arXiv subjects

Aleksandar Donev

Publications and source records attributed to Aleksandar Donev.

At least 37 records · Page 2Linked to original sources

arXiv2017

Fluctuation-enhanced electric conductivity in electrolyte solutions

In this letter we analyze the effects of an externally applied electric field on thermal fluctuations for a fluid containing charged species. We show in particular that the fluctuating Poisson-Nernst-Planck equations for charged multispecies diffusion coupled with the fluctuating fluid momentum equation, result in enhanced charge transport. Although this transport is advective in nature, it can macroscopically be represented as electrodiffusion with renormalized electric conductivity. We calculate the renormalized electric conductivity by deriving and integrating the structure factor coefficients of the fluctuating quantities and show that the renormalized electric conductivity and diffusion coefficients are consistent although they originate from different noise terms. In addition, the fluctuating hydrodynamics approach recovers the electrophoretic and relaxation corrections obtained by Debye-Huckel-Onsager theory, and provides a quantitative theory that predicts a non-zero cross-diffusion Maxwell-Stefan coefficient that agrees well with experimental measurements. Finally, we show that strong applied electric fields result in anisotropically enhanced velocity fluctuations and reduced fluctuations of salt concentrations.

physics.flu-dyn↗

arXiv2017

An Immersed Boundary Method with Divergence-Free Velocity Interpolation and Force Spreading

The Immersed Boundary (IB) method is a mathematical framework for constructing robust numerical methods to study fluid-structure interaction in problems involving an elastic structure immersed in a viscous fluid. The IB formulation uses an Eulerian representation of the fluid and a Lagrangian representation of the structure. The Lagrangian and Eulerian frames are coupled by integral transforms with delta function kernels. The discretized IB equations use approximations to these transforms with regularized delta function kernels to interpolate the fluid velocity to the structure, and to spread structural forces to the fluid. It is well-known that the conventional IB method can suffer from poor volume conservation since the interpolated Lagrangian velocity field is not generally divergence-free, and so this can cause spurious volume changes. In practice, the lack of volume conservation is especially pronounced for cases where there are large pressure differences across thin structural boundaries. The aim of this paper is to greatly reduce the volume error of the IB method by introducing velocity-interpolation and force-spreading schemes with the properties that the interpolated velocity field in which the structure moves is at least C1 and satisfies a continuous divergence-free condition, and that the force-spreading operator is the adjoint of the velocity-interpolation operator. We confirm through numerical experiments in two and three spatial dimensions that this new IB method is able to achieve substantial improvement in volume conservation compared to other existing IB methods, at the expense of a modest increase in the computational cost. Further, the new method provides smoother Lagrangian forces (tractions) than traditional IB methods. The method presented here is restricted to periodic computational domains. Its generalization to non-periodic domains is important future work.

math.NA↗

arXiv2017

Brownian Dynamics of Confined Suspensions of Active Microrollers

We develop efficient numerical methods for performing many-body Brownian dynamics simulations of a recently-observed fingering instability in an active suspension of colloidal rollers sedimented above a wall [M. Driscoll, B. Delmotte, M. Youssef, S. Sacanna, A. Donev and P. Chaikin, Nature Physics, 2016, doi:10.1038/nphys3970]. We present a stochastic Adams-Bashforth integrator for the equations of Brownian dynamics, which has the same cost as but is more accurate than the widely-used Euler-Maruyama scheme, and uses a random finite difference to capture the stochastic drift proportional to the divergence of the configuration-dependent mobility matrix. We generate the Brownian increments using a Krylov method, and show that for particles confined to remain in the vicinity of a no-slip wall by gravity or active flows the number of iterations is independent of the number of particles. Our numerical experiments with active rollers show that the thermal fluctuations set the characteristic height of the colloids above the wall, both in the initial condition and the subsequent evolution dominated by active flows. The characteristic height in turn controls the timescale and wavelength for the development of the fingering instability.

cond-mat.soft↗

arXiv2017

Stochastic Simulation of Reaction-Diffusion Systems: A Fluctuating-Hydrodynamics Approach

We develop numerical methods for reaction-diffusion systems based on the equations of fluctuating hydrodynamics (FHD). While the FHD formulation is formally described by stochastic partial differential equations (SPDEs), it becomes similar to the reaction-diffusion master equation (RDME) description when those SPDEs are spatially discretized and reactions are modeled as a source term having Poisson fluctuations. However, unlike the RDME, the FHD description naturally extends from the regime where fluctuations are strong, i.e., each hydrodynamic cell has few (reactive) molecules, to regimes with moderate or weak fluctuations, and ultimately to the deterministic limit. By treating diffusion implicitly, we avoid the severe restriction on time step size that limits all methods based on explicit treatments of diffusion, and construct numerical methods that are more efficient than RDME methods, without compromising accuracy. We find that an implicit midpoint tau leaping scheme attains second-order weak accuracy for the linearized FHD, and gives an accurate and stable structure factor for a time step size an order of magnitude larger than the hopping time scale of diffusing molecules. We study the numerical accuracy of our methods for the Schlögl reaction-diffusion model both in and out of thermodynamic equilibrium. We demonstrate and quantify the importance of thermodynamic fluctuations to the formation of a two-dimensional Turing-like pattern, and examine the effect of fluctuations on three-dimensional chemical front propagation. By comparing FHD simulations to deterministic reaction-diffusion simulations, we show that fluctuations accelerate pattern formation in spatially homogeneous systems, and lead to a qualitatively-different disordered pattern behind a traveling wave.

physics.flu-dyn↗

arXiv2016

Unstable fronts and stable "critters" formed by microrollers

Condensation of objects into stable clusters occurs naturally in equilibrium and driven systems. It is commonly held that potential interactions, depletion forces, or sensing are the only mechanisms which can create long-lived compact structures. Here we show that persistent motile structures can form spontaneously from hydrodynamic interactions alone with no sensing or potential interactions. We study this structure formation in a system of colloidal rollers suspended and translating above a floor, using both experiments and large-scale 3D simulations. In this system, clusters originate from a previously unreported fingering instability, where fingers pinch off from an unstable front to form autonomous "critters", whose size is selected by the height of the particles above the floor. These critters are a stable state of the system, move much faster than individual particles, and quickly respond to a changing drive. With speed and direction set by a rotating magnetic field, these active structures offer interesting possibilities for guided transport, flow generation, and mixing at the microscale.

cond-mat.soft↗

arXiv2016

Low Mach Number Fluctuating Hydrodynamics for Electrolytes

We formulate and study computationally the low Mach number fluctuating hydrodynamic equations for electrolyte solutions. We are interested in studying transport in mixtures of charged species at the mesoscale, down to scales below the Debye length, where thermal fluctuations have a significant impact on the dynamics. Continuing our previous work on fluctuating hydrodynamics of multicomponent mixtures of incompressible isothermal miscible liquids (A. Donev, et al., Physics of Fluids, 27, 3, 2015), we now include the effect of charged species using a quasielectrostatic approximation. Localized charges create an electric field, which in turn provides additional forcing in the mass and momentum equations. Our low Mach number formulation eliminates sound waves from the fully compressible formulation and leads to a more computationally efficient quasi-incompressible formulation. We demonstrate our ability to model saltwater (NaCl) solutions in both equilibrium and nonequilibrium settings. We show that our algorithm is second-order in the deterministic setting, and for length scales much greater than the Debye length gives results consistent with an electroneutral/ambipolar approximation. In the stochastic setting, our model captures the predicted dynamics of equilibrium and nonequilibrium fluctuations. We also identify and model an instability that appears when diffusive mixing occurs in the presence of an applied electric field.

physics.flu-dyn↗

arXiv2015

Dynamic scaling for the growth of non-equilibrium fluctuations during thermophoretic diffusion in microgravity

Diffusion processes are widespread in biological and chemical systems, where they play a fundamental role in the exchange of substances at the cellular level and in determining the rate of chemical reactions. Recently, the classical picture that portrays diffusion as random uncorrelated motion of molecules has been revised, when it was shown that giant non-equilibrium fluctuations develop during diffusion processes. Under microgravity conditions and at steady-state, non-equilibrium fluctuations exhibit scale invariance and their size is only limited by the boundaries of the system. In this work, we investigate the onset of non-equilibrium concentration fluctuations induced by thermophoretic diffusion in microgravity, a regime not accessible to analytical calculations but of great relevance for the understanding of several natural and technological processes. A combination of state of the art simulations and experiments allows us to attain a fully quantitative description of the development of fluctuations during transient diffusion in microgravity. Both experiments and simulations show that during the onset the fluctuations exhibit scale invariance at large wave vectors. In a broader range of wave vectors simulations predict a spinodal-like growth of fluctuations, where the amplitude and length-scale of the dominant mode are determined by the thickness of the diffuse layer.

cond-mat.soft↗

arXiv2015

Coupling a nano-particle with isothermal fluctuating hydrodynamics: Coarse-graining from microscopic to mesoscopic dynamics

We derive a coarse-grained description of the dynamics of a nanoparticle immersed in an isothermal simple fluid by performing a systematic coarse graining of the underlying microscopic dynamics. As coarse-grained or relevant variables we select the position of the nanoparticle and the \emph{total} mass and momentum density field of the fluid, which are locally conserved slow variables because they are defined to include the contribution of the nanoparticle. The theory of coarse graining based on the Zwanzing projection operator leads us to a system of stochastic \emph{ordinary} differential equations (SODEs) that are closed in the relevant variables. We demonstrate that our discrete coarse-grained equations are consistent with a Petrov-Galerkin finite-element discretization of a system of formal stochastic \emph{partial} differential equations (SPDEs) which resemble previously-used phenomenological models based on fluctuating hydrodynamics. Under suitable approximations we obtain \emph{closed} approximations of the coarse-grained dynamics in a manner which gives them a clear physical interpretation, and provides \emph{explicit} microscopic expressions for all of the coefficients appearing in the closure. Our work leads to a model for dilute nanocolloidal suspensions that can be simulated effectively using feasibly short molecular dynamics simulations as input to a FEM fluctuating hydrodynamic solver.

cond-mat.mes-hall↗

arXiv2015

Brownian Dynamics of Confined Rigid Bodies

We introduce numerical methods for simulating the diffusive motion of rigid bodies of arbitrary shape immersed in a viscous fluid. We parameterize the orientation of the bodies using normalized quaternions, which are numerically robust, space efficient, and easy to accumulate. We construct a system of overdamped Langevin equations in the quaternion representation that accounts for hydrodynamic effects, preserves the unit-norm constraint on the quaternion, and is time reversible with respect to the Gibbs-Boltzmann distribution at equilibrium. We introduce two schemes for temporal integration of the overdamped Langevin equations of motion, one based on the Fixman midpoint method and the other based on a random finite difference approach, both of which ensure the correct stochastic drift term is captured in a computationally efficient way. We study several examples of rigid colloidal particles diffusing near a no-slip boundary, and demonstrate the importance of the choice of tracking point on the measured translational mean square displacement (MSD). We examine the average short-time as well as the long-time quasi-two-dimensional diffusion coefficient of a rigid particle sedimented near a bottom wall due to gravity. For several particle shapes we find a choice of tracking point that makes the MSD essentially linear with time, allowing us to estimate the long-time diffusion coefficient efficiently using a Monte Carlo method. However, in general such a special choice of tracking point does not exist, and numerical techniques for simulating long trajectories, such as the ones we introduce here, are necessary to study diffusion on long timescales.

cond-mat.soft↗

arXiv2015

Finite element discretization of non-linear diffusion equations with thermal fluctuations

We present a finite element discretization of a non-linear diffusion equation used in the field of critical phenomena and, more recently, in the context of Dynamic Density Functional Theory. The discretized equation preserves the structure of the continuum equation. Specifically, it conserves the total number of particles and fulfills an H-theorem as the original partial differential equation. Guided by the Theory of Coarse-Graining, we discuss the inclusion of thermal fluctuations in the non-linear diffusion equation. This sheds light on the meaning of such a fluctuating hydrodynamics equation and to the limitations of the approximations involved. The methodology proposed for the introduction of thermal fluctuations in finite element methods is general and valid for both regular and irregular grids in arbitrary dimensions. We focus here on simulations of the Ginzburg-Landau free energy functional using both regular and irregular 1D grids. Convergence of the numerical results is obtained for the static and dynamic structure factors as the resolution of the grid is increased.

cond-mat.stat-mech↗

arXiv2015

Slowing-down of non-equilibrium concentration fluctuations in confinement

Fluctuations in a fluid are strongly affected by the presence of a macroscopic gradient making them long-ranged and enhancing their amplitude. While small-scale fluctuations exhibit diffusive lifetimes, larger-scale fluctuations live shorter because of gravity, as theoretically and experimentally well-known. We explore here fluctuations of even larger size, comparable to the extent of the system in the direction of the gradient, and find experimental evidence of a dramatic slowing-down in their dynamics. We recover diffusive behaviour for these strongly-confined fluctuations, but with a diffusion coefficient that depends on the solutal Rayleigh number. Results from dynamic shadowgraph experiments are complemented by theoretical calculations and numerical simulations based on fluctuating hydrodynamics, and excellent agreement is found. The study of the dynamics of non-equilibrium fluctuations allows to probe and measure the competition of physical processes such as diffusion, buoyancy and confinement.

cond-mat.soft↗

arXiv2014

Modeling Multi-phase Flow using Fluctuating Hydrodynamics

Fluctuating hydrodynamics provides a model for fluids at mesoscopic scales where thermal fluctuations can have a significant impact on the behavior of the system. Here we investigate a model for fluctuating hydrodynamics of a single component, multiphase flow in the neighborhood of the critical point. The system is modeled using a compressible flow formulation with a van der Waals equation of state, incorporating a Korteweg stress term to treat interfacial tension. We present a numerical algorithm for modeling this system based on an extension of algorithms developed for fluctuating hydrodynamics for ideal fluids. The scheme is validated by comparison of measured structure factors and capillary wave spectra with equilibrium theory. We also present several non-equilibrium examples to illustrate the capability of the algorithm to model multi-phase fluid phenomena in a neighborhood of the critical point. These examples include a study of the impact of fluctuations on the spinodal decomposition following a rapid quench, as well as the piston effect in a cavity with supercooled walls. The conclusion in both cases is that thermal fluctuations affect the size and growth of the domains in off-critical quenches.

physics.flu-dyn↗

arXiv2014

Metropolis Integration Schemes for Self-Adjoint Diffusions

We present explicit methods for simulating diffusions whose generator is self-adjoint with respect to a known (but possibly not normalizable) density. These methods exploit this property and combine an optimized Runge-Kutta algorithm with a Metropolis-Hastings Monte-Carlo scheme. The resulting numerical integration scheme is shown to be weakly accurate at finite noise and to gain higher order accuracy in the small noise limit. It also permits to avoid computing explicitly certain terms in the equation, such as the divergence of the mobility tensor, which can be tedious to calculate. Finally, the scheme is shown to be ergodic with respect to the exact equilibrium probability distribution of the diffusion when it exists. These results are illustrated on several examples including a Brownian dynamics simulation of DNA in a solvent. In this example, the proposed scheme is able to accurately compute dynamics at time step sizes that are an order of magnitude (or more) larger than those permitted with commonly used explicit predictor-corrector schemes.

math.NA↗

arXiv2014

Fluctuating hydrodynamics of multi-species, non-reactive mixtures

In this paper we discuss the formulation of the fuctuating Navier-Stokes (FNS) equations for multi-species, non-reactive fluids. In particular, we establish a form suitable for numerical solution of the resulting stochastic partial differential equations. An accurate and efficient numerical scheme, based on our previous methods for single species and binary mixtures, is presented and tested at equilibrium as well as for a variety of non-equilibrium problems. These include the study of giant nonequilibrium concentration fluctuations in a ternary mixture in the presence of a diffusion barrier, the triggering of a Rayleigh-Taylor instability by diffusion in a four-species mixture, as well as reverse diffusion in a ternary mixture. Good agreement with theory and experiment demonstrates that the formulation is robust and can serve as a useful tool in the study of thermal fluctuations for multi-species fluids. The extension to include chemical reactions will be treated in a sequel paper.

physics.flu-dyn↗

arXiv2008

Asynchronous Event-Driven Particle Algorithms

We present, in a unifying way, the main components of three asynchronous event-driven algorithms for simulating physical systems of interacting particles. The first example, hard-particle molecular dynamics, is well-known. We also present a recently-developed diffusion kinetic Monte Carlo algorithm, as well as a novel stochastic molecular-dynamics algorithm that builds on the Direct Simulation Monte Carlo. We explain how to effectively combine asynchronous event-driven with classical time-driven or with synchronous event-driven handling. Finally, we discuss some promises and challenges for event-driven simulation of realistic physical systems.

cs.OH↗

arXiv2008

Stochastic Hard-Sphere Dynamics for Hydrodynamics of Non-Ideal Fluids

A novel stochastic fluid model is proposed with non-ideal structure factor consistent with compressibility, and adjustable transport coefficients. This Stochastic Hard Sphere Dynamics (SHSD) algorithm is a modification of the Direct Simulation Monte Carlo (DSMC) algorithm and has several computational advantages over event-driven hard-sphere molecular dynamics. Surprisingly, SHSD results in an equation of state and pair correlation function identical to that of a deterministic Hamiltonian system of penetrable spheres interacting with linear core pair potentials. The fluctuating hydrodynamic behavior of the SHSD fluid is verified for the Brownian motion of a nano-particle suspended in a compressible solvent.

cond-mat.stat-mech↗

arXiv2007

An Event-Driven Hybrid Molecular Dynamics and Direct Simulation Monte Carlo Algorithm

A novel Stochastic Event-Driven Molecular Dynamics (SEDMD) algorithm is developed for the simulation of polymer chains suspended in a solvent. The polymers are represented as chains of hard spheres tethered by square wells and interact with the solvent particles with hard core potentials. The algorithm uses Event-Driven Molecular Dynamics (EDMD) for the simulation of the polymer chain and the interactions between the chain beads and the surrounding solvent particles. The interactions between the solvent particles themselves are not treated deterministically as in event-driven algorithms, rather, the momentum and energy exchange in the solvent is determined stochastically using the Direct Simulation Monte Carlo (DSMC) method. The coupling between the solvent and the solute is consistently represented at the particle level, however, unlike full MD simulations of both the solvent and the solute, the spatial structure of the solvent is ignored. The algorithm is described in detail and applied to the study of the dynamics of a polymer chain tethered to a hard wall subjected to uniform shear. The algorithm closely reproduces full MD simulations with two orders of magnitude greater efficiency. Results do not confirm the existence of periodic (cycling) motion of the polymer chain.

cond-mat.mtrl-sci↗

arXiv2004

Neighbor List Collision-Driven Molecular Dynamics Simulation for Nonspherical Particles. I. Algorithmic Details II. Applications to Ellipses and Ellipsoids

In the first part of a series of two papers, we present in considerable detail a collision-driven molecular dynamics algorithm for a system of nonspherical particles, within a parallelepiped simulation domain, under both periodic or hard-wall boundary conditions. The algorithm extends previous event-driven molecular dynamics algorithms for spheres. We present a novel partial-update near-neighbor list (NNL) algorithm that is superior to previous algorithms at high densities, without compromising the correctness of the algorithm. This efficiency of the algorithm is further increased for systems of very aspherical particles by using bounding sphere complexes (BSC). In the second part of this series of papers we apply the algorithm presented in the first part of this series of papers to systems of hard ellipses and ellipsoids. The theoretical machinery needed to treat such particles, including the overlap potentials, is developed in full detail. We describe an algorithm for predicting the time of collision for two moving ellipses or ellipsoids. We present performance results for our implementation of the algorithm. The practical utility of the algorithm is demonstrated by presenting several interesting physical applications, including the generation of jammed packings inside spherical containers, the study of contact force chains in jammed packings, and melting the densest-known equilibrium crystals of prolate spheroids.

physics.comp-ph↗