Fluctuating hydrodynamics and Brownian motion

We compare computer simulation results for the angular velocity autocorrelation function ͑AVACF͒ of a colloidal particle with theoretical predictions. We consider both spherical and nonspherical particles in two and three dimensions. The theoretical prediction for the long-time decay of the AVACF in three dimensions is well known, here we also give the two-dimensional result, along with a sketch of how it was derived. For spherical particles we find excellent agreement between the simulations results and theoretical predictions in both two and three dimensions. We also find that the same expressions apply to the nonspherical particles when the particles have had time to undergo a significant angular displacement. This observation is again in agreement with theory.

Section: Introductionmentioning

confidence: 70%

Long-time tails in angular momentum correlations

Lowe

Frenkel

Masters

1995

“…In particular, we observe that the computed value of constants a 0 (translational) and b 0 (rotational) differ from those predicted by Hauge and Martin-Löf. 23 The main reason for this difference is that the short time behavior of the Mittag Leffler thermostat predicts a stretched exponential behavior as opposed to an exponential behavior. This important difference highlights how the Mittag Leffler thermostat alters the hydrodynamic correlations (and the diffusion coefficient, see below) of the nanoparticle.…”

Section: Dynamics Of the Nanoparticle Coupled To The Gle Thermostatmentioning

confidence: 99%

“…Hauge and Martin-Löf have considered the Brownian motion of particles of arbitrary shape and have shown that in the Langevin approach, the momentum equation for the nanoparticle can be appropriately modified to satisfy the generalized fluctuationdissipation theorem. 23 Numerical schemes for studying the nanoparticle motion in a fluid must simultaneously consider the momentum (Langevin) equation for the particle and the Navier-Stokes equation for the fluid. The random force/torque in the particle equation can then be related to the frictional force/torque via the generalized fluctuation-dissipation theorem.…”

Section: Introductionmentioning

confidence: 99%

Generalized Langevin dynamics of a nanoparticle using a finite element approach: Thermostating with correlated noise

Batra

Swaminathan

Ayyaswamy

et al. 2011

A direct numerical simulation (DNS) procedure is employed to study the thermal motion of a nanoparticle in an incompressible Newtonian stationary fluid medium with the generalized Langevin approach. We consider both the Markovian (white noise) and non-Markovian (Ornstein-Uhlenbeck noise and Mittag-Leffler noise) processes. Initial locations of the particle are at various distances from the bounding wall to delineate wall effects. At thermal equilibrium, the numerical results are validated by comparing the calculated translational and rotational temperatures of the particle with those obtained from the equipartition theorem. The nature of the hydrodynamic interactions is verified by comparing the velocity autocorrelation functions and mean square displacements with analytical results. Numerical predictions of wall interactions with the particle in terms of mean square displacements are compared with analytical results. In the non-Markovian Langevin approach, an appropriate choice of colored noise is required to satisfy the power-law decay in the velocity autocorrelation function at long times. The results obtained by using non-Markovian Mittag-Leffler noise simultaneously satisfy the equipartition theorem and the long-time behavior of the hydrodynamic correlations for a range of memory correlation times. The Ornstein-Uhlenbeck process does not provide the appropriate hydrodynamic correlations. Comparing our DNS results to the solution of an one-dimensional generalized Langevin equation, it is observed that where the thermostat adheres to the equipartition theorem, the characteristic memory time in the noise is consistent with the inherent time scale of the memory kernel. The performance of the thermostat with respect to equilibrium and dynamic properties for various noise schemes is discussed.

“…[6][7][8] The latter follows from linearized hydrodynamics. The friction coefficient, and hence the admittance, depends on frequency due to inertia of the fluid.…”

Section: ͓S0021-9606͑96͒02116-2͔mentioning

confidence: 99%

Comment on ‘‘Long-time tails in angular momentum correlations’’ [J. Chem. Phys. 103, 1582 (1995)]

Cichocki

Felderhof

1996

It is shown that the shape-dependence of the coefficient of the long-time tail of the angular velocity autocorrelation function of a Brownian particle, as predicted for both two and three dimensions from the fluctuation–dissipation theorem and linearized hydrodynamics, agrees with recent computer simulations. The disagreement with a mode-coupling calculation suggests that the latter should be revised.