Publications

Time delays are fundamental in many real systems. When these delays themselves vary periodically in time, they can lead to a special form of chaos called laminar chaos. It is characterized by long, quiet phases interrupted by sudden bursts. Earlier studies showed that laminar chaos arises because the system can fall into a resonance with its own past: as the delay varies, the timing of feedback aligns in just the right way to generate these alternating calm and burst phases. Our new work, reveals that this resonance, and the resulting laminar chaos, emerges not only when delays vary periodically, but even when they change in completely random or chaotically generated ways. Our work also extends practical tools for detecting laminar chaos in experimental data, and for distinguishing it from related phenomena such as pseudolaminar chaos observed in Lorenz-like walking-droplet dynamics.

Active particles, tiny objects that propel themselves by using energy, often swim through complex fluid environments, yet their motion can reveal surprising order. In this work, we developed a unified mathematical framework to describe how self-propelled particles move in smooth, steady flows through straight channels of different cross-sectional shapes. Through analytical and numerical methods, we show that active particles, whether spherical, elongated, or flattened, follow intricate trajectories that nevertheless remain confined within well-defined, predictable regions of the channel. This reveals an underlying structure in what might otherwise appear as complex or chaotic motion.

Quincke rotation, where a particle in a fluid spontaneously spins under a strong electric field, is governed by the famous Lorenz system. We show that including the fluid’s inertia, a “memory” of past motion, modifies the dynamics into memory Lorenz equations, resolving discrepancies between classical predictions and experiments. This memory delays chaos, expands multistability, and can restore periodic motion at higher fields. More broadly, memory effects may shape Lorenz-type systems in general, with implications for chaos control and active matter.

We use a minimal theoretical model to show that when deformable, elongated particles are placed in an oscillatory shear flow, they can synchronize their shape oscillations leading to spontaneous nematic alignment without any particle-particle interactions. Rigid elongated particles don’t show this behavior, whereas deformable particles do due to their ability to undergo shape changes and phase-lock with the driving flow.

We consider a nonlinear oscillator with state-dependent time-delay that displays a countably infinite number of nested limit cycle attractors, i.e. megastability. We demonstrate transitions between different quantized orbits, i.e. different energy levels, by subjecting the system to an external finite-time harmonic driving. Resonance can drivestransitions to higher energy levels whereas beating effects can lead to transitions to lower energy levels. Such driven transitions between quantized orbits form a classical analog of quantum jumps. From a practical viewpoint, our work might find applications in physical and engineering system where controlled transitions between several limit cycles of a multistable dynamical system is desired.

We consider a simple setup of a classical, active wave-particle entity (inspired from walking droplets) encountering a barrier. Since the particle is active, it does not conserve energy and can modulate it when interacting with the barrier. This setup maps to the dynamics of a perturbed Lorenz system (same Lorenz system with the well-known “butterfly effect”). We find that nonlinear features of this system can give rise to unpredictable “tunneling” across the barrier.

A classical particle in a harmonic potential gives rise to a continuous energy spectra, whereas the corresponding quantum particle exhibits countably infinite quantized energy levels. By considering a truncated-memory stroboscopic pilot-wave model walking droplets in the low dissipation regime, we obtain a classical harmonic oscillator perturbed by oscillatory nonconservative forces that display countably infinite coexisting limit-cycle states, also known as megastability.

On applying a small bias force, nonequilibrium systems may respond in paradoxical ways such as with negative mobility – a net drift opposite to the applied bias. We consider a minimal model of a memory-driven active particle inspired from experiments with walking and superwalking droplets, whose equation of motion maps to the celebrated Lorenz system. By adding a small bias force to this Lorenz model for the active particle, we uncover a dynamical mechanism for emergence of negative mobility. Our work highlights a general dynamical mechanism for the emergence of anomalous transport behaviors for active particles described by low-dimensional nonlinear models.

We investigated the motion of a simple active particle suspended in fluid flow through a straight channel. We observe a diverse set of active particle trajectories, both regular and chaotic, which we classify into different types of swinging, trapping, tumbling and wandering motion. Outcomes of this work may have implications for dynamics of natural and artificial microswimmers in confined regions. 

We theoretically and numerically investigated tipping points in a system of small particles flowing inside spiral microfluidic channels. Such microfluidic systems are being used in experiments to separate particles according to their size in biodemical and industrial technologies. We show that tipping points exist for particles moving in such spiral microfluidic channels, and this may have implications for optimizing particle separation in such devices. Further, we leverage these tipping points and use them to propose new ways of separating particles by size. 

Vibrating a liquid bath can result in droplets that extract energy from the vibrations of bath and convert it into self-propulsion. Such active droplets, known as walkers/superwalkers, not only move persistently but also sculpt their own dynamical landscape by imprinting fading waves on the liquid surface as they move. Using a simple mathematical model of such an active particle inspired from walkers/superwalkers, we show that it exhibits quantum-like behaviours in a double-well potential. These include multistable quantized states, intermittent tunneling and wave-like statistics. 

We investigate an ODE model that governs the focusing dynamics of small particles in curved duct fluid flows. We investigate both analytically and numerically, the particle equilibria and their bifurcations for a curved duct having a 2×1 and a 1×2 rectangular cross-section. We observe a number of different bifurcations in particle equilibria such as saddle-node, pitchfork and Hopf, as the model parameters are varied. These results may aid in the design of inertial microfluidic devices aimed at particle separation by size.

We investigated the dynamics of a damped particle inside an external double-well potential under the influence of state-dependent time-delayed feedback. In certain regions of the parameter space, we observe multistability with the existence of two different attractors (limit cycle or strange attractor) with well separated mean Lyapunov energies forming a two-level system. Bifurcation analysis reveals that, as the effects of the time-delay feedback are enhanced, chaotic transitions emerge between the two wells of the double-well potential for the attractor corresponding to the fundamental energy level. By computing the residence time distributions and the scaling laws near the onset of chaotic transitions, we rationalize this apparent tunneling-like effect in terms of the crisis-induced intermittency phenomenon.

Strange attractors emerge in the phase space of nonlinear dynamical systems. We consider a converse case where attractors, strange or otherwise, are used as a fundamental driver of the dynamics of a single-particle or multi-particle classical system. By coupling the dynamical variables of a particle with an attractor associated with its internal state-space, we present a formalism to generate a class of matter coined “attractor-driven matter.” We illustrate the rich dynamical and emergent behaviors that can arise from such particles and show behaviors reminiscent of active matter. The formalism provides a flexible means to generate complex dynamical and collective behaviors that may be broadly applied in various contexts.

In finite-dimensional, chaotic, Lorenz-like wave-particle dynamical systems one can find diffusive trajectories, which share their appearance with that of laminar chaotic diffusion known from delay systems with lag-time modulation. Applying, however, to such systems a test for laminar chaos, these signals fail such a test, thus leading to the notion of pseudolaminar chaos. The latter can be interpreted as integrated periodically driven on-off intermittency. We demonstrate that, on a signal level, true laminar and pseudolaminar chaos are hardly distinguishable in systems with and without dynamical noise. However, very pronounced differences become apparent when correlations of signals and increments are considered. We compare and contrast these properties of pseudolaminar chaos with true laminar chaos.

A new class of self-propelled droplets, coined superwalkers, has been shown to emerge when a bath of silicone oil is vibrated simultaneously at a given frequency and its subharmonic tone with a relative phase difference between them. To understand the emergence of superwalking droplets, we explore their vertical and horizontal dynamics by extending previously established theoretical models for walkers driven by a single frequency to superwalkers driven by two frequencies. We provide an explanation for the emergence of superwalking at two frequencies and compare our simulated superwalkers with experiments.

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.