1. Shock-Wave Simulations Using Molecular Dynamics Shock-Wave Simulations Using Molecular Dynamics CCP5 and Marie Curie Actions: Methods in Molecular Simulation Summer School 2006 1 Matthew R. Farrow Department of Physics, University of York, United Kingdom

2. 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 2

3. What am I doing?! 3

4. 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

5. 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! 5

6. How am I supposed to do THAT?! 6

7. 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 10 9 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) 7

8. What is a shock-wave? 8

9. 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 Shock u 0 = 0 P 0 = 0 V 0 = 1/p 0 E 0 = 0 After Shock P = Uu/V 0 V = V 0 (1-u/U) E = 1/2P(V 0 -V) u 9

10. 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

11. Recent Work with Argon 11

12. Shock-waves in Argon For Argon we can use the well known Lennard-Jones potential [5] : 12 [5] M.P. Allen and D.J Tildesley, “Computer Simulation of Liquids”, Oxford University Press (1987)

13. Shock-wave movies 13 No shockwave

14. Shock-wave movies 14 5X Velocity of Sound

15. Shock-wave movies 15 10X Velocity of Sound

16. 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 16

17. Future Work To model a shock-wave through  Metals (e.g. Aluminium)  Insulators Much bigger system of atoms (~10,000)  NB: one cubic cm ~ 10 23 atoms. Create the EOS and predictions! 17

18. Thanks for listening! Any questions? 18