An equation of state for insect swarms

Collective behaviour in flocks, crowds, and swarms occurs throughout the biological world. Animal groups are generally assumed to be evolutionarily adapted to robustly achieve particular functions, so there is widespread interest in exploiting collective behaviour for bio-inspired engineering. However, this requires understanding the precise properties and function of groups, which remains a challenge. Here, we demonstrate that collective groups can be described in a thermodynamic framework. We define an appropriate set of state variables and extract an equation of state for laboratory midge swarms. We then drive swarms through “thermodynamic” cycles via external stimuli, and show that our equation of state holds throughout. Our findings demonstrate a new way of precisely quantifying the nature of collective groups and provide a cornerstone for potential future engineering design

Path lengths in turbulence

By tracking tracer particles at high speeds and for long times, we study the geometric statistics of Lagrangian trajectories in an intensely turbulent laboratory flow. In particular, we consider the distinction between the displacement of particles from their initial positions and the total distance they travel. The difference of these two quantities shows power-law scaling in the inertial range. By comparing them with simulations of a chaotic but non-turbulent flow and a Lagrangian Stochastic model, we suggest that our results are a signature of turbulence.Comment: accepted for publication in Journal of Statistical Physic

Mechanical spectroscopy of insect swarms

Social animals routinely form groups, which are thought to display emergent, collective behavior. This hypothesis suggests that animal groups should have properties at the group scale that are not directly linked to the individuals, much as bulk materials have properties distinct from those of their constituent atoms. Materials are often probed by measuring their response to controlled perturbations, but such experiments are difficult to conduct on animal groups, particularly in the wild. Here we show that laboratory midge swarms possess emergent continuum mechanical properties, displaying a collective viscoelastic response to applied oscillatory visual stimuli that allows us to extract storage and loss moduli for the swarm. We find that the swarms strongly damp perturbations, both viscously and inertially. Thus, unlike bird flocks, which appear to use collective behavior to promote lossless information flow through the group, our results suggest that midge swarms use it to stabilize themselves against environmental perturbations

Velocity correlations in laboratory insect swarms

In contrast to animal groups such as bird flocks or migratory herds that display net, directed motion, insect swarms do not possess global order. Without such order, it is difficult to define and characterize the transition to collective behavior in swarms; nevertheless, visual observation of swarms strongly suggests that swarming insects do behave collectively. It has recently been suggested that correlation rather than order is the hallmark of emergent collective behavior. Here, we report measurements of spatial velocity correlation functions in laboratory mating swarms of the non-biting midge Chironomus riparius. Although we find some correlation at short distances, our swarms are in general only weakly correlated, in contrast to what has been observed in field studies. Our results hint at the potentially important role of environmental conditions on collective behavior, and suggest that general indicators of the collective nature of swarming are still needed

Local linearity, coherent structures, and scale-to-scale coupling in turbulent flow

Turbulent and other nonlinear flows are highly complex and time dependent, but are not fully random. To capture this spatiotemporal coherence, we introduce the idea of a linear neighborhood, defined as a region in an arbitrary flow field where the velocity gradient varies slowly in space over a finite time. Thus, by definition, the flow in a linear neighborhood can be approximated arbitrarily well by only a subset of the fluid-element trajectories inside it. This slow spatiotemporal variation also allows short-time prediction of the flow. We demonstrate that these linear neighborhoods are computable in real data using experimental measurements from a quasi-two-dimensional turbulent flow and find support for our theoretical arguments. We also show that our kinematically defined linear neighborhoods have an additional dynamical significance, in that the scale-to-scale spectral energy flux that is a hallmark of turbulent flows behaves differently inside the neighborhoods. Our results add additional support to the conjecture that turbulent flows locally tend to transport energy and momentum in space or in scale but not both simultaneously.Lei Fang, Sanjeeva Balasuriya and Nicholas T. Ouellett

The role of pair dispersion in turbulent flow

Mixing and transport in turbulent flows—which have strong local concentration fluctuations—are essential in many natural and industrial systems including reactions in chemical mixers, combustion in engines and burners, droplet formation in warm clouds, and biological odor detection and chemotaxis. Local concentration fluctuations, in turn, are intimately tied to the problem of the separation of pairs of fluid elements. We have measured this separation rate in an intensely turbulent laboratory flow and have found, in quantitative agreement with the seminal predictions of Batchelor, that the initial separation of the pair plays an important role in the subsequent spreading of the fluid elements. These results have surprising consequences for the decay of concentration fluctuations and have applications to biological and chemical systems