Transient hydrodynamical behavior by dynamical nonequilibrium molecular dynamics: the formation of convective cells.

We present a method based on dynamical nonequilibrium molecular dynamics (D-NEMD) that allows one to produce rigorous ensemble averages for the transient regimes. We illustrate the method by describing the formation of convective cells within a two-dimensional fluid system of soft disks in which a gravity field and a thermal gradient are present. We analyze two different physical settings, with the thermal gradient orthogonal or parallel to the gravity field. In both settings, we follow the formation of the convective flows from the initial time, when the perturbation is turned on, to the steady state. In the first setting (orthogonal fields) we investigate several different cases, varying the initial stationary ensemble and the perturbing field. We find that the final steady-state convective cell is independent of the specific sequence of perturbation fields, which only affects the transient behavior. In all cases, we find that the convective roll is formed through a sequence of damped oscillations of the local fields (density, temperature, and velocity), superimposed to an overall relaxation toward the local steady-state values. Then, we show how D-NEMD can be applied to the Rayleigh-Bénard (RB) setting (parallel fields). In these conditions, the convective flow only establishes above a threshold, without a preferred verse of rotation. We analyze only the response to the ignition of the gravity field in a stationary system under the action of a vertical thermal gradient. Also in this case we characterize the transient response by following the evolution of the density, temperature, and velocity fields until the steady-state RB convective cell is formed. The observed transients are similar to those observed in the case of orthogonal fields. However, the final steady states are quite different. Finally, we briefly discuss the conditions for the general applicability of the D-NEMD method.

Pores in bilayer membranes of amphiphilic molecules: coarse-grained molecular dynamics simulations compared with simple mesoscopic models.

We investigate pores in fluid membranes by molecular dynamics simulations of an amphiphile-solvent mixture, using a molecular coarse-grained model. The amphiphilic membranes self-assemble into a lamellar stack of amphiphilic bilayers separated by solvent layers. We focus on the particular case of tensionless membranes, in which pores spontaneously appear because of thermal fluctuations. Their spatial distribution is similar to that of a random set of repulsive hard disks. The size and shape distribution of individual pores can be described satisfactorily by a simple mesoscopic model, which accounts only for a pore independent core energy and a line tension penalty at the pore edges. In particular, the pores are not circular: their shapes are fractal and have the same characteristics as those of two-dimensional ring polymers. Finally, we study the size-fluctuation dynamics of the pores, and compare the time evolution of their contour length to a random walk in a linear potential.

Confinement effects on the slow dynamics of a supercooled polymer melt: Rouse modes and the incoherent scattering function.

Results of large-scale molecular-dynamics simulations of a supercooled polymer film are presented (F. Varnik, J. Baschnagel, K. Binder, J. Phys. IV 10, 239 (2000)). The dynamic and static properties of the system are studied for a wide range of film thicknesses (from 3 to about 55 times the bulk radius of gyration) and temperatures (from the normal liquid state to the supercooled region). The system is confined between two completely smooth and purely repulsive walls. Motivated by the previous results on the enhancement of the local relaxation dynamics due to the confinement (F. Varnik, J. Baschnagel, K. Binder, Eur. Phys. J. E 8, 175 (2002); Phys. Rev. E. 65, 021507 (2002)), we now study the effect of the walls on the dynamics of the Rouse modes. It has been reported from Monte Carlo studies of the Bond Fluctuation Model (BFM) that, contrary to the enhancement of the "cage dynamics" (exemplified by a faster relaxation of the incoherent scattering function in the film), Rouse modes exhibit a slower relaxation in the confined system (C. Mischler, J. Baschnagel, K. Binder, Adv. Colloid Interface Sci. 94, 197 (2001)). However, we do not observe such a discrepancy for our continuum model: At a given temperature, the relaxation of a given Rouse mode is faster in the film than in the bulk in accordance with the acceleration of the dynamics around the cage.

Origin of the hydrodynamic Lyapunov modes.

Recent studies of the Lyapunov spectrum of the hard sphere fluid reveal that there are "hydrodynamic" Lyapunov exponents corresponding to collective perturbations in phase space. We show that these collective perturbations are due to the conservation of certain quantities during collisions. These new conservation laws generate new hydrodynamic fields, just as the conservation of mass, momentum, and energy generate the density, velocity, and temperature fields. We then construct a detailed theory of the new hydrodynamic fields using a kinetic theory approach. This theory predicts several properties of the modes, but not all of them. This suggests that the underlying idea is correct, but a detailed theory must be elaborated in another way. The hydrodynamic exponents are not related in a simple way to the transport coefficients.

Precollisional velocity correlations in a hard-disk fluid with dissipative collisions.

Velocity correlations are studied in granular fluids, modeled by the inelastic hard sphere gas. Making a density expansion of the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy for the evolution of the reduced distributions, we predict the presence of precollisional velocity correlations. They are created by the propagation through correlated sequences of collisions (ring events) of the velocity correlations generated after dissipative collisions. The correlations have their origin in the dissipative character of collisions, being always present in granular fluids. The correlations, that manifest microscopically as an alignment of the velocities of a colliding pair produce modifications of collisional averages, in particular, the virial pressure. The pressure shows a reduction with respect to the elastic case as a consequence of the velocity alignment. Good qualitative agreement is obtained for the comparison of the numerical evaluations of the obtained analytical expressions and molecular dynamics results that showed evidence of precollisional velocity correlations [R. Soto and M. Mareschal, Phys. Rev. E 63, 041303 (2001)].

Lyapunov spectrum of granular gases.

We calculate and study the Lyapunov spectrum of a granular gas maintained in a steady state by an isokinetic thermostat. Considering restitution coefficients greater than unity allows us to show that the spectra change smoothly and continuously at equilibrium. The shearing instability of the granular gas, however, provokes an abrupt change in the structure of the spectrum. The relationship between various physically relevant quantities and the energy dissipation rate differs from previously studied nonequilibrium steady states.

Statistical mechanics of fluidized granular media: short-range velocity correlations.

A statistical mechanical study of fluidized granular media is presented. Using a special energy injection mechanism, homogeneous fluidized stationary states are obtained. Molecular dynamics simulations and theoretical analysis of the inelastic hard-disk model show that there is a large asymmetry in the two-particle distribution function between pairs that approach and separate. Large velocity correlations appear in the postcollisional states due to the dissipative character of the collision rule. These correlations can be well-characterized by a state dependent pair correlation function at contact. It is also found that velocity correlations are present for pairs that are about to collide. Particles arrive at collisions with a higher probability that their velocities are parallel rather than antiparallel. These dynamical correlations lead to a decrease of the pressure and of the collision frequency as compared to their Enskog values. A phenomenological modified equation of state is presented.

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.

Nonlinear analysis of the shearing instability in granular gases

It is known that a finite-size homogeneous granular fluid develops a hydrodynamiclike instability when dissipation crosses a threshold value. This instability is analyzed in terms of modified hydrodynamic equations: first, a source term is added to the energy equation which accounts for the energy dissipation at collisions and the phenomenological Fourier law is generalized according to previous results. Second, a rescaled time formalism is introduced that maps the homogeneous cooling state into a nonequilibrium steady state. A nonlinear stability analysis of the resulting equations is done which predicts the appearance of flow patterns. A stable modulation of density and temperature is produced that does not lead to clustering. Also a global decrease of the temperature is obtained, giving rise to a decrease of the collision frequency and dissipation rate. Good agreement with molecular dynamics simulations of inelastic hard disks is found for low dissipation.