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Non-Markovian out-of-equilibrium dynamics: A general numerical procedure to construct time-dependent memory kernels for coarse-grained observables Meyer, Hugues ; ; in Europhysics Letters (2020), 128(4), 40001 We present a numerical method to compute non-equilibrium memory kernels based on experimental data or molecular dynamics simulations. The procedure uses a recasting of the non-stationary generalized ... [more ▼] We present a numerical method to compute non-equilibrium memory kernels based on experimental data or molecular dynamics simulations. The procedure uses a recasting of the non-stationary generalized Langevin equation, in which we expand the memory kernel in a series that can be reconstructed iteratively. Each term in the series can be computed based solely on knowledge of the two-time auto-correlation function of the observable of interest. We discuss how to optimize this method in order to be the most numerically convenient. As a proof of principle, we test the method on the problem of crystallization from a super-cooled Lennard-Jones melt. We analyze the nucleation and growth dynamics of crystallites and observe that the memory kernel has a time extent that is about one order of magnitude larger than the typical timescale needed for a particle to be attached to the crystallite in the growth regime. [less ▲] Detailed reference viewed: 76 (0 UL)Derivation of an exact, nonequilibrium framework for nucleation: Nucleation is a priori neither diffusive nor Markovian ; Meyer, Hugues ; et al in Physical Review. E. (2019), 100(5), 052140 We discuss the structure of the equation of motion that governs nucleation processes at first order phase transitions. From the underlying microscopic dynamics of a nucleating system, we derive by means ... [more ▼] We discuss the structure of the equation of motion that governs nucleation processes at first order phase transitions. From the underlying microscopic dynamics of a nucleating system, we derive by means of a nonequilibrium projection operator formalism the equation of motion for the size distribution of the nuclei. The equation is exact, ie, the derivation does not contain approximations. To assess the impact of memory, we express the equation of motion in a form that allows for direct comparison to the Markovian limit. As a numerical test, we have simulated crystal nucleation from a supersaturated melt of particles interacting via a Lennard-Jones potential. The simulation data show effects of non-Markovian dynamics. [less ▲] Detailed reference viewed: 147 (0 UL)On the dynamics of reaction coordinates in classical, time-dependent, many-body processes Meyer, Hugues ; ; in Journal of Chemical Physics (2019), 150(17), 174118 Complex microscopic many-body processes are often interpreted in terms of so-called “reaction coordinates,” i.e., in terms of the evolution of a small set of coarse-grained observables. A rigorous method ... [more ▼] Complex microscopic many-body processes are often interpreted in terms of so-called “reaction coordinates,” i.e., in terms of the evolution of a small set of coarse-grained observables. A rigorous method to produce the equation of motion of such observables is to use projection operator techniques, which split the dynamics of the observables into a main contribution and a marginal one. The basis of any derivation in this framework is the classical Heisenberg equation for an observable. If the Hamiltonian of the underlying microscopic dynamics and the observable under study do not explicitly depend on time, this equation is obtained by a straightforward derivation. However, the problem is more complicated if one considers Hamiltonians which depend on time explicitly as, e.g., in systems under external driving, or if the observable of interest has an explicit dependence on time. We use an analogy to fluid dynamics to derive the classical Heisenberg picture and then apply a projection operator formalism to derive the nonstationary generalized Langevin equation for a coarse-grained variable. We show, in particular, that the results presented for time-independent Hamiltonians and observables in the study by Meyer, Voigtmann, and Schilling, J. Chem. Phys. 147, 214110 (2017) can be generalized to the time-dependent case. [less ▲] Detailed reference viewed: 110 (4 UL)Memory Effects in the Fermi–Pasta–Ulam Model ; Meyer, Hugues ; in Journal of Statistical Physics (2019), 174(1), 219-257 We study the intermediate scattering function (ISF) of the strongly-nonlinear Fermi–Pasta–Ulam Model at thermal equilibrium, using both numerical and analytical methods. From the molecular dynamics ... [more ▼] We study the intermediate scattering function (ISF) of the strongly-nonlinear Fermi–Pasta–Ulam Model at thermal equilibrium, using both numerical and analytical methods. From the molecular dynamics simulations we distinguish two limit regimes, as the system behaves as an ideal gas at high temperature and as a harmonic chain for low excitations. At intermediate temperatures the ISF relaxes to equilibrium in a nontrivial fashion. We then calculate analytically the Taylor coefficients of the ISF to arbitrarily high orders (the specific, simple shape of the two-body interaction allows us to derive an iterative scheme for these). The results of the recursion are in good agreement with the numerical ones. Via an estimate of the complete series expansion of the scattering function, we can reconstruct within a certain temperature range its coarse-grained dynamics. This is governed by a memory-dependent Generalized Langevin Equation (GLE), which can be derived via projection operator techniques. Moreover, by analyzing the first series coefficients of the ISF, we can extract a parameter associated to the strength of the memory effects in the dynamics. [less ▲] Detailed reference viewed: 145 (3 UL)Simulation study of the electrical tunneling network conductivity of suspensions of hard spherocylinders ; ; Rahm, Alexander et al in Physical Review. E. (2018), 98 Using Monte Carlo simulations, we investigate the electrical conductivity of networks of hard rods with aspect ratios 10 and 20 as a function of the volume fraction for two tunneling conductance models ... [more ▼] Using Monte Carlo simulations, we investigate the electrical conductivity of networks of hard rods with aspect ratios 10 and 20 as a function of the volume fraction for two tunneling conductance models. For a simple, orientationally independent tunneling model, we observe nonmonotonic behavior of the bulk conductivity as a function of volume fraction at the isotropic-nematic transition. However, this effect is lost if one allows for anisotropic tunneling. The relative conductivity enhancement increases exponentially with volume fraction in the nematic phase. Moreover, we observe that the orientational ordering of the rods in the nematic phase induces an anisotropy in the conductivity, i.e., enhanced values in the direction of the nematic director field. We also compute the mesh number of the Kirchhoff network, which turns out to be a simple alternative to the computationally expensive conductivity of large systems in order to get a qualitative estimate. [less ▲] Detailed reference viewed: 119 (4 UL)On the non-stationary generalized Langevin Equation Meyer, Hugues ; ; in Journal of Chemical Physics (2017), 147(21), 214110 In molecular dynamics simulations and single molecule experiments, observables are usually measured along dynamic trajectories and then averaged over an ensemble (“bundle”) of trajectories. Under ... [more ▼] In molecular dynamics simulations and single molecule experiments, observables are usually measured along dynamic trajectories and then averaged over an ensemble (“bundle”) of trajectories. Under stationary conditions, the time-evolution of such averages is described by the generalized Langevin equation. By contrast, if the dynamics is not stationary, it is not a priori clear which form the equation of motion for an averaged observable has. We employ the formalism of time-dependent projection operator techniques to derive the equation of motion for a non-equilibrium trajectory-averaged observable as well as for its non-stationary auto-correlation function. The equation is similar in structure to the generalized Langevin equation but exhibits a time-dependent memory kernel as well as a fluctuating force that implicitly depends on the initial conditions of the process. We also derive a relation between this memory kernel and the autocorrelation function of the fluctuating force that has a structure similar to a fluctuation-dissipation relation. In addition, we show how the choice of the projection operator allows us to relate the Taylor expansion of the memory kernel to data that are accessible in MD simulations and experiments, thus allowing us to construct the equation of motion. As a numerical example, the procedure is applied to Brownian motion initialized in non-equilibrium conditions and is shown to be consistent with direct measurements from simulations. [less ▲] Detailed reference viewed: 104 (2 UL)Monolayers of hard rods on planar substrates. II. Growth ; ; Dixit, Mohit et al in Journal of Chemical Physics (2017), 146 Growth of hard-rod monolayers via deposition is studied in a lattice model using rods with discrete orientations and in a continuum model with hard spherocylinders. The lattice model is treated with ... [more ▼] Growth of hard-rod monolayers via deposition is studied in a lattice model using rods with discrete orientations and in a continuum model with hard spherocylinders. The lattice model is treated with kinetic Monte Carlo simulations and dynamic density functional theory while the continuum model is studied by dynamic Monte Carlo simulations equivalent to diffusive dynamics. The evolution of nematic order (excess of upright particles, “standing-up” transition) is an entropic effect and is mainly governed by the equilibrium solution, rendering a continuous transition [Paper I, M. Oettel et al., J. Chem. Phys. 145, 074902 (2016)]. Strong non-equilibrium effects (e.g., a noticeable dependence on the ratio of rates for translational and rotational moves) are found for attractive substrate potentials favoring lying rods. Results from the lattice and the continuum models agree qualitatively if the relevant characteristic times for diffusion, relaxation of nematic order, and deposition are matched properly. Applicability of these monolayer results to multilayer growth is discussed for a continuum-model realization in three dimensions where spherocylinders are deposited continuously onto a substrate via diffusion. [less ▲] Detailed reference viewed: 170 (10 UL) |
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