From molecular dynamics to hydrodynamics: A novel Galilean invariant thermostat

Abstract

This article proposes a novel thermostat applicable to any particle-based dynamic simulation. Each pair of particles is thermostated either (with probability P) with a pairwise Lowe-Andersen thermostat [C.P.Lowe, Europhys. Lett. 47, 145 (1999)], or (with probability 1-P) with a thermostat that is introduced here, which is based on a pairwise interaction similar to the Nosé-Hoover thermostat. When the pairwise Nosé-Hoover thermostat dominates (low P), the liquid has a high diffusion coefficient and low viscosity, but when the Lowe-Andersen thermostat dominates, the diffusion coefficient is low and viscosity is high. This novel Nosé-Hoover-Lowe-Andersen thermostat is Galilean invariant and preserves both total linear and angular momentum of the system, due to the fact that the thermostatic forces between each pair of the particles are pairwise additive and central. We show by simulation that this thermostat also preserves hydrodynamics. For the (non-interacting) ideal gas at P=0, the diffusion coefficient diverges and viscosity is zero, while for P>0 it has a finite value. By adjusting probability P, the Schmidt number can be varied by orders of magnitude. The temperature deviation from the required value is at least an order of magnitude smaller than in Dissipative Particle Dynamics (DPD), while the equilibrium properties of the system are very well reproduced. The thermostat is easy to implement and offers a computational efficiency better than DPD, with better temperature control and greater flexibility in terms of adjusting the diffusion coefficient and viscosity of the simulated system. Applications of this thermostat include all standard molecular dynamic simulations of dense liquids and solids with any type of force field, as well as hydrodynamic simulation of multi-phase systems with largely different bulk viscosities, including surface viscosity, and of dilute gases and plasmas. PACS. 02.70.Ns − Molecular dynamics and particle methods.

Multiscale modeling of emergent materials: biological and soft matter

“…161 Intra-molecular forces other than harmonic ''springs'' have been implemented including 2-4 interactions, 140 FENE springs 161 and the accuracy of the surfactant simulation has been increased by Shillcock et al 155 through the addition of a three body potential acting between consecutive bead triples. We are finally not limited to the thermostating being provided by dissipative and random forces, as the now widely used Lowe-Andersen themostat 162 and the extension of this method proposed by Stoyanov and Groot 163 attest.…”

“…As stated previously the use of random and dissipative forces is not the only effective thermostat for DPD simulation. The methods of Lowe 162 and the extension of this method proposed by Stoyanov and Groot 163 propose a very different alternative. In the same way that the above described DPD algorithm takes Langevin dynamics as the starting point, the algorithm proposed by Lowe takes the Andersen thermostat as the starting point, hence the name by which it is commonly known, the ''Lowe-Andersen'' thermostat.…”

Water flow in carbon nanotubes: The effect of tube flexibility and thermostat

“…All the thermostats considered in our study are widely used in molecular simulations, but they are not suitable to fully account for the system hydrodynamics, when subjected to an external force. 50,51 However, the drawback of the Langevin thermostat, in comparison to the Nosé-Hoover and Berendsen thermostats, is that the frictional and random forces of the Langevin thermostat can damp the system dynamics, thus reducing the flow velocity in nonequilibrium simulations. In fact, the forces exerted by fluid onto the walls were highest in systems coupled to the Langevin thermostat, i.e., the interfacial friction has been increased considerably.…”

Strong influence of periodic boundary conditions on lateral diffusion in lipid bilayer membranes

“…53 Although this integrator is not ideal for studying hydrodynamic effects, 54,55 attempts to implement strict energy and momentum conserving simulations within GROMACS were not successful and were ultimately abandoned. While use of the NPT thermostat is recognized to be a potential issue, the below results do seem to indicate support for the predictions in Secs.…”

“…Other thermostats, including the commonly used Nosé-Hoover approach, may also potentially disrupt hydrodynamic flows. 54,55 To study transport properties, either an NVE integrator or a thermostat specifically designed to preserve hydrodynamics (e.g., dissipative particle dynamics thermostats 59,60 ) would be most appropriate. Unfortunately, most largescale simulation packages suitable for studying realistic lipid architectures do not support this functionality without some degree of modification and tinkering.…”