arXiv subjects

Rahil N. Valani

Publications and source records attributed to Rahil N. Valani.

At least 19 recordsLinked to original sources

arXiv2026

An active Lorentz gas: walking droplets in periodic media

The Lorentz gas is a paradigmatic model in dynamical systems theory for understanding the origin of nonequilibrium transport in terms of microscopic deterministic chaos. In the periodic setting, a point particle scatters elastically off disks arranged on a two-dimensional lattice. Here we replace the disks by smooth potentials and the particle by the widely studied walking droplet, which propels itself on a vertically vibrating fluid. In the low-memory limit, this droplet reduces to a particle with nonlinear active friction. We call this system an active Lorentz gas. Using extensive numerical simulations, we analyze how dissipation generated by the active deterministic dynamics alters the phase-space structure of the corresponding conservative Lorentz gas. We find that islands of stability collapse into attracting and repelling sets. To characterize these structures, we introduce an energy-variance filtering method that distinguishes localized periodic, quasi-ballistic periodic, and chaotic trajectories, enabling the construction of bifurcation diagrams in a non-conservative setting. We identify parameter regimes exhibiting strong bifurcation cascades, anomalous diffusion, and significant phase-space contraction. Our results establish the active Lorentz gas as a rich framework for studying transport in dissipative dynamical systems and provide a bridge between active matter and classical models of chaotic transport, with potential implications for hydrodynamic quantum analogs in periodic media.

nlin.CD↗

arXiv2026

Synchronization induces Bell violations in a model of walking droplets

We consider a reduced Lorenz-like model that describes two walking droplets interacting through their mutual wave field, and investigate the emergence of strong bipartite correlations in this classical wave-particle system. The coupled nonlinear dynamics admit two invariant synchronization manifolds associated with correlated and anticorrelated states, within which the droplets display synchronized chaotic intermittency. Employing measurement protocols inspired by Bell experiments, we compute position correlations from the long-time dynamics and identify parameter regimes for which the CHSH-Bell parameter $S$ exceeds 2, corresponding to violations of Bell's Inequality. We further introduce a procedure for isolating the two subsystems, thereby ensuring the absence of wave-mediated signaling between them. Changing measurement settings following this isolation allows us to execute dynamic Bell tests in which violations persist. Our results demonstrate that nonlinear deterministic dynamics can produce Bell violations through wave-mediated synchronization mechanisms; moreover, these violations may be rationalized on the grounds that the wave form is influenced by the measurement settings. We thus provide a consistent dynamical framework for the appearance of classical entanglement in pilot-wave systems.

nlin.CD↗

arXiv2026

Intermittent Flocking and Fractal Collective Order Induced by Time-Varying Delays

Time-varying interaction delays are ubiquitous in active matter, yet their collective effects remain largely unexplored. We show that active particles with internal dynamics and Vicsek-like delayed alignment exhibit intermittent flocking, characterized by long episodes of coherent motion interrupted by brief disordering events. This collective behavior arises from laminar chaos, a form of chaotic dynamics unique to systems with time-varying delays. Changing only the delay parameters qualitatively reshapes collective motion, producing fractal changes in global flocking order. Our results establish the temporal structure of interaction delays as a new control parameter for active matter.

nlin.CD↗

arXiv2026

Shear-Induced Collective Shape Oscillations in Dense Soft Suspensions

Dense suspensions of deformable particles can exhibit rich nonequilibrium dynamics arising from complex flow-structure coupling. Using a multi-phase field model, we show that steady shear drives an initially disordered, dense, soft suspension into a positionally and orientationally ordered state, within which particles undergo robust self-sustained shape oscillations. These oscillations originate from repeated T1 neighbor exchanges that force the ordered particle lattice to cyclically traverse different ordered configurations, coupling particle deformation to evolving lattice topology. By identifying the lattice angle as a key variable, we construct a minimal one-degree-of-freedom model that quantitatively captures the limit cycle oscillation. Because these mechanisms rely only on deformability, packing, and shear, they provide a generic route to collective time-dependent behavior in dense soft suspensions.

cond-mat.soft↗

arXiv2025

Wave-Like Statistics from Classical Active Particles with Internal Degrees Of Freedom

Wave-like spatial statistics in walking-droplet systems are often associated with wave-mediated interactions and wave-memory effects. Here we explore how similar statistical structure can arise from the low-dimensional nonlinear dynamics of an inertial active particle with internal degrees of freedom. In this framework, steady propulsion corresponds to internal-state fixed points whose spiral or transiently chaotic relaxation organizes oscillatory ensemble densities. Local perturbations then generate wave-like statistics in both open and closed geometries, suggesting that wave-like ensemble behavior may emerge more generally from internal-state attractor dynamics in inertial active matter.

cond-mat.soft↗

arXiv2025

Intermittent Motility of a Synthetic Active Particle in Changing Environments

We experimentally investigate the dynamics of synthetic active particles composed of gravitationally bouncing, superwalking droplets confined within an annular fluid bath. Driven by a topologically pumping dual-frequency waveform, the droplets exhibit alternating active (walking) and dormant (bouncing) phases, producing intermittent azimuthal motion. Tracking individual droplets reveals pseudolaminar chaotic dynamics in the time series of particle's angular position, characterized by laminar plateaus that are interrupted by short irregular bursts of activity. Increasing the driving amplitude induces a qualitative change in the active particle's intermittent dynamics, arising from a symmetry-breaking transition in its Faraday-wave field environment: continuous SO(2)-symmetric "channelling" waves give way to discrete "trapping" patterns. These findings demonstrate how environmental symmetry and spatiotemporal structure modulate motility and intermittency in synthetic active matter.

physics.flu-dyn↗

arXiv2025

From Equilibrium Multistability to Spatiotemporal Chaos in Channel Flows of Nematic Fluids

We investigate channel-confined, nematic liquid crystals using the Beris-Edwards model of nematohydrodynamics. Using strong homeotropic anchoring at the walls, we find multistability i.e. multiple coexisting states where the uniform nematic state coexists with states having spatially varying scalar nematic order and director fields. When a pressure gradient is applied, flows develop, and the inherent multistability of the system organizes a variety of complex dynamics. For low pressure gradients, steady flows are established, and the director fields that emerge from the multistable states at equilibrium correspond to Bowser and Dowser configurations similar to those reported in experiments. An increasing pressure-gradient destabilizes steady Bowser and Dowser flow states sequentially, leading to unsteady periodic and chaotic regimes featuring cyclical topological transitions, pulsating flows, advecting defects and spatiotemporal chaos. These findings demonstrate that modest variations in the scalar nematic order, as captured by the Beris-Edwards model, can qualitatively modify equilibrium structures and give rise to complex nonequilibrium behaviour in confined nematics-contrasting with the Ericksen-Leslie model, which assumes a constant scalar order parameter. Our key model predictions - multistability, periodically oscillating states and advecting defect-mediated turbulence can be experimentally investigated in pressure-driven channel flows of nematic fluids.

cond-mat.soft↗

arXiv2025

A Hamiltonian formulation for the motion of an active spheroidal particle suspended in laminar straight duct flow

We analyse a generalisation of Z\"{o}ttl and Stark's model of active spherical particles [Phys. Rev. Lett. 108, 218104 (2012)] and prolate spheroidal particles [Eur. Phys. J. E 36(1), 4 (2013)] suspended in cylindrical Poiseuille flow, to particle dynamics in an arbitrary unidirectional steady laminar flow through a straight duct geometry. Our primary contribution is to describe a Hamiltonian formulation of these systems and provide explicit forms of the constants of motions in terms of the arbitrary fluid velocity field. The Hamiltonian formulation provides a convenient and robust approach to the computation of particle orbits whilst also providing new insights into the dynamics, specifically the way in which orbits are trapped within basins defined by a potential well. In addition to considering spherical and prolate spheroidal particles, we also illustrate that the model can be adapted to oblate spheroidal particles.

physics.flu-dyn↗

arXiv2025

Energy self-balance as the physical basis of orbit quantization

We show that work done by the non conservative forces along a stable limit cycle attractor of a dissipative dynamical system is always equal to zero. Thus, mechanical energy is preserved on average along periodic orbits. This balance between energy gain and energy loss along different phases of the self sustained oscillation is responsible for the existence of quantized orbits in such systems. Furthermore, we show that the instantaneous preservation of projected phase space areas along quantized orbits describes the neutral dynamics of the phase, allowing us to derive from this equation the Wilson Sommerfeld like quantization condition. We apply our general results to near Hamiltonian systems, identifying the fixed points of Krylov Bogoliubov radial equation governing the dynamics of the limit cycles with the zeros of the Melnikov function. Moreover, we relate the instantaneous preservation of the phase space area along the quantized orbits to the second Krylov Bogoliubov equation describing the dynamics of the phase. We test the two quantization conditions in the context of hydrodynamic quantum analogs, where a megastable spectra of quantized orbits have recently been discovered. Specifically, we use a generalized pilot wave model for a walking droplet confined in a harmonic potential, and find a countably infinite set of nested limit cycle attractors representing a classical analog of quantized orbits. We compute the energy spectrum and the eigenfunctions of this self excited system.

nlin.AO↗

arXiv2025

Laminar chaos in systems with random and chaotically time-varying delay

A type of chaos called laminar chaos was found in singularly perturbed dynamical systems with periodically [Phys. Rev. Lett. 120, 084102 (2018)] and quasiperiodically [Phys. Rev. E 107, 014205 (2023)] time-varying delay. Compared to high-dimensional turbulent chaos that is typically found in such systems with large constant delay, laminar chaos is a very low-dimensional phenomenon. It is characterized by a time series with nearly constant laminar phases that are interrupted by irregular bursts, where the intensity level of the laminar phases varies chaotically from phase to phase. In this paper, we demonstrate that laminar chaos, and its generalizations, can also be observed in systems with random and chaotically time-varying delay. Moreover, while for periodic and quasiperiodic delays the appearance of (generalized) laminar chaos and turbulent chaos depends in a fractal manner on the delay parameters, it turns out that short-time correlated random and chaotic delays lead to (generalized) laminar chaos in almost the whole delay parameter space, where the properties of circle maps with quenched disorder play a crucial role. It follows that introducing such a delay variation typically leads to a drastic reduction of the dimension of the chaotic attractor of the considered systems. We investigate the dynamical properties and generalize the known methods for detecting laminar chaos in experimental time series to random and chaotically time-varying delay.

nlin.CD↗

arXiv2025

Active wave-particle clusters

Active particles are non-equilibrium entities that uptake energy and convert it into self-propulsion. A dynamically rich class of inertial active particles having features of wave-particle coupling and wave memory are walking/superwalking droplets. Such classical, active wave-particle entities (WPEs) have previously been shown to exhibit hydrodynamic analogs of many single-particle quantum systems. Inspired by the rich dynamics of strongly interacting superwalking droplets in experiments, we numerically investigate the dynamics of WPE clusters using a stroboscopic model. We find that several interacting WPEs self-organize into a stable bound cluster, reminiscent of an atomic nucleus. This active cluster exhibits a rich spectrum of collective excitations, including shape oscillations and chiral rotating modes, akin to vibrational and rotational modes of nuclear excitations, as the spatial extent of the waves and their temporal decay rate (memory) are varied. Dynamically distinct excitation modes create a common time-averaged collective wave field potential, bearing qualitative similarities with the nuclear shell model and the bag model of hadrons. For high memory and rapid spatial decay of waves, the active cluster becomes unstable and disintegrates; however, within a narrow regime of the parameter space, the cluster ejects single particles whose decay statistics follow exponential laws, reminiscent of radioactive nuclear decay. Our study uncovers a rich spectrum of dynamical behaviors in clusters of active particles, opening new avenues for exploring hydrodynamic quantum analogs in active matter systems.

cond-mat.soft↗

arXiv2025

Nematic order from phase synchronization of shape oscillations

We show that a suspension of non-interacting deformable particles subjected to an oscillatory shear flow leads to development of nematic order that arises from the phenomenon of phase synchronization. The synchronized state corresponds to a unique, stable limit cycle confined in the toroidal state space. The limit cycle exists since, unlike rigid particles, deformable particles can modulate aspect ratio, adjust their tumbling rate and thus, achieve phase synchronization. These synchronized regions emerge as Arnold tongues in the parameter-space of the driving amplitude and frequency. Considering the rheological implications of ordering dynamics in soft and active matter, our results motivate oscillatory shear flow experiments with deformable particles.

cond-mat.soft↗

arXiv2025

Hydrodynamic memory and Quincke rotation

The spontaneous (so-called Quincke) rotation of an uncharged, solid, dielectric, spherical particle under a steady electric field is analyzed, accounting for the inertia of the particle and the transient fluid inertia, or ``hydrodynamic memory,'' due to the unsteady Stokes flow around the particle. The dynamics of the particle are encapsulated in three coupled nonlinear integro-differential equations for the evolution of the angular velocity of the particle, and the components of the induced dipole of the particle that are parallel and transverse to the applied field. These equations represent a generalization of the celebrated Lorenz system. A numerical solution of these `modified Lorenz equations' (MLE) shows that hydrodynamic memory leads to an increase in the threshold field strength for chaotic particle rotation, which is in qualitative agreement with experimental observations. Furthermore, hydrodynamic memory leads to an increase in the range of field strengths where multi-stability between steady and chaotic rotation occurs. At large field strengths, chaos ceases and the particle is predicted to execute periodic rotational motion.

physics.flu-dyn↗

arXiv2024

Megastable quantization in generalized pilot-wave hydrodynamics

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. In recent years, classical non-Markovian wave-particle entities that materialize as walking droplets have been shown to exhibit various hydrodynamic quantum analogs, including quantization in a harmonic potential by displaying few coexisting limit cycle orbits. By considering a truncated-memory stroboscopic pilot-wave model of the system in the low dissipation regime, we obtain a classical harmonic oscillator perturbed by oscillatory non-conservative forces that displays countably infinite coexisting limit-cycle states, also known as \emph{megastability}. Using averaging techniques in the low-memory regime, we derive analytical approximations of the orbital radii, orbital frequency and Lyapunov energy function of this megastable spectrum, and further show average energy conservation along these quantized states. Our formalism extends to a general class of self-excited oscillators and can be used to construct megastable spectrum with different energy-frequency relations.

nlin.AO↗

arXiv2024

Tunneling in a Lorenz-like model for an active wave-particle entity

Active wave-particle entities (WPEs) emerge as self-propelled oil droplets on the free surface of a vibrating oil bath. The particle (droplet) periodically imprints decaying waves on the liquid surface which in turn guide the particle motion, resulting in a two-way coupling between the particle and its self-generated waves. Such WPEs have been shown to exhibit hydrodynamic analogs of various quantum features. In this work, we theoretically and numerically explore a dynamical analog of tunneling by considering a simple setup of a one-dimensional WPE incident on an isolated Gaussian potential barrier. Our idealized model takes the form of a perturbed Lorenz system which we use to explore the dynamics and statistics of barrier crossing as a function of initial conditions and system parameters. Our work highlights that velocity fluctuations of the WPE at high memories that are rooted in non-equilibrium features of the Lorenz system, such as spiraling motion towards equilibrium points and transient chaos, give rise to - (i) sensitivity and unpredictability in barrier crossing, (ii) smooth variations in transmission probability as a function of system parameters, and (iii) wave-like features in the transmitted and reflected probability density profiles.

nlin.CD↗

arXiv2024

Asymmetric limit cycles within Lorenz chaos induce anomalous mobility for a memory-driven active particle

On applying a small bias force, non-equilibrium systems may respond in paradoxical ways such as with giant negative mobility (GNM) -- a large net drift opposite to the applied bias, or giant positive mobility (GPM) -- an anomalously large drift in the same direction as the applied bias. Such behaviors have been extensively studied in idealized models of externally driven passive inertial particles. Here, 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 simultaneous emergence of GNM and GPM in the parameter space. Within the chaotic sea of the parameter space, a symmetric pair of coexisting asymmetric limit cycles separate and migrate under applied bias force, resulting in anomalous transport behaviors that are sensitive to the active particle's memory. Our work highlights a general dynamical mechanism for the emergence of anomalous transport behaviors for active particles described by low-dimensional nonlinear models.

cond-mat.soft↗

arXiv2024

Driven transitions between megastable quantized orbits

We consider a nonlinear oscillator with state-dependent time-delay that displays a countably infinite number of nested limit cycle attractors, \emph{i.e.} megastability. In the low-memory regime, the equation reduces to a self-excited nonlinear oscillator and we use averaging methods to analytically show quasilinear increasing amplitude of the megastable spectrum of quantized quasicircular orbits. We further assign a mechanical energy to each orbit using the Lyapunov energy function and obtain a quadratically increasing energy spectrum and (almost) constant frequency spectrum. We demonstrate transitions between different quantized orbits, i.e. different energy levels, by subjecting the system to an external finite-time harmonic driving. For large driving amplitude with frequency close to the limit cycle frequency, resonance drives transitions to higher energy levels. Alternatively, for large driving amplitude with frequency slightly detuned from limit-cycle frequency, beating effects can lead to transitions to lower energy levels. Such driven transitions between quantized orbits form a classical analog of quantum jumps. For excitations to higher energy levels, we show amplitude locking where nearby values of driving amplitudes result in the same response amplitude, i.e. the same final higher energy level. We rationalize this effect based on the basins of different limit cycles in phase space. 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.

quant-ph↗

arXiv2024

Active particle motion in Poiseuille flow through rectangular channels

We investigate the dynamics of a point-like active particle suspended in fluid flow through a straight channel. For this particle-fluid system, we derive a constant of motion for a general unidirectional fluid flow, and apply it to an approximation of Poiseuille flow through channels with rectangular cross-sections. We obtain a $4$D nonlinear conservative dynamical system with one constant of motion and a dimensionless parameter describing the ratio of maximum flow speed to intrinsic active particle speed. Applied to square channels, we observe a diverse set of active particle trajectories with variations in system parameters and initial conditions which we classify into different types of swinging, trapping, tumbling and wandering motion. Regular (periodic/quasiperiodic) motion as well as chaotic active particle motion are observed for these trajectories and quantified using largest Lyapunov exponents. We explore the transition to chaotic motion using Poincar\'e maps and show ``sticky" chaotic tumbling trajectories that have long transients near a periodic state. We briefly illustrate how these results extend to rectangular cross-sections with width/height ratio larger than one. Outcomes of this work may have implications for dynamics of natural and artificial microswimmers in experimental microfluidic channels that typically have rectangular cross-sections.

physics.flu-dyn↗