Shock-Wave Shock-Wave Simulations Simulations

Using Molecular Using Molecular DynamicsDynamics

CCP5 and Marie Curie Actions: Methods in Molecular Simulation Summer School 20061

Matthew R. Farrow

Department of Physics, University of York,United Kingdom

Outline• Introduction:

- What is it I am doing?

- Why am I doing it?

- How will I do it?

• What is a Shock-wave?

• Recent work:

- Shock-wave in Argon;

• Discussion and conclusions

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What am I doing?!

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Shock-wave research

My research is to use shock-waves in solids to investigate material properties, using molecular dynamics (MD) simulations;

- Aim to probe the Equations of State to enhance understanding of material properties;

- Perhaps find new applications? 4

Why shock-wave research?

•Allows us to go places inaccessible to the current level of experiment;

•Astrophysics:

- Planetary core modelling;

- High temperature physics

•Explosives modelling!

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How am I supposed to do

THAT?!

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Classical or Ab-initio MD?• Classical MD uses empirical potentials and so is

computationally cheap;

•Classical MD simulations should scale linearly with number of processors; for both speed of computation and number of atoms;

•Shock waves in systems with 109 atoms have been simulated[1] using Classical MD.

• Ab-initio MD calculations are limited in the number of atoms that can be simulated due to the extreme computational cost of calculating the many-body interactions;

•Ab-initio is more accurate!

[1] K.Kadau,T.C.Germann,P.S.Lomdahl,B.L.Holian,Science,296,1681 (2002)

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What is a shock-wave?

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Shock-waves• Possible to have the propagation of the pertubation move faster

than the acoustic velocity of discontinuous pressure waves[2]

• Shock-waves through solids, liquids and gases

- Navier-Stokes Equations

- Rankine-Hugoniot equations

[2] G.G.Stokes, M. Poisson (1800’s)

Shock Front

U

Before Shocku0= 0P0 = 0

V0 = 1/p0

E0 = 0

After ShockP = Uu/V0

V = V0(1-u/U) E = 1/2P(V0-

V)

u

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Shock-waves and Equations of State (EOS)

• The Equations of State (EOS) gives the all the properties of the material in terms of Pressure, P, Volume, V and Energy, E (or Temperature, T);

- For example, the ideal gas EOS: PV = RT

• However, the full EOS for most materials are very difficult to determine.

• Hugoniot is a line on the EOS:

- All possible states after a material has been shocked

Hugoniot Curve Exemplar[3]

[3] “Equations of State” Article in Discovery, the AWE Science and Technology Journal (1989)10

Recent Work with Argon

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Shock-waves in Argon• For Argon we can use the well known Lennard-

Jones potential[5] :

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[5] M.P. Allen and D.J Tildesley, “Computer Simulation of Liquids”, Oxford University Press (1987)

Shock-wave movies

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QuickTime™ and aYUV420 codec decompressor

are needed to see this picture.

No shockwave

Shock-wave movies

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QuickTime™ and aYUV420 codec decompressor

are needed to see this picture.

5X Velocity of Sound

Shock-wave movies

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QuickTime™ and aYUV420 codec decompressor

are needed to see this picture.

10X Velocity of Sound

Discussion and Conclusions•Shock-waves are characterised by

their Hugoniot:

- Line on the Equations of State surface;

•Have plenty of materials to choose from;

•Different shock-wave velocities seen to produce different responses

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Future Work•To model a shock-wave through

- Metals (e.g. Aluminium)

- Insulators

•Much bigger system of atoms (~10,000)

- NB: one cubic cm ~ 1023 atoms.

•Create the EOS and predictions!

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Thanks for listening!

Any questions?

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