Publications

We show that laminar chaos, characterised by long quiescent phases interrupted by bursts, can arise not only from periodically varying time delays, but also from randomly or chaotically varying delays. The results demonstrate that laminar chaos originates from a resonance with a system’s own past and provide practical tools to identify it and distinguish it from related phenomena in experimental data.

We develop a unified mathematical framework to describe the motion of microswimmers (e.g. microorganisms or microrobots) in steady channel flows of varying cross-section. Despite complex trajectories, particles of different shapes remain confined to well-defined, predictable regions, revealing hidden structure in active transport through fluids.

We show that incorporating fluid inertia into the Lorenz description of Quincke rotation leads to “memory Lorenz” equations that reconcile theory with experiments. Memory effects delay the onset of chaos, enhance multistability, and can restore periodic motion, with broader implications for Lorenz-type systems and chaos control in active matter.

We show that deformable elongated particles in oscillatory shear flow can synchronize their shape oscillations and spontaneously form nematic order, even in the absence of particle–particle interactions. This behaviour arises from phase-locking between particle deformation and the driving flow and is absent in rigid particles.

We show that a nonlinear oscillator with state-dependent delay can exhibit an infinite hierarchy of nested limit-cycle attractors (megastability) and undergo controlled transitions between quantized orbits under external driving. Resonance and beating enable upward and downward transitions between these states, forming a classical analogue of quantum jumps with potential applications in multistable engineering systems.

We show that a classical active wave–particle system encountering a barrier can exhibit unpredictable tunneling due to its mapping onto a perturbed Lorenz system. Nonlinear dynamics and sensitivity to initial conditions enable barrier crossing without energy conservation, providing a classical analogue of tunneling.

We show that a classical pilot-wave model with truncated memory can produce a countably infinite set of coexisting limit-cycle states (megastability) in a harmonic potential. This provides a classical analogue of quantized energy levels arising from nonconservative, oscillatory forcing.

We identify a dynamical mechanism for negative mobility in a memory-driven active particle by mapping its motion to a biased Lorenz system. A small applied force can induce transport opposite to the bias, revealing how low-dimensional nonlinear dynamics generate anomalous transport in active matter.

We study the motion of an active particle in channel flow and identify a range of regular and chaotic trajectories, including swinging, trapping, tumbling, and wandering states. These results provide insight into the dynamics of natural and artificial microswimmers in confined environments.

We identify tipping points in the dynamics of particles flowing through spiral microfluidic channels and show how these transitions can be exploited to control particle trajectories. This provides new strategies for optimising size-based particle separation in biomedical and industrial microfluidic devices.

We show that a simple mathematical model of a self-propelled droplet interacting with its own wave field can exhibit quantum-like behaviour in a double-well potential. The system displays multistable quantized states, intermittent tunnelling, and wave-like statistics, despite being entirely classical.

We analyse an ODE model for particle focusing in curved duct flows and identify equilibrium states and their bifurcations using analytical and numerical methods. Saddle-node, pitchfork, and Hopf bifurcations emerge as system parameters vary, with implications for the design of inertial microfluidic devices for size-based particle separation.

We show that a particle subject to state-dependent delayed feedback in a double-well potential can exhibit multistability between distinct dynamical attractors forming an effective two-level system. Bifurcation analysis reveals chaotic transitions between wells driven by crisis-induced intermittency, providing a dynamical explanation for tunnelling-like behaviour.

We introduce a formalism in which a particle’s dynamics are driven directly by an attractor in its internal state space, giving rise to a new class of systems termed attractor-driven matter. This framework generates rich single-particle and collective behaviours reminiscent of active matter and provides a flexible way to model complex dynamical systems.

We distinguish true laminar chaos from visually similar diffusion-like dynamics in Lorenz-type wave–particle systems, introducing the concept of pseudolaminar chaos. While the two behaviours appear nearly indistinguishable at the signal level, correlation analysis reveals clear dynamical differences, even in the presence of noise.

We develop a theoretical model for superwalking droplets driven by two-frequency vibration and explain how coupled vertical and horizontal dynamics give rise to sustained self-propulsion. Numerical results agree with experiments and clarify the mechanism underlying the emergence of superwalking states.

Millimetre-sized walking droplets that emerge on the surface of a vertically vibrating liquid bath can exhibit certain features that were previously thought to be exclusive to the microscopic quantum realm. This thesis investigates a new class of walking droplets, coined superwalkers, and also studies the rich dynamical behaviour of droplets in a generalised pilot-wave framework. Insights from this research may help further our understanding in the areas of hydrodynamic quantum analogues and active matter.

A walker is a droplet of liquid that self-propels on the free surface of an oscillating bath of the same liquid through feedback between the droplet and its wave field. We have studied walking droplets in the presence of two driving frequencies and have observed a new class of walking droplets, which we coin superwalkers. Superwalkers may be more than double the size of the largest walkers, may travel at more than triple the speed of the fastest ones, and enable a plethora of novel multidroplet behaviors.

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. 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.