Attractor-driven matter
arXiv:2110.03776 · doi:10.1063/5.0107401
Abstract
The state of a classical point-particle system may often be specified by giving the position and momentum for each constituent particle. For non-pointlike particles, the center-of-mass position may be augmented by an additional coordinate that specifies the internal state of each particle. The internal state space is typically topologically simple, in the sense that the particle's internal coordinate belongs to a suitable symmetry group. In this paper we explore the idea of giving internal complexity to the particles, by attributing to each particle an internal state space that is represented by a point on a strange (or otherwise) attracting set. It is of course very well known that strange attractors arise in a variety of nonlinear dynamical systems. However, rather than considering strange attractors as emerging from complex dynamics, we may employ strange attractors to {\em drive} such dynamics. In particular, by using an attractor (strange or otherwise) to model each particle's internal state space, we present a class of matter coined ``attractor-driven matter''. We outline the general formalism for attractor-driven matter and explore several specific examples, some of which are reminiscent of active matter. Beyond the examples studied in this paper, our formalism for attractor-driven dynamics may be applicable more broadly, to model complex dynamical and emergent behaviors in a variety of contexts.
arXiv comment25 pages, 17 figures
References in corpus (37)
- Novel type of phase transition in a system of self-driven particles
- Collective motion
- Self-motile colloidal particles: from directed propulsion to random walk
- Motility-Induced Phase Separation
- Active Brownian Particles. From Individual to Collective Stochastic Dynamics
- Inertial effects of self-propelled particles: from active Brownian to active Langevin motion
- Steady state, relaxation and first-passage properties of a run-and-tumble particle in one-dimension
- Run-and-tumble particle in one-dimensional confining potential: Steady state, relaxation and first passage properties
- Run-and-tumble in a crowded environment: persistent exclusion process for swimmers
- First-passage time of run-and-tumble particles
- Alternating steady state in one-dimensional flocking
- Run-and-tumble particles in two-dimensions : Marginal position distributions
- Emergence of bimodal motility in active droplets
- Confined run-and-tumble swimmers in one dimension
- Generalised `Arcsine' laws for run-and-tumble particle in one dimension
- The convex hull of the run-and-tumble particle in a plane
- Superwalking droplets
- Analysis of a new chaotic system, electronic realization and use in navigation of differential drive mobile robot
- Deterministic Brownian Motion: The Effects of Perturbing a Dynamical System by a Chaotic Semi-Dynamical System
- Universal scaling in active single-file dynamics
- Laminar Chaos
- Multi-stable free states of an active particle from a coherent memory dynamics
- Coarsening and clustering in run-and-tumble dynamics with short-range exclusion
- Hard core run and tumble particles on a one dimensional lattice
- Unsteady dynamics of a classical particle-wave entity
- Tunable bimodal explorations of space from memory-driven deterministic dynamics
- Run-and-Tumble particle in inhomogeneous media in one dimension
- Deterministic Brownian motion generated from differential delay equations
- Lorenz-like systems emerging from an integro-differential trajectory equation of a one-dimensional wave-particle entity
- Ultra-chaos: an insurmountable objective obstacle of reproducibility and replicability
- Chaotic Diffusion in Delay Systems: Giant Enhancement by Time Lag Modulation
- Emergence of superwalking droplets
- Laminar Chaos in experiments and nonlinear delayed Langevin equations: A time series analysis toolbox for the detection of Laminar Chaos
- Anomalous transport of a classical wave-particle entity in a tilted potential
- Pseudo-laminar chaos from on-off intermittency
- Lorenz deterministic diffusion
- A 3D Strange Attractor with a Distinctive Silhouette. The Butterfly Effect Revisited