Force correlations in molecular and stochastic dynamics

A molecular gas system in three dimensions is numerically studied by the energy conserving molecular dynamics (MD). The autocorrelation functions for the velocity and the force are computed and the friction coefficient is estimated. From the comparison with the stochastic dynamics (SD) of a Brownian particle, it is shown that the force correlation function in MD is different from the delta-function force correlation in SD in short time scale. However, as the measurement time scale is increased further, the ensemble equivalence between the microcanonical MD and the canonical SD is restored. We also discuss the practical implication of the result.Comment: 9 pages, 4 figures and Computer Physics Communcations (in press

Master equation for the probability distribution functions of forces in soft particle packings

Employing molecular dynamics simulations of jammed soft particles, we study microscopic responses of force-chain networks to quasi-static isotropic (de)compressions. We show that not only contacts but also interparticle gaps between the nearest neighbors must be considered for the stochastic evolution of the probability distribution functions (PDFs) of forces, where the mutual exchange of contacts and interparticle gaps, i.e. opening and closing contacts, are also crucial to the incremental system behaviors. By numerically determining the transition rates for all changes of contacts and gaps, we formulate a Master equation for the PDFs of forces, where the insight one gets from the transition rates is striking: The mean change of forces reflects non-affine system response, while their fluctuations obey uncorrelated Gaussian statistics. In contrast, interparticle gaps are reacting mostly affine in average, but imply multi-scale correlations according to a wider stable distribution function.Comment: 5 pages, 4 figures, submitted to Soft Matte

Dynamic Implicit-Solvent Coarse-Grained Models of Lipid Bilayer Membranes : Fluctuating Hydrodynamics Thermostat

Many coarse-grained models have been developed for equilibrium studies of lipid bilayer membranes. To achieve in simulations access to length-scales and time-scales difficult to attain in fully atomistic molecular dynamics, these coarse-grained models provide a reduced description of the molecular degrees of freedom and often remove entirely representation of the solvent degrees of freedom. In such implicit-solvent models the solvent contributions are treated through effective interaction terms within an effective potential for the free energy. For investigations of kinetics, Langevin dynamics is often used. However, for many dynamical processes within bilayers this approach is insufficient since it neglects important correlations and dynamical contributions that are missing as a result of the momentum transfer that would have occurred through the solvent. To address this issue, we introduce a new thermostat based on fluctuating hydrodynamics for dynamic simulations of implicit-solvent coarse-grained models. Our approach couples the coarse-grained degrees of freedom to a stochastic continuum field that accounts for both the solvent hydrodynamics and thermal fluctuations. We show our approach captures important correlations in the dynamics of lipid bilayers that are missing in simulations performed using conventional Langevin dynamics. For both planar bilayer sheets and bilayer vesicles, we investigate the diffusivity of lipids, spatial correlations, and lipid flow within the bilayer. The presented fluctuating hydrodynamics approaches provide a promising way to extend implicit-solvent coarse-grained lipid models for use in studies of dynamical processes within bilayers

A Stochastic Immersed Boundary Method for Fluid-Structure Dynamics at Microscopic Length Scales

In this work it is shown how the immersed boundary method of (Peskin2002) for modeling flexible structures immersed in a fluid can be extended to include thermal fluctuations. A stochastic numerical method is proposed which deals with stiffness in the system of equations by handling systematically the statistical contributions of the fastest dynamics of the fluid and immersed structures over long time steps. An important feature of the numerical method is that time steps can be taken in which the degrees of freedom of the fluid are completely underresolved, partially resolved, or fully resolved while retaining a good level of accuracy. Error estimates in each of these regimes are given for the method. A number of theoretical and numerical checks are furthermore performed to assess its physical fidelity. For a conservative force, the method is found to simulate particles with the correct Boltzmann equilibrium statistics. It is shown in three dimensions that the diffusion of immersed particles simulated with the method has the correct scaling in the physical parameters. The method is also shown to reproduce a well-known hydrodynamic effect of a Brownian particle in which the velocity autocorrelation function exhibits an algebraic tau^(-3/2) decay for long times. A few preliminary results are presented for more complex systems which demonstrate some potential application areas of the method.Comment: 52 pages, 11 figures, published in journal of computational physic

The Stochastic Dynamics of an Array of Atomic Force Microscopes in a Viscous Fluid

We consider the stochastic dynamics of an array of two closely spaced atomic force microscope cantilevers in a viscous fluid for use as a possible biomolecule sensor. The cantilevers are not driven externally, as is common in applications of atomic force microscopy, and we explore the stochastic cantilever dynamics due to the constant buffeting of fluid particles by Brownian motion. The stochastic dynamics of two adjacent cantilevers are correlated due to long range effects of the viscous fluid. Using a recently proposed thermodynamic approach the hydrodynamic correlations are quantified for precise experimental conditions through deterministic numerical simulations. Results are presented for an array of two readily available atomic force microscope cantilevers. It is shown that the force on a cantilever due to the fluid correlations with an adjacent cantilever is more than 3 times smaller than the Brownian force on an individual cantilever. Our results indicate that measurements of the correlations in the displacement of an array of atomic force microscopes can detect piconewton forces with microsecond time resolution.Comment: 7 page article with 11 images submitted to the International Journal of Nonlinear Mechanic

Probing complex RNA structures by mechanical force

RNA secondary structures of increasing complexity are probed combining single molecule stretching experiments and stochastic unfolding/refolding simulations. We find that force-induced unfolding pathways cannot usually be interpretated by solely invoking successive openings of native helices. Indeed, typical force-extension responses of complex RNA molecules are largely shaped by stretching-induced, long-lived intermediates including non-native helices. This is first shown for a set of generic structural motifs found in larger RNA structures, and then for Escherichia coli's 1540-base long 16S ribosomal RNA, which exhibits a surprisingly well-structured and reproducible unfolding pathway under mechanical stretching. Using out-of-equilibrium stochastic simulations, we demonstrate that these experimental results reflect the slow relaxation of RNA structural rearrangements. Hence, micromanipulations of single RNA molecules probe both their native structures and long-lived intermediates, so-called "kinetic traps", thereby capturing -at the single molecular level- the hallmark of RNA folding/unfolding dynamics.Comment: 9 pages, 9 figure

Comparison of dynamical multifragmentation models

Multifragmentation scenarios, as predicted by antisymmetrized molecular dynamics (AMD) or momentum-dependent stochastic mean-field (BGBD) calculations are compared. While in the BGBD case fragment emission is clearly linked to the spinodal decomposition mechanism, i.e. to mean-field instabilities, in AMD many-body correlations have a stronger impact on the fragmentation dynamics and clusters start to appear at earlier times. As a consequence, fragments are formed on shorter time scales in AMD, on about equal footing of light particle pre-equilibrium emission. Conversely, in BGBD pre-equilibrium and fragment emissions happen on different time scales and are related to different mechanisms

Equilibrium free energies from fast-switching trajectories with large time steps

Jarzynski's identity for the free energy difference between two equilibrium states can be viewed as a special case of a more general procedure based on phase space mappings. Solving a system's equation of motion by approximate means generates a mapping that is perfectly valid for this purpose, regardless of how closely the solution mimics true time evolution. We exploit this fact, using crudely dynamical trajectories to compute free energy differences that are in principle exact. Numerical simulations show that Newton's equation can be discretized to low order over very large time steps (limited only by the computer's ability to represent resulting values of dynamical variables) without sacrificing thermodynamic accuracy. For computing the reversible work required to move a particle through a dense liquid, these calculations are more efficient than conventional fast switching simulations by more than an order of magnitude. We also explore consequences of the phase space mapping perspective for systems at equilibrium, deriving an exact expression for the statistics of energy fluctuations in simulated conservative systems