Rahul Pandit

We provide an overview of the Cahn–Hilliard–Navier–Stokes (CHNS) framework that has been used to study multi-phase flows. We concentrate on recent advances in modelling active-fluid mixtures and the non-reciprocal CHNS system. We first use the zero-field Ising model to illustrate two-phase coexistence, below the critical temperature, and to recall how equilibrium properties can be studied approximately by using mean-field or Curie–Weiss theory and its gradient expansion, namely, Landau–Ginzburg theory for a scalar order-parameter ϕ, which distinguishes between the two coexisting phases. We then move to the spatio-temporal evolution of ϕ, which requires time-dependent Ginzburg–Landau theory (Model A), if the order parameter is not conserved, or Cahn–Hilliard theory (CH or Model B), if the order parameter is conserved. Next, we consider the combination of CH models with the Navier–Stokes equation for an incompressible fluid; this yields the CHNS system. We give a synoptic view of recent generalizations of this CHNS system that include different active models (e.g. Active Models B) or non-reciprocity. This article is part of the theme issue ‘Anti-diffusive transport and layering: from sub-cellular to astrophysical scales’.

Anti-diffusion refers to a remarkable class of processes, in which particles, fluid elements, etc., tend to migrate up-gradient, contrary to expected diffusive relaxation. A particularly dramatic and fascinating anti-diffusive phenomenon is layering or staircase formation, in which turbulent stirring leads to the formation of mixed regions, interspersed by layers of steepened gradients. Anti-diffusive dynamics is of interest across a wide range of physical systems—e.g. in geophysical and astrophysical fluid dynamics, in magnetically confined plasmas and in active matter. To bring together researchers from a variety of different backgrounds, the Isaac Newton Institute hosted a six-month programme in 2024 entitled Anti-Diffusive Dynamics: from Sub-Cellular to Astrophysical Scales. This special issue is a product of that programme, containing papers aimed at a broad readership covering observations, experiments, and theoretical and computational developments in a range of topics in fluid dynamics, plasma physics and active matter. This article is part of the theme issue ‘Anti-diffusive transport and layering: from sub-cellular to astrophysical scales’.

Ventricular arrhythmias, like ventricular tachycardia (VT) and ventricular fibrillation (VF), precipitate sudden cardiac death, which is the leading cause of mortality in the industrialized 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 analogs of low-amplitude defibrillation by the application of currents that can eliminate spiral waves. We develop an efficient deep-neural-network 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 ξ 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 ξ is large and vice versa.

In our solar system, Jupiter possesses the strongest magnetosphere, with radiation belts filled with ultrarelativistic charged particles. These particles are trapped along Jupiter’s closed magnetic field lines, where they undergo gyration, bounce, and drift motions. Traditionally, the quasiperiodic behavior associated with each of these motions has been explained using gyrocenter approximation–based theoretical or simulation models. However, ultrarelativistic charged particles (with energies in the MeV–GeV range) have large gyroradii, which can give rise to nonadiabatic behavior. In such cases, while the particles remain confined within Jupiter’s magnetic field, their motion may no longer remain periodic. As a result, conventional theoretical models fail to describe their trajectories accurately. We investigate the intermittent behavior that emerges in this ultrarelativistic system of charged particles by analyzing the velocity structure function of energetic charged particles in a manner that is akin to the study of the intermittency of Lagrangian-particle trajectories in fluid turbulence. For this purpose, we have performed three-dimensional relativistic test-particle simulations, introducing protons with energies ranging from 1 to 500 GeV into Jupiter’s inner radiation belt. We have examined both the adiabatic case (1 GeV) and the nonadiabatic cases (100 and 500 GeV) in detail. Our results show that, in the nonadiabatic regime, ultrarelativistic charged-particle trajectories exhibit intermittency on timescales of 10–272 ms, which are significantly shorter than the expected gyroperiods in this region. These findings provide conclusive evidence for the multiscale nature of ultrarelativistic particle dynamics in Jupiter’s radiation belts.

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 (DMHs). 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 A and the Poisson equation for self-gravity. This article is part of the theme issue ‘Frontiers of turbulence and statistical physics’.

The 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.

Focal arrhythmias, which arise from delayed afterdepolarizations (DADs), are observed in various pathophysiological heart conditions; these can lead to sudden cardiac death. A clear understanding of the interplay of electrophysiological factors of cardiac myocytes, which lead to DADs, can suggest pharmacological targets that can eliminate DAD-induced arrhythmias. Therefore, we carry out multiscale investigations of two mathematical models for human-ventricular myocytes, namely, the ten Tusscher-Panfilov TP06 model and the HuVEC15 model of Himeno, et al., at the levels of single myocytes, one- and two-dimensional (1D and 2D) tissue, and anatomically realistic bi-ventricular domains. We demonstrate that the Sarco/endoplasmic reticulum Ca ²⁺ -ATPase (SERCA) pump uptake rate and the Ca ²⁺ leak through the ryanodine-receptor (RyR) channel impact this transition significantly. We show that the frequencies and amplitudes of the DADs are key features that can be used to classify them into three types, at the single-myocyte level. By carrying out detailed parameter-sensitivity analyses, we identify the electrophysiological parameters, in the myocyte models, that most affect these key features. We then obtain stability (or phase) diagrams that show the regions of parameter space in which different types of DADs occur. By comparing differences in model compartmentalizations, we show that these structural features can significantly influence both the occurrence and the types of DADs. We demonstrate in the TP06 model, the Na ⁺ /Ca ²⁺ exchanger can also play a protective role in the elimination of DADs, and the presence of late calcium releases can enhance this effect. We present representative tissue simulations of the spatiotemporal evolution of waves of electrical activation, in these models, to illustrate how arrhythmogenic premature ventricular complexes (PVCs) emerge from patches of DAD cells, when we pace the tissue.