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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]

Waddington envisioned stem cell differentiation as a marble rolling down a hill, passing through hierarchically branched valleys representing the cell's temporal state. The terminal valleys at the bottom of the hill indicate the possible committed cells of the multicellular organism. Although originally proposed as a metaphor, Waddington's hypothesis establishes the fundamental principles for characterizing the differentiation process as a dynamic system: the generated equilibrium points must exhibit hierarchical branching, robustness to perturbations (homeorhesis), and produce the appropriate number of cells for each cell type. This article aims to capture these characteristics using a mathematical model based on two fundamental hypotheses. First, it is assumed that the gene regulatory network consists of hierarchically coupled subnetworks of genes (modules), each modeled as a dynamical system exhibiting supercritical pitchfork or cusp bifurcation. Second, the gene modules are spatiotemporally regulated by feedback mechanisms originating from epigenetic factors. Analytical and numerical results show that the proposed model exhibits self-organized multistability with hierarchical branching. Moreover, these branches of equilibrium points are robust to perturbations, and the number of different cells produced can be determined by the system parameters. [ABSTRACT FROM AUTHOR]

Thermal fluctuation and hydrophobicity are two hallmarks of fluid hydrodynamics on the nano-scale. It is a challenge to consistently couple the small length and time scale phenomena associated with molecular interaction with larger scale phenomena. The development of this consistency is the essence of mesoscale science. In this study, we use a nanoscale fluid model based on smoothed dissipative particle dynamics that accounts for the phenomena associated with density fluctuations and hydrophobicity. We show consistency in the fluctuation spectrum across scales. In doing so, it is necessary to account for finite fluid particle size. Furthermore, we demonstrate that the present model can capture the void probability and solvation free energy of nonpolar hard particles of different sizes. The present fluid model is well suited for an understanding of emergent phenomena in nano-scale fluid systems. [ABSTRACT FROM AUTHOR]

Fluctuating hydrodynamics (FHD) is a general framework of mesoscopic modeling and simulation based on conservational laws and constitutive equations of linear and nonlinear responses. However, explicit representation of electrical forces in FHD has yet to appear. In this work, we devised an Ansatz for the dynamics of dipole moment densities that is linked with the Poisson equation of the electrical potential Φ in coupling to the other equations of FHD. The resulting Φ-FHD equations then serve as a platform for integrating the essential forces, including electrostatics in addition to hydro-dynamics, pressure-volume equation of state, surface tension, and solvent-particle interactions that govern the emergent behaviors of molecular systems at an intermediate scale. This unique merit of Φ-FHD is illustrated by showing that the water dielectric function and ion hydration free energies in homogeneous and heterogenous systems can be captured accurately via the mesoscopic simulation. Furthermore, we show that the field variables of Φ-FHD can be mapped from the trajectory of an all-atom molecular dynamics simulation such that model development and parametrization can be based on the information obtained at a finer-grained scale. With the aforementioned multiscale capa-bilities and a spatial resolution as high as 5 Å, the Φ-FHD equations represent a useful semi-explicit solvent model for the modeling and simulation of complex systems, such as biomolecular machines and nanofluidics. [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]

Transport in complex fluidic environments often exhibits transient subdiffusive dynamics accompanied by non-Gaussian probability density profiles featuring a nonmonotonic non-Gaussian parameter. Such properties cannot be adequately explained by the original theory of Brownian motion. Based on an extension of kinetic theory, this study introduces a chain of hierarchically coupled random walks approach that effectively captures all these intriguing characteristics. If the environment consists of a series of independent white noise sources, then the problem can be expressed as a system of hierarchically coupled Ornstein-Uhlenbech equations. Due to the linearity of the system, the most essential transport properties have a closed analytical form.