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Variational formulation for the dynamics of soft matter including inertia
Abstract
The motion of liquids and soft matter is over-damped and `slow' when viscosity dominates. In this (low Reynolds-number) limit and when the system is isothermal, the equations of motion may be generated via Onsager's variational principle, which neglects inertia. This variational approach is immensely powerful, being used to obtain equations of motion for colloidal fluids, droplets on surfaces and much more. However, inertia can play a role, manifesting as vibrations and under-damped motion. Here we show how to extend this variational framework so that it remains valid for when damping/dissipation and inertia are both equally important.
Versions
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BibTeX
@misc{archer2026variational,
title = {{Variational formulation for the dynamics of soft matter including inertia}},
author = {Andrew J Archer},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.18457},
eprint = {2607.18457},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.18457},
}
RIS
TY - UNPB
TI - Variational formulation for the dynamics of soft matter including inertia
AU - Andrew J Archer
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2607.18457
UR - https://arxiv.org/abs/2607.18457
AB - The motion of liquids and soft matter is over-damped and `slow' when viscosity dominates. In this (low Reynolds-number) limit and when the system is isothermal, the equations of motion may be generated via Onsager's variational principle, which neglects inertia. This variational approach is immensely powerful, being used to obtain equations of motion for colloidal fluids, droplets on surfaces and much more. However, inertia can play a role, manifesting as vibrations and under-damped motion. Here we show how to extend this variational framework so that it remains valid for when damping/dissipation and inertia are both equally important.
ER -