2, University of Colorado Boulder, Boulder, Colorado, United States
3, Georgia Institute of Technology, Atlanta, Georgia, United States
Active networks are omnipresent in nature, ranging from the molecular level (with polymeric networks powered by molecular motors), micron scale (with cell and microbial colonies) and macroscopic level (with swarms of insects and larvae). Owing to their transient bond dynamics and intrinsic energy input, these networks display a rich class of behaviors, including elasticity, viscous flow, self-healing and growth. Although classical theories in rheology and mechanics have enabled us to characterize these materials, there is still a gap in our understanding on how the individual properties, i.e. the mechanics of the building blocks and their interconnections, affect the emerging response of the network.
In this presentation, we will discuss an alternative way to think about these networks from a statistical point of view. More specifically, a network will be seen as a collection of individual building blocks connected by elastic chains that can associate and dissociate over time. From the knowledge of these individual chains (elasticity, transient attachment, and detachment events), we will construct a statistical description of the population and derive an evolution equation of their distribution based on applied deformation and their local interactions. Upon appropriate averaging operations, we will then show that these distributions can be used to determine important macroscopic measures such as stress, energy storage, and dissipation in the network.
Using this approach, we will then discuss the mechanics of fire-ant aggregations, whose swarming behavior has shown impressive dynamics that culminates with the aggregation’s capacity to self-heal and adapt to the environment. In this context, we will show how the physical characteristics and behavior of single ants lead to the elasticity, rheological properties, and activity of the aggregation. Numerical simulations of the aggregation’s response in diverse situations will be presented and compared to experimental observations and measurements.