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The nonlinear dependence of the mean-squared displacement (MSD) on time is a common characteristic of particle transport in complex environments. Frequently, this anomalous behavior only occurs transiently before the particle reaches a terminal Fickian diffusion. This study shows that a system of hierarchically coupled Ornstein–Uhlenbeck equations is able to describe both transient subdiffusion and transient superdiffusion dynamics, as well as their sequential combinations. To validate the model, five distinct experimental, molecular dynamics simulation, and theoretical studies are successfully described by the model. The comparison includes the transport of particles in random optical fields, supercooled liquids, bedrock, soft colloidal suspensions, and phonons in solids. The model's broad applicability makes it a convenient tool for interpreting the MSD profiles of particles exhibiting transient anomalous diffusion. [ABSTRACT FROM AUTHOR]

We introduce a multiscale framework to simulate inhomogeneous fluids by coarse-graining an all-atom molecular dynamics (MD) trajectory onto sequential snapshots of hydrodynamic fields. We show that the field representation of an atomistic trajectory is quantitatively described by a dynamic field-theoretic model that couples hydrodynamic fluctuations with a Ginzburg-Landau free energy. For liquid-vapor interfaces of argon and water, the parameters of the field model can be adjusted to reproduce the bulk compressibility and surface tension calculated from the positions and forces of atoms in an MD simulation. These optimized parameters also enable the field model to reproduce the static and dynamic capillary wave spectra calculated from atomistic coordinates at the liquid-vapor interface. In addition, we show that a density-dependent gradient coefficient in the Ginzburg-Landau free energy enables bulk and interfacial fluctuations to be controlled separately. For water, this additional degree of freedom is necessary to capture both the bulk compressibility and surface tension emergent from the atomistic trajectory. The proposed multiscale framework illustrates that bottom-up coarse-graining and top-down phenomenology can be integrated with quantitative consistency to simulate the interfacial fluctuations in nanoscale transport processes. [ABSTRACT FROM AUTHOR]

A multiscale computational method is developed to model the nanoscale viscoelasticity of fluids by bridging non-Markovian fluctuating hydrodynamics (FHD) and molecular dynamics (MD) simulations. To capture the elastic responses that emerge at small length scales, we attach an additional rheological model parallel to the macroscopic constitutive equation of a fluid. The widely used linear Maxwell model is employed as a working choice; other models can be used as well. For a fluid that is Newtonian in the macroscopic limit, this approach results in a parallel Newtonian–Maxwell model. For water, argon, and an ionic liquid, the power spectrum of momentum field autocorrelation functions of the parallel Newtonian–Maxwell model agrees very well with those calculated from all-atom MD simulations. To incorporate thermal fluctuations, we generalize the equations of FHD to work with non-Markovian rheological models and colored noise. The fluctuating stress tensor (white noise) is integrated in time in the same manner as its dissipative counterpart and numerical simulations indicate that this approach accurately preserves the set temperature in a FHD simulation. By mapping position and velocity vectors in the molecular representation onto field variables, we bridge the non-Markovian FHD with atomistic MD simulations. Through this mapping, we quantitatively determine the transport coefficients of the parallel Newtonian–Maxwell model for water and argon from all-atom MD simulations. For both fluids, a significant enhancement in elastic responses is observed as the wave number of hydrodynamic modes is reduced to a few nanometers. The mapping from particle to field representations and the perturbative strategy of developing constitutive equations provide a useful framework for modeling the nanoscale viscoelasticity of fluids. [ABSTRACT FROM AUTHOR]

A new multiscale coarse-graining (CG) methodology is developed to bridge molecular and hydrodynamic models of a fluid. The hydrodynamic representation considered in this work is based on the equations of fluctuating hydrodynamics (FH). The essence of this method is a mapping from the position and velocity vectors of a snapshot of a molecular dynamics (MD) simulation to the field variables on Eulerian cells of a hydrodynamic representation. By explicit consideration of the effective lengthscale dmol that characterizes the volume of a molecule, the computed density fluctuations from MD via our mapping procedure have volume dependence that corresponds to a grand canonical ensemble of a cold liquid even when a small cell length (5–10 Å) is used in a hydrodynamic representation. For TIP3P water at 300 K and 1 atm, dmol is found to be 2.4 Å, corresponding to the excluded radius of a water molecule as revealed by its center-of-mass radial distribution function. By matching the density fluctuations and autocorrelation functions of momentum fields computed from solving the FH equations with those computed from MD simulation, the sound velocity and shear and bulk viscosities of a CG hydrodynamic model can be determined directly from MD. Furthermore, a novel staggered discretization scheme is developed for solving the FH equations of an isothermal compressive fluid in a three dimensional space with a central difference method. This scheme demonstrates high accuracy in satisfying the fluctuation-dissipation theorem. Since the causative relationship between field variables and fluxes is captured, we demonstrate that the staggered discretization scheme also predicts correct physical behaviors in simulating transient fluid flows. The techniques presented in this work may also be employed to design multiscale strategies for modeling complex fluids and macromolecules in solution. [ABSTRACT FROM AUTHOR]

In this work, we have studied the effects of thermal fluctuations on the stability of polaron motion under the influence of an external electric field. Zero temperature calculations have been reported previously showing the existence of critical electric field, E cr , where the system transitions from a stable polaron motion to a Bloch-like oscillation. In this study, we further report that for intermediate polaron sizes the lifetime of such Bloch-like oscillations decay with time due to excessive phonon emission. Our numerical simulations show that the value of E cr is finite for small temperatures. However, E cr rapidly decreases with increasing T and becomes practically zero for T > T cr . In this small but finite temperature window, we report how temperature affects (a) the electric current density, and (b) the Bloch-like frequencies. [ABSTRACT FROM AUTHOR]

The development of a hybrid fluctuating hydrodynamics (FHD) and molecular dynamics (MD) simulation method that combines the molecular dynamics of moving particles with the fluctuating hydrodynamics of solvent fields on Eulerian grid cells is presented. This method allows resolution of solute-solvent interfaces and realization of excluded volumes of particles in the presence of hydrodynamic coupling. With these capabilities, we show that the ubiquitous forces mediated by the solvent, hydrophobicity and hydrodynamics, can be linked in a mesoscopic simulation. The strategies we devise to overcome the numerical issues of mixing variables in the Eulerian and Lagrangian coordinate systems, i.e., using a pair of auxiliary fluids to realize the excluded volumes of particles and assigning collocating gridding systems on solutes to interface with solvent fields, are also presented. Simulation results show that the hybrid FHD and MD method can reproduce the solvation free energies and scaling laws of particles dynamics for hydrophobes of different sizes. The collapse of two hydrophobic particles was also simulated to illustrate that the hybrid FHD and MD method has the potential to be generally applied to study nanoscale self-assembly and dynamics-structure-function relationships of biomolecules. [ABSTRACT FROM AUTHOR]

Simulation methodologies for modelling the viscoelasticity and thermal fluctuations of molecular fluids at nanoscale are presented. In particular, we bridge the distinct frameworks of fluctuating hydrodynamics (FHD) and molecular dynamics (MD) simulations using a coarse-graining procedure that properly considers the effective size of each fluid molecule in mapping a phase space vector of the all-atom model to field variables in the FHD representation. We also generalise the FHD equations to model non-Markovian rheological responses by incorporating coloured noise. To capture the increasing elastic responses that emerge at the nanoscale, a composite Newtonian-Maxwell rheological model is developed. Numerical simulations using a staggered discretisation scheme demonstrate that the thermodynamic states and dynamic properties (power spectra) of FHD equations match with those of all-atom MD simulations quantitatively. This agreement also unambiguously determines the wavenumber-dependent transport coefficients of the composite Newtonian-Maxwell model. To avoid the complexities associated with using wavenumber-dependent transport coefficients, we characterise the approximation of using a single set of transport coefficients. We find that for collective fluctuations with a wavelength longer than 25 Å, wavenumber-independent models can accurately describe the power spectra. For fluctuations with shorter wavelengths, relative errors in power spectra increase monotonically with wavenumber. [ABSTRACT FROM AUTHOR]

This work illustrates that fluctuating hydrodynamics (FHD) simulations can be used to capture the thermodynamic and hydrodynamic responses of molecular fluids at the nanoscale, including those associated with energy and heat transfer. Using all-atom molecular dynamics (MD) trajectories as the reference data, the atomistic coordinates of each snapshot are mapped onto mass, momentum, and energy density fields on Eulerian grids to generate a corresponding field trajectory. The molecular length-scale associated with finite molecule size is explicitly imposed during this coarse-graining by requiring that the variances of density fields scale inversely with the grid volume. From the fluctuations of field variables, the response functions and transport coefficients encoded in the all-atom MD trajectory are computed. By using the extracted fluid properties in FHD simulations, we show that the fluctuations and relaxation of hydrodynamic fields quantitatively match with those observed in the reference all-atom MD trajectory, hence establishing compatibility between the atomistic and field representations. We also show that inclusion of energy transfer in the FHD equations can more accurately capture the thermodynamic and hydrodynamic responses of molecular fluids. The results indicate that the proposed MD-to-FHD mapping with explicit consideration of finite molecule size provides a robust framework for coarse-graining the solution phase of complex molecular systems. [ABSTRACT FROM AUTHOR]