Honey Bees Don't Fail in Geometry While Making a Honeycomb

While Honey Bees Are Forming the Honeycomb, Geometry Doesn't Fall Out of the Classroom
Honey Bees Do Not Fall Out Of Geometry While They Are Forming The Comb - Honey bees are starting to work on producing honeycombs under geometric constraints. Credit: Golnar Gharooni Fard

To find out, the scientists collected imaging data from 10 hives that had deliberate flaws in their honeycombs, which the bees had built on hexagonal frames.
The honeycomb made of beeswax built by countless bees is very important to the existence of a colony. In addition, because beeswax is so expensive, they need to reduce the ratio of beeswax to storage in the honeycomb – bees must consume about four kilos of honey to excrete less than half a kilo of beeswax. The natural tessellation of the hexagons of a honeycomb reduces the length of the border per unit of storage capacity. However, when bees build their nests in already existing tree holes, they have to mix cells of various sizes and shapes due to geometric limitations, resulting in irregular hexagons and topological defects in the honeycomb.

The mechanisms governing the formation of honeycombs with geometric constraints are still unknown.

Golnar Gharooni Fard, a doctoral student at the University of Colorado Boulder, studied how bees adapt to this natural environment, under the supervision of biophysicist Orit Peleg and aerospace engineer Francisco López Jiménez.

Gharooni Fard used three-dimensional printing to create experimental frameworks that precisely control the geometric sources of frustration applied on the hexagonal lattice (tilt angle (A) and offsets (L and h) in the horizontal and vertical axes), as shown in the first figure below. This was done to mimic geometric constraints. It has added constraints only to clearly defined spaced elements of the framework.

Cage Frustration
Cage Frustration

This frame geometry prevented the bees from simply expanding the hexagonal foundations to fill the voids.

After a series of experiments on 10 hives, the researchers measured the bees' strategies for overcoming mismatches in their cage planes. Gharooni Fard and colleagues used computer vision techniques to identify individual honeycomb cells, after taking pictures of the fully constructed frames. With these images, they reconstructed the comb structure, revealing the irregularity of the cell shapes built within the cavity, as shown in the figure below. Inspired by the similarities between grain boundaries in reconstructed combs and those in graphene, the researchers developed a crystallography-based algorithm to place cell centers in the lattice at locations that minimize some variation of the Lennard-Jones potential.

The researchers created a crystallography-based approach to locate cell centers at points within the lattice that minimized a given Lennard-Jones potential. This algorithm was developed based on the similarities between grain boundaries in reconstructed combs and grain boundaries in graphene.

The results of the researchers' experiments and the model's predictions showed a quantitative agreement. For example, topological defects (cells with more or less than six neighbors) are due to a set of geometric constraints, and the researchers found a significant correlation between the density of defects and the angle of inclination of the two hexagonal lattices. Unsurprisingly, errors were rare when there was no slope between the cages, and the bees regularly built regular hexagons to connect them.

Consistency between experiments and simulations has also demonstrated the value of using crystallographic tools to understand honeycomb spherical structures resulting from local interaction between cells and their environment.

Source: physicstoday.scitation.org/do/10.1063/PT.6.1.20221201a/

Günceleme: 02/12/2022 21:57

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