Microscopic simulations of shock propagation in condensed media: comparison between real time and frequency domains Page: 3 of 9
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The recognition of this limitation stems from a proper understanding of
gaseous behavior which acknowledges that thermodynamic concepts, such as
pressure and temperature, can only be defined for regions large compared with
the mean free path of molecules in the gaseous phase. Since shock fronts
arise from non-linearities In the basic (Navler-Stokes) equations, they will
automatically steepen until their wldtn Is at the mean free path limit. Thus
the front Is recognized as a special region whose full understanding can only
be achieved by a detailed examination of the microscopic behavior of the
molecules in the shock region. Specifically, It comes as no surprise that
collisions between them can lead to bond rupture, even though the temperatures
behind and in front of the shock are well below that required for thermal
The study of shocks in condensed matter has suffered from the lack of any
such clear-cut criterion. Thus, hydrocode studies of shock propagation in
solids are carried through with the Inclusion of a viscous (lossy) damping in
the equations and typically give shock widths of millimeters and rise times of
microseconds, both of which appear to agree with experiment. However, 0.5
mm/psec =5.0 A/picosecond. Thus, If we have a front which 1s composed of
a sequence of "steps" of width •v interatomic spacing, it will appear to show
a microsecond rise time If It Is examined by probes which are of millimeter
dimensions; however, what these observations are actually reflecting are the
natural time and frequency scales of interatomic motion.
Once this Is realized it 1s apparent that the hydro-codes are being
forced beyond the same natural limit as that for gaseous media; namely, the
mean Interatomic spacing which, 1n condensed materials, fills the same role as
the mean free path 1n gases. The proper way to resolve this difficulty is to
examine the propagating shock front at the microscopic (atomic) level; experi-
mentally, this Is beyond the limits of spatial and temporal resolution
currently available simultaneously, although recent work has demonstrated that
when both "windows" (limits) are reduced, the shock width shrinks in the manner
we would predict. However, it 1s both easier and much cheaper to do a computer
experiment using the techniques of computer molecular dynamics (CMD). These
involve setting up in the computer the Newton's law equations of motion for an
assembly of atoms bound in regular or irregular arrays and numerically
integrating them to determine the system's temporal history, following initial
Over the past ten years, we have carried out many such studiesJ but most
recently**>3 we have been concerned with developing post-processing techniques
that will enable us to present in a compact and manageable form the temporal
histories of each simulation, without resorting to such broad averaging that
the detailed behavior of the shock 1s lost or obscured. It is 1n the nature of
the these simulations that they contain all possible information, and one can
scan this by generating a movie of each history—however, this provides
qualitative rather than quantitative insight.
In this paper we wish to present early results of applying two post-
processing techniques both to one of our original canonical studies and to a
related simulation designed to show the effects of lattice irregularities or
2. NATURE OF THE SIMULATIONS
The techniques of CMD are now well documented by both others and our-
selves.^4 The only novel features are the use of "neighborhood look-up"
Here’s what’s next.
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Karo, A.M.; Hardy, J.R. & Mehlman, M.H. Microscopic simulations of shock propagation in condensed media: comparison between real time and frequency domains, article, July 1, 1985; United States. (digital.library.unt.edu/ark:/67531/metadc1093724/m1/3/: accessed January 18, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.