Pseudolaminar chaos from on-off intermittency

Müller-Bender, David; Valani, Rahil N.; Radons, Günter

doi:10.1103/physreve.107.014208

Cited by 4 publications

(2 citation statements)

References 85 publications

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“…Deterministic diffusive motion also arises in Lorenz-like dynamical systems 65 as well as in systems of delay differential equations. [66][67][68] Recently, deterministic diffusion was observed in simulations of walking droplet dynamics governed by an integrodifferential equation of motion. 16,17,[69][70][71][72]…”

Section: A An Alternate Viewpoint For Active Mattermentioning

confidence: 99%

“…Features of laminar chaos are robust, being preserved even when noise is added to the system. 68,111 Using systems that exhibit laminar chaos, to model our internal state-space, will allow us to construct attractordriven particles that preserve correlations even when disturbed by external noise. • In normal chaos, small changes in initial conditions lead to very different trajectories but the statistics normally remain the same.…”

Section: Articlementioning

confidence: 99%

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Attractor-driven matter

Valani

Paganin

2023

Chaos: An Interdisciplinary Journal of Nonlinear Science

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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 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.

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Section: A An Alternate Viewpoint For Active Mattermentioning

confidence: 99%

Section: Articlementioning

confidence: 99%

Attractor-driven matter

Valani

Paganin

2023

Chaos: An Interdisciplinary Journal of Nonlinear Science

Self Cite

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Dynamics, interference effects, and multistability in a Lorenz-like system of a classical wave–particle entity in a periodic potential

Perks

Valani

2023

Chaos: An Interdisciplinary Journal of Nonlinear Science

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A classical wave–particle entity (WPE) can be realized experimentally as a droplet walking on the free surface of a vertically vibrating liquid bath, with the droplet’s horizontal walking motion guided by its self-generated wave field. These self-propelled WPEs have been shown to exhibit analogs of several quantum and optical phenomena. Using an idealized theoretical model that takes the form of a Lorenz-like system, we theoretically and numerically explore the dynamics of such a one-dimensional WPE in a sinusoidal potential. We find steady states of the system that correspond to a stationary WPE as well as a rich array of unsteady motions, such as back-and-forth oscillating walkers, runaway oscillating walkers, and various types of irregular walkers. In the parameter space formed by the dimensionless parameters of the applied sinusoidal potential, we observe patterns of alternating unsteady behaviors suggesting interference effects. Additionally, in certain regions of the parameter space, we also identify multistability in the particle’s long-term behavior that depends on the initial conditions. We make analogies between the identified behaviors in the WPE system and Bragg’s reflection of light as well as electron motion in crystals.

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Infinite-memory classical wave-particle entities, attractor-driven active particles, and the diffusionless Lorenz equations

Valani

2024

Chaos: An Interdisciplinary Journal of Nonlinear Science

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A classical wave-particle entity (WPE) can materialize as a millimeter-sized droplet walking horizontally on the free surface of a vertically vibrating liquid bath. This WPE comprises a particle (droplet) that shapes its environment by locally exciting decaying standing waves, which, in turn, guides the particle motion. At high amplitude of bath vibrations, the particle-generated waves decay very slowly in time and the particle motion is influenced by the history of waves along its trajectory. In this high-memory regime, WPEs exhibit hydrodynamic quantum analogs where quantum-like statistics arise from underlying chaotic dynamics. Exploration of WPE dynamics in the very high-memory regime requires solving an integrodifferential equation of motion. By using an idealized one-dimensional WPE model where the particle generates sinusoidal waves, we show that in the limit of infinite memory, the system dynamics reduce to a 3D nonlinear system of ordinary differential equations (ODEs) known as the diffusionless Lorenz equations (DLEs). We use our algebraically simple ODE system to explore in detail, theoretically and numerically, the rich set of periodic and chaotic dynamical behaviors exhibited by the WPE in the parameter space. Specifically, we link the geometry and dynamics in the phase-space of the DLE system to the dynamical and statistical features of WPE motion, paving a way to understand hydrodynamic quantum analogs using phase-space attractors. Our system also provides an alternate interpretation of an attractor-driven particle, i.e., an active particle driven by internal state-space variables of the DLE system. Hence, our results might also provide new insights into modeling active particle locomotion.

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Pseudolaminar chaos from on-off intermittency

Cited by 4 publications

References 85 publications

Attractor-driven matter

Attractor-driven matter

Dynamics, interference effects, and multistability in a Lorenz-like system of a classical wave–particle entity in a periodic potential

Infinite-memory classical wave-particle entities, attractor-driven active particles, and the diffusionless Lorenz equations

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