Related papers: Rigidity and persistence for ensuring shape mainte…

Matrix stiffness expressions are derived for the particle movements in an assembly of rigid granules having compliant contacts. The derivations include stiffness terms that arise from the particle shapes at their contacts. These geometric…

In formation control, an ensemble of autonomous agents is required to stabilize at a given configuration in the plane, doing so while agents are allowed to observe only a subset of the ensemble. As such, formation control provides a rich…

This work considers the distance constrained formation control problem with an additional constraint requiring that the formation exhibits a specified spatial symmetry. We employ recent results from the theory of symmetry-forced rigidity to…

This paper examines stability properties of distance-based formation control when the underlying topology consists of a rigid graph and a flex node addition. It is shown that the desired equilibrium set is locally asymptotically stable but…

This paper introduces new structures called conic frameworks and their rigidity. They are composed by agents and a set of directed constraints between pairs of agents. When the structure cannot be flexed while preserving the constraints, it…

We study diffusion-driven pattern-formation in networks of networks, a class of multilayer systems, where different layers have the same topology, but different internal dynamics. Agents are assumed to disperse within a layer by undergoing…

Generally, the normal displacement-based formation control has a sensing mode that requires the agent not only to have certain knowledge of its direction, but also to gather its local information characterized by nonnegative coupling…

This paper considers a formation shape control problem for point agents in a two-dimensional ambient space, where the control is distributed, is based on achieving desired distances between nominated agent pairs, and avoids the possibility…

We introduce a simple network formation model for social networks. Agents are nodes, connecting to another agent by building a directed edge (or accepting a connection from another agent) has a cost, and reaching (or being reached by) other…

A generic feature of bounded confidence type models is the formation of clusters of agents. We propose and study a variant of bounded confidence dynamics with the goal of inducing unconditional convergence to a consensus. The defining…

Persistent homology is a topological data analysis tool that has been widely generalized, extending its scope beyond the field of topology. Among its extensions, steady and ranging persistence were developed to study a wide variety of graph…

Persistent currents and magnetization are considered for a two-dimensional electron (or gas of electrons) coupled to various magnetic fields. Thermodynamic formulae for the magnetization and the persistent current are established and the…

This work focuses on the bearing rigidity theory, namely the branch of knowledge investigating the structural properties necessary for multi-element systems to preserve the inter-units bearings when exposed to deformations. The original…

Motivated by data on coauthorships in scientific publications, we analyze a team formation process that generalizes matching models and network formation models, allowing for overlapping teams of heterogeneous size. We apply different…

In structural rigidity, one studies frameworks of bars and joints in Euclidean space. Such a framework is an articulated structure consisting of rigid bars, joined together at joints around which the bars may rotate. In this paper, we will…

A rigidity theory is developed for bar-joint frameworks in $\mathbb{R}^{d+1}$ whose vertices are constrained to lie on concentric $d$-spheres with independently variable radii. In particular, combinatorial characterisations are established…

We study Tao's finitary viewpoint of convergence in metric spaces, as captured by the notion of metastability. We adopt the perspective of continuous model theory. We show that, in essence, metastable convergence with a given rate is the…

Group behavior has received much attention as a test case of self-organization. There has been much written in recent years to investigate interactions within groups of agents. These agents can be animals moving in an interactive way, such…

This work introduces a distributed formation control strategy for multi-agent systems based solely on rotation symmetry constraints. We propose a potential function that enforces inter-agent \textbf{rotational} symmetries, whose gradient…

Magnetic particles underpin a broad range of technologies, from water purification and mineral processing to bioseparations and targeted drug delivery. The dynamics of magnetic particles in high-gradient magnetic fields-encompassing both…