Related papers: Rigidity and persistence for ensuring shape mainte…
Traditionally the effects of MHD instabilities and micro-instabilities on plasma confinement are investigated separately. However, these two instabilities often occur simultaneously, with the overlap of the dynamics on a broad range of…
Comparing with traditional fixed formation for a group of dynamical systems, time-varying formation can produce the following benefits: i) covering the greater part of complex environments; ii) collision avoidance. This paper studies the…
On a global level, ecological communities are being perturbed at an unprecedented rate by human activities and environmental instabilities. Yet, we understand little about what factors facilitate or impede long-term persistence of these…
We consider the question of defining interleaving metrics on generalized persistence modules over arbitrary preordered sets. Our constructions are functorial, which implies a form of stability for these metrics. We describe a large class of…
The present research is devoted to the problem of stability of the fluid flow moving in a channel with flexible walls and interacting with the walls, which are subject to traveling waves. Experimental data shows that the energy of the…
Evolving magnetic fields are frequently embedded in plasmas that are turbulent. When the primary interest is in effects that are on a large scale compared to that of the turbulence, it is desirable to average over the turbulence to obtain…
Combinatorial rigidity theory seeks to describe the rigidity or flexibility of bar-joint frameworks in R^d in terms of the structure of the underlying graph G. The goal of this article is to broaden the foundations of combinatorial rigidity…
This paper presents a novel planning method that achieves navigation of multi-robot formations in cluttered environments, while maintaining the formation throughout the robots motion. The method utilises a decentralised approach to find…
Phase separation in passive systems leads to uncontrolled droplet growth, limiting structural control in soft materials and cells. We identify a generic mechanism to arrest coarsening based on chemical interconversion between molecular…
Magnetic reconnection, a fundamental plasma process, is pivotal in understanding energy conversion and particle acceleration in astrophysical systems. While extensively studied in two-dimensional (2D) configurations, the dynamics of…
In this paper, we present a machine learning approach to move a group of robots in a formation. We model the problem as a multi-agent reinforcement learning problem. Our aim is to design a control policy for maintaining a desired formation…
This work investigates experimentally and numerically the dynamics of rigid particles settling under gravity in a highly viscous fluid. We demonstrate that certain shapes: cones, crescent moons, arrowheads, and open flat rings reorient and…
The complexity of condensed matter arises from emergent behaviors that cannot be understood by analyzing individual constituents in isolation. While traditional condensed-matter approaches-developed primarily for ideal crystalline…
A ring is rigid if there is no nonzero locally nilpotent derivation on it. In terms of algebraic geometry, a rigid coordinate ring corresponds to an algebraic affine variety which does not allow any nontrivial algebraic additive group…
Nonlinear waves are a robust phenomenon observed in complex systems ranging from mechanics to ecology. Fronts are fundamental due to their robustness against perturbations and capacity to propagate one state over another. Controlling and…
This letter presents two bearing-constrained formation tracking control protocols for multiple nonholonomic agents based respectively on the bearing vectors and displacements between the agents. The desired formation pattern of the system…
The multi-agent system has been a hot topic in the past few decades owing to its lower cost, higher robustness, and higher flexibility. As a particular multi-agent system, the multiple rigid body system received a growing interest for its…
We consider the rigidity and global rigidity of bar-joint frameworks in Euclidean $d$-space under additional dilation constraints in specified coordinate directions. In this setting we obtain a complete characterisation of generic rigidity.…
Magnetohydrodynamic (MHD) turbulence is a ubiquitous dynamical state of astrophysical plasmas and a primary agent in the redistribution, dissipation, and conversion of energy into particle populations. Yet turbulence is still most often…
This paper presents an alternative approach to the study of distance rigidity in networks of mobile agents, based on a subframework scheme. The advantage of the proposed strategy lies in expressing framework rigidity, which is inherently…