Simulation of detection and scattering of sound waves by the lateral line of a fish

TL;DR

This paper presents an exactly solvable mathematical model for how fish detect sound and how sound waves scatter around their lateral line, using advanced operator theory to understand these biological sensing mechanisms.

Contribution

It introduces a novel, explicit mathematical model based on self-adjoint perturbations of the Laplace operator for sound detection and scattering by the lateral line.

Findings

Model provides exact solutions for sound detection scenarios.

Offers insights into the scattering behavior of sound waves near the lateral line.

Enhances understanding of biological sound sensing mechanisms.

Abstract

An explicitly solvable model of sound sources detection and sound wave scattering by the lateral line of a fish or amphibian based on the theory of self-adjoint perturbations of the Laplace operator by arrays of additional boundary conditions at isolated points is proposed and discussed.