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Active nematics on the surface of a toroid

Perry Ellis, Ya-Wen Chang, and Alberto Fernandez-Nieves

Why Ants?
Active matter is a special class of systems where energy is constantly added on the individual particle level. This sets an active system apart from traditional thermodynamic systems (such as gasses) where energy can only be added by heat exchange or work from the surroundings, both of which affect on the all of the particles at once. Examples are common in nature, such as swimming bacteria, herds of cattle, and most of your body; but there has also been recent work to create synthetic active systems, including rolling colloids, vibrated assymetrical disks, and Janus particles.

An important result of the specifics of the energy input is that active matter can never settle into an equilibrium state. Since much of what we know in thermodynamics relies on equilibrium, we are not very good at predicting the macroscopic behavior of a particular active matter from knowledge of its microscopics. Our work consists of observing ants in sistuations where we would understand thermodynamic behavior, and then comparing and contrasting the behavior of the ants with, say, an ideal gas. Ants themselves have been chosen because they operate on everyday time and lengthscales and are, of course, readily available to anyone living in Georgia!

Fig. 1: Free expansion of an ideal gas. It moves from an initial state to a final state by a path that is out of equilibrium

Video. 2: Free expansion ot ants. The video is played at 6000x speed

Free Expansion: When an ideal gas undergoes free expansion, it moves from an initial equilibrium state to a final equilibrium state. Both of these states can be characterized by equilibrium state variables, such as the temperature and entropy, but these variables will be different as a result of the expansion. However, on its way from the initial to final state, the gas is out of equilibrium and ruled by large fluctuations. This means the state variables can no longer be defined. In other words, the gas has no temperature. For a gas, this is rarely observed because the transition between states happens faster than every day timescales.

This is an interesting experiment to paralell with ants, because ants are always out of equilibrium! Despite this, we see that when ants are allowed to exapnd freely, they move from an initial steady state to a final steady state, much like a gas would. However this final steady state is nonuniform, suggesting that the ants be modeled with some kind of attractive potential.

Fig. 2: Reversible Expansion of an ideal gas. The expansion is controlled and the gas must do work against a piston.
The expansion happens slowly enought that the gas can be considered to remain in equilibrium

Video. 3: Ants expanding against the work of gravity. Video is played at 250x speed

Constrained Expansion: When an ideal gas undergoes reversible expansion, it performs work on its surroundings. For example, that goes may push against a piston. Moreover, because it is constrained, occurs slowly enough that the gas can be considered to remain in equilibrium through the duration of the process. This means that it state variables can be defined throughout the experiment. Even though the gas may cool down or lose pressure over the course of the expansion, nevertheless the temperature and pressure can still be measured.

This experiment is interesting to perform with ants for the opositte reason as free expansion. The ants are now placed in a situation where an ideal gas would remain in equilibrium. In the experiment shown in Video 3, the column is placed vertically to force the ants to expand against their own weight. They perform work against gravity as they complete their expansion. Suprisingly, we can see that the ants expand at a relatively constant rate which suggests some kind of oreder. We think this near constant rate of expansion is related to how quickly the ants unjam themselves from their initial state. Once again the ants seeam to reach a steady state, where the height remains over the course of hours. This suggests that there is some average natural amount of force exerted by each ant.

Soft Condensed Matter Laboratory, School of Physics, Georgia Institute of Technology
770 State Street NW, Atlanta, GA, 30332-0430, USA
Phone: 404-385-3667 Fax: 404-894-9958
alberto.fernandez [at] physics.gatech.edu