2002}
{Lewis}, M.~C., and {Stewart}, G.~R. 2002.
\newblock {A new methodology for granular flow simulations of planetary rings -
  coordinates and boundary conditions}.
\newblock {Pages  292--297 of:} H., {Hamza}~M. (ed), {\em {Proceedings of the
  IASTED International Conference, Modeling and Simulation}}.
\newblock {ACTA Press}.

\bibitem[\protect\citename{{Lewis} and {Stewart}, }2003]{lewis2003}
{Lewis}, M.~C., and {Stewart}, G.~R. 2003.
\newblock {A new methodology for granular flow simulations of planetary rings -
  collision handling}.
\newblock {Pages  292--297 of:} H., {Hamza}~M. (ed), {\em {Proceedings of the
  IASTED International Conference, Modeling and Simulation, Palm Springs}}.
\newblock {ACTA Press}.

\bibitem[\protect\citename{{Lewis} and {Stewart}, }2005]{lewis2005}
{Lewis}, M.~C., and {Stewart}, G.~R. 2005.
\newblock {Expectations for Cassini observations of ring material with nearby
  moons}.
\newblock {\em Icarus}, {\bf 178}, 124--143.

\bibitem[\protect\citename{{Lewis} and {Stewart}, }2007]{lewis07}
{Lewis}, M.~C., and {Stewart}, G.~R. 2007.
\newblock {Collisional simulations of the F ring with Prometheus and Pandora}.
\newblock {Page  26.08 of:} {\em AAS/Division for Planetary Sciences Meeting
  Abstracts},  vol. 39.

\bibitem[\protect\citename{{Lewis} and {Stewart}, }2009]{lewis2009}
{Lewis}, M.~C., and {Stewart}, G.~R. 2009.
\newblock {Features around embedded moonlets in Saturn's rings: The role of
  self-Gravity and particle size distributions}.
\newblock {\em Icarus}, {\bf 199}, 387--412.

\bibitem[\protect\citename{Lewis and Massingill, }2006]{lewis2006multithreaded}
Lewis, Mark, and Massingill, Berna~L. 2006.
\newblock Multithreaded Collision Detection in Java.
\newblock {Pages  583--592 of:} {\em PDPTA}.

\bibitem[\protect\citename{Lewis {et~al.}, }2009]{lewis2009hybrid}
Lewis, Mark, Maly, Matthew, and Massingill, Berna~L. 2009.
\newblock Hybrid Parallelization of N-Body Simulations Involving Collisions and
  Self-Gravity.
\newblock {Pages  324--330 of:} {\em PDPTA}.

\bibitem[\protect\citename{Lewis {et~al.}, }2011]{lewis2011negative}
Lewis, Mark, Stewart, Glen, Leezer, Jason, and West, Amy. 2011.
\newblock Negative diffusion in planetary rings with a nearby Moon.
\newblock {\em Icarus}, {\bf 213}(1), 201--217.

\bibitem[\protect\citename{Lewis and Stewart, }2006a]{lewis2006simulatingA}
Lewis, Mark~C, and Stewart, Glen~R. 2006a.
\newblock Simulating Saturn’s Keeler Gap Region.
\newblock {\em Proceedings of the 17th IASTED international conference on
  Modeling and Simulation, Montreal, Canada},  268--273.

\bibitem[\protect\citename{Lewis and Stewart, }2006b]{lewis2006simulatingB}
Lewis, Mark~C, and Stewart, GR. 2006b.
\newblock Simulating the Keeler gap in Saturn's rings: Wake and edge dynamics.
\newblock {Page  560 of:} {\em Bulletin of the American Astronomical Society},
  vol. 38.

\bibitem[\protect\citename{Lewis and Wing, }2002]{lewis2002distributed}
Lewis, Mark~C, and Wing, Nick. 2002.
\newblock A distributed methodology for hard sphere collisional simulations.
\newblock {Pages  404--409 of:} {\em Proceedings of the International
  Conference on Parallel and Distributed Processing Techniques and
  Applications-Volume 1}.
\newblock CSREA Press.

\bibitem[\protect\citename{{Lin} and {Bodenheimer}, }1981]{lin1981}
{Lin}, D. N.~C., and {Bodenheimer}, P. 1981.
\newblock {On the stability of Saturn's rings}.
\newblock {\em Astrophys. J. Lett.}, {\bf 248}, L83--L86.

\bibitem[\protect\citename{{Longaretti} and {Rappaport}, }1995]{longaretti1995}
{Longaretti}, P.-Y., and {Rappaport}, N. 1995.
\newblock {Viscous overstabilities in dense narrow planetary rings.}
\newblock {\em Icarus}, {\bf 116}, 376--396.

\bibitem[\protect\citename{Lukkari, }1981]{lukkari1981}
Lukkari, J. 1981.
\newblock Collisional amplification of density fluctuations in {S}aturn's
  rings.
\newblock {\em Nature}, {\bf 292}, 433--435.

\bibitem[\protect\citename{{Lumme} and {Bowell}, }1981]{lumme1981}
{Lumme}, K., and {Bowell}, E. 1981.
\newblock {Radiative transfer in the surfaces of atmosphereless bodies. I -
  Theory. II - Interpretation of phase curves}.
\newblock {\em Astron. J.}, {\bf 86}, 1694--1721.

\bibitem[\protect\citename{{Lumme} {et~al.}, }1977]{Lumme1977}
{Lumme}, K., {Esposito}, L.~W., {Irvine}, W.~M., and {Baum}, W.~A. 1977.
\newblock {Azimuthal brightness variations of Saturn's rings. II - Observations
  at an intermediate tilt angle}.
\newblock {\em Astrophys. J. Lett.}, {\bf 216}, L123--L126.

\bibitem[\protect\citename{{Lumme} {et~al.}, }1983]{lumme1983}
{Lumme}, K., {Irvine}, W.~M., and {Esposito}, L.~W. 1983.
\newblock {Theoretical interpretation of the ground-based photometry of
  Saturn's B ring}.
\newblock {\em Icarus}, {\bf 53}, 174--184.

\bibitem[\protect\citename{Lynden-Bell and Kalnajs, }1972]{lynden-bell1972}
Lynden-Bell, D., and Kalnajs, A.J. 1972.
\newblock On the Generating Mechanism of Spiral Structure.
\newblock {\em Mon. Not. R. Astron. Soc.}, {\bf 157}, 1--30.

\bibitem[\protect\citename{{Makino} and {Funato}, }1993]{makino1993}
{Makino}, J., and {Funato}, Y. 1993.
\newblock {The GRAPE Software System}.
\newblock {\em Publications of the Astronomical Society of Japan}, {\bf 45},
  279--288.

\bibitem[\protect\citename{{Michikoshi} {et~al.}, }2015]{michikoshi2015}
{Michikoshi}, S., {Fujii}, A., {Kokubo}, E., and {Salo}, H. 2015.
\newblock {Dynamics of Self-gravity Wakes in Dense Planetary Rings. I. Pitch
  Angle}.
\newblock {\em Astrophys. J}, {\bf 812}, 151.

\bibitem[\protect\citename{{Mishchenko}, }1992]{mishchenko1992}
{Mishchenko}, M.~I. 1992.
\newblock {The angular width of the coherent back-scatter opposition effect -
  an application to icy outer planet satellites}.
\newblock {\em Ap\&SS}, {\bf 194}, 327--333.

\bibitem[\protect\citename{{Morishima} and {Salo}, }2004]{morishima2004}
{Morishima}, R., and {Salo}, H. 2004.
\newblock {Spin rates of small moonlets embedded in planetary rings: I.
  Three-body calculations}.
\newblock {\em Icarus}, {\bf 167}, 330--346.

\bibitem[\protect\citename{{Morishima} and {Salo}, }2006]{morishima2006}
{Morishima}, R., and {Salo}, H. 2006.
\newblock {Simulations of dense planetary rings IV. Spinning self-gravitating
  particles with size distributions}.
\newblock {\em Icarus}, {\bf 181}, 272--291.

\bibitem[\protect\citename{{Morishima} {et~al.}, }2010]{morishima2010}
{Morishima}, R., {Spilker}, L., {Salo}, H., {Ohtsuki}, K., {Altobelli}, N., and
  {Pilortz}, S. 2010.
\newblock {A multilayer model for thermal infrared emission of Saturn's rings
  II: Albedo, spins, and vertical mixing of ring particles inferred from
  Cassini CIRS}.
\newblock {\em Icarus}, {\bf 210}, 330--345.

\bibitem[\protect\citename{{Morishima} {et~al.}, }2011]{morishima2011}
{Morishima}, R., {Spilker}, L., and {Ohtsuki}, K. 2011.
\newblock {A multilayer model for thermal infrared emission of Saturn's rings.
  III: Thermal inertia inferred from Cassini CIRS}.
\newblock {\em Icarus}, {\bf 215}(Sept.), 107--127.

\bibitem[\protect\citename{{Morishima} {et~al.}, }2014]{morishima2014}
{Morishima}, R., {Spilker}, L., and {Turner}, N. 2014.
\newblock {Azimuthal temperature modulations of Saturn's A ring caused by
  self-gravity wakes}.
\newblock {\em Icarus}, {\bf 228}, 247--259.

\bibitem[\protect\citename{{Mosqueira}, }1996]{mosqueira1996}
{Mosqueira}, I. 1996.
\newblock {Local simulations of perturbed dense planetary rings}.
\newblock {\em Icarus}, {\bf 122}, 128--152.

\bibitem[\protect\citename{{Muinonen} {et~al.}, }1991]{muinonen1991}
{Muinonen}, K.~O., {Sihvola}, A.~H., {Lindell}, I.~V., and {Lumme}, K.~A. 1991.
\newblock {Scattering by a small object close to an interface. II. Study of
  backscattering}.
\newblock {\em Journal of the Optical Society of America A}, {\bf 8}, 477--482.

\bibitem[\protect\citename{{Nelson} {et~al.}, }2000]{nelson2000}
{Nelson}, R.~M., {Hapke}, B.~W., {Smythe}, W.~D., and {Spilker}, L.~J. 2000.
\newblock {The Opposition Effect in Simulated Planetary Regoliths. Reflectance
  and Circular Polarization Ratio Change at Small Phase Angle}.
\newblock {\em Icarus}, {\bf 147}, 545--558.

\bibitem[\protect\citename{{Nicholson} {et~al.}, }2005]{nicholson2005}
{Nicholson}, P.~D., {French}, R.~G., {Campbell}, D.~B., {Margot}, J.-L.,
  {Nolan}, M.~C., {Black}, G.~J., and {Salo}, H.~J. 2005.
\newblock {Radar imaging of Saturn's rings}.
\newblock {\em Icarus}, {\bf 177}, 32--62.

\bibitem[\protect\citename{Ohtsuki, }1992]{Ohtsuki92}
Ohtsuki, K. 1992.
\newblock {Equilibrium velocities in planetary rings with low optical depth}.
\newblock {\em Icarus}, {\bf 95}, 265--282.

\bibitem[\protect\citename{Ohtsuki, }1993]{ohtsuki1993}
Ohtsuki, K. 1993.
\newblock {Capture probability of colliding planetesimals: Dynamical
  constraints on accretion of planets, satellites, and ring particles}.
\newblock {\em Icarus}, {\bf 106}, 228--246.

\bibitem[\protect\citename{Ohtsuki, }1999]{ohtsuki1999}
Ohtsuki, K. 1999.
\newblock {Evolution of particle velocity dispersion in a circumplanetary disk
  due to inelastic collisions and gravitational interactions}.
\newblock {\em Icarus}, {\bf 137}, 152--177.

\bibitem[\protect\citename{Ohtsuki, }2004a]{Ohtsuki04a}
Ohtsuki, K. 2004a.
\newblock {Formulation and analytic calculation for the spin angular momentum
  of a moonlet due to inelastic collisions of ring particles}.
\newblock {\em Earth Planets Space}, {\bf 56}, 909--919.

\bibitem[\protect\citename{Ohtsuki, }2004b]{Ohtsuki04b}
Ohtsuki, K. 2004b.
\newblock {On the rotation of a moonlet embedded in planetary rings}.
\newblock {\em Icarus}, {\bf 172}, 432--445.

\bibitem[\protect\citename{Ohtsuki, }2005]{Ohtsuki05}
Ohtsuki, K. 2005.
\newblock {Rotation rates of particles in Saturn's rings}.
\newblock {\em Astrophys. J.}, {\bf 626}, L61--L64.

\bibitem[\protect\citename{Ohtsuki, }2006a]{ohtsuki2006a}
Ohtsuki, K. 2006a.
\newblock {Rotation rate and velocity dispersion of planetary ring particles
  with size distribution. I. Formulation and analytic calculation}.
\newblock {\em Icarus}, {\bf 183}, 373--383.

\bibitem[\protect\citename{Ohtsuki, }2006b]{ohtsuki2006b}
Ohtsuki, K. 2006b.
\newblock {Rotation rate and velocity dispersion of planetary ring particles
  with size distribution. II. Numerical simulation for gravitating particles}.
\newblock {\em Icarus}, {\bf 183}, 384--395.

\bibitem[\protect\citename{{Ohtsuki}, }2012]{ohtsuki2012}
{Ohtsuki}, K. 2012.
\newblock {Collisions and gravitational interactions between particles in
  planetary rings}.
\newblock {\em Prog. Theor. Phys. Suppl.}, {\bf 195}, 29--47.

\bibitem[\protect\citename{{Ohtsuki} and {Emori}, }2000]{ohtsuki2000}
{Ohtsuki}, K., and {Emori}, H. 2000.
\newblock {Local N-Body Simulations for the Distribution and Evolution of
  Particle Velocities in Planetary Rings}.
\newblock {\em Astron. J.}, {\bf 119}, 403--416.

\bibitem[\protect\citename{Ohtsuki and Emori, }2000]{OhtsukiEmori}
Ohtsuki, K., and Emori, H. 2000.
\newblock {Local N-body simulations for the distribution and evolution of
  particle velocities in planetary rings}.
\newblock {\em Astron. J.}, {\bf 119}, 403--416.

\bibitem[\protect\citename{Ohtsuki and Toyama, }2005]{ohtsuki2005}
Ohtsuki, K., and Toyama, D. 2005.
\newblock {Local N-body simulations for the rotation rates of particles in
  planetary rings}.
\newblock {\em Astron. J.}, {\bf 130}, 1302--1310.

\bibitem[\protect\citename{{Ohtsuki} {et~al.}, }2002]{ohtsuki2002}
{Ohtsuki}, K., {Stewart}, G.~R., and {Ida}, S. 2002.
\newblock {Evolution of Planetesimal Velocities Based on Three-Body Orbital
  Integrations and Growth of Protoplanets}.
\newblock {\em Icarus}, {\bf 155}(Feb.), 436--453.

\bibitem[\protect\citename{{Ohtsuki} {et~al.}, }2013]{ohtsuki2013}
{Ohtsuki}, K., {Yasui}, Y., and {Daisaka}, H. 2013.
\newblock {Accretion Rates of Moonlets Embedded in Circumplanetary Particle
  Disks}.
\newblock {\em Astronomical Journal}, {\bf 146}, 25.

\bibitem[\protect\citename{{Perrine} and {Richardson}, }2006]{perrine2006}
{Perrine}, R.~P., and {Richardson}, D.~C. 2006.
\newblock {A Computational Model of Moons in Planetary Ring Gaps}.
\newblock {Page  560 of:} {\em AAS/Division for Planetary Sciences Meeting
  Abstracts \#38}.
\newblock Bulletin of the American Astronomical Society, vol. 38.

\bibitem[\protect\citename{{Perrine} and {Richardson}, }2007]{perrine2007}
{Perrine}, R.~P., and {Richardson}, D.~C. 2007.
\newblock {Numerical Studies of Satellite-Ring Interactions}.
\newblock {Page  425 of:} {\em AAS/Division for Planetary Sciences Meeting
  Abstracts \#39}.
\newblock Bulletin of the American Astronomical Society, vol. 39.

\bibitem[\protect\citename{{Perrine} and {Richardson}, }2012]{perrine2012}
{Perrine}, R.~P., and {Richardson}, D.~C. 2012.
\newblock {N-body simulations of cohesion in dense planetary rings: A study of
  cohesion parameters}.
\newblock {\em Icarus}, {\bf 219}, 515--533.

\bibitem[\protect\citename{{Perrine} {et~al.}, }2011]{perrine2011}
{Perrine}, R.~P., {Richardson}, D.~C., and {Scheeres}, D.~J. 2011.
\newblock {A numerical model of cohesion in planetary rings}.
\newblock {\em Icarus}, {\bf 212}, 719--735.

\bibitem[\protect\citename{{Petit} and {H\'enon}, }1987]{petit1987}
{Petit}, J.~M., and {H\'enon}, M. 1987.
\newblock {A numerical simulation of planetary rings. I. Binary encounters}.
\newblock {\em Astron. \& Astrophys.}, {\bf 173}, 389--404.

\bibitem[\protect\citename{{Porco} {et~al.}, }2008]{porco2008}
{Porco}, C.~C., {Weiss}, J.~W., {Richardson}, D.~C., {Dones}, L., {Quinn}, T.,
  and {Throop}, H. 2008.
\newblock {Simulations of the dynamical and light-scattering behavior of
  Saturn's rings and the derivation of ring particle and disk properties}.
\newblock {\em Astron. J.}, {\bf 136}, 2172--2200.

\bibitem[\protect\citename{Porco {et~al.}, }2007]{porco2007}
Porco, C.C., Thomas, P.C., Weiss, J.~W., and Richardson, D.~C. 2007.
\newblock {Saturn's small inner satellites: Clues to their origins}.
\newblock {\em Science}, {\bf 318}, 1602--1607.

\bibitem[\protect\citename{{P{\"o}schel} and {Schwager}, }2005]{Poschel2005}
{P{\"o}schel}, T., and {Schwager}, T. 2005.
\newblock {\em {Computational Granular Dynamics}}.
\newblock Springer-Verlag Berlin Heidelberg.

\bibitem[\protect\citename{{Poulet} {et~al.}, }2002]{poulet2002}
{Poulet}, F., {Cuzzi}, J.~N., {French}, R.~G., and {Dones}, L. 2002.
\newblock {A Study of Saturn's Ring Phase Curves from HST Observations}.
\newblock {\em Icarus}, {\bf 158}, 224--248.

\bibitem[\protect\citename{{Rein} and {Latter}, }2013]{rein2013}
{Rein}, H., and {Latter}, H.~N. 2013.
\newblock {Large-scale N-body simulations of the viscous overstability in
  Saturn's rings}.
\newblock {\em Mon. Not. Royal Astron. Soc.}, {\bf 431}, 145--158.

\bibitem[\protect\citename{{Rein} and {Liu}, }2012]{rein2012}
{Rein}, H., and {Liu}, S.-F. 2012.
\newblock {REBOUND: an open-source multi-purpose N-body code for collisional
  dynamics}.
\newblock {\em Astron. \& Astrophys.}, {\bf 537}, A128.

\bibitem[\protect\citename{Rein and Liu, }2012]{rein2012rebound}
Rein, Hanno, and Liu, S-F. 2012.
\newblock REBOUND: an open-source multi-purpose N-body code for collisional
  dynamics.
\newblock {\em Astronomy \& Astrophysics}, {\bf 537}, A128.

\bibitem[\protect\citename{{Reitsema} {et~al.}, }1976]{reitsema1976}
{Reitsema}, H.~J., {Beebe}, R.~F., and {Smith}, B.~A. 1976.
\newblock {Azimuthal brightness variations in Saturn's rings}.
\newblock {\em Astron. J.}, {\bf 81}, 209--215.

\bibitem[\protect\citename{{Richardson}, }1993]{richardson1993}
{Richardson}, D.~C. 1993.
\newblock {A new tree code method for simulation of planetesimal dynamics}.
\newblock {\em Mon. Not. R. Astron. Soc.}, {\bf 261}, 396--414.

\bibitem[\protect\citename{{Richardson} {et~al.}, }2000]{richardson2000}
{Richardson}, D.~C., {Quinn}, T., {Stadel}, J., and {Lake}, G. 2000.
\newblock {Direct Large-Scale N-Body Simulations of Planetesimal Dynamics}.
\newblock {\em Icarus}, {\bf 143}, 45--59.

\bibitem[\protect\citename{Richardson, }1994]{richardson1994}
Richardson, D.C. 1994.
\newblock {Tree code simulations of planetary rings}.
\newblock {\em Mon. Not. R. Astron. Soc.}, {\bf 269}, 493--511.

\bibitem[\protect\citename{{Robbins} {et~al.}, }2010]{robbins2010}
{Robbins}, S.~J., {Stewart}, G.~R., {Lewis}, M.~C., {Colwell}, J.~E., and
  {Srem{\v c}evi{\'c}}, M. 2010.
\newblock {Estimating the masses of Saturn's A and B rings from high-optical
  depth N-body simulations and stellar occultations}.
\newblock {\em Icarus}, {\bf 206}, 431--445.

\bibitem[\protect\citename{{Safranov}, }1969]{safranov1969}
{Safranov}, V. 1969.
\newblock {\em {Evolution of the protoplanetary cloud and the formation of the
  earth and planets}}.
\newblock Nauka, NASA TTF-667.

\bibitem[\protect\citename{{Salmon} {et~al.}, }2010]{salmon2010}
{Salmon}, J., {Charnoz}, S., {Crida}, A., and {Brahic}, A. 2010.
\newblock {Long-term and large-scale viscous evolution of dense planetary
  rings}.
\newblock {\em Icarus}, {\bf 209}, 771--785.

\bibitem[\protect\citename{Salo, }1987a]{salo1987a}
Salo, H. 1987a.
\newblock {Collisional evolution of rotating, non-identical particles}.
\newblock {\em Moon Planets}, {\bf 38}, 149--181.

\bibitem[\protect\citename{Salo, }1987b]{salo1987b}
Salo, H. 1987b.
\newblock {Numerical simulations of collisions between rotating particles}.
\newblock {\em Icarus}, {\bf 70}, 37--51.

\bibitem[\protect\citename{{Salo}, }1991]{salo1991}
{Salo}, H. 1991.
\newblock {Numerical simulations of dense collisional systems}.
\newblock {\em Icarus}, {\bf 92}, 367--368.

\bibitem[\protect\citename{Salo, }1992a]{salo1992b}
Salo, H. 1992a.
\newblock {Gravitational wakes in Saturn's rings}.
\newblock {\em Nature}, {\bf 359}, 619--621.

\bibitem[\protect\citename{Salo, }1992b]{salo1992a}
Salo, H. 1992b.
\newblock {Numerical simulations of dense collisional systems. II. Extended
  distribution of particle sizes}.
\newblock {\em Icarus}, {\bf 96}, 85--106.

\bibitem[\protect\citename{Salo, }1995]{salo1995}
Salo, H. 1995.
\newblock {Simulations of dense planetary rings. III. Self-gravitating
  identical particles}.
\newblock {\em Icarus}, {\bf 117}, 287--312.

\bibitem[\protect\citename{Salo, }2001]{salo2001gg}
Salo, H. 2001.
\newblock Numerical Simulations of the Collisional Dynamics of Planetary Rings.
\newblock {Pages  330--349 of:} {P{\"o}schel}, T., and {Luding}, S. (eds), {\em
  Granular Gases}.
\newblock Lecture Notes in Physics, Berlin Springer Verlag, vol. 564.

\bibitem[\protect\citename{{Salo} and {French}, }2010]{salo2010b}
{Salo}, H., and {French}, R.~G. 2010.
\newblock {The opposition and tilt effects of Saturn's rings from HST
  observations}.
\newblock {\em Icarus}, {\bf 210}, 785--816.

\bibitem[\protect\citename{Salo and Karjalainen, }2003]{salo2003}
Salo, H., and Karjalainen, R. 2003.
\newblock {Photometric modeling of Saturn's rings. I. Monte Carlo method and
  the effect of nonzero volume filling factor}.
\newblock {\em Icarus}, {\bf 164}, 428--460.

\bibitem[\protect\citename{{Salo} and {Schmidt}, }2010]{salo2010a}
{Salo}, H., and {Schmidt}, J. 2010.
\newblock {N-body simulations of viscous instability of planetary rings}.
\newblock {\em Icarus}, {\bf 206}, 390--409.

\bibitem[\protect\citename{Salo {et~al.}, }2001]{salo2001}
Salo, H., Schmidt, J., and Spahn, F. 2001.
\newblock Viscous overstability in {S}aturn's {B} ring: {I}. {D}irect
  simulations and measurement of transport coefficients.
\newblock {\em Icarus}, {\bf 153}, 295--315.

\bibitem[\protect\citename{{Salo} {et~al.}, }2004]{salo2004}
{Salo}, H., {Karjalainen}, R., and {French}, R.~G. 2004.
\newblock {Photometric modeling of Saturn's rings. II. Azimuthal asymmetry in
  reflected and transmitted light}.
\newblock {\em Icarus}, {\bf 170}, 70--90.

\bibitem[\protect\citename{{Salo} and {Schmidt}, }2007]{salo2007}
{Salo}, H.~J., and {Schmidt}, J. 2007.
\newblock {Release of impact-debris in perturbed ring regions: Dynamical and
  photometric simulations.}
\newblock {Page  425 of:} {\em Bull. American Astron. Soc.}
\newblock Bull. American Astron. Soc., vol. 38.

\bibitem[\protect\citename{Schmidt and Salo, }2003]{schmidt2003}
Schmidt, J., and Salo, H. 2003.
\newblock A weakly nonlinear model for viscous overstability in Saturn's dense
  rings.
\newblock {\em Physical Review Letters}, {\bf 90}(6), 061102.

\bibitem[\protect\citename{Schmidt {et~al.}, }2001]{schmidt2001}
Schmidt, J., Salo, H., Spahn, F., and Petzschmann, Olaf. 2001.
\newblock Viscous overstability in {S}aturn's {B} ring: {II}. {H}ydrodynamic
  theory and comparison to simulations.
\newblock {\em Icarus}, {\bf 153}, 316--331.

\bibitem[\protect\citename{{Schmidt} {et~al.}, }2009]{schmidt2009}
{Schmidt}, J., {Ohtsuki}, K., {Rappaport}, N., {Salo}, H., and {Spahn}, F.
  2009.
\newblock {Dynamics of Saturn's Dense Rings}.
\newblock {Page  413 of:} {Dougherty}, M.~K., {Esposito}, L.~W., and
  {Krimigis}, S.~M. (eds), {\em Saturn from Cassini-Huygens}.

\bibitem[\protect\citename{{Schmit} and {Tscharnuter}, }1995]{schmit1995}
{Schmit}, U., and {Tscharnuter}, W.M. 1995.
\newblock {A fluid dynamical treatment of the common action of
  self-gravitation, collisions, and rotation in {S}aturn's B-ring}.
\newblock {\em Icarus}, {\bf 115}, 304--319.

\bibitem[\protect\citename{{Schmit} and {Tscharnuter}, }1999]{schmit1999}
{Schmit}, U., and {Tscharnuter}, W.M. 1999.
\newblock {On the formation of the fine--scale structure in {S}aturn's B ring}.
\newblock {\em Icarus}, {\bf 138}, 173--187.

\bibitem[\protect\citename{{Sellwood}, }2014]{sellwood2014}
{Sellwood}, J.~A. 2014.
\newblock {GALAXY package for N-body simulation}.
\newblock {\em ArXiv e-prints 1406.6606}.

\bibitem[\protect\citename{{Showalter}, }1991]{showalter1991a}
{Showalter}, M.~R. 1991.
\newblock {Visual detection of 1981S13, Saturn's eighteenth satellite, and its
  role in the Encke gap}.
\newblock {\em Nature}, {\bf 351}, 709--713.

\bibitem[\protect\citename{Showalter, }1998]{Showalter98}
Showalter, M.~R. 1998.
\newblock {Detection of centimeter-sized meteoroid impact events in Saturn's F
  ring}.
\newblock {\em Science}, {\bf 282}, 1099--1102.

\bibitem[\protect\citename{{Showalter} {et~al.}, }1986]{showalter1986}
{Showalter}, M.~R., {Cuzzi}, J.~N., {Marouf}, E.~A., and {Esposito}, L.~W.
  1986.
\newblock {Satellite 'wakes' and the orbit of the Encke Gap moonlet}.
\newblock {\em Icarus}, {\bf 66}, 297--323.

\bibitem[\protect\citename{{Shu}, }1984]{shu1984}
{Shu}, F.~H. 1984.
\newblock {Waves in planetary rings}.
\newblock {Pages  513--561 of:} {Greenberg}, R., and {Brahic}, A. (eds), {\em
  Planetary Rings}.
\newblock Tucson Arizona: Univ. of Arizona Press.

\bibitem[\protect\citename{{Shu} and {Stewart}, }1985]{shu1985}
{Shu}, F.~H., and {Stewart}, G.~R. 1985.
\newblock {The collisional dynamics of particulate disks}.
\newblock {\em Icarus}, {\bf 62}, 360--383.

\bibitem[\protect\citename{Shukhman, }1984]{shukhman1984}
Shukhman, I.G. 1984.
\newblock Collisional dynamics of particles in {S}aturn's rings.
\newblock {\em Sov. Astron.}, {\bf 28}, 574--585.

\bibitem[\protect\citename{Spahn and Srem{\v c}evi{\'c}, }2000]{spahn2000}
Spahn, F., and Srem{\v c}evi{\'c}, M. 2000.
\newblock {Density patterns induced by small moonlets in Saturn's rings?}
\newblock {\em Astron. \& Astrophys.}, {\bf 358}, 368--372.

\bibitem[\protect\citename{{Spahn} {et~al.}, }1995]{spahn1995}
{Spahn}, F., {Hertzsch}, J.-M., and {Brilliantov}, N.V. 1995.
\newblock {The role of particle collisions for the dynamics in planetary
  rings}.
\newblock {\em Chaos, Solitons and Fractals}, {\bf 5}, 1945--1964.

\bibitem[\protect\citename{{Springel}, }2005]{springel2005}
{Springel}, V. 2005.
\newblock {The cosmological simulation code GADGET-2}.
\newblock {\em Mon. Not. Royal Astron. Soc.}, {\bf 364}, 1105--1134.

\bibitem[\protect\citename{{Srem{\v c}evi{\'c}} {et~al.}, }2007]{sremcevic2007}
{Srem{\v c}evi{\'c}}, M., {Schmidt}, J., {Salo}, H., {Sei{\ss}}, M., {Spahn},
  F., and {Albers}, N. 2007.
\newblock {A belt of moonlets in Saturn's A ring}.
\newblock {\em Nature}, {\bf 449}, 1019--1021.

\bibitem[\protect\citename{Stadel {et~al.}, }2002]{stadel2002high}
Stadel, Joachim, Wadsley, James, and Richardson, Derek~C. 2002.
\newblock High performance computational astrophysics with pkdgrav/gasoline.
\newblock {Pages  501--523 of:} {\em High Performance Computing Systems and
  Applications}.
\newblock Springer.

\bibitem[\protect\citename{{Stewart}, }1991]{Stewart1991}
{Stewart}, G.~R. 1991.
\newblock {Nonlinear satellite wakes in planetary rings. I - Phase-space
  kinematics}.
\newblock {\em Icarus}, {\bf 94}, 436--450.

\bibitem[\protect\citename{{Stewart} {et~al.}, }1984]{stewart1984}
{Stewart}, G.~R., {Lin}, D. N.~C., and {Bodenheimer}, P. 1984.
\newblock Collision-induced transport processes in planetary rings.
\newblock {Pages  447--512 of:} Greenberg, R., and Brahic, A. (eds), {\em
  Planetary Rings}.
\newblock Tucson Arizona: Univ. of Arizona Press.

\bibitem[\protect\citename{{Stewart} and {Leinhardt}, }2009]{stewart2009}
{Stewart}, S.~T., and {Leinhardt}, Z.~M. 2009.
\newblock {Velocity-Dependent Catastrophic Disruption Criteria for
  Planetesimals}.
\newblock {\em Astrophys. J. Lett.}, {\bf 691}, L133--L137.

\bibitem[\protect\citename{Supulver {et~al.}, }1995]{supulver1995}
Supulver, K.~D., Bridges, F.~G., and Lin, D. N.~C. 1995.
\newblock {The coefficient of restitution of ice particles in glancing
  collisions: Experimental results for unfrosted surfaces}.
\newblock {\em Icarus}, {\bf 113}, 188--199.

\bibitem[\protect\citename{{Tanaka} {et~al.}, }2003]{tanaka2003}
{Tanaka}, H., {Ohtsuki}, K., and {Daisaka}, H. 2003.
\newblock {A new formulation of the viscosity in planetary rings}.
\newblock {\em Icarus}, {\bf 161}, 144--156.

\bibitem[\protect\citename{{Thompson} {et~al.}, }1981]{thompson1981}
{Thompson}, W.~T., {Lumme}, K., {Irvine}, W.~M., {Baum}, W.~A., and {Esposito},
  L.~W. 1981.
\newblock {Saturn's rings - Azimuthal variations, phase curves, and radial
  profiles in four colors}.
\newblock {\em Icarus}, {\bf 46}, 187--200.

\bibitem[\protect\citename{{Thomson} {et~al.}, }2007]{thomson2007}
{Thomson}, F.~S., {Marouf}, E.~A., {Tyler}, G.~L., {French}, R.~G., and
  {Rappoport}, N.~J. 2007.
\newblock {Periodic microstructure in Saturn's rings A and B}.
\newblock {\em Gephys. Res. Lett.}, {\bf 34}, 24203--+.

\bibitem[\protect\citename{Tiscareno {et~al.}, }2006]{tiscareno2006}
Tiscareno, M.~S., Burns, J.~A., Hedman, M.~M., Porco, C.~C., Weiss, J.~W.,
  Murray, C.~D., and Dones, L. 2006.
\newblock Observation of ``propellers'' indicates 100-metre diameter moonlets
  reside in Saturn's A-ring.
\newblock {\em Nature}, {\bf 440}, 648--650.

\bibitem[\protect\citename{{Tiscareno} {et~al.}, }2007]{tiscareno2007}
{Tiscareno}, M.~S., {Burns}, J.~A., {Nicholson}, P.~D., {Hedman}, M.~M., and
  {Porco}, C.~C. 2007.
\newblock {Cassini imaging of Saturn's rings: II. A wavelet technique for
  analysis of density waves and other radial structure in the rings}.
\newblock {\em Icarus}, {\bf 189}, 14--34.

\bibitem[\protect\citename{{Tiscareno} {et~al.}, }2010]{tiscareno2010}
{Tiscareno}, M.~S., {Perrine}, R.~P., {Richardson}, D.~C., {Hedman}, M.~M.,
  {Weiss}, J.~W., {Porco}, C.~C., and {Burns}, J.~A. 2010.
\newblock {An Analytic Parameterization of Self-Gravity Wakes in Saturn's
  Rings, with Application to Occultations and Propellers}.
\newblock {\em Astron. J.}, {\bf 139}, 492--503.

\bibitem[\protect\citename{{Tiscareno} {et~al.}, }2013a]{tiscareno2013a}
{Tiscareno}, M.~S., {Hedman}, M.~M., {Burns}, J.~A., and {Castillo-Rogez}, J.
  2013a.
\newblock {Compositions and Origins of Outer Planet Systems: Insights from the
  Roche Critical Density}.
\newblock {\em Astrophys. J. Lett.}, {\bf 765}, L28.

\bibitem[\protect\citename{{Tiscareno} {et~al.}, }2013b]{tiscareno2013}
{Tiscareno}, M.~S., {Hedman}, M.~M., {Burns}, J.~A., {Weiss}, J.~W., and
  {Porco}, C.~C. 2013b.
\newblock {Probing the inner boundaries of Saturn's A ring with the Iapetus
  -1:0 nodal bending wave}.
\newblock {\em Icarus}, {\bf 224}, 201--208.

\bibitem[\protect\citename{Toomre, }1964]{toomre1964}
Toomre, A. 1964.
\newblock On the gravitational stability of a disk of stars.
\newblock {\em Astrophys. J.}, {\bf 139}, 1217--1238.

\bibitem[\protect\citename{{Toomre}, }1981]{toomre1981}
{Toomre}, A. 1981.
\newblock {What amplifies the spirals}.
\newblock {Pages  111--136 of:} {Fall}, S.~M., and {Lynden-Bell}, D. (eds),
  {\em Structure and Evolution of Normal Galaxies}.

\bibitem[\protect\citename{{Toomre} and {Kalnajs}, }1991]{toomre1991}
{Toomre}, A., and {Kalnajs}, A.~J. 1991.
\newblock {Spiral chaos in an orbiting patch}.
\newblock {Pages  341--358 of:} {Sundelius}, B. (ed), {\em Dynamics of Disc
  Galaxies}.
\newblock Almquist-Wiksell, G{\"o}teborg.

\bibitem[\protect\citename{{Tremaine}, }2003]{tremaine2003}
{Tremaine}, S. 2003.
\newblock {On the origin of irregular structure in Saturn's rings}.
\newblock {\em Astron. J.}, {\bf 125}(Feb.), 894--901.

\bibitem[\protect\citename{Trulsen, }1972]{trulsen1972b}
Trulsen, J. 1972.
\newblock Numerical simulation of jetstreams,1:The three-dimensional case.
\newblock {\em Astrophys. Space Sci.}, {\bf 17}, 241--262.

\bibitem[\protect\citename{Ward, }1981]{ward1981}
Ward, W.~R. 1981.
\newblock {On the radial structure of Saturn's rings}.
\newblock {\em Geophys. Res. Lett.}, {\bf 8}, 641--643.

\bibitem[\protect\citename{Weidenschilling {et~al.}, }1984]{weidenschilling84}
Weidenschilling, S.~J., Chapman, C.~R., Davis, D.~R., and Greenberg, R. 1984.
\newblock Ring particles: Collisional interactions and physical nature.
\newblock {Pages  367--415 of:} Greenberg, R., and Brahic, A. (eds), {\em
  Planetary Rings}.
\newblock Tucson Arizona: Univ. of Arizona Press.

\bibitem[\protect\citename{{Wisdom} and {Tremaine}, }1988]{wisdom1988}
{Wisdom}, J., and {Tremaine}, S. 1988.
\newblock {Local simulations of planetary rings}.
\newblock {\em Astron. J.}, {\bf 95}, 925--940.

\bibitem[\protect\citename{{Yasui} {et~al.}, }2012]{yasui2012}
{Yasui}, Y., {Ohtsuki}, K., and {Daisaka}, H. 2012.
\newblock {Viscosity in Planetary Rings with Spinning Self-gravitating
  Particles}.
\newblock {\em Astron. J.}, {\bf 143}, 110.

\bibitem[\protect\citename{{Yasui} {et~al.}, }2014]{yasui2014}
{Yasui}, Y., {Ohtsuki}, K., and {Daisaka}, H. 2014.
\newblock {Gravitational Accretion of Particles onto Moonlets Embedded in
  Saturn's Rings}.
\newblock {\em Astrophys. J.}, {\bf 797}, 93.

\end{thebibliography}