The applications of the Rayleigh-Taylor instability---i.e. the mixing of a heavy fluid on top of a light in a gravitational field ---range from astrophysics (supernova explosions), to geophysics
(formation of salt domes), all the way to inertial confinement fusion (collapse of ICF
capsules), as well as the general turbulent mixing of fluids. Therefore, its fundamental understanding is of relevance not only to the foundations of hydrodynamics but also to a broad range of subjects, including physics, chemistry, biology, and geology.
We show that quantitative theoretical investigations on the atomistic level of the Rayleigh-Taylor instability --- as the classical example of complex turbulent hydrodynamic flows --- compare favorably to recent experiments. Using the latest generation of supercomputers (the LANL Q machine) we solve Newtonian equations of motion for up to 100 million particles for as many as 250,000 integration steps --- an enormous numerical venture. A quantitative comparison of these ``nanohydrodynamic'' flows with continuum descriptions (Navier-Stokes equations) and macroscopic experiments demonstrates that large-scale atomistic simulations can provide insight into complex hydrodynamic phenomena.
The movie gives a nice impression of what happens during such instabilities;
it shows a quasi 2 dimensional simulation including about 12 million atoms
interacting via Lenard-Jones potentials (only the repulsive part for the
AB interaction in order to maximize surface tension)
Proc. Natl. Acad. Sci. 104, 7741 (2007), The Importance of Fluctuations in Fluid Mixing by K. Kadau, C. Rosenblatt, J.L. Barber, T.C. Germann, Z. Huang, P. Carles, and Berni J. Alder. (for supporting on-line material including movies click here)Int. J. Mod. Phys. C 17, 1755 (2006), Molecular-Dynamics Comes of Age: 320 Billion Atom Simulation on BlueGene/L by K. Kadau, T.C. Germann, and P.S. Lomdahl.
Supercomputing `05 (2005)(SC05, ACM 1-59593-061-2/05/0011).[Gordon Bell Prize finalist paper] 25 Tflop/s Multibillion-Atom Molecular Dynamics Simulations and Visualization/Analysis on BlueGene/L, by T.C. Germann, K. Kadau, P.S. Lomdahl
Proc. Natl. Acad. Sci. 101, 5851 (2004), Nanohydrodynamics simulations: An atomistic view of the Rayleigh-Taylor instability by K. Kadau, T.C. Germann, N.G. Hadjiconstantinou, P.S. Lomdahl, G. Dimonte, B.L. Holian, and B.J. Alder. (for supporting on-line material including movies click here)Int. J. Mod. Phys. C 15, 193 (2004), Large-Scale Molecular-Dynamics Simulation of 19 Billion particles by K. Kadau, T.C. Germann, and P.S. Lomdahl
DPG pro-physik.de, 08.04.2004, Supercomputer laesst 100 Millionen Atome tanzen by Rainer Scharf.
Shock waves were initiated by a 'momentum mirror' (B.L. Holian and P.S. Lomdahl, Science 280, 965 (1998)), which specularly reflects any atoms atoms reaching reaching the face of of the perfectly flat infinitely massive piston (left) moving at a piston velocity. The resulting shock waves in the iron single crystal moves (from left to right) along the (001) direction in the initial bcc structure (gray). Above the threshold for the structural transformation (about 15GPa, about 10 percent uniaxial compression, or about a piston velocity of 5 percent of the longitudinal sound velocity) into the close-packed structure (red) many grains of the close-packed material nucleate in a displacive manner (martensitic-like) within the uniaxially compressed bcc structure (blue). Crystallographic different oriented grains are separated by grain boundaries (yellow). Depending on the shock strength the transformed region can be a mixed phase region and the resulting shock wave structure is a split two-wave structure consisting of an elastic precursor and a slower transformation wave. The initial nucleation takes place along the (bcc011) close-packed planes transforming into the close-packed planes of the close-packed material. The comparison of the nucleation process for three different shock strength (increasing from left to right in the movie) is shown in the last movie where only atoms with a lateral displacement larger than about 1/6 of the nearest neighbor distance are shown. The samples consist of aprox 8 million atoms (i.e. 40.2nm x 40.2nm x 57.4nm) and was simulated for 8.76ps.
Nucleation of close-packed material for 3 different shock-strength
Phys. Rev. B 72, 064120 (2005), Atomistic Simulations of Shock-Induced Structural Transformations in bcc Iron Single Crystals for Different Crystallographic Orientations by K. Kadau, T.C. Germann, P.S. Lomdahl, Brad Lee Holian.
Phys. Rev. Lett. 95, 075502 (2005), Direct Observation of the alpha-epsilon Transition in Shock-Compressed Iron via Nanosecond X-ray Diffraction by D.H. Kalantar, J.F. Belak, G. W. Collins, J. D. Colvin, H.M. Davies, J.H. Eggert, T.C. Germann, J. Hawreliak, B.L. Holian, K. Kadau, P.S. Lomdahl, H.E. Lorenzana, M.A. Meyers, K. Rosolankova, M.S. Schneider, J. Sheppard, J.S. Stoelken, J.S. Wark.Science 296, 1681 (2002), Microscopic View of Structural Phase Transitions Induced by Shock Waves by K. Kadau, T.C. Germann, P.S. Lomdahl, and B.L. Holian.
Frankfurter Allgemeine Zeitung, 12.06.2002, Nr. 133 / Seite N2, Schock im Eisenkristall by Rainer Scharf.
Science 280, 965 (1998), Plasticity Induced by Shock Waves in Nonequilibrium Molecular-Dynamics Simulations by B.L. Holian and P.S. Lomdahl.
Cubic iron-nickel alloy nano-particles (only half of the sample is shown in order to see the interior) undergo a martensitic transformation (first movie) from the high temperature fcc austenitic phase (red) into the low temperature bcc martensitic phase (green) (due to technical reasons the surface is green or blue depending on the orientation of the surface). The heterogeneous nucleation starts at defects like corners and grows into the interior of the nano-particle with a fraction of the sound velocity (that is, the growth velocity depends on the crystallographic direction.) with a transient mixed phase region having a needle-like pattern. The final structure is twinned and can undergo a transformation back to the original austenite structure (second movie). The sample contains one million atoms (edge length=24nm) and was simulated for 67.5ps.
J. Phys. IV France 11, Pr8-17 (2001), Large-scale molecular-dynamics study of the nucleation process of martensite in Fe-Ni alloys by K. Kadau, P. Entel, T.C. Germann, P.S. Lomdahl, and B.L. Holian.
Phys. Rev. B 57, 5140 (1998), Martensite-austenite transition and phonon dispersion curves of Fe1-xNix studied by molecular dynamics simulations by R. Meyer and P. Entel.
J. Magn. Magn. Mater. 177-181, 1409 (1998), Numerical simulation of
martensitic transformations in magnetic transition-metal alloys by P.
Entel, R. Meyer, K. Kadau, H.C. Herper, M. Acet, E.F. Wassermann.
Nature 391, 561-563 (1998), Softening of nanocrystalline metals at very small grain sizes by J. Schiøtz, F. D. Di Tolla and K. W. Jacobsen.
Science 296, 66 (2002), Grain Boundaries and Dislocations by H. van Swygenhoven.