# Body-attitude coordination in arbitrary dimension

@inproceedings{Degond2021BodyattitudeCI, title={Body-attitude coordination in arbitrary dimension}, author={Pierre Degond and Antoine Diez and Amic Frouvelle}, year={2021} }

We consider a system of self-propelled agents interacting through body attitude coordination in arbitrary dimension n ≥ 3. We derive the formal kinetic and hydrodynamic limits for this model. Previous literature was restricted to dimension n = 3 only and relied on parametrizations of the rotation group that are only valid in dimension 3. To extend the result to arbitrary dimensions n ≥ 3, we develop a different strategy based on Lie group representations and the Weyl integration formula. These…

## 3 Citations

### Topological states and continuum model for swarmalators without force reciprocity

- PhysicsAnalysis and Applications
- 2022

Swarmalators are systems of agents which are both self-propelled particles and oscillators. Each particle is endowed with a phase which modulates its interaction force with the other particles. In…

### Hyperbolicity and non-conservativity of a hydrodynamic model of swarming rigid bodies

- Mathematics
- 2022

In this paper, we study a nonlinear system of first order partial differential equations describing the macroscopic behavior of an ensemble of interacting self-propelled rigid bodies. Such system may…

### Radial Laplacian on rotation groups

- Mathematics
- 2023

The Laplacian on the rotation group is invariant by conjugation. Hence, it maps class functions to class functions. A maximal torus consists of block diagonal matrices whose blocks are planar…

## References

SHOWING 1-10 OF 69 REFERENCES

### Quaternions in Collective Dynamics

- PhysicsMultiscale Model. Simul.
- 2018

This work introduces a model of multiagent dynamics for self-organized motion; individuals travel at a constant speed while trying to adopt the averaged body attitude of their neighbors, based on nematic (rather than polar) alignment.

### Phase Transitions and Macroscopic Limits in a BGK Model of Body-Attitude Coordination

- MathematicsJ. Nonlinear Sci.
- 2020

This work shows that in the spatially homogeneous case, self-organisation may appear or not depending on the local density of agents involved, and deduces the complete description of the possible equilibria.

### A continuum model for alignment of self-propelled particles with anisotropy and density-dependent parameters

- Mathematics
- 2012

We consider the macroscopic model derived by Degond and Motsch from a time-continuous version of the Vicsek model, describing the interaction orientation in a large number of self-propelled…

### Asymptotic Fixed-Speed Reduced Dynamics for Kinetic Equations in Swarming

- Mathematics
- 2012

We perform an asymptotic analysis of general particle systems arising in collective behavior in the limit of large self-propulsion and friction forces. These asymptotics impose a fixed speed in the…

### Reduced fluid models for self-propelled particles interacting through alignment

- Physics
- 2017

The asymptotic analysis of kinetic models describing the behavior of particles interacting through alignment is performed. We will analyze the asymptotic regime corresponding to large alignment…

### Body-Attitude Alignment: First Order Phase Transition, Link with Rodlike Polymers Through Quaternions, and Stability

- PhysicsRecent Advances in Kinetic Equations and Applications
- 2021

We present a simple model of alignment of a large number of rigid bodies (modeled by rotation matrices) subject to internal rotational noise. The numerical simulations exhibit a phenomenon of first…

### Phase transition and diffusion among socially interacting self-propelled agents

- Mathematics
- 2012

We consider a hydrodynamic model of swarming behavior derived from the kinetic description of a particle system combining a noisy Cucker-Smale consensus force and self-propulsion. In the large…

### Alignment of Self-propelled Rigid Bodies: From Particle Systems to Macroscopic Equations

- Computer ScienceStochastic Dynamics Out of Equilibrium
- 2019

From the various microscopic models, the same macroscopic model is derived, which is a good indicator of its universality.

### Hydrodynamic equations for self-propelled particles: microscopic derivation and stability analysis

- Physics
- 2009

Considering a gas of self-propelled particles with binary interactions, we derive the hydrodynamic equations governing the density and velocity fields from the microscopic dynamics, in the framework…

### Hydrodynamic limits for kinetic flocking models of Cucker-Smale type.

- PhysicsMathematical biosciences and engineering : MBE
- 2019

It is shown that the set of generalized collision invariants, introduced in [1], is equivalent in this setting to the more classical notion of collision invariant, i.e., the kernel of a suitably linearized collision operator.