### Inertial particle focusing in curved microchannels

Particles suspended in a fluid flow through a curved duct can focus to equilibrium locations within the duct cross-section. This particle focusing is a result of a balance between two dominant forces acting on the particle: (i) the inertial lift force arising from small but non-negligible inertia of the fluid, and (ii) the secondary drag force due to the cross-sectional vortices induced by the curvature of the duct. Such particle focusing is exploited in various medical and industrial technologies aimed at separating particles by size. We are investigating the bifurcations in these particle equilibria and particle dynamics as the system parameters are varied. Understanding of particle dynamics and their equilibria will assist in the design of inertial microfluidic devices that can separate particles efficiently.

**R. N. Valani**, B. Harding and Y. M. Stokes, Utilizing bifurcations to separate particles in spiral inertial microfluidics,*Physics of Fluids*,**35**, 011703 (2023)**arXiv****R. N. Valani**, B. Harding and Y. M. Stokes, Bifurcations and dynamics in inertial focusing of particles in curved rectangular ducts*, SIADS*, 21, 2371-2392 (2022)**arXiv****R. N. Valani**, B. Harding and Y. M. Stokes, Bifurcations in inertial focusing of a particle suspended in flow through curved rectangular ducts (under review)**arXiv**

### Attractor-driven matter

Murmurations of birds, schooling of fish, insect swarms, bacterial suspensions, human crowd and swarming of robots/drones are all examples of complex and dynamical collective behaviours that result from complex interactions among individuals. We have explored a collection of particles, coined attractor-driven matter, where we model each particle’s internal complexity by attributing to it an internal state space that is represented by a point on an attracting set of a chaotic dynamical system. We illustrate the rich dynamical and emergent behaviors that can arise from such particles. The formalism provides a flexible means to generate complex dynamical and collective behaviors that may be broadly applied in various contexts.

and D. M. Paganin**R. N. Valani****,**Attractor-driven matter,*Chaos*, 33, 023125 (2023)

### Superwalking droplets

Vertically vibrating a bath of silicone oil can give rise to walking droplets on the free surface of the liquid. These walking droplets have been shown to mimic several features from the quantum regime. By vibrating the bath at two frequencies, a new class of walking droplets emerge, coined *superwalkers*. Two-frequency driven superwalkers are typically bigger and faster than single-frequency driven walkers and interactions of many superwalkers give rise to novel multidroplet behaviors. Moreover, slight detuning of two driving frequencies can give rise to intermittent locomotion of superwalkers called *stop-and-go motion*.

**R. N. Valani**, A.C. Slim and T. Simula, Stop-and-go locomotion of superwalking droplets,*Physical Review E*, 103, 043102 (2021)**arXiv****R. N. Valani**, J. Dring, A.C. Slim and T. Simula, Emergence of superwalking droplets,*Journal of Fluid Mechanics*, 906, A3 (2021)**arXiv****R. N. Valani**, Superwalking Droplets and Generalised Pilot-Wave Dynamics, PhD Thesis, Monash University (2020)**R. N. Valani**, A. C. Slim and T. Simula, Superwalking droplets,*Physical Review Letters*, 123, 024503 (2019)**arXiv**

### Dynamics of wave-particle entities

A classical wave-particle entity in the form of a millimetric walking droplet can emerge on the free surface of a vertically vibrating liquid bath. Such wave-particle entities have been shown to exhibit hydrodynamic analogs of quantum systems. We are exploring, theoretically and numerically, the rich dynamical behaviours emerging for a single as well as a pair of interacting wave-particle entities.

Lorenz-like systems emerging from an integro-differential trajectory equation of a one-dimensional wave-particle entity,**R. N. Valani**,*Chaos*, 32, 023129 (2022)**arXiv****R. N. Valani**, Anomalous transport of a classical wave-particle entity in a tilted potential,*Physical Review E*, 105, L012101 (2022)**arXiv****R. N. Valani**, A. C. Slim, D. M. Paganin, T. P. Simula, and T. Vo, Unsteady dynamics of a classical particle-wave entity,*Physical Review E*, 104, 015106 (2021)**arXiv****R. N. Valani**and A.C. Slim, Pilot-wave dynamics of two identical, in-phase bouncing droplets,*Chaos*, 28 (9), 096114 (2018)*Editor’s pick***arXiv****R. N. Valani**, A.C. Slim and T. Simula, Hong-Ou-Mandel-like two-droplet correlations,*Chaos*, 28 (9), 096104 (2018)**arXiv**