Interplay of unit-speed constraint and singular communication in the thermodynamic Cucker–Smale model

Abstract

We study collision avoidance resulting from unit-speed constraint and singular communication weight in a thermo-mechanical Cucker–Smale (TCS) flocking ensemble moving in a Euclidean space. The TCS model governs the flocking dynamics of the CS particles in the presence of a self-consistent temperature field. The issue of collision avoidance has been addressed in the realistic modeling of collective particle models, and it has been investigated in the CS and TCS models without unit-speed constraint. In this paper, we take one further step by examining how unit-speed constraint and singular communication weights can result in collision avoidance between particles. For this, we introduce a sufficient framework to ensure collision avoidance in terms of system parameters and initial data.