arXiv subjects

Anand U. Oza

Publications and source records attributed to Anand U. Oza.

14 recordsLinked to original sources

arXiv2026

Vertical motion of a periodically driven floating disc

We present the results of a combined theoretical and experimental investigation into the vertical dynamics of floating discs subjected to an imposed time-periodic forcing. The axisymmetric and inviscid wavefield is governed by a linear elliptic boundary value problem with mixed boundary conditions, wherein the no-penetration boundary condition is satisfied under the disc while the free surface boundary conditions are enforced away from it. The problem is solved by recasting the system of partial differential equations as a second-kind Fredholm integral equation which is then solved numerically. The solution furnishes a prediction for the dependence of the disc's oscillation amplitude on the forcing frequency, which exhibits good agreement with experiments. We interpret our results physically by computing the added mass, wave damping and effective spring coefficients of the disc, both numerically for a range of forcing frequencies and analytically in the low-frequency limit.

physics.flu-dyn↗

arXiv2026

Exponential mixing in a hydrodynamic pilot--wave theory with singular potentials

We conduct an analysis of a stochastic hydrodynamic pilot-wave theory, which is a Langevin equation with a memory kernel that describes the dynamics of a walking droplet (or "walker") subjected to a repulsive singular potential and random perturbations through additive Gaussian noise. Under suitable assumptions on the singularities, we show that the walker dynamics is exponentially attracted toward the unique invariant probability measure. The proof relies on a combination of the Lyapunov technique and an asymptotic coupling specifically tailored to our setting. We also present examples of invariant measures, as obtained from numerical simulations of the walker in two-dimensional Coulomb potentials. Our results extend previous work on the ergodicity of stochastic pilot-wave dynamics established for smooth confining potentials.

math.PR↗

arXiv2026

Traveling waves in a continuum model of schooling swimmers

The complex formations exhibited by schooling fish have long been the object of fascination for biologists and physicists. However, the physical and sensory mechanisms leading to organized collective behavior remain elusive. On the physical side in particular, it is unknown how the flows generated by individual fish influence the collective patterns that emerge in large schools. To address this question, we here present a continuum theory for a school of swimmers in an inline formation. The swimmers are modeled as flapping wings that interact through temporally nonlocal hydrodynamic forces, as arise when one swimmer moves through the lingering vortex wakes shed by the others, leading to a system of time-delay-differential equations. Through coarse-graining, we derive a system of partial differential equations for the evolution of swimmer density and collective vorticity-induced hydrodynamic force. Linear stability analysis of the governing equations shows that there is a range of swimmer densities for which the uniform (constant-density) state is unstable to perturbations. Numerical simulations {in periodic domains} reveal families of stable traveling wave solutions, where a uniform school destabilizes into a collection of densely populated "sub-schools" separated by relatively sparse regions that move as a propagating wave. We find that distinct propagating waves may be stable for the same set of kinematic parameters. We also find that finite schools can evolve into packets of coarsening traveling waves whose overall spreading is described by a rarefaction fan moving upstream and a terminating downstream shock. Generally, our results show that temporally nonlocal hydrodynamic interactions can lead to rich collective behavior in schools of swimmers.

physics.flu-dyn↗

arXiv2026

On the stability of an in-line formation of hydrodynamically interacting flapping plates

The motion of several plates in an inviscid and incompressible fluid is studied numerically using a vortex sheet model. Two to four plates are initially placed in-line, separated by a specified distance, and actuated in the vertical direction with a prescribed oscillatory heaving motion. The vertical motion induces the plates' horizontal acceleration due to their self-induced thrust and fluid drag forces. In certain parameter regimes, the plates adopt equilibrium "schooling modes," wherein they translate at a steady horizontal velocity while maintaining a constant separation distance between them. The separation distances are found to be quantized on the flapping wavelength. As either the number of plates increases or the oscillation amplitude decreases, the schooling modes destabilize via oscillations that propagate downstream from the leader and cause collisions between the plates, an instability that is similar to that observed in recent experiments on flapping wings in a water tank (Newbolt et al., 2024). A simple control mechanism is implemented, wherein each plate accelerates or decelerates according to its velocity relative to the plate directly ahead by modulating its own flapping amplitude. This mechanism is shown to successfully stabilize the schooling modes, with remarkable impact on the regularity of the vortex pattern in the wake. Several phenomena observed in the simulations are obtained by a reduced model based on linear thin-airfoil theory.

physics.flu-dyn↗

arXiv2024

Phase-field modeling of colloid-polymer mixtures in microgravity

Colloid-polymer mixtures are an archetype for modeling phase transition processes, as they a exhibit low-density gas phase, high-density crystalline phase and an intervening liquid phase. While their equilibrium behavior has been studied extensively, the role of hydrodynamics in driving their phase separation is not yet understood. We present a theoretical model that describes hydrodynamic interactions in colloid-polymer mixtures in a microgravity environment. Our phase-field model consists of the Cahn-Hilliard equation, which describes phase separation processes in multicomponent mixtures, coupled with the Stokes equation for viscous fluid flow. We account for the dependence of the suspension viscosity on the colloid concentration, and the so-called Korteweg stresses that arise at the interfaces of colloidal phases. We process video microscopy images from NASA's Binary Colloid Alloy Test (BCAT) experiments, which were performed on the International Space Station. While terrestrial experiments would be dominated by gravitational forces and buoyancy-driven flows, the microgravity environment of the BCAT experiments allows for the visualization of phase separation by low interfacial tension, and thus enables a quantitative comparison between experiment and our model predictions.

cond-mat.soft↗

arXiv2024

Single-particle diffraction with a hydrodynamic pilot-wave model

A macroscopic hydrodynamic system that couples a particle and a wave has recently renewed interest in the question as to what extent a classical system may reproduce quantum phenomena. Here we investigate single-particle diffraction with a pilot-wave model originally developed to describe the hydrodynamic system. We study single-particle interactions with a barrier and slits of increasing width by focusing on the near field. We find single-particle diffraction arising as wavelike patterns in the particles' position statistics, which we compare to the predictions of quantum mechanics. We provide a mechanism that rationalizes the diffractive behavior in our system.

physics.flu-dyn↗

arXiv2024

The invariant measure of a walking droplet in hydrodynamic pilot-wave theory

We study the long time statistics of a walker in a hydrodynamic pilot-wave system, which is a stochastic Langevin dynamics with an external potential and memory kernel. While prior experiments and numerical simulations have indicated that the system may reach a statistically steady state, its long-time behavior has not been studied rigorously. For a broad class of external potentials and pilot-wave forces, we construct the solutions as a dynamics evolving on suitable path spaces. Then, under the assumption that the pilot-wave force is dominated by the potential, we demonstrate that the walker possesses a unique statistical steady state. We conclude by presenting an example of such an invariant measure, as obtained from a numerical simulation of a walker in a harmonic potential.

math.PR↗

arXiv2023

Theoretical modeling of capillary surfer interactions on a vibrating fluid bath

We present and analyze a theoretical model for the dynamics and interactions of "capillary surfers," which are millimetric objects that self-propel while floating at the interface of a vibrating fluid bath. In our companion paper [1], we reported the results of an experimental investigation of the surfer system, which showed that surfer pairs may lock into one of seven bound states, and that larger collectives of surfers self-organize into coherent flocking states. Our theoretical model for the surfers' positional and orientational dynamics approximates a surfer as a pair of vertically oscillating point sources of weakly viscous gravity-capillary waves. We derive an analytical solution for the associated interfacial deformation and thus the hydrodynamic force exerted by one surfer on another. Our model recovers the bound states found in experiments and exhibits good quantitative agreement with experimental data. Moreover, a linear stability analysis shows that the bound states are quantized on the capillary wavelength, with stable branches of equilibria separated by unstable ones. Generally, our work shows that self-propelling objects coupled by interfacial flows constitute a promising platform for studying active matter systems in which both inertial and viscous effects are relevant.

physics.flu-dyn↗

arXiv2023

Capillary surfers: wave-driven particles at a vibrating fluid interface

We present an experimental study of capillary surfers, a new fluid-mediated active system that bridges the gap between dissipation- and inertia-dominated regimes. Surfers are wave-driven particles that self-propel and interact on a fluid interface via an extended field of surface waves. A surfer's speed and interaction with its environment can be tuned broadly through the particle, fluid, and vibration parameters. The wave nature of interactions among surfers allows for multistability of interaction modes and promises a number of novel collective behaviors.

physics.flu-dyn↗

arXiv2021

Generalization of waving-plate theory to multiple interacting swimmers

Early research in aerodynamics and biological propulsion was dramatically advanced by the analytical solutions of Theodorsen, von Kármán, Wu and others. While these classical solutions apply only to isolated swimmers, the flow interactions between multiple swimmers are relevant to many practical applications, including the schooling and flocking of animal collectives. In this work, we derive a class of solutions that describe the hydrodynamic interactions between an arbitrary number of swimmers in a two-dimensional inviscid fluid. Our approach is rooted in multiply-connected complex analysis and exploits several recent results. Specifically, the transcendental (Schottky-Klein) prime function serves as the basic building block to construct the appropriate conformal maps and leading-edge-suction functions, which allows us to solve the modified Schwarz problem that arises. As such, our solutions generalize classical thin aerofoil theory, specifically Wu's waving-plate analysis, to the case of multiple swimmers. For the case of a pair of interacting swimmers, we develop an efficient numerical implementation that allows rapid computations of the forces on each swimmer. We investigate flow-mediated equilibria and find excellent agreement between our new solutions and previously reported experimental results. Our solutions recover and unify disparate results in the literature, thereby opening the door for future studies into the interactions between multiple swimmers.

physics.flu-dyn↗

arXiv2021

Flow rectification in loopy network models of bird lungs

We demonstrate flow rectification, valveless pumping or AC-to-DC conversion in macroscale fluidic networks with loops. Inspired by the unique anatomy of bird lungs and the phenomenon of directed airflow throughout the respiration cycle, we hypothesize, test and validate that multi-loop networks exhibit persistent circulation or DC flows when subject to oscillatory or AC forcing at high Reynolds numbers. Experiments reveal that disproportionately stronger circulation is generated for higher frequencies and amplitudes of the imposed oscillations, and this nonlinear response is corroborated by numerical simulations. Visualizations show that flow separation and vortex shedding at network junctions serve the valving function of directing current with appropriate timing in the oscillation cycle. These findings suggest strategies for controlling inertial flows through network topology and junction connectivity.

physics.flu-dyn↗

arXiv2019

Lattices of hydrodynamically interacting flapping swimmers

Fish schools and bird flocks exhibit complex collective dynamics whose self-organization principles are largely unknown. The influence of hydrodynamics on such collectives has been relatively unexplored theoretically, in part due to the difficulty in modeling the temporally long-lived hydrodynamic interactions between many dynamic bodies. We address this through a novel discrete-time dynamical system (iterated map) that describes the hydrodynamic interactions between flapping swimmers arranged in one- and two-dimensional lattice formations. Our 1D results exhibit good agreement with previously published experimental data, in particular predicting the bistability of schooling states and new instabilities that can be probed in experimental settings. For 2D lattices, we determine the formations for which swimmers optimally benefit from hydrodynamic interactions. We thus obtain the following hierarchy: while a side-by-side single-row "phalanx" formation offers a small improvement over a solitary swimmer, 1D in-line and 2D rectangular lattice formations exhibit substantial improvements, with the 2D diamond lattice offering the largest hydrodynamic benefit. Generally, our self-consistent modeling framework may be broadly applicable to active systems in which the collective dynamics is primarily driven by a fluid-mediated memory.

cond-mat.soft↗

arXiv2016

Antipolar ordering of topological defects in active liquid crystals

ATP-driven microtubule-kinesin bundles can self-assemble into two-dimensional active liquid crystals (ALCs) that exhibit a rich creation and annihilation dynamics of topological defects, reminiscent of particle-pair production processes in quantum systems. This recent discovery has sparked considerable interest but a quantitative theoretical description is still lacking. We present and validate a minimal continuum theory for this new class of active matter systems by generalizing the classical Landau-de Gennes free-energy to account for the experimentally observed spontaneous buckling of motor-driven extensile microtubule bundles. The resulting model agrees with recently published data and predicts a regime of antipolar order. Our analysis implies that ALCs are governed by the same generic ordering principles that determine the non-equilibrium dynamics of dense bacterial suspensions and elastic bilayer materials. Moreover, the theory manifests an energetic analogy with strongly interacting quantum gases. Generally, our results suggest that complex non-equilibrium pattern-formation phenomena might be predictable from a few fundamental symmetry-breaking and scale-selection principles.

cond-mat.soft↗

arXiv2016

Pilot-wave dynamics in a harmonic potential: Quantization and stability of circular orbits

We present the results of a theoretical investigation of the dynamics of a droplet walking on a vibrating fluid bath under the influence of a harmonic potential. The walking droplet's horizontal motion is described by an integro-differential trajectory equation, which is found to admit steady orbital solutions. Predictions for the dependence of the orbital radius and frequency on the strength of the radial harmonic force field agree favorably with experimental data. The orbital quantization is rationalized through an analysis of the orbital solutions. The predicted dependence of the orbital stability on system parameters is compared with experimental data and the limitations of the model are discussed.

physics.flu-dyn↗