Geometric Mechanics of Active Particles
type: CreativeWork
description: Abstract Geometrical methods play an important role in classical dynamics, most notably in the dynamical preservation of symplecticity in Hamiltonian systems. In this way, dynamics derived from a Hamiltonian function admit energy-conserving integration schemes with an error that remains bounded in the infinite time limit. Furthermore, the existence of this scalar first integral greatly simplifies analysis of a system's dynamics. On the other hand, active systems imply power-injection at the microscale and thus dynamics that can not be encapsulated within the Hamiltonian formalism. It is therefore surprising that Hamiltonian functions should occured in a variety of active matter problems. Even more surprising is that these appearances often manifest in overdamped systems, where viscous damping forces dominate inertia driven effects. Abstract Starting at the equations of motion for active systems, where constituent active particles provide energy input at the microscopic level, the emergence of symplectic structure is investigated. In the presence of overdamped forces and torques, inertial forces are negligible and time-evolution become purely kinematical in nature. This dissipative structure precludes the existence of a dynamical Hamiltonian and there is therefore no a priori reason for the existence of a conserved symplectic form. Yet in many active systems, pairs of kinematic variables may be identified as conjugate to one another, and thus a kinematically symplectic structure may be conserved throughout time-evolution. Particular examples of kinematic symplecticity include both two- and infinite-body sedimenting active systems. Here, the constituent active particles break microscopic rotational symmetry through a preferred axis of translation due to their internal activity manifesting as self-propulsion in a dissipative environment while sedimenting through a viscous medium under the influence of an external gravitational force. This produces hydrodynamically medi…
abstract: Abstract Geometrical methods play an important role in classical dynamics, most notably in the dynamical preservation of symplecticity in Hamiltonian systems. In this way, dynamics derived from a Hamiltonian function admit energy-conserving integration schemes with an error that remains bounded in the infinite time limit. Furthermore, the existence of this scalar first integral greatly simplifies analysis of a system's dynamics. On the other hand, active systems imply power-injection at the microscale and thus dynamics that can not be encapsulated within the Hamiltonian formalism. It is therefore surprising that Hamiltonian functions should occured in a variety of active matter problems. Even more surprising is that these appearances often manifest in overdamped systems, where viscous damping forces dominate inertia driven effects. Abstract Starting at the equations of motion for active systems, where constituent active particles provide energy input at the microscopic level, the emergence of symplectic structure is investigated. In the presence of overdamped forces and torques, inertial forces are negligible and time-evolution become purely kinematical in nature. This dissipative structure precludes the existence of a dynamical Hamiltonian and there is therefore no a priori reason for the existence of a conserved symplectic form. Yet in many active systems, pairs of kinematic variables may be identified as conjugate to one another, and thus a kinematically symplectic structure may be conserved throughout time-evolution. Particular examples of kinematic symplecticity include both two- and infinite-body sedimenting active systems. Here, the constituent active particles break microscopic rotational symmetry through a preferred axis of translation due to their internal activity manifesting as self-propulsion in a dissipative environment while sedimenting through a viscous medium under the influence of an external gravitational force. This produces hydrodynamically medi…
author: Bolitho, Austen
language: eng
keywords: Active Matter, Classical Mechanics, Symplectic Dynamics, Volvox, Viscous Fluids
license: https://www.rioxx.net/licenses/all-rights-reserved/
date published: 2021-09-30
date modified: 2026-07-22T22:24:06Z
provider: Cambridge University
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: University of Cambridge

PropertyValue
property ID: DOI
value: 10.17863/CAM.83455