molecular-dynamics simulations movie page (this page)

graphic page

sport page

Most of the simulations were performed by using an embedded-atom method (EAM) potential (M.S. Daw and M.I. Baskes PRL 50, 1285 (1983.), M.S. Daw and M.I. Baskes PRB 29, 1285 (1983.)) which consist of a density depend and a two body potential term. The EAM potential is able to reproduce fundamental properties of metals in contrast to pure pair-potentials like the Lenard-Jones (LJ) potential.

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),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),

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.

Shock along Fe-bcc(001), piston velocity=471m/s

Shock along Fe-bcc(001), piston velocity=689m/s

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.

austenitic (back) transformation at high temperatures

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.

We model tensile testing of nano-phase Al (Al modelled by an EAM potential described in: Phase Transitions 75, 265 (2002), Atomistic modeling of diffusion in Aluminum by S. Grabowski, K. Kadau, and P. Entel.) by either sintering from spherical nano-particles or setting up by a Voronoi construction.

Different crystallographic oriented grains (red) are separated by grain boundaries or pores (yellow). Under tensile testing different modes of plasticity such as grain rotation and grain-boundary movements are observed. In addition to that and in contrast to other materials like Cu, No, and Pd (see Literature) crack propagation along the grain-boundaries at high strains (around 10 percent depending on grain size) is observed. As in the case of Cu,Pd, and Ni an inverse Hall-Petch effect (i.e. softening at smallest grain size) is observed. the case of the sintered nano phase material the remaining pores significantly reduce the strength of the material (growth of pores). For some quantitative results check here.

tensile test nanophase Aluminum (Voronoi-constructed)

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.

Motivated by a visit at the Meteor Crater or Barringer Crater near Flagstaff in Arizona we model an impact of a nano-meteor consisting of 418 iron atoms smashing into a slab of one million bcc ordered iron atoms. The impact velocity was chosen to 11 miles/sec which was the impact velocity of the Meteor Crater, the incident angle in the simulation is 45 degree. It's amazing how fast the kinetic energy is transformed into potential energy (i.e. deformation). As early as 4 pico seconds after the impact a crater has formed which consumed about half of the kinetic energy of the meteor (see graph) . Another interesting aspect is the formed aspect ratio (the ratio between the crater depth and width) which is for the meteor crater about 1/5 for the time being (that might has been different directly after the impact). The nano-meteor has an aspect ratio of 1/3 four pico seconds after the impact. As you can see in the movies the crater seems to get larger in diameter, so things are going into the right direction. We also find that a perpendicular impact doesn't change that much the crater formation and the energy transformation. For this simulations we worked with an integration time step of 0.125 femto second s -and increase to 0.25 femto seconds didn't change the picture but rather led to numerical instabilities at later times ...

By the way the Barringer Crater has a diameter of about a mile and was impacted some 50,000 years ago by a meteor consisting of an iron nickel compound with a diameter of 150 feet and weighed no less than 300,000 tons. Between miles and nanometers there is a factor of 10 to the power of 12, but still there are similarities, at least for certain situations ...

side view

airplane view

Theoretical Division (T-11) (LANL, USA)

Kai Kadau's home page