Going beyond an old shockwave conjecture for improving upon Navier-Stokes.

Nonequilibrium molecular dynamics (NEMD) computer simulations of steady shockwaves in dense fluids and rarefied gases produce detailed shockwave profiles of mechanical and thermal properties. The Boltzmann equation, under the assumption of local thermodynamic equilibrium (LTE), leads to the first-order (linear) continuum theory of hydrodynamic flow: Navier-Stokes-Fourier (NSF). (Expansion of the LTE Boltzmann equation in higher powers of gradients yields so-called Burnett second-order terms, etc.

Mesodynamics with implicit degrees of freedom.

Mesoscale phenomena--involving a level of description between the finest atomistic scale and the macroscopic continuum--can be studied by a variation on the usual atomistic-level molecular dynamics (MD) simulation technique. In mesodynamics, the mass points, rather than being atoms, are mesoscopic in size, for instance, representing the centers of mass of polycrystalline grains or molecules. In order to reproduce many of the overall features of fully atomistic MD, which is inherently more expensive, the equations of motion in mesodynamics must be derivable from an interaction potential that is faithful to the compressive equation of state, as well as to tensile de-cohesion that occurs along the boundaries of the mesoscale units.

Burnett-Cattaneo continuum theory for shock waves.

We model strong shock-wave propagation, both in the ideal gas and in the dense Lennard-Jones fluid, using a refinement of earlier work, which accounts for the cold compression in the early stages of the shock rise by a nonlinear, Burnett-like, strain-rate dependence of the thermal conductivity, and relaxation of kinetic-temperature components on the hot, compressed side of the shock front. The relaxation of the disequilibrium among the three components of the kinetic temperature, namely, the difference between the component in the direction of a planar shock wave and those in the transverse directions, particularly in the region near the shock front, is accomplished at a much more quantitative level by a rigorous application of the Cattaneo-Maxwell relaxation equation to a reference solution, namely, the steady shock-wave solution of linear Navier-Stokes-Fourier theory, along with the nonlinear Burnett heat-flux term. Our new continuum theory is in nearly quantitative agreement with nonequilibrium molecular-dynamics simulations under strong shock-wave conditions, using relaxation parameters obtained from the reference solution.

Heat-flow equation motivated by the ideal-gas shock wave.

We present an equation for the heat-flux vector that goes beyond Fourier's Law of heat conduction, in order to model shockwave propagation in gases. Our approach is motivated by the observation of a disequilibrium among the three components of temperature, namely, the difference between the temperature component in the direction of a planar shock wave, versus those in the transverse directions. This difference is most prominent near the shock front.

Test of a new heat-flow equation for dense-fluid shock waves.

Using a recently proposed equation for the heat-flux vector that goes beyond Fourier's Law of heat conduction, we model shockwave propagation in the dense Lennard-Jones fluid. Disequilibrium among the three components of temperature, namely, the difference between the kinetic temperature in the direction of a planar shock wave and those in the transverse directions, particularly in the region near the shock front, gives rise to a new transport (equilibration) mechanism not seen in usual one-dimensional heat-flow situations. The modification of the heat-flow equation was tested earlier for the case of strong shock waves in the ideal gas, which had been studied in the past and compared to Navier-Stokes-Fourier solutions.

Atomistic methods in fluid simulation.

Atomistic methods, such as molecular dynamics and direct simulation Monte Carlo, constitute a powerful and growing set of techniques for fluid-dynamics simulation. The more fundamental nature of such methods, which exhibit nonlinear transport effects and small-scale fluctuations, extends their modelling accuracy to a significantly wider range of scales and regimes than the more traditional Navier-Stokes-based continuum fluid-simulation techniques. In this paper, we describe the current state of the art in atomistic fluid simulation, from both a theoretical and a computational standpoint, and outline the advantages and limitations of such methods.

Influence of interatomic bonding potentials on detonation properties.

The dependences of the macroscopic detonation properties of a two-dimensional (2D) diatomic (AB) molecular system on the fundamental molecular properties were investigated. This includes examining the detonation velocity, reaction zone thickness, and critical width as functions of the exothermicity (Q) of the gas-phase reaction [AB --> (1/2)(A(2) + B(2))] and the gas-phase dissociation energy (D(e)(AB)) for AB --> A + B . Following previous work, molecular dynamics (MD) simulations with a reactive empirical bond-order potential were used to characterize the shock-induced response of a diatomic AB molecular solid, which exothermically reacts to produce A2 and B2 gaseous products.

Shock waves in polycrystalline iron.

The propagation of shock waves through polycrystalline iron is explored by large-scale atomistic simulations. For large enough shock strengths the passage of the wave causes the body-centered-cubic phase to transform into a close-packed phase with most structure being isotropic hexagonal-close-packed (hcp) and, depending on shock strength and grain orientation, some fraction of face-centered-cubic (fcc) structure. The simulated shock Hugoniot is compared to experiments.

Direct observation of the alpha-epsilon transition in shock-compressed iron via nanosecond x-ray diffraction.

In situ x-ray diffraction studies of iron under shock conditions confirm unambiguously a phase change from the bcc (alpha) to hcp (epsilon) structure. Previous identification of this transition in shock-loaded iron has been inferred from the correlation between shock-wave-profile analyses and static high-pressure x-ray measurements. This correlation is intrinsically limited because dynamic loading can markedly affect the structural modifications of solids.

Energy exchange between mesoparticles and their internal degrees of freedom.

We present mesoscale equations of motion that lead to a thermodynamically accurate description of the energy exchange between mesoparticles and their internal degrees of freedom. In our approach, energy exchange is done through particle coordinates, rather than momenta, resulting in Galilean invariant equations of motion. The total linear momentum and total energy (including the internal energy of the mesoparticles) are conserved, and no coupling occurs when a mesoparticle is in free flight.

Nanohydrodynamics simulations: an atomistic view of the Rayleigh-Taylor instability.

Nanohydrodynamics simulations, hydrodynamics on the nanometer and nanosecond scale by molecular dynamics simulations for up to 100 million particles, are performed on the latest generation of supercomputers. Such simulations exhibit Rayleigh-Taylor instability, the mixing of a heavy fluid on top of a light in the presence of a gravitational field, initiated by thermal fluctuations at the interface, leading to the chaotic regime in the long-time evolution of the mixing process. The early-time behavior is in general agreement with linear analysis of continuum theory (Navier-Stokes), and the late-time behavior agrees quantitatively with experimental observations.

Onset of incommensurate interfacial instability in a minimal model of dry friction.

We present a minimal model of dry friction between two incommensurate interfaces sliding at high relative velocity. Many of the features of the friction force for the full two-dimensional many-body dynamical system-particularly in the sub-critical velocity regime-are captured by our one-dimensional Einstein model, where the motion of a typical interfacial atom is constrained to be vertical to the sliding plane. Beyond the linear response of force versus sliding velocity, the anharmonic Einstein model predicts a doublet resonance peak, whereupon a catastrophe in the model signals the onset of a plastic deformation mechanism for frictional sliding, namely, the instability of the interface.

Atomistic mechanism for hot spot initiation.

We propose a picture of the role of shock-wave interactions with microscopic voids that leads to significant heating, sufficient to thermally initiate chemical reactions in solid explosives, or phase transitions in metals. The key ingredients to this dramatic overshoot in temperature are: (i) a strong enough shock wave to cause vaporization of material into the void; (ii) the stagnation of low-density vapor (for a wide enough gap) at the far side; and (iii) recompression of the gas (pressure-volume work) from low density back to the original shocked density. We explore dependencies on both shock strength and one-dimensional gap width in atomistic simulations of a two-dimensional unreactive Lennard-Jones solid, comparing observed thermal overshoot with a straightforward model, to show how hot spots can be generated under shock-wave conditions.

Microscopic view of structural phase transitions induced by shock waves.

Multimillion-atom molecular-dynamics simulations are used to investigate the shock-induced phase transformation of solid iron. Above a critical shock strength, many small close-packed grains nucleate in the shock-compressed body-centered cubic crystal growing on a picosecond time scale to form larger, energetically favored grains. A split two-wave shock structure is observed immediately above this threshold, with an elastic precursor ahead of the lagging transformation wave.

Droplet formation by rapid expansion of a liquid.

Molecular dynamics of two- and three-dimensional liquids undergoing a homogeneous adiabatic expansion provides a direct numerical simulation of the atomization process. The Lennard-Jones potential is used with different force cutoff distances; the cluster distributions do not depend strongly on the cutoff parameter. Expansion rates, scaled by the natural molecular time unit (about a picosecond), are investigated from unity down to 0.

Uniaxial Hugoniostat: a method for atomistic simulations of shocked materials.

An new equilibrium molecular-dynamics method (the uniaxial Hugoniostat) is proposed to study the energetics and deformation structures in shocked crystals. This method agrees well with nonequilibrium molecular-dynamics simulations used to study shock-wave propagation in solids and liquids.

Universality in fragmentation.

Fragmentation of a two-dimensional brittle solid by impact and "explosion," and a fluid by "explosion" are all shown to become critical. The critical points appear at a nonzero impact velocity, and at infinite explosion duration, respectively. Within the critical regimes, the fragment-size distributions satisfy a scaling form qualitatively similar to that of the cluster-size distribution of percolation, but they belong to another universality class.

Orientation dependence in molecular dynamics simulations of shocked single crystals.

We use multimillion-atom molecular dynamics simulations to study shock wave propagation in fcc crystals. As shown recently, shock waves along the <100> direction form intersecting stacking faults by slippage along 111 close-packed planes at sufficiently high shock strengths. We find even more interesting behavior of shocks propagating in other low-index directions: for the <111> case, an elastic precursor separates the shock front from the slipped (plastic) region.

Plasticity induced by shock waves in nonequilibrium molecular-dynamics simulations.

Nonequilibrium molecular-dynamics simulations of shock waves in three-dimensional 10-million atom face-centered cubic crystals with cross-sectional dimensions of 100 by 100 unit cells show that the system slips along all of the available 111 slip planes, in different places along the nonplanar shock front. Comparison of these simulations with earlier ones on a smaller scale not only eliminates the possibility that the observed slippage is an artifact of transverse periodic boundary conditions, but also reveals the richness of the nanostructure left behind. By introducing a piston face that is no longer perfectly flat, mimicking a line or surface inhomogeneity in the unshocked material, it is shown that for weaker shock waves (below the perfect-crystal yield strength), stacking faults can be nucleated by preexisting extended defects.