arXiv subjects

Rahul Pandit

Publications and source records attributed to Rahul Pandit.

At least 19 recordsLinked to original sources

arXiv2026

How well can Diffusion Models learn Lagrangian-Tracer Statistics in Non-reciprocal Turbulence?

Recent advances in generative artificial intelligence have led to significant potential applications in conventional fluid flows, including those that are turbulent. Can these methods be carried over to studies of novel types of turbulence, such as turbulence induced by non-reciprocity in binary-fluid systems? To answer this question, we analyze the statistics of Lagrangian-tracer particles in non-reciprocal binary-fluid turbulence, which has been studied recently in the non-reciprocal Cahn-Hilliard-Navier-Stokes (NRCHNS). We obtain our ground-truth data via extensive pseudospectral direct numerical simulations (DNSs) of the two-dimensionsl (2D) NRCHNS model. Our study yields a variety of intriguing results for probability distribution functions (PDFs) for particle accelerations and velocity-component PDFs; the latter turn out to be bimodal, completely unlike their 2D-fluid-turbulence counterparts. We relate this bimodality to lane-type structures in Eulerian-velocity components. Furthermore, we characterize Lagrangian multiscaling via Lagrangian velocity increments, their structure functions and flatnesses, and multiscaling exponent ratios, for the first time in non-reciprocal hydrodynamics. Finally, we use generative diffusion models to obtain synthetic Lagrangian trajectories for the NRCHNS system, assess how effectively they can emulate the Lagrangian statistics that we obtain from our DNSs, and highlight open challenges in the application of generative artificial intelligence in non-reciprocal systems.

physics.flu-dyn↗

arXiv2026

Obstacle-aware navigation of smart microswimmers in a turbulent flow

Microswimmers in turbulent flows often navigate complex, heterogeneous, and obstacle-rich environments, where they exhibit intricate behaviors such as trapping at and escape from obstacles. We generalize recent $\mathcal{Q}-$learning methods of J.K. Alageshan \textit{et al.} [Phys.Rev.E \textbf{101}, 043110 (2020)] and A. Gupta \textit{et al.} [Physics of Fluids \textbf{37}, 045107 (2025)] developed for non-interacting microswimmers that aim to move optimally from an initial position to a target, to account for the additional complication of an obstacle in the flow. We begin by considering one circular obstacle in forced two-dimensional (2D) Navier-Stokes turbulence in which the energy spectrum displays a forward cascade. We employ the volume-penalization method to introduce this obstacle within our doubly periodic simulation domain. We augment our adversarial $\mathcal{Q}-$learning Refs.~\cite{Alageshan_2020,Akanksha_2025} by suppressing the tendency of microswimmers to get trapped in stagnation points in the vicinity of the obstacle. We demonstrate that smart microswimmers ($SS$), which adopt our obstacle-aware adversarial $\mathcal{Q}-$learning strategy, outperform both na\"ive swimmers ($NS$) and surfers ($SuS$).

physics.flu-dyn↗

arXiv2026

Vortex Retention Mediated Turbulent Transitions in Self-Gravitating Bosonic and Axionic Condensates

We investigate turbulent spin-down dynamics in self-gravitating Bose-Einstein condensates, comparing purely bosonic and axionic (higher-order interacting) systems. Through simulations of the Gross-Pitaevskii-Poisson system, we study condensates pinned to a crust potential undergoing rapid rotation slowdown. We find that axionic condensates exhibit more uniform density profiles and smaller sizes compared to their bosonic counterparts for similar interaction strengths, which facilitates earlier vortex entry. The sudden spin-down triggers vortex depinning and a turbulent cascade. For comparable sizes, both systems exhibit a short-lived Kolmogorov energy cascade ($k^{-5/3}$ scaling) followed by a transition to Vinen turbulence ($k^{-1}$ scaling). Crucially, their responses diverge with increasing interaction strength (and thus condensate size): the axionic system increasingly deviates from Kolmogorov scaling because of enhanced vortex retention, a trend quantitatively confirmed by analyzing the vortex fraction and its dependence on the final rotation frequency. Spectral analysis reveals that the growth of incompressible energy is primarily driven by quantum pressure during vortex detachment, rather than by compressible flows. The compressible spectrum shows thermalization ($k$ scaling). Our results demonstrate how distinct nonlinearities govern vortex dynamics and turbulent dissipation in self-gravitating quantum fluids.

cond-mat.quant-gas↗

arXiv2026

Non-reciprocal Binary-fluid Turbulence

Although effective non-reciprocal interactions have been investigated in a variety of fields, their consequences have not been explored in hydrodynamical turbulence. We initiate such an exploration by introducing non-reciprocal binary-fluid tubulence and uncover its properties by developing a two-dimensional (2D) Non-Reciprocal Cahn-Hilliard-Navier-Stokes (NRCHNS) model. We show that, as we increase the strength of the non-reciprocal terms, this model displays a hitherto unanticipated type of turbulence, with an inverse cascade of energy and an energy spectrum $E(k)\sim k^{-5/3}$, reminiscent of the well-known inverse cascade in forced, 2D fluid turbulence, but distinct from it, in so far as it develops a non-reciprocal flux $\mathbf J$. We demonstrate how NRCHNS turbulence suppresses $J(t) = |\mathbf J|$, as the Reynolds number increases. We compare and contrast 2D NRCHNS turbulence with its fluid-turbulence counterpart by examining spectra, fluxes, spectral balances, flow topologies, and signatures of multifractality.

physics.flu-dyn↗

arXiv2026

The global attractor of the Toner-Tu-Swift-Hohenberg equations of active turbulence and its properties

The Toner-Tu-Swift-Hohenberg (TTSH) equations are one of the basic equations that are used to model turbulent behaviour in active matter, specifically the swarming of bacteria in suspension. They combine features of the incompressible Navier-Stokes, the Toner-Tu and Swift-Hohenberg equations, together with the important properties that they are linearly driven, and that the Laplacian diffusion is taken to be negative in combination with hyper-dissipation. We prove that the TTSH equations possess a finite-dimensional compact global attractor on the periodic domain $\mathbb{T}^d$ ($d=2,3$) and we establish explicit estimates for its Lyapunov dimension which agree with the heuristic prediction based on the Swift-Hohenberg length scale. The predominance of this length scale (as a vortex length scale) has been observed in both numerical and experimental studies of bacterial turbulence, so our methods and results provide a rigorous theoretical foundation for this phenomenon. We also carry out pseudospectral direct numerical simulations of these PDEs in dimension $d=2$ through which we obtain Lyapunov spectra for representative parameter values. We show that our numerical results are consistent with the analytically derived rigorous bounds.

physics.flu-dyn↗

arXiv2025

Self-gravitating Superfluids: The Gross-Pitaevskii-Poisson Framework

We provide an overview of the Gross-Pitaevskii-Poisson equation (GPPE) that is used to model self-gravitating superfluid systems, which include gravitationally collapsed boson and axion stars and dark-matter haloes. We outline how this framework can be used to develop minimal models for neutron stars and for pulsars and their glitches. We account not only for vortices in the neutron superfluid inside these stars, but also for the flux tubes in the proton-superconductor subsystem, using a coupled model with the neutron superfluid, proton superconductor, the Maxwell equations for the vector potential ${\bf A}$, and the Poisson equation for self-gravity.

astro-ph.HE↗

arXiv2025

Vortex triplets, symmetry breaking, and emergent nonequilibrium plastic crystals in an active-spinner fluid

The formation of patterns and exotic nonequilibrium steady states in active-fluid systems continues to pose challenging problems -- theoretical, numerical, and experimental -- for statistical physicists and fluid dynamicists. We combine theoretical ideas from statistical mechanics and fluid mechanics to uncover a new type of self-assembled crystal of vortex triplets in an active-spinner fluid. We begin with the two-dimensional Cahn-Hilliard-Navier-Stokes (CHNS) model for a binary-fluid system of active rotors that has two important ingredients: a scalar order parameter field phi that distinguishes regions with clockwise (CW) and counter-clockwise (CCW) spinners; and an incompressible velocity field u. In addition to the conventional CHNS coupling between phi and u, this model has a torque-induced activity term, with coefficient tau, whose consequences we explore. We demonstrate that, if we increase the activity tau, it overcomes dissipation and this system displays a hitherto unanticipated emergent triangular crystal, with spinning vortex triplets at its vertices. We show that this is a nonequilibrium counterpart of an equilibrium plastic crystal. We characterise the statistical properties of this novel crystal and suggest possible experimental realisations of this new state of active matter.

cond-mat.soft↗

arXiv2025

Deep Neural Networks can eliminate Spiral-wave Turbulence in Cardiac Tissue Models

Ventricular arrhythmias, like ventricular tachycardia (VT) and ventricular fibrillation (VF), precipitate sudden cardiac death (SCD), which is the leading cause of mortality in the industrialised world. Thus, the elimination of VT and VF is a problem of paramount importance, which is studied experimentally, theoretically, and numerically. Numerical studies use partial-differential-equation models, for cardiac tissue, which admit solutions with spiral- or broken-spiral-wave solutions that are the mathematical counterparts of VT and VF. In silico investigations of such mathematical models of cardiac tissue allow us not only to explore the properties of such spiral-wave turbulence, but also to develop mathematical analogues of low-amplitude defibrillation by the application of currents that can eliminate spiral waves. We develop an efficient deep-neural-network U-Net-based method for the control of spiral-wave turbulence in mathematical models of cardiac tissue. Specifically, we use the simple, two-variable Aliev-Panfilov and the ionically realistic TP06 mathematical models to show that the lower the correlation length {\xi} for spiral-turbulence patterns, the easier it is to eliminate them by the application of control currents on a mesh electrode. We then use spiral-turbulence patterns from the TP06 model to train a U-Net to predict the sodium current, which is most prominent along thin lines that track the propagating front of a spiral wave. We apply currents, in the vicinities of the predicted sodium-current lines to eliminate spiral waves efficiently. The amplitudes of these currents are adjusted automatically, so that they are small when {\xi} is large and vice versa. We show that our U-Net-aided elimination of spiral-wave turbulence is superior to earlier methods.

nlin.PS↗

arXiv2025

Ideal incompressible axisymmetric MHD: Uncovering finite-time singularities

We provide compelling numerical evidence for the development of (potential) finite-time singularities in the three-dimensional (3D) axisymmetric, ideal, incompressible magnetohydrodynamic (IMHD) equations, in a wall-bounded cylindrical domain, starting from smooth initial data, for the velocity and magnetic fields. We demonstrate that the nature of the singularity depends crucially on the relative strength C of the velocity and magnetic fields at the time of initialisation: (i) if C < 1, then the swirl components, at the wall, evolve towards square profiles that lead to the intensification of shear at the meridional plane (r = 1, z = L/2) and the development of a finite-time singularity; (ii) if C = 1, there is no temporal evolution; (iii) if C > 1, then the swirl components, at the wall, evolve towards a cusp-type singularity. By examining the spatiotemporal evolution of the pressure, we obtain insights into the development of these singularities.

physics.flu-dyn↗

arXiv2025

Uncovering the Varieties of Three-dimensional Hall-MHD Turbulence

We carry out extensive pseudospectral direct numerical simulations (DNSs) of decaying three-dimensional (3D) Hall magnetohydrodynamics (3D HMHD) plasma turbulence at three magnetic Prandtl numbers $Pr_{m}=0.1$, $1.0$ and $10.0$. Our DNSs have been designed to uncover the dependence of the statistical properties of 3D HMHD turbulence on $Pr_m$ and to bring out the subtle interplay between three lengths, the kinetic and magnetic dissipation length scales $\eta_u$, and $\eta_b$ and the ion-inertial scale $d_i$, below which we see the manifestations of the Hall term. This interplay, qualitatively apparent from isosurface plots of the moduli of the vorticity and the current density, is exposed clearly by the kinetic-energy and magnetic-energy spectra, $E_u(k)$ and $E_b(k)$, respectively. We find two different inertial regions, In the first inertial region $k k_{i}$, the scaling of $E_b(k)$ depends upon $Pr_M$: At $Pr_{m}=0.1$, the spectral-scaling exponent is $-17/3$, but for $Pr_{m}=1$ and $10$ this exponent is $-11/3$. We then show theoretically that $E_u(k) \sim k^2 E_b(k)$ for $Pr_m \ll 1$ and $E_b(k) \sim k^2 E_u(k)$ for $Pr_m \gg 1$; our DNS results are consistent with our theoretical predictions. We examine, furthermore, left- and right-polarised fluctuations of the fields that lead, respectively, to the dominance of ion-cyclotron or whistler waves.

physics.space-ph↗

arXiv2025

Intermittency and non-universality of pair dispersion in isothermal compressible turbulence

Statistical properties of the pair dispersion of Lagrangian particles (tracers) in incompressible turbulent flows provide insights into transport and mixing. We explore the same in transonic to supersonic compressible turbulence of an isothermal ideal gas in two dimensions, driven by large-scale solenoidal and irrotational stirring forces, via direct numerical simulations. We find that the scaling exponents of the order-$p$ negative moments of the distribution of exit times -- in particular, the doubling and halving times of pair separations -- are nonlinear functions of $p$. Furthermore, the doubling and halving time statistics are different. The halving-time exponents are universal -- they satisfy their multifractal model-based prediction, irrespective of the nature of the stirring. However, the doubling-time exponents are not. In the solenoidally-stirred flows, the doubling time exponents can be expressed solely in terms of the multifractal scaling exponents obtained from the structure functions of the solenoidal component of the velocity. Moreover, they depend strongly on the Mach number, Ma, as elongated patches of high vorticity emerge along shock fronts at high Ma. In contrast, in the irrotationally-stirred flows, the doubling-time exponents do not satisfy any known multifractal model-based relation, and are independent of Ma. Our findings are of potential relevance to astrophysical disks and molecular clouds wherein turbulent transport and mixing of gases often govern chemical kinetics and the rates of formation of stars and planetesimals.

physics.flu-dyn↗

arXiv2025

Dynamics of Superfluid-Superconducting Magnetars: Magnetic Field Evolution and Gravitational Waves

Magnetars, highly magnetized neutron stars, host superconducting and superfluid phases. We develop a minimal model that captures the interplay between neutron superfluidity, proton superconductivity, and electromagnetic fields using the Gross-Pitaevskii-Poisson, Ginzburg-Landau, and Maxwell equations. Our numerical simulations show that strong rotation enhances the net magnetic field inside the magnetar, suppresses superconductivity there, and amplifies the field near the surface. We explain this by a theory that makes testable predictions, including gravitational-wave signatures.

astro-ph.HE↗

arXiv2025

Large-scale multifractality and lack of self-similar decay for Burgers and 3D Navier-Stokes turbulence

We study decaying turbulence in the 1D Burgers equation (Burgulence) and 3D Navier-Stokes (NS) turbulence. We first investigate the decay in time $t$ of the energy $E(t)$ in Burgulence, for a fractional Brownian initial potential, with Hurst exponent $H$, and demonstrate rigorously a self-similar time-decay of $E(t)$, previously determined heuristically. This is a consequence of the nontrivial boundedness of the energy for any positive time. We define a spatially forgetful \textit{oblivious fractional Brownian motion} (OFBM), with Hurst exponent $H$, and prove that Burgulence, with an OFBM as initial potential $\varphi_0(x)$, is not only intermittent, but it also displays, a hitherto unanticipated, large-scale bifractality or multifractality; the latter occurs if we combine OFBMs, with different values of $H$. This is the first rigorous proof of genuine multifractality for turbulence in a nonlinear hydrodynamical partial differential equation. We then present direct numerical simulations (DNSs) of freely decaying turbulence, capturing some aspects of this multifractality. For Burgulence, we investigate such decay for two cases: (A) $\varphi_0(x)$ a multifractal random walk that crosses over to a fractional Brownian motion beyond a crossover scale $\mathcal{L}$, tuned to go from small- to large-scale multifractality; (B) initial energy spectra $E_0(k)$, with wavenumber $k$, having one or more power-law regions, which lead, respectively, to self-similar and non-self-similar energy decay. Our analogous DNSs of the 3D NS equations also uncover self-similar and non-self-similar energy decay. Challenges confronting the detection of genuine large-scale multifractality, in numerical and experimental studies of NS and MHD turbulence, are highlighted.

physics.flu-dyn↗

arXiv2025

The Cahn-Hilliard-Navier-Stokes Framework for Multiphase Fluid Flows: Laminar, Turbulent, and Active

The Cahn-Hilliard-Navier-Stokes (CHNS) partial differential equations (PDEs) provide a powerful framework for the study of the statistical mechanics and fluid dynamics of multiphase fluids. We provide an introduction to the equilibrium and nonequilibrium statistical mechanics of systems in which coexisting phases, distinguished from each other by scalar order parameters, are separated by an interface. We then introduce the coupled Cahn-Hilliard-Navier-Stokes (CHNS) PDEs for two immiscible fluids and generalisations for (a) coexisting phases with different viscosities, (b) CHNS with gravity, (c) the three-component fluids (CHNS3), and (d) the CHNS for active fluids. We discuss mathematical issues of the regularity of solutions of the CHNS PDEs. Finally we provide a survey of the rich variety of results that have been obtained by numerical studies of CHNS-type PDEs for diverse systems, including bubbles in turbulent flows, antibubbles, droplet and liquid-lens mergers, turbulence in the active-CHNS model, and its generalisation that can lead to a self-propelled droplet.

physics.flu-dyn↗

arXiv2025

First observation of turbulence-like state in dense algal suspensions

Active turbulence arises typically in systems ranging from microorganisms and biopolymers to synthetic colloids, where chaotic flows are closely associated with motile topological defects in collectively swarming suspensions. Here, we report the first experimental observation of turbulence-like dynamics in a fundamentally different class of systems: dense monolayers of motile unicellular alga Chlamydomonas reinhardtii that exhibit neither orientational order nor topological defects. Nevertheless, the system displays rich spatiotemporal flow patterns with pronounced small-scale intermittency. We uncover strongly non-Gaussian velocity distribution, a feature distinct from both bacterial and classical fluid turbulence. Furthermore, we observe power-law regimes in the kinetic energy spectra, characterized by unique scaling exponents. Not only do our results provide compelling evidence for active spatiotemporal chaos in systems devoid of nematic or polar structures, but they also challenge current theoretical models. Our work opens new avenues for understanding emergent dynamics in active-matter systems and suggests intriguing biological implications, including enhanced mixing and transport in dense cell suspensions.

cond-mat.soft↗

arXiv2025

Emergent turbulence and coarsening arrest in active-spinner fluids

We uncover activity-driven crossover from phase separation to a new turbulent state in a two-dimensional system of counter-rotating spinners. We study the statistical properties of this active-rotor turbulence using the active-rotor Cahn-Hilliard-Navier-Stokes model, and show that the vorticity $\omega \propto \phi$, the scalar field that distinguishes regions with different rotating states. We explain this intriguing proportionality theoretically, and we characterize power-law energy and concentration spectra, intermittency, and flow-topology statistics. We suggest biological implications of such turbulence.

physics.flu-dyn↗

arXiv2025

A machine-learning study of phase transitions in Ising, Blume-Capel, and Ising-metamagnet models

We combine machine-learning (ML) techniques with Monte Carlo (MC) simulations and finite-size scaling (FSS) to study continuous and first-order phase transitions in Ising, Blume-Capel, and Ising-metamagnet spin models. We go beyond earlier studies that had concentrated on obtaining the correlation-length exponent $\nu$. In particular, we show (a) how to combine neural networks (NNs), trained with data from MC simulations of Ising-type spin models on finite lattices, with FSS to obtain both thermal magnetic exponents $y_t = 1/\nu$ and $y_h$, respectively, at both critical and tricritical points, (b) how to obtain the NN counterpart of two-scale-factor universality at an Ising-type critical point, and (c) FSS at a first-order transition. We also obtain the FSS forms for the output of our trained NNs as functions of both the temperature and the magnetic field.

cond-mat.stat-mech↗

arXiv2024

Can flocking aid the path planning of microswimmers in turbulent flows?

We show that flocking of microswimmers in a turbulent flow can enhance the efficacy of reinforcement-learning-based path-planning of microswimmers in turbulent flows. In particular, we develop a machine-learning strategy that incorporates Vicsek-model-type flocking in microswimmer assemblies in a statistically homogeneous and isotropic turbulent flow in two dimensions (2D). We build on the adversarial-reinforcement-learning of Ref.~\cite{alageshan2020machine} for non-interacting microswimmers in turbulent flows. Such microswimmers aim to move optimally from an initial position to a target. We demonstrate that our flocking-aided version of the adversarial-reinforcement-learning strategy of Ref.~\cite{alageshan2020machine} can be superior to earlier microswimmer path-planning strategies.

physics.flu-dyn↗