Dr Rahil Valani

Abstract:

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 organises 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 destabilises 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 non-equilibrium 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.

Abstract:

Active particles are nonequilibrium 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.

Abstract:

A type of chaos called laminar chaos was found in singularly perturbed dynamical systems with periodically [D. Müller , ] and quasiperiodically [D. Müller-Bender and G. Radons, ] 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.

Abstract:

We analyze a generalization of Zöttl and Stark's model of active spherical particles [Phys. Rev. Lett. 108, 218104 (2012)0031-900710.1103/PhysRevLett.108.218104] and prolate spheroidal particles [Eur. Phys. J. E 36, 4 (2013)1292-894110.1140/epje/i2013-13004-5] 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 while 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.

Abstract:

Differential equations containing memory terms that depend nonlinearly on past states model a variety of non-Markovian processes. In this study, we present a Markovian embedding procedure for a subclass of such equations with distributed delay by utilising an exact spectral representation of the nonlinear memory function. This allows us to transform the nonlocal system to an equivalent local-in-time system in an abstract extended space. We demonstrate our embedding procedure for two one-dimensional physical models: (i) the walking droplet and (ii) the single-phase Stefan problem. In addition to providing an alternative representation of the underlying physical system, the local representation finds applications in designing efficient time-integrators with time-independent computational costs for memory-dependent systems which typically suffer from growing-in-time costs.