# LETTER TO THE EDITOR: Alternating steady state in one-dimensional flocking

@article{OLoan1998LETTERTT, title={LETTER TO THE EDITOR: Alternating steady state in one-dimensional flocking}, author={O. J. O'Loan and Martin R. Evans}, journal={Journal of Physics A}, year={1998}, volume={32} }

We study flocking in one dimension, introducing a lattice model in which particles can move either left or right. We find that the model exhibits a continuous non-equilibrium phase transition from a condensed phase, in which a single `flock' contains a finite fraction of the particles, to a homogeneous phase; we study the transition using numerical finite-size scaling. Surprisingly, in the condensed phase the steady state is alternating, with the mean direction of motion of particles reversing…

## 27 Citations

### Phase separation and emergence of collective motion in a one-dimensional system of active particles.

- PhysicsThe Journal of chemical physics
- 2019

It is proved the existence of two fundamentally different types of active phase separation, which are referred to as neutral phase separation (NPS) and polar phase separation and indicate that NPS is subdivided in two classes with distinct critical exponents.

### Cohesive motion in one-dimensional flocking

- Physics
- 2011

A one-dimensional rule-based model for flocking, which combines velocity alignment and long-range centering interactions, is presented and studied. The induced cohesion in the collective motion of…

### Factorised steady states and condensation transitions in nonequilibrium systems

- Physics
- 2005

Systems driven out of equilibrium can often exhibit behaviour not seen in systems in thermal equilibrium —for example phase transitions in one-dimensional systems. In this talk I will review a simple…

### Minimal stochastic field equations for one-dimensional flocking

- PhysicsPhysical Review E
- 2018

We consider the collective behaviour of active particles that locally align with their neighbours. Agent-based simulation models have previously shown that in one dimension, these particles can form…

### Symmetry breaking and ordering in driven diffusive systems

- Physics
- 2003

Driven diffusive systems provide a simple framework which captures some of the complex collective phenomena shown by non-equilibrium systems. Even in one dimension, they exhibit phase transitions,…

### Collective steady-state patterns of swarmalators with finite-cutoff interaction distance.

- PhysicsChaos
- 2021

We study the steady-state patterns of population of the coupled oscillators that sync and swarm, where the interaction distances among the oscillators have a finite-cutoff in the interaction…

### Mean field model for collective motion bistability

- PhysicsDiscrete & Continuous Dynamical Systems - B
- 2019

We consider the Czir\'ok model for collective motion of locusts along a one-dimensional torus. In the model, each agent's velocity locally interacts with other agents' velocities in the system, and…

### Asymmetric Random Average Processes

- Physics
- 2002

In the present work the asymmetric random average process (ARAP) is considered. This nonequilibrium model is defined on a one-dimensional periodic lattice and equipped with a stochastic nearest…

## References

SHOWING 1-10 OF 13 REFERENCES

### Spontaneously ordered motion of self-propelled particles

- Physics
- 1997

We study a biologically inspired, inherently non-equilibrium model consisting of self-propelled particles. In the model, particles move on a plane with a velocity of constant magnitude; they locally…

### Novel type of phase transition in a system of self-driven particles.

- Materials SciencePhysical review letters
- 1995

Numerical evidence is presented that this model results in a kinetic phase transition from no transport to finite net transport through spontaneous symmetry breaking of the rotational symmetry.

### Flocks, herds, and schools: A quantitative theory of flocking

- Physics
- 1998

We present a quantitative continuum theory of ``flocking'': the collective coherent motion of large numbers of self-propelled organisms. In agreement with everyday experience, our model predicts the…

### Mean-Field Analysis of a Dynamical Phase Transition in a Cellular Automaton Model for Collective Motion

- Physics
- 1997

When in the course of evolutionary events it became possible for cells to actively crawl and move towards more favorable habitats, this led to an acceleration of evolutionary change. Another…

### Collective motion in a system of motile elements.

- Physics, Computer SciencePhysical review letters
- 1996

A mathematical model of cluster motion seen in nature, including collective rotation, chaos, wandering, occur in computer simulations of this deterministic model by introducing a set dimensionless parameters.

### Self-Organized Collective Displacements of Self-Driven Individuals.

- PsychologyPhysical review letters
- 1996

An archetype model for the collective displacements of self-driven individuals, aimed to describe dynamic of flocking behavior among living things, is presented and studied and shows that systems rule the model self-organize into a critical state exhibiting power-law behavior in both the distribution population avalanches and the spatial correlation between individuals.

### Phys. Rev. Lett

- Phys. Rev. Lett
- 1996

### Phys. Rev. Lett

- Phys. Rev. Lett
- 1996

### J. Phys. A: Math. Gen

- J. Phys. A: Math. Gen
- 1997

### Phys. Rev. Lett

- Phys. Rev. Lett
- 1997