Recent results on prey detection in a spider orb web

In this paper, we present a review of some results concerning the inverse problem of detecting a prey in a spider orb web. First, an overview of the discrete and numerical models in the literature is provided to understand the mechanics of the orb web and a descriiption of their structural features is presented. Then, a continuous model was introduced in which the orb web was described as a membrane with a specific fibrous structure and subject to tensile prestress in the referential configuration. The prey's impact was modeled as a pressure field acting on the orb web with magnitude of the form $ g(t)f(x) $, where $ g(t) $ is a known function of the time and $ f(x) $ is the unknown spatial term that depends on the position variable $ x $. Next, for axially symmetric orb webs supported at the boundary and undergoing infinitesimal deformations, a uniqueness results for $ f(x) $ was proven in terms of dynamic displacement measurements taken on an arbitrarily small and thin ring centered at the origin of the web, for a sufficiently large interval of time. A reconstruction algorithm suggested by the uniqueness result was implemented for $ f(x) $, and how the results of identification are affected by the key geometric and mechanical parameters were studied. The results, obtained on a realistic family of orb webs, revealed that the dynamic signals propagating through the web immediately after impact contained enough information for the spider to capture the prey. In the final part of the paper, we discuss an alternative method for prey localization and include some extension to account for different boundary conditions. A short list of open problems is proposed in the conclusions section. This paper is dedicated to Professor Emilio Turco for his 60th Birthday.