Inverse problems and optimal design of asymmetrical spider orb webs

• Grant number: 23/08152-6
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: January 15, 2024
• End date: March 14, 2024
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Alexandre Kawano
• Grantee: Alexandre Kawano
• Visiting researcher: Antonino Morassi
• Visiting researcher institution: Università degli Studi di Udine, Italy
• Host Institution: Escola Politécnica (EP). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

The spider orb web is a complex biological-mechanical system that has attracted increasing interest in the scientific literature of the last decades. Its primary functions are for catching prey and sensory information, and the study of the mechanisms guiding the spider in prey capture and gathering information through web vibration has been - and actually is - one of the main objectives of the research in this field. Basic questions posed by the researchers mainly concern: (i) how spidersmight discriminate between the large set of web-borne vibrations and, particularly, between prey-produced signals and irrelevant vibrations such as those generated by wind; and (ii) how the spider adjusts the web mechanics to the environmental conditions where the web is built, such as, the pre-stress tensile forces to be assigned at specific locations of the web, in order to improve its ability to prey capture. In a series of recent works, also by the authors, some partial answers to these questions have been given, mainly through the development of a mechanical model of spider web described as a continuous membrane subjected to an appropriate pre-traction state. All results available in the literature, both for modeling and for the inverse problem of prey identification, have only been obtained for axially symmetrical webs. In this research, we abandon the axial symmetry hypothesis and we face with the case of vertical asymmetry, a situation found in almost all vertical orb webs. This important extension will raise non-trivial questions in the mechanical modelling and optimal design of pre-tractions. The study of the corresponding inverse problem of detecting and locating a prey from dynamic data also promises to be highly non-trivial and will require the development of new and original analytical tools. (AU)