Viewing Transformers as interacting particle systems, we describe the geometry of learned
representations when the weights are not time-dependent. We show that particles …

The book aims to present the recent developments in Rational Extended Thermodynamics
(RET) of gases in both classical and relativistic cases. The RET theory is a …

This paper addresses some preliminary steps toward the modeling and qualitative analysis
of swarms viewed as living complex systems. The approach is based on the methods of …

We present the complete predictability of clustering for the Cucker–Smale (C–S) model on
the line. Emergence of multi-cluster flocking is often observed in numerical simulations for …

We present a thermodynamically consistent particle (TCP) model motivated by the theory of
multi-temperature mixture of fluids in the case of spatially homogeneous processes. The …

1. Introduction. Collective behaviors of many-body systems are ubiquitous in the ensemble
of self-propelled particles, eg, flocking of birds, herding of sheep, and synchronicity of …

We study the flocking dynamics of a generalized Cucker--Smale (CS) model for
thermodynamic particles. The original CS model deals with flocking dynamics of mechanical …

This work focuses on the fixed-time bipartite flocking control problem for multi-agent
systems. By employing the structurally balanced signed graph theory and a fixed-time …

We study the communication time-delay effect on the emergent dynamics of thermodynamic
Cucker–Smale (TCS) ensemble with temperature as an internal state. In the presence of …

For the long-range-communicated Cucker-Smale (CS) model, asymptotic flocking can be
obtained by taking full use of a key equality about the kinetic energy. However, such …