A growth model driven by curvature reproduces geometric features of arboreal termite nests

Abstract

We present a simple three-dimensional model to describe the autonomous expansion of a substrate whose growth is driven by the local mean curvature of its surface. The model aims to reproduce the nest construction process in arboreal Nasutitermes termites, whose cooperation may similarly be mediated by the shape of the structure they are walking on, for example focusing the building activity of termites where local mean curvature is high. We adopt a phase-field model where the nest is described by one continuous scalar field and its growth is governed by a single nonlinear equation with one adjustable parameter d . When d is large enough the equation is linearly unstable and fairly reproduces a growth process in which the initial walls expand, branch and merge, while progressively invading all the available space, which is consistent with the intricate structures of real nests. Interestingly, the linear problem associated with our growth equation is analogous to the buckling of a thin elastic plate under symmetric in-plane compression, which is also known to produce rich patterns through nonlinear and secondary instabilities. We validated our model by collecting nests of two species of arboreal Nasutitermes from the field and imaging their structure with a micro-computed tomography scanner. We found a strong resemblance between real and simulated nests, characterized by the emergence of a characteristic length scale and by the abundance of saddle-shaped surfaces with zero-mean curvature, which validates the choice of the driving mechanism of our growth model.

Substrate evaporation drives collective construction in termites

“…Note that, in the picture of depositions being attracted by evaporation flux, depositions observed at the edges of the clay disk, also agree with our previous growth model driven only by curvature (Facchini et al, 2020). In fact, the edge of the clay disk is almost flat (weak convexity)…”

Ariadne’s thread and the extension of cognition: A common but overlooked phenomenon in nature?

“…The construction of termite nests was demonstrated to be a complex, self-organised process, built upon a set of simple rules that each termite follows individually, which ultimately leads to the architectural complexity of the nest (Camazine et al, 2003;Facchini et al, 2020). Nevertheless, when building nests, termites are known for relying more on environmental cues than their own 10.3389/fevo.2022.1069349 Frontiers in Ecology and 10 frontiersin.org memory for making decisions (Fouquet et al, 2014).…”

Generative Design of Internal Cooling Channels for Gas Turbine Blades

“…In this study, a self-organized growth equation proposed by Facchini et al [17] was used to generate the inner structure of each cooling channel. The algorithm assumed the geometry was controlled by a phase filed f, in which f < 0.5 referred to solid while f ≥ 0.5 referred to fluid.…”

“…Mathematically, the 4th ordered diffusion equation could be decomposed into the convolution of a diffusion equation and an anti-diffusion equation, which meant that the growth was driven by diffusion and constrained by antidiffusion. Specially in this study, two control factor k1 and k2 was introduced to the original equation of [17], so as to increase the diversity of the equations. The factor k1 was an exponent of f to control the difficulty of growth, which had a range of [0.01 2].…”

“…This study introduced a unique bionic algorithm proposed by Facchini et al [17] to gas turbine airfoils internal cooling channels. The algorithm simulated the constructing process of termite nests.…”