# Momentum conserving Brownian dynamics propagator for complex soft matter fluids

## Abstract

We present a Galilean invariant, momentum conserving first order Brownian dynamics scheme for coarse-grained simulations of highly frictional soft matter systems. Friction forces are taken to be with respect to moving background material. The motion of the background material is described by locally averaged velocities in the neighborhood of the dissolved coarse coordinates. The velocity variables are updated by a momentum conserving scheme. The properties of the stochastic updates are derived through the Chapman-Kolmogorov and Fokker-Planck equations for the evolution of the probability distribution of coarse-grained position and velocity variables, by requiring the equilibrium distribution to be a stationary solution. We test our new scheme on concentrated star polymer solutions and find that the transverse current and velocity time auto-correlation functions behave as expected from hydrodynamics. In particular, the velocity auto-correlation functions display a long time tail in complete agreement with hydrodynamics.

- Authors:

- Department of Chemical Engineering and Chemistry, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven (Netherlands)
- Computational Biophysics, University of Twente, P.O. Box 217, 7500 AE Enschede (Netherlands)

- Publication Date:

- OSTI Identifier:
- 22415405

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Chemical Physics; Journal Volume: 141; Journal Issue: 24; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BROWNIAN MOVEMENT; CORRELATION FUNCTIONS; EQUILIBRIUM; FLUIDS; FOKKER-PLANCK EQUATION; FRICTION; HYDRODYNAMICS; MATHEMATICAL SOLUTIONS; POLYMERS; PROBABILITY; PROPAGATOR; STOCHASTIC PROCESSES; VELOCITY

### Citation Formats

```
Padding, J. T., and Briels, W. J.
```*Momentum conserving Brownian dynamics propagator for complex soft matter fluids*. United States: N. p., 2014.
Web. doi:10.1063/1.4904315.

```
Padding, J. T., & Briels, W. J.
```*Momentum conserving Brownian dynamics propagator for complex soft matter fluids*. United States. doi:10.1063/1.4904315.

```
Padding, J. T., and Briels, W. J. Sun .
"Momentum conserving Brownian dynamics propagator for complex soft matter fluids". United States.
doi:10.1063/1.4904315.
```

```
@article{osti_22415405,
```

title = {Momentum conserving Brownian dynamics propagator for complex soft matter fluids},

author = {Padding, J. T. and Briels, W. J.},

abstractNote = {We present a Galilean invariant, momentum conserving first order Brownian dynamics scheme for coarse-grained simulations of highly frictional soft matter systems. Friction forces are taken to be with respect to moving background material. The motion of the background material is described by locally averaged velocities in the neighborhood of the dissolved coarse coordinates. The velocity variables are updated by a momentum conserving scheme. The properties of the stochastic updates are derived through the Chapman-Kolmogorov and Fokker-Planck equations for the evolution of the probability distribution of coarse-grained position and velocity variables, by requiring the equilibrium distribution to be a stationary solution. We test our new scheme on concentrated star polymer solutions and find that the transverse current and velocity time auto-correlation functions behave as expected from hydrodynamics. In particular, the velocity auto-correlation functions display a long time tail in complete agreement with hydrodynamics.},

doi = {10.1063/1.4904315},

journal = {Journal of Chemical Physics},

number = 24,

volume = 141,

place = {United States},

year = {Sun Dec 28 00:00:00 EST 2014},

month = {Sun Dec 28 00:00:00 EST 2014}

}