Multimedia Gallery

We have a number of ongoing projects at various stages of publication using the new granular dynamics code. Dr. Steve Schwartz (Nice Observatory) is carrying out granular impact simulations in support of the Hayabusa-2 mission. Dr. Soko Matsumura (University of Dundee) is studying the Brazil-nut effect in granular materials with application to seismic shaking on asteroids. Graduate student Yang Yu (Tsingua University) is simulating the 2029 encounter of Apophis with Earth to determine whether gravity tides could disturb surface grains on the asteroid. And Maryland graduate student Ron Ballouz is investigating the effect of pre-impact spin and different material properties on rubble pile collision outcome, as well as carrying out simulations of the OSIRIS-REx regolith sampling mechanism. All of these projects are also in collaboration with Dr. Patrick Michel (Nice Observatory). Movie clips illustrating some of this work are presented below, followed by a list of related publications in progress.

Related papers (alphabetical by first author):

• Ballouz, R.-L., Richardson, D.C., Michel, P., Schwartz, S.R. 2014. Rotation-dependent catastrophic disruption of gravitational aggregates. ApJ 789:158
• Ballouz, R.-L., Richardson, D.C., Michel, P., Schwartz, S.R., Yu, Y. 2014. The effects of shear strength on the catastrophic disruption of gravitational aggregates. P&SS, in press (preprint)
• Matsumura, S., Richardson, D.C., Michel, P., Schwartz, S.R., Ballouz, R.-L. 2014. The Brazil nut effect and its application to asteroids. MNRAS 443, 3368-3380
• Schwartz, S.R., Michel, P., Richardson, D.C., Yano, H. 2014. Low-speed impact simulations into regolith in support of asteroid sampling mechanism design: I. Comparison with 1-g experiments. P&SS, in press (preprint)
• Yu, Y., Richardson, D.C., Michel, P., Schwartz, S.R., Ballouz, R.-L. 2014. Numerical predictions of surface effects during the 2029 close approach of asteroid 99942 Apophis. Icarus 242, 82-96

Graduate student Steve Schwartz is leading our effort to add soft-sphere granular mechanics to pkdgrav. In his first paper (Schwartz et al. 2012, Granular Matter 14, 363), Steve describes the implementation and shows that the method successfully reproduces the flow rate of grains through a cylindrical hopper as a function of aperture size. Below are two movies provided as supplemental material to the paper. On the left is an animation of a hopper being filled with 1.5 million particles; once the hopper is full, an aperture at the bottom is opened and the material drains out. On the right is a similar simulation, but this time showing the force network in the grains (light particles are experiencing more stress, dark particles less stress; the red particles are in free fall). Stayed tuned for more results from our granular dynamics experiments!

Undergraduate Brett Morris is conducting a detailed study of how rigid bodies (asteroid components) in contact evolve as angular momentum is added to the system. We can also examine the complex interplay of rigid bodies in mutual orbit. Compared to earlier simulations (see the last item in the July 2009 entry below), these have much higher resolution and feature very symmetric bodies constructed using an algrorithm Brett designed. Shown here is a movie illustrating the orbital and rotational evolution of two identical, promixal, flattened ellipsoids (perturbed slightly at the start to make things more interesting). The result is a fascinating cosmic dance. Enjoy!

We have implemented a new "soft-sphere" method in pkdgrav to model dense granular systems with proper treatment of friction, including rolling friction. Graduate student Steve Schwartz is leading the coding effort. The aim is to apply this technique to models of granular flow in low-gravity environments, such as asteroid surfaces. Shown here are two movies demonstrating the method in action with a gentle landslide past an obstacle. Many intriguing aspects of granular flow are evident, including jamming.

Randall Perrine has added the ability of planetary ring particles in local patch simulations to stick together to form rigid aggregates (which can also break apart), depending on configurable parameters. The simulations below represent portions of the A ring, with equal-size (1-meter-radius) particles. Bond strengths are 100 Pascals. The movie on the left allows particles to stick if they hit as speeds less than half their mutual escape speed, and break off at 1.5 times the mutual escape speed. The movie on the right is less plausible (merge limit 1.5 times the escape speed, fragmentation limit twice the escape speed), but results in larger aggregates that persist longer. A paper describing the method and early results has just been submitted -- watch this space for a link to the preprint! UPDATE: This is now published as Perrine, R.P., Richardson, D.C., Scheeres, D.J., 2011. A numerical model of cohesion in planetary rings. Icarus 212, 719-735. Also see Perrine, R.P., Richardson, D.C. 2012. N-body simulations of cohesion in dense planetary rings: A study of cohesion parameters. Icarus 219, 515-533.

Stephen Schwartz has been experimenting with weak cohesion to reproduce laboratory measurements of high-speed impacts into macroscopic glass beads that have been glued together. The movies below (animated GIFs) show simulations of impacts into weak (left) and strong (right) configurations. We are exploring the many configurable parameters to see which best reproduce the laboratory experiments. The nifty visuals were produced with POV-Ray.

Just for fun, here's a comparison between a set of real glued beads (left) and the simulated version (right):

Related paper:

• Schwartz, S.R., Michel, P., Richardson, D.C. 2013. Numerically simulating impact disruptions of cohesive glass bead agglomerates using the soft-sphere discrete element method. Icarus 226, 67-76

There is strong renewed interest in applying insights from granular dynamics to the study of asteroid (and other small solar system body) surfaces. I have greatly enhanced my code's ability to do problems in this area. Here are a couple fun examples. More to come!

Related papers:

• Richardson, D.C., Walsh, K.J., Murdoch, N., Michel, P. 2011. Numerical simulations of granular dynamics: I. Hard-sphere discrete element method and tests. Icarus 212, 427-437
• Murdoch, N., Michel, P., Richardson, D.C., Nordstrom, K., Berardi, C.R., Green, S.F, Losert, W. 2012. Numerical simulations of granular dynamics: II. Particle dynamics in a shaken granular material. Icarus 219, 321-335 [corrigendum 220, 296]

With a team led by Dan Durda (SwRI), we carried out impact experiments with meter-diameter granite spheres. Pictures along with a cool movie of the low-speed experiments can be found here. Below are two movies of shooting projectiles into our spheres in a (failed!) attempt to fully fragment them. Paper coming soon!

UPDATE 9/9/10: The new Discovery program Bad Universe featured these impacts in the pilot episode, clips from which are available here (search for the "Doomsday" clip).

UPDATE 6/12/12: Here's a short video clip of run #99 from the slow-speed experiments, with sound! (Listen for the distinct "tink!" as the spheres come into contact.)

UPDATE 4/11/13: Here's a long video clip of run #90, our highest-speed impact, with sound!

Related papers:

• Durda, D.D., Movshovitz, N., Richardson, D.C., Asphaug, E., Morgan, A., Rawlings, A.R., Vest, C. 2011. Experimental determination of the coefficient of restitution for meter-scale granite spheres. Icarus 211, 849-855
• Walker, J.D., Chocron, S., Durda, D.D., Grosch, D.J., Movshovitz, N., Richardson, D.C., Asphaug, E. 2013. Momentum enhancement from aluminum striking granite and the scale size effect. International Journal of Impact Engineering 56, 12-18

Some of my research talks at conferences and other venues have been recorded for posterity. Here are the ones I have been able to find:

• "N Rigid-body Dynamics" (Prospects in Theoretical Physics: Computational Astrophysics; Princeton, NJ; Jul 17, 2009) -- streaming video, also available as hi-res and lo-res QuickTime videos.
• "Forming NEA Binaries: Tidal Disruption May Not Be Enough" (IAU Symposium 236: Near Earth Objects, Our Celestial Neighbors: Opportunity and Risk; Prague, Czech Republic; Aug 16, 2006) -- 423 MB MPEG(!)
• "Gravitational Reaccumulation in the Solar System" (KITP Conference: Planet Formation: Terrestrial and Extra-solar; Santa Barbara, CA; Mar 19, 2004) -- web page

Here are some fun movies illustrating the concept of rigid aggregates. Most recently, a simulation of asteroid family formation (QuickTime, 800 MB!!):

Related paper:

• Michel, P., Richardson, D.C. 2013. Collision and gravitational reaccumulation: Possible formation mechanism of the asteroid Itokawa. A&A 554, L1

Some cubes colliding (which ones are rigid?...):

And an old but pedagogical movie of gravity torques on rigid aggregates:

Selected paper related to all of the above: Richardson, D.C., Michel, P., Walsh, K.J., Flynn, K.W. 2009. Numerical simulations of asteroids modeled as gravitational aggregates. Plan. & Space Sci. 57, 183-192

This is a movie of the dynamics in a patch of a planetary ring. In the snapshot, the central patch is shown in green while shearing replicas are shown in magenta. Wake formation on a scale of about 100 m is easily seen in this simulation, which consisted of over 220,000 self-gravitating, colliding particles. This work was performed on the ARSC Cray T3E.

And here's a side view of a ring patch (ray-traced still image):

Related paper: Porco, C.C., Weiss, J.W., Richardson, D.C., Dones, L., Quinn, T., Throop, H. 2008. Simulations of the dynamical and light-scattering behavior of Saturn's rings and the derivation of ring particle and disk properties. Astron. J. 136, 2172-2200

My former student Kevin Walsh, myself, and Patrick Michel published a Nature paper demonstrating how a binary asteroid like 1999 KW4 could be formed by the gradual spinup from thermal forces of a rubble-pile asteroid (gravitational aggregate). Here's the UMd press release. Below is a movie illustrating the process.

Related paper: Walsh, K.J., Richardson, D.C., Michel, P. 2008. Rotational breakup as the origin of small binary asteroids. Nature 454, 188-191

Also see: Walsh, K.J., Richardson, D.C., Michel, P. 2012. Spin-up of rubble-pile asteroids: Disruption, satellite formation, and equilibrium shapes. Icarus 220, 514-529

Here's an animation of a moonlet embedded in a patch of planetary ring, generating a "propeller" structure:

Related paper: Tiscareno, M.S., Burns, J.A., Hedman, M.M., Porco, C.C., Weiss, J.W., Dones, L., Richardson, D.C., Murray, C.D. 2006. 100-metre-diameter moonlets in Saturn's A ring from observations of `propeller' structures. Nature 440, 648-650

Handy for when you can't show a movie, here are some strips showing rigid cubes colliding, rubble piles colliding, and tidal disruption.

Simulations of planet formation usually require assumptions about what happens when planetesimals collide (do they stick, bounce, or fragment?). As part of her thesis, my former student Zoë Leinhardt incorporated simulations of rubble piles collisions into our code in the first self-consistent model of planet formation. Here is a movie illustrating the idea:

Selected related paper: Leinhardt, Z.M., Richardson, D.C. 2005. Planetesimals to protoplanets. I. Effect of fragmentation on terrestrial planet formation. Astrophys. J. 625, 427-440

A large suite of rubble pile collision simulations was needed to provide a full range of planetesimal collision outcomes for the above work. Here are some select movies from that campaign. The entire suite of movies is available here.

Selected related paper: Leinhardt, Z.M., Richardson, D.C., Quinn, T. 2000. Direct N-body simulations of rubble pile collisions. Icarus 146, 133-151

Work that I have been involved with has been featured on the covers of major journals. Click on the images to access the associated articles.

Here are some old tests of my code's ability to perform granular dynamics: dropping balls in a cylinder; dropping balls in a funnel; making a sandpile; and mixing balls in a tumbler. This work has been superceded recently (2010) by far more sophisticated treatments of granular dynamics with the code. See the "Granular Dyanmics, Revisited" entry above.

A movie and graph animation showing a 1000-year planet formation simulation performed on the NASA Goddard SGI T3E using 128 nodes for about 200 wallclock hours. The run consisted of 1 million planetesimals in a thin cold disk around the Sun, and included the effects of the giant planets. In 100 years Jupiter has already begun to carve out resonance structure in the disk. Meanwhile, particles in the Earth-Mars region have started to agglomerate on the way to building planets.

Related paper: Richardson, D.C., Quinn, T., Stadel, J., Lake, G. 2000. Direct large-scale N-body simulations of planetesimal dynamics. Icarus 143, 45-59

If many asteroids (and comets) are piles of rubble, they are susceptible to stresses such as tidal disruption. Here's a movie made long ago that I show all the time in which a tidally distorted asteroid forms a binary. A blob effect smooths over the underlying particles. Next to that is a two-frame illustration of the tidal disruption process during a close planetary fly-by.

Selected related paper: Richardson, D.C., Bottke Jr., W.F., Love, S.G. 1998. Tidal distortion and disruption of Earth-crossing asteroids. Icarus 134, 47-76

Note that tidal disruption simulations can be sensitive to the resolution (number of particles used):

All of this was inspired by the disruption and impact of Comet D/Shoemaker-Levy 9 at Jupiter. Here are animations of prograde (left) and retrograde (right) encounters of a rubble-pile comet with Jupiter, with the former leading to the formation of the famous "string of pearls." (Animations created with the assistance of Rudy Ziegler at the old High Performance Research Computing (HPRC) Visualization Lab at the University of Toronto.)

By allowing particles to stick at the point of contact in an N-body simulation, it is possible to build up fluffy aggregates that are reminiscent of fluffy grains studied in the laboratory. Such grains may be important in the early stages of planetesimal growth, since their fractal nature allow a limited kind of runaway agglomeration even while being stirred up by the turbulent gas in the primordial nebula. Eventually these grains would grow large enough to decouple from the gas, settle to the midplane, and begin to coagulate into larger planetesimals. We think!

Related paper: Richardson, D.C. 1995. A self-consistent treatment of fractal aggregate dynamics. Icarus 115, 320-335