Hydrodynamic fluctuations in thermostatted multiparticle collision dynamics

A hybrid method for micro-mesoscopic stochastic simulation of reaction-diffusion systems

The present paper introduces a new micro-meso hybrid algorithm based on the Ghost Cell Method concept in which the microscopic subdomain is governed by the Reactive Multi-Particle Collision (RMPC) dynamics. The mesoscopic subdomain is modeled using the Reaction-Diffusion Master Equation (RDME). The RDME is solved by means of the Inhomogeneous Stochastic Simulation Algorithm. No hybrid algorithm has hitherto used the RMPC dynamics for modeling reactions and the trajectories of each individual particle. The RMPC is faster than other molecular based methods and has the advantage of conserving mass, energy and momentum in the collision and free streaming steps. The new algorithm is tested on three reaction-diffusion systems. In all the systems studied, very good agreement with the deterministic solutions of the corresponding differential equations is obtained. In addition, it has been shown that proper discretization of the computational domain results in significant speed-ups in comparison with the full RMPC algorithm.

Spatial correlations of hydrodynamic fluctuations in simple fluids under shear flow: A mesoscale simulation study

Hydrodynamic fluctuations in simple fluids under shear flow are demonstrated to be spatially correlated, in contrast to the fluctuations at equilibrium, using mesoscopic hydrodynamic simulations. The simulation results for the equal-time hydrodynamic correlations in a multiparticle collision dynamics (MPC) fluid in shear flow are compared with the explicit expressions obtained from fluctuating hydrodynamics calculations. For large wave vectors k, the nonequilibrium contributions to transverse and longitudinal velocity correlations decay as k^{-4} for wave vectors along the flow direction and as k^{-2} for the off-flow directions. For small wave vectors, a crossover to a slower decay occurs, indicating long-range correlations in real space. The coupling between the transverse velocity components, which vanishes at equilibrium, also exhibits a k^{-2} dependence on the wave vector. In addition, we observe a quadratic dependency on the shear rate of the nonequilibrium contribution to pressure.

Harmonically bound Brownian motion in fluids under shear: Fokker-Planck and generalized Langevin descriptions

We study the Brownian motion of a particle bound by a harmonic potential and immersed in a fluid with a uniform shear flow. We describe this problem first in terms of a linear Fokker-Planck equation which is solved to obtain the probability distribution function for finding the particle in a volume element of its associated phase space. We find the explicit form of this distribution in the stationary limit and use this result to show that both the equipartition law and the equation of state of the trapped particle are modified from their equilibrium form by terms increasing as the square of the imposed shear rate. Subsequently, we propose an alternative description of this problem in terms of a generalized Langevin equation that takes into account the effects of hydrodynamic correlations and sound propagation on the dynamics of the trapped particle. We show that these effects produce significant changes, manifested as long-time tails and resonant peaks, in the equilibrium and nonequilibrium correlation functions for the velocity of the Brownian particle. We implement numerical simulations based on molecular dynamics and multiparticle collision dynamics, and observe a very good quantitative agreement between the predictions of the model and the numerical results, thus suggesting that this kind of numerical simulations could be used as complement of current experimental techniques.

Thermostat for nonequilibrium multiparticle-collision-dynamics simulations

Multiparticle collision dynamics (MPC), a particle-based mesoscale simulation technique for complex fluid, is widely employed in nonequilibrium simulations of soft matter systems. To maintain a defined thermodynamic state, thermalization of the fluid is often required for certain MPC variants. We investigate the influence of three thermostats on the nonequilibrium properties of a MPC fluid under shear or in Poiseuille flow. In all cases, the local velocities are scaled by a factor, which is either determined via a local simple scaling approach (LSS), a Monte Carlo-like procedure (MCS), or by the Maxwell-Boltzmann distribution of kinetic energy (MBS). We find that the various scaling schemes leave the flow profile unchanged and maintain the local temperature well. The fluid viscosities extracted from the various simulations are in close agreement. Moreover, the numerically determined viscosities are in remarkably good agreement with the respective theoretically predicted values. At equilibrium, the calculation of the dynamic structure factor reveals that the MBS method closely resembles an isothermal ensemble, whereas the MCS procedure exhibits signatures of an adiabatic system at larger collision-time steps. Since the velocity distribution of the LSS approach is non-Gaussian, we recommend to apply the MBS thermostat, which has been shown to produce the correct velocity distribution even under nonequilibrium conditions.

Tracking control of colloidal particles through non-homogeneous stationary flows

We consider the problem of controlling the trajectory of a single colloidal particle in a fluid with steady non-homogeneous flow. We use a Langevin equation to describe the dynamics of this particle, where the friction term is assumed to be given by the Faxén's Theorem for the force on a sphere immersed in a stationary flow. We use this description to propose an explicit control force field to be applied on the particle such that it will follow asymptotically any given desired trajectory, starting from an arbitrary initial condition. We show that the dynamics of the controlled particle can be mapped into a set of stochastic harmonic oscillators and that the velocity gradient of the solvent induces an asymmetric coupling between them. We study the particular case of a Brownian particle controlled through a plane Couette flow and show explicitly that the velocity gradient of the solvent renders the dynamics non-stationary and non-reversible in time. We quantify this effect in terms of the correlation functions for the position of the controlled particle, which turn out to exhibit contributions depending exclusively on the non-equilibrium character of the state of the solvent. In order to test the validity of our model, we perform simulations of the controlled particle moving in a simple shear flow, using a hybrid method combining molecular dynamics and multi-particle collision dynamics. We confirm numerically that the proposed guiding force allows for controlling the trajectory of the micro-sized particle by obligating it to follow diverse specific trajectories in fluids with homogeneous shear rates of different strengths. In addition, we find that the non-equilibrium correlation functions in simulations exhibit the same qualitative behavior predicted by the model, thus revealing the presence of the asymmetric non-equilibrium coupling mechanism induced by the velocity gradient.

Hydrodynamic correlations in multiparticle collision dynamics fluids

The emergent fluctuating hydrodynamics of the multiparticle collision dynamics (MPC) approach, a particle-based mesoscale simulation technique for fluid dynamics, is analyzed theoretically and numerically. We focus on the stochastic rotation dynamics implementation of the MPC method. The fluid is characterized by its longitudinal and transverse velocity correlation functions in Fourier space and velocity autocorrelation functions in real space. Particular attention is paid to the role of sound, which leads to piecewise negative correlation functions. Moreover, finite system-size effects are addressed with an emphasis on the role of sound. Analytical expressions are provided for the transverse and longitudinal velocity correlations, which are derived from the linearized Landau-Lifshitz Navier-Stokes equation adopted for an isothermal MPC fluid. The comparison of the analytical results with simulations shows excellent agreement above a minimal length scale. The simulations indicate a breakdown in hydrodynamics on length scales smaller than this minimal length. This demonstrates that we have an excellent analytical description and understanding of the MPC method and its limitations in terms of time and length scales.