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. Moreover, mesodynamics differs from Newton's equations of motion in that dissipation--the exchange of energy between mesoparticles and their internal degrees of freedom (DoFs)--must be described, and so should the transfer of energy between the internal modes of neighboring mesoparticles. We present a formulation where energy transfer between the internal modes of a mesoparticle and its external center-of-mass DoFs occurs in the phase space of mesoparticle coordinates, rather than momenta, resulting in a Galilean invariant formulation that conserves total linear momentum and energy (including the energy internal to the mesoparticles). We show that this approach can be used to describe, in addition to mesoscale problems, conduction electrons in atomic-level simulations of metals, and we demonstrate applications of mesodynamics to shockwave propagation and thermal transport.

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. Now, the Lennard-Jones fluid, whose equation of state and transport properties have been determined from independent calculations, allows us to study the case where potential, as well as kinetic contributions are important. The new heat-flow treatment improves the agreement with nonequilibrium molecular-dynamics simulations under strong shock wave conditions, compared to Navier-Stokes.

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. Nonequilibrium MD simulations reveal that there is a linear dependence between the square of the detonation velocity and both of these molecular parameters. The detonation velocities were shown to be consistent with the Chapman-Jouguet (CJ) model, demonstrating that these dependences arise from how the equation of state of the products and reactants are affected. Equilibrium MD simulations of microcanonical ensembles were used to determine the CJ states for varying Q 's, and radial distribution functions characterize the atomic structure. The character of this material near the CJ conditions was found to be somewhat unusual, consisting of polyatomic clusters rather than discrete molecular species. It was also found that there was a minimum value of Q and a maximum value of (D(e)(AB)) for which a pseudo-one-dimensional detonation could not be sustained. The reaction zone of this material was characterized under both equilibrium (CJ) and transient (underdriven) conditions. The basic structure is consistent with the Zeldovich-von Neumann-Döring model, with a sharp shock rise and a reaction zone that extends to 200-300 Angstrom. The underdriven systems show a buildup process which requires an extensive time to approach equilibrium conditions. The rate stick failure diameter (critical width in 2D) was also found to depend on Q and (D(e)(AB)). The dependence on Q could be explained in terms of the reaction zone properties.

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. Higher velocities than this critical value require a much more sophisticated description of the production and coalescence of dislocations into a microstructure.

Heat transfer between two degrees of freedom.

A particularly simple chaotic nonequilibrium open system with two Cartesian degrees of freedom, characterized by two distinct temperatures T(x) and T(y), is introduced. The two temperatures are maintained by Nose-Hoover canonical-ensemble thermostats. Both the equilibrium (no net heat transfer) and nonequilibrium (dissipative) Lyapunov spectra are characterized for this simple system.

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. We test our heat-flow equation for the case of strong shock waves in the ideal gas, which has been studied in the past and compared to Navier-Stokes solutions. The new heat-flow treatment improves the agreement with nonequilibrium molecular-dynamics simulations of hard spheres under strong shockwave conditions.

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. By calculating the extended x-ray absorption fine structure (EXAFS) directly from the atomic configurations, a comparison to experimental EXAFS measurements of nanosecond-laser shocks shows that the experimental data is consistent with such a phase transformation. However, the atomistically simulated EXAFS spectra also show that an experimental distinction between the hcp or fcc phase is not possible based on the spectra alone.

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. We test our method for shock wave propagation in a crystalline polymer, poly(vinylidene fluoride); the mesodynamics results agree very well with all-atom molecular dynamics.

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. For even higher shock strengths, a single, overdriven wave is obtained. The dynamics and orientation of the developing close-packed grains depend on the shock strength and especially on the crystallographic shock direction. Orientational relations between the unshocked and shocked regions are similar to those found for the temperature-driven martensitic transformation in iron and its alloys.

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.

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. Nanohydrodynamics provides insights into the turbulent mixing process that are inaccessible to either continuum calculations or to experiment.