Emergence of perversions in helical rods : from tendrils of plants to the interaction of topological defects
| When |
Nov 12, 2024
from 11:00 to 12:00 |
|---|---|
| Where | Amphi L |
| Attendees |
Émilien Dilly |
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Helical rods (elastic springs) provide a simple system that highlights complex non-linear phenomena related to topological defects, occurring right at our fingertips. The unwinding of helical rods leads to the presence of a perversion. This topological defect connects a helix of positive chirality to a helix of negative chirality, as seen in the tendrils of climbing plants such as cucumbers or vines. The perversion can be seen as a kink, a topological defects linking two different phases—namely, helices of opposite chiralities. This kink solution, situated near a Hamilton-Hopf bifurcation, can be analytically solved within the framework of Kirchhoff’s rod theory, in the asymptotic condition of low load. The emergence of this kink solution, along with its associated antikink, allows for the existence of stabilized kink-antikink pairs—that is, helical rods presenting two perversions. The interaction between the kink and antikink is studied experimentally, numerically, and analytically solved in the case of widely separated perversions. If the kink and antikink are brought closer together, they ultimately annihilate, radiating the energy stored in the kink and antikink. Finally, the interaction between perversions is shown to lead to stabilized solutions at discrete distances between the perversions. These results resonate with broader findings on kink-antikink systems with spatially oscillating tails, such as the emergence of spatially periodic structures : the godet solutions.