Molecular hydrodynamics: Vortex formation and sound wave propagation

A perspective on the microscopic pressure (stress) tensor: History, current understanding, and future challenges

The pressure tensor (equivalent to the negative stress tensor) at both microscopic and macroscopic levels is fundamental to many aspects of engineering and science, including fluid dynamics, solid mechanics, biophysics, and thermodynamics. In this Perspective, we review methods to calculate the microscopic pressure tensor. Connections between different pressure forms for equilibrium and nonequilibrium systems are established. We also point out several challenges in the field, including the historical controversies over the definition of the microscopic pressure tensor; the difficulties with many-body and long-range potentials; the insufficiency of software and computational tools; and the lack of experimental routes to probe the pressure tensor at the nanoscale. Possible future directions are suggested.

Bootstrapping time correlation functions of molecular dynamics

Molecular dynamics is often considered as a numerical experiment. The error bars on the results are therefore mandatory, but sometimes difficult to determine and computationally demanding. As a low-cost approach, we describe the application of the bootstrap (BS) method to the quantification of uncertainties pertaining to the time correlation functions. We chose the autocorrelation functions of velocity and interdiffusion current for a binary ionic mixture as a test bed, and we assessed the merit of the Darken approximation relating both of them. The intrinsic errors related to phase space sampling is investigated comparing the BS method with the reference method of replica. We also study how the BS method can assist in addressing the finite-size effects.

Bridging the gap between molecular dynamics and hydrodynamics in nanoscale Brownian motions

Through molecular dynamics simulations, we examined the hydrodynamic behavior of the Brownian motion of fullerene particles based on molecular interactions. The solvation free energy and velocity autocorrelation function (VACF) were calculated by using the Lennard-Jones (LJ) and Weeks-Chandler-Andersen (WCA) potentials for the solute-solvent and solvent-solvent interactions and by changing the size of the fullerene particles. We also measured the diffusion constant of the fullerene particles and the shear viscosity of the host fluid, and then the hydrodynamic radius aHD was quantified from the Stokes-Einstein relation. The aHD value exceeds that of the gyration radius of the fullerene when the solvation free energy exhibits largely negative values using the LJ potential. In contrast, aHD is similar to the size of bare fullerene when the solvation free energy is positive using the WCA potential. Furthermore, the VACF of the fullerene particles is directly comparable with the analytical expressions utilizing the Navier-Stokes equations both in incompressible and compressible forms. A hydrodynamic long-time tail t-3/2 is demonstrated for timescales longer than the kinematic time of the momentum diffusion over the particle size. However, the VACF at shorter timescales deviates from the hydrodynamic description, particularly for smaller fullerene particles and for the LJ potential. This occurs even though the compressible effect is considered when characterizing the decay of the VACF around the sound-propagation timescale over the particle size. These results indicate that the nanoscale Brownian motion is influenced by the solvation structure around the solute particles originating from the molecular interaction.