Superadiabatic torques and forces in anisotropic colloidal systems
Final Report Abstract
Many-body systems of interacting particles exhibit collective phenomena which is not present in the individual constituents. The origin of these emergent phenomena is the non-trivial interactions between the particles. Integrating over the degrees of freedom of all but one particle in a classical many-body system of interacting particles yields as a result an exact one-body force balance equation. For anisotropic particles, the force balance equation is complemented with an exact torque balance equation. The coupled force and torque balance equations are resolved in space and in time, and they determine together the structure and the dynamical evolution of the system at the one-body level in equilibrium and non-equilibrium situations. In this project we have investigated the non-trivial contributions to the one-body balance equations: the kinetic stress tensor, the internal force field, and the torque field. To investigate the effect of inertia in the dynamical evolution of the one-body fields, we have developed a custom flow method for particles following molecular dynamics. Custom flow allows us to prescribe the desired dynamical evolution of a system at the one-body level by numerically finding the generating external force field. Using custom flow we have designed compressional and shear flows in which we were able to unambiguously determined the contribution of the one-body acceleration field to the kinetic stress tensor and the one-body internal force field. We have for example demonstrated the occurrence of shear and bulk viscosities associated to spatial inhomogeneities of the acceleration field. For system with orientational degrees of freedom we have presented a power functional theory for Brownian active particles that accurately predicts the mobility induced phase separation. Based on the one-body torque balance equation we have developed a torque sampling method that constructs the orientational distribution function via an orientational integral of the torque acting on the particles. The method produces profiles of the orientational distribution function with better accuracy than those obtained with the traditional counting method. Torque sampling also makes it possible to sample the orientational distribution function with arbitrarily small angular resolution. Finally, we have started an alternative route to the study superadiabatic effects at the one-body level. Instead of developing analytical approximations to the generating power functional, we use a neural network to learn the kinematic mapping predicted in power functional theory from the density and the velocity profiles to the one-body internal force field. The network is trained with steady-state simulation data of many-body systems subject to randomized external forces. The trained network accurately represents the kinematic mapping and therefore the superadiabatic contributions to the dynamics of the one-body fields.
Publications
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Custom flow in molecular dynamics. Physical Review Research, 3(1).
Renner, Johannes; Schmidt, Matthias & de las Heras, Daniel
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Phase separation of active Brownian particles in two dimensions: anything for a quiet life. Molecular Physics, 119(15-16).
Hermann, Sophie; de las Heras, Daniel & Schmidt, Matthias
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Shear and Bulk Acceleration Viscosities in Simple Fluids. Physical Review Letters, 128(9).
Renner, Johannes; Schmidt, Matthias & Heras, Daniel de las
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Perspective: How to overcome dynamical density functional theory. Journal of Physics: Condensed Matter, 35(27), 271501.
de las Heras, Daniel; Zimmermann, Toni; Sammüller, Florian; Hermann, Sophie & Schmidt, Matthias
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Reduced-variance orientational distribution functions from torque sampling. Journal of Physics: Condensed Matter, 35(23), 235901.
Renner, Johannes; Schmidt, Matthias & de las Heras, Daniel
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From many-body systems to the one-body force and torque balance equations in and out of equilibrium. J. Renner. Dissertation, Universität Bayreuth
J. Renner
