ORCID Profile
0000-0001-8346-0739
Current Organisation
University of Adelaide
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Publisher: AIP Publishing
Date: 09-2018
DOI: 10.1063/1.5032114
Abstract: We present a numerical study of two-droplet pair correlations for in-phase droplets walking on a vibrating bath. Two such walkers are launched toward a common point of intersection. As they approach, their carrier waves may overlap and the droplets have a non-zero probability of forming a two-droplet bound state. The likelihood of such pairing is quantified by measuring the probability of finding the droplets in a bound state at late times. Three generic types of two-droplet correlations are observed: promenading, orbiting, and chasing pair of walkers. For certain parameters, the droplets may become correlated for certain initial path differences and remain uncorrelated for others, while in other cases, the droplets may never produce droplet pairs. These observations pave the way for further studies of strongly correlated many-droplet behaviors in the hydrodynamical quantum analogs of bouncing and walking droplets.
Publisher: American Physical Society (APS)
Date: 08-07-2021
Publisher: AIP Publishing
Date: 09-2018
DOI: 10.1063/1.5032128
Abstract: A droplet bouncing on the surface of a vibrating liquid bath can move horizontally guided by the wave it produces on impacting the bath. The wave itself is modified by the environment, and thus, the interactions of the moving droplet with the surroundings are mediated through the wave. This forms an ex le of a pilot-wave system. Taking the Oza–Rosales–Bush description for walking droplets as a theoretical pilot-wave model, we investigate the dynamics of two interacting identical, in-phase bouncing droplets theoretically and numerically. A remarkably rich range of behaviors is encountered as a function of the two system parameters, the ratio of inertia to drag, κ, and the ratio of wave forcing to drag, β. The droplets typically travel together in a tightly bound pair, although they unbind when the wave forcing is large and inertia is small or inertia is moderately large and wave forcing is moderately small. Bound pairs can exhibit a range of trajectories depending on parameter values, including straight lines, sub-diffusive random walks, and closed loops. The droplets themselves may maintain their relative positions, oscillate toward and away from one another, or interchange positions regularly or chaotically as they travel. We explore these regimes and others and the bifurcations between them through analytic and numerical linear stability analyses and through fully nonlinear numerical simulation.
Publisher: American Physical Society (APS)
Date: 05-01-2022
Publisher: AIP Publishing
Date: 02-2023
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 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 ex les, some of which are reminiscent of active matter. Beyond the ex les 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.
Publisher: AIP Publishing
Date: 03-2023
DOI: 10.1063/5.0125727
Abstract: 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.
Publisher: Cambridge University Press (CUP)
Date: 09-11-2021
DOI: 10.1017/JFM.2020.742
Publisher: AIP Publishing
Date: 2023
DOI: 10.1063/5.0132151
Abstract: Particles suspended in fluid flow through a closed duct can focus to specific stable locations in the duct cross section due to hydrodynamic forces arising from the inertia of the disturbed fluid. Such particle focusing is exploited in biomedical and industrial technologies to separate particles by size. In curved ducts, the particle focusing is a result of balance between two dominant forces on the particle: (i) inertial lift arising from small inertia of the fluid and (ii) drag arising from cross-sectional vortices induced by the centrifugal force on the fluid. Bifurcations of particle equilibria take place as the bend radius of the curved duct varies. By using the mathematical model of Harding et al. [J. Fluid Mech. 875, 1–43 (2019)], we illustrate via numerical simulations that these bifurcations can be leveraged in a spiral duct to achieve a large separation between different sized neutrally buoyant particles and identify a separation mechanism, not previously reported, which exploits the transient focusing of smaller particles near saddle points. We demonstrate this for similar sized particles, as well as particles that have a large difference in size, using spiral ducts with a square cross section. The novel formalism of using bifurcations to manipulate particle focusing can be applied more broadly to different geometries in inertial microfluidics, which may open new avenues in particle separation techniques.
Publisher: Cassyni
Date: 05-01-2023
Publisher: American Physical Society (APS)
Date: 12-07-2019
Publisher: AIP Publishing
Date: 02-2022
DOI: 10.1063/5.0076162
Abstract: Vertically vibrating a liquid bath can give rise to a self-propelled wave–particle entity on its free surface. The horizontal walking dynamics of this wave–particle entity can be described adequately by an integro-differential trajectory equation. By transforming this integro-differential equation of motion for a one-dimensional wave–particle entity into a system of ordinary differential equations (ODEs), we show the emergence of Lorenz-like dynamical systems for various spatial wave forms of the entity. Specifically, we present and give ex les of Lorenz-like dynamical systems that emerge when the wave form gradient is (i) a solution of a linear homogeneous constant coefficient ODE, (ii) a polynomial, and (iii) a periodic function. Understanding the dynamics of the wave–particle entity in terms of Lorenz-like systems may prove to be useful in rationalizing emergent statistical behavior from underlying chaotic dynamics in hydrodynamic quantum analogs of walking droplets. Moreover, the results presented here provide an alternative physical interpretation of various Lorenz-like dynamical systems in terms of the walking dynamics of a wave–particle entity.
Publisher: American Physical Society (APS)
Date: 13-01-2023
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 02-12-2022
DOI: 10.1137/21M1451919
Publisher: American Physical Society (APS)
Date: 12-04-2021
Publisher: IOP Publishing
Date: 15-05-2018
No related grants have been discovered for Rahil Valani.