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

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dc.contributor.authorValani, R.N.
dc.date.issued2024
dc.descriptionPublished Online: 22 January 2024
dc.description.abstractA 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.
dc.description.statementofresponsibilityR. N. Valani
dc.identifier.citationChaos, 2024; 34(1):013133-1-013133-17
dc.identifier.doi10.1063/5.0171007
dc.identifier.issn1054-1500
dc.identifier.issn1089-7682
dc.identifier.orcidValani, R.N. [0000-0001-8346-0739]
dc.identifier.urihttps://hdl.handle.net/2440/142091
dc.language.isoen
dc.publisherAmerican Institute of Physics
dc.relation.granthttp://purl.org/au-research/grants/arc/DP200100834
dc.rights© 2024 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
dc.source.urihttp://dx.doi.org/10.1063/5.0171007
dc.titleInfinite-memory classical wave-particle entities, attractor-driven active particles, and the diffusionless Lorenz equations
dc.typeJournal article
pubs.publication-statusPublished

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