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Rahul Pandit

Publications and source records attributed to Rahul Pandit.

At least 37 records · Page 2Linked to original sources
arXiv2025

Capture and release of quantum vortices using mechanical devices in low-temperature superfluids

We show that the Gross-Pitaevskii equation coupled with the wave equation for a wire (GP-W) provides a natural theoretical framework for understanding recent experiments employing a nanowire to detect a single quantum vortex in superfluid $^4 {\rm He}$. We uncover the complete spatiotemporal evolution of such wire-based vortex detection via direct numerical simulations of the GP-W system. Furthermore, by computing the spatiotemporal spectrum, we obtain the vortex-capture-induced change in the oscillation frequency of the wire. We quantify this frequency shift by plotting the wire's oscillation frequency versus time and obtain results that closely match experimental observations. In addition, we provide analytical support for our numerical results by deriving the dispersion relation for the oscillating wire, with and without a trapped vortex. We show that the Magnus force opens a gap in the wire dispersion relation. The size of the gap becomes the characteristic frequency of the wire when a vortex is trapped.

cond-mat.other↗
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 $ν$. 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 $y_t = 1/ν$ 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↗
arXiv2024

Turbulent cascade arrests and the formation of intermediate-scale condensates

Energy cascades lie at the heart of the dynamics of turbulent flows. In a recent study of turbulence in fluids with odd-viscosity [de Wit \textit{et al.}, Nature \textbf{627}, 515 (2024)], the two-dimensionalization of the flow at small scales leads to the arrest of the energy cascade and selection of an intermediate scale, between the forcing and the viscous scales. To investigate the generality of this phenomenon, we study a shell model that is carefully constructed to have three-dimensional turbulent dynamics at small wavenumbers and two-dimensional turbulent dynamics at large wavenumbers. The large scale separation that we can achieve in our shell model allows us to examine clearly the interplay between these dynamics, which leads to an arrest of the energy cascade at a transitional wavenumber and an associated accumulation of energy at the same scale. Such pile-up of energy around the transitional wavenumber is reminiscent of the formation of condensates in two-dimensional turbulence, \textit{but, in contrast, it occurs at intermediate wavenumbers instead of the smallest wavenumber

physics.flu-dyn↗
arXiv2024

Neutron-superfluid vortices and proton-superconductor flux tubes: Development of a minimal model for pulsar glitches

We develop a theoretical framework that allows us to explore the coupled motion of neutron-superfluid vortices and proton-superconductor flux tubes in a gravitationally collapsed condensate, which describe neutron stars that form pulsars. Our framework uses the 3D Gross-Pitaevskii-Poisson-Equation (GPPE) for neutron Cooper pairs, the Real-Time-Ginzburg-Landau equation (RTGLE) for proton Cooper pairs, the Maxwell equations for the vector potential ${\bf A}$, and Newtonian gravity and interactions, both direct and induced by the Poisson equation, between the neutron and proton subsystems. For a pulsar we include a crust potential, characterized by an angle $θ$, and frictional drag. By carrying out extensive direct numerical simulations, we obtain a variety of interesting results. We show that a rotating proton superconductor generates a uniform London magnetic field, which changes the field distribution inside flux tubes. In the absence of any direct interaction between the two species, they interact through the gravitational Poisson equation. The presence of attractive (repulsive) density-density interaction leads to the attraction (repulsion) between neutron vortices and proton flux tubes. The inclusion of the current-current interaction and the complete Maxwell equations allows us to quantify the entrainment effect that leads to induced magnetization of neutron vortices. We show that, with a strong external magnetic field ${\bf B}_{\rm ext}$, proton flux tubes are anchored to the crust, whereas neutron vortices leave the condensate and lead to abrupt changes of the crust angular momentum ${\rm J}_c$. The frictional term in the dynamical equation for $θ$ yields stick-slip dynamics that leads, in turn, to glitches in the time series of ${\rm J}_c$. By calculating various statistical properties of this time series, we demonstrate that they display self-organised criticality(SOC).

astro-ph.HE↗
arXiv2024

Liquid-Droplet Coalescence: CNN-based Reconstruction of Flow Fields from Concentration Fields

Liquid-droplet coalescence and the mergers of liquid lenses are problems of great practical and theoretical interest in fluid dynamics and the statistical mechanics of multi-phase flows. During such mergers, there is an interesting and intricate interplay between the shapes of the interfaces, separating two phases, and the background flow field. In experiments, it is easier to visualize concentration fields than to obtain the flow field. We demonstrate that two-dimensional (2D) encoder-decoder CNNs, 2D U-Nets, and three-dimensional (3D) U-Nets can be used to obtain flow fields from concentration fields here. To train these networks, we use concentration and flow fields, which we obtain from extensive direct numerical simulations (DNSs) of (a) the coalescence of two circular droplets in the two-component 2D Cahn-Hilliard-Navier-Stokes (CHNS) partial differential equations (PDEs), (b) liquid-lens mergers in the three-component 2D CHNS PDEs, and (c) spherical-droplet coalescence in the two-component 3D CHNS PDEs. We then show that, given test images of concentration fields, our trained models accurately predict the flow fields at both high and low Ohnesorge numbers $Oh$ (a dimensionless ratio of viscous stresses to the inertial and surface-tension forces). Using autoencoders and fully connected neural networks, we also investigate the mapping between the concentration and vorticity fields via low-dimensional latent variables for droplet mergers in the 2D CHNS system. We compare the accuracies of flow-field reconstruction based on the two approaches we employ. Finally, we use data from recent experiments on droplet coalescence to show how our method can be used to obtain the flow field from measurements of the concentration field.

physics.flu-dyn↗
arXiv2024

Early-time resonances in the three-dimensional wall-bounded axisymmetric Euler and related equations

We investigate the complex-time analytic structure of solutions of the 3D-axisymmetric, wall-bounded, incompressible Euler equations, by starting with the initial data proposed in Luo and Hou (2014), to study a possible finite-time singularity. We use our pseudospectral Fourier-Chebyshev method, with quadruple-precision arithmetic, to compute the time-Taylor series coefficients of the flow fields, up to a high order. We show that the resulting approximations display early-time resonances; the initial spatial location of these structures is different from that for the tygers, which we have obtained in Kolluru et al. (2022). We then perform asymptotic analysis of the Taylor-series coefficients, by using generalised ratio methods, to extract the location and nature of the convergence-limiting singularities and demonstrate that these singularities are distributed around the origin, in the complex-t2 plane, along two curves that resemble the shape of an eye. We obtain similar results for the 1D wall-approximation (of the full 3D-axisymmetric Euler equation) called the 1D HL model, for which we use Fourier-pseudospectral methods to compute the time-Taylor series coefficients of the flow fields. Our work examines the link between tygers, in Galerkin-truncated pseudospectral studies, and early-time resonances, in truncated time-Taylor expansions of solutions of PDEs, such as those we consider.

physics.flu-dyn↗
arXiv2024

Interfaces as transport barriers in two-dimensional Cahn-Hilliard-Navier-Stokes turbulence

We investigate the role of interfaces as transport barriers in binary-fluid turbulence by employing Lagrangian tracer particles. The Cahn-Hilliard-Navier-Stokes (CHNS) system of partial differential equations provides a natural theoretical framework for our investigations. For specificity, we utilize the two-dimensional (2D) CHNS system. We capture efficiently interfaces and their fluctuations in 2D binary-fluid turbulence by using extensive pseudospectral direct numerical simulations (DNSs) of the 2D CHNS equations. We begin with $n$ tracers within a droplet of one phase and examine their dispersal into the second phase. The tracers remain within the droplet for a long time before emerging from it, so interfaces act as transport barriers in binary-fluid turbulence. We show that the fraction of the number of particles inside the droplet decays exponentially and is characterized by a decay time $τ_ξ\sim R_0^{3/2}$ that increases with $R_0$, the radius of the initially circular droplet. Furthermore, we demonstrate that the average first-passage time $\langle τ\rangle$ for tracers inside a droplet is orders of magnitude larger than it is for transport out of a hypothetical circle with the same radius as the initially circular droplet. We examine the roles of the Okubo-Weiss parameter $Λ$, the fluctuations of the droplet perimeter, and the probability distribution function of $\cos(θ)$, with $θ$ the angle between the fluid velocity and the normal to a droplet interface, in trapping tracers inside droplets. We mention possible generalisations of our study.

physics.flu-dyn↗
arXiv2024

Phases, morphologies, and transitions in a membrane model for the endoplasmic reticulum

We introduce a novel model, comprising self-avoiding surfaces and incorporating edges and tubules, that is designed to characterize the structural morphologies and transitions observed within the endoplasmic reticulum (ER). By employing discretized models, we model smooth membranes with triangulated surfaces, and we utilize numerical variational methods to minimize energies associated with periodic morphologies. Our study obtains phases, their morphologies, and their transitions and examines their dependence on the membrane chemical potential, the line tensions, and the positive Gaussian curvature stiffness. By starting with diverse topological structures, we explore shape variations by using Surface Evolver, while maintaining fixed topology. Notably, we identify the region of parameter space where the model displays lamellae, with a lattice of helical edges connecting the layers; this resembles structures that have been observed in the rough ER. Furthermore, our investigation reveals an intricate phase diagram with periodic structures, including flat lamellar sheets, sponge phases, and configurations comprising tubules with junctions, which are akin to the morphology of the smooth ER. An estimation of lattice parameters is achieved through fluctuation analysis. Significantly, our model predicts a transition between homotopically equivalent lamellae, with helical edges and configurations featuring tubules with junctions.

cond-mat.soft↗
arXiv2024

Novel spectral methods for shock capturing and the removal of tygers in computational fluid dynamics

Spectral methods yield numerical solutions of the Galerkin-truncated versions of nonlinear partial differential equations involved especially in fluid dynamics. In the presence of discontinuities, such as shocks, spectral approximations develop Gibbs oscillations near the discontinuity. This causes the numerical solution to deviate quickly from the true solution. For spectral approximations of the 1D inviscid Burgers equation, nonlinear wave resonances lead to the formation of tygers in well-resolved areas of the flow, far from the shock. Recently, Besse(to be published) has proposed novel spectral relaxation (SR) and spectral purging (SP) schemes for the removal of tygers and Gibbs oscillations in spectral approximations of nonlinear conservation laws. For the 1D inviscid Burgers equation, it is shown that the novel SR and SP approximations of the solution converge strongly in L2 norm to the entropic weak solution, under an appropriate choice of kernels and related parameters. In this work, we carry out a detailed numerical investigation of SR and SP schemes when applied to the 1D inviscid Burgers equation and report the efficiency of shock capture and the removal of tygers. We then extend our study to systems of nonlinear hyperbolic conservation laws - such as the 2x2 system of the shallow water equations and the standard 3x3 system of 1D compressible Euler equations. For the latter, we generalise the implementation of SR methods to non-periodic problems using Chebyshev polynomials. We then turn to singular flow in the 1D wall approximation of the 3D-axisymmetric wall-bounded incompressible Euler equation. Here, in order to determine the blowup time of the solution, we compare the decay of the width of the analyticity strip, obtained from the pure pseudospectral method, with the improved estimate obtained using the novel spectral relaxation scheme.

math.NA↗
arXiv2024

Novel turbulence and coarsening arrest in active-scalar fluids

We uncover a new type of turbulence -- activity-induced homogeneous and isotropic turbulence in a model that has been employed to investigate motility-induced phase separation (MIPS) in a system of microswimmers. The active Cahn-Hilliard-Navier-Stokes equations (CHNS), also called active model H, provides a natural theoretical framework for our study. In this CHNS model, a single scalar order parameter $ϕ$, positive (negative) in regions of high (low) microswimmer density, is coupled with the velocity field $\bm u$. The activity of the microswimmers is governed by an activity parameter $ζ$ that is positive for \textit{extensile} swimmers and negative for \textit{contractile} swimmers. With extensile swimmers, this system undergoes complete phase separation, which is similar to that in binary-fluid mixtures. By carrying out pseudospectral direct numerical simulations (DNSs), we show, for the first time, that this model (a) develops an emergent nonequilibrium, but statistically steady, state (NESS) of active turbulence, for the case of contractile swimmers, if $ζ$ is sufficiently large and negative and (b) this turbulence arrests the phase separation. We quantify this suppression by showing how the coarsening-arrest length scale does not grow indefinitely, with time $t$, but saturates at a finite value at large times. We characterise the statistical properties of this active-scalar turbulence by employing energy spectra and fluxes and the spectrum of $ϕ$. For sufficiently high Reynolds numbers, the energy spectrum $\mathcal E(k)$ displays an inertial range, with a power-law dependence on the wavenumber $k$. We demonstrate that, in this range, the flux $Π(k)$ assumes a nearly constant, negative value, which indicates that the system shows an inverse cascade of energy, even though energy injection occurs over a wide range of wavenumbers in our active-CHNS model.

physics.flu-dyn↗
arXiv2023

Uncovering the multifractality of Lagrangian pair dispersion in shock-dominated turbulence

Lagrangian pair dispersion provides insights into mixing in turbulent flows. By direct numerical simulations (DNS) we show that the statistics of pair dispersion in the randomly forced two-dimensional Burgers equation, which is a typical model of shock-dominated turbulence, is very different from its incompressible counterpart because Lagrangian particles get trapped in shocks. We develop a heuristic theoretical framework that accounts for this -- a generalization of the multifractal model -- whose prediction of the scaling of Lagrangian exit times agrees well with our DNS.

physics.flu-dyn↗
arXiv2023

Gravity- and temperature-driven phase transitions in a model for collapsed axionic condensates

We show how to use the cubic-quintic Gross-Pitaevskii-Poisson equation (cq-GPPE) and the cubic-quintic Stochastic Ginzburg-Landau-Poisson equation (cq-SGLPE) to investigate the gravitational collapse of a tenuous axionic gas into a collapsed axionic condensate for both zero and finite temperature $T$. At $T=0$, we use a Gaussian Ansatz for a spherically symmetric density to obtain parameter regimes in which we might expect to find compact axionic condensates. We then go beyond this Ansatz, by using the cq-SGLPE to investigate the dependence of the axionic condensate on the gravitational strength $G$ at $T = 0$. We demonstrate that, as $G$ increases, the equilibrium configuration goes from a tenuous axionic gas, to flat sheets or $\textit{Zeldovich pancakes}$, cylindrical structures, and finally a spherical axionic condensate. By varying $G$, we show that there are first-order phase transitions, as the system goes from one of these structures to the next one; we find hysteresis loops that are associated with these transitions. We examine these states and the transitions between these states via the Fourier truncated cq-GPPE; and we also obtain the thermalized $T > 0$ states from the cq-SGLPE; the transitions between these states yield thermally driven first-order phase transitions and their associated hysteresis loops. Finally, we discuss how our cq-GPPE approach can be used to follow the spatiotemporal evolution of a rotating axionic condensate and also a rotating binary-axionic-condensate system; in particular, we demonstrate, in the former, the emergence of vortices at large angular speeds $Ω$ and, in the latter, the rich dynamics of the mergers of the components of this binary system, which can yield vortices in the process of merging.

astro-ph.CO↗
arXiv2023

Unveiling the Spatiotemporal Evolution of Liquid-Lens Coalescence: Self-Similarity, Vortex Quadrupoles, and Turbulence in a Three-Phase Fluid System

We demonstrate that the three-phase Cahn-Hilliard-Navier-Stokes (CHNS3) system provides a natural theoretical framework for studying liquid-lens coalescence, which has been investigated in recent experiments. Our extensive direct numerical simulations (DNSs) of lens coalescence, in the two and three dimensional (2D and 3D) CHNS3, uncover the rich spatiotemporal evolution of the fluid velocity $\bf u$ and vorticity $ω$, the concentration fields $c_1, \, c_2,$ and $c_3$ of the three liquids, and a generalized Laplace pressure $P^G_\mathcal{L}$, which we define in terms of these concentrations via a Poisson equation. We find, in agreement with experiments, that as the lenses coalesce, their neck height $h(t) \sim t^{α_v}$, with $α_v \simeq 1$ in the viscous regime, and $h(t) \sim t^{α_i}$, with $α_i \simeq 2/3$ in the inertial regime. We obtain the crossover from the viscous to the inertial regimes as a function of the Ohnesorge number $Oh$, a dimensionless combination of viscous stresses and inertial and surface tension forces. We show that a vortex quadrupole, which straddles the neck of the merging lenses, and $P^G_\mathcal{L}$ play crucial roles in distinguishing between the viscous- and inertial-regime growths of the merging lenses. In the inertial regime we find signatures of turbulence, which we quantify via kinetic-energy and concentration spectra. Finally, we examine the merger of asymmetric lenses, in which the initial stages of coalescence occur along the circular parts of the lens interfaces; in this case, we obtain power-law forms for the $h(t)$ with inertial-regime exponents that lie between their droplet-coalescence and lens-merger counterparts.

physics.flu-dyn↗
arXiv2023

The Statistical Properties of Superfluid Turbulence in $^4$He from the Hall-Vinen-Bekharevich-Khalatnikov Model

We obtain the von Kármán-Howarth relation for the stochastically forced three-dimensional Hall-Vinen-Bekharvich-Khalatnikov (3D HVBK) model of superfluid turbulence in Helium ($^4$He) by using the generating-functional approach. We combine direct numerical simulations (DNSs) and analyitcal studies to show that, in the statistically steady state of homogeneous and isotropic superfluid turbulence, in the 3D HVBK model, the probability distribution function (PDF) $P(γ)$, of the ratio $γ$ of the magnitude of the normal fluid velocity and superfluid velocity, has power-law tails that scale as $P(γ) \sim γ^3$, for $γ\ll 1$, and $P(γ) \sim γ^{-3}$, for $γ\gg 1$. Furthermore, we show that the PDF $P(θ)$, of the angle $θ$ between the normal-fluid velocity and superfluid velocity exhibits the following power-law behaviors: $P(θ)\sim θ$ for $θ\ll θ_*$ and $P(θ)\sim θ^{-4}$ for $θ_* \ll θ\ll 1$, where $θ_*$ is a crossover angle that we estimate. From our DNSs we obtain energy, energy-flux, and mutual-friction-transfer spectra, and the longitudinal-structure-function exponents for the normal fluid and the superfluid, as a function of the temperature $T$, by using the experimentally determined mutual-friction coefficients for superfluid Helium $^4$He, so our results are of direct relevance to superfluid turbulence in this system.

physics.flu-dyn↗
arXiv2023

Multiscale studies of delayed afterdepolarizations II: Calcium-overload-induced ventricular arrhythmias

Disturbances in calcium homeostasis in a cardiac myocyte can lead to calcium-overload conditions and abnormal calcium releases, which occur primarily in the following two phases of the action potential (AP): (a) triggered or late calcium release (LCR) during the plateau phase; (b) spontaneous calcium release (SCR) during the diastolic interval (DI). Experimental and numerical studies of LCRs and SCRs have suggested that these abnormal calcium releases can lead to triggered excitations and, thence to life-threatening ventricular arrhythmias. We explore this suggestion in detail by building on our work in the previous accompanying Paper I, where we have studied abnormal calcium releases and delayed afterdepolarizations (DADs) in two state-of-the-art mathematical models for human ventricular myocytes. Here, we carry out a detailed \textit{in-silico} study of one of these models, namely, the ten Tusscher-Panfilov TP06~\cite{ten2006alternans} model. We increase the L-type Ca-channel current $I_{\rm{CaL}}$ to trigger LCRs, and calcium leak through the ryanodine receptor (RyR) to trigger SCRs, in the myocyte. We then perform multiscale simulations of coupled TP06-model myocytes in tissue in one-, two-, and three-dimensional (1D, 2D, and 3D) domains, with clumps of DAD-capable myocytes, to demonstrate how these clumps precipitate premature ventricular complexes (PVCs) that lead, in turn, to fibrillatory excitations like spiral and scroll waves. We examine possible pharmacological implications of our study for the class of ventricular arrhythmias that result from Ca\textsuperscript{2+} overload.

q-bio.TO↗
arXiv2023

Multiscale studies of delayed afterdepolarizations I: A comparison of two biophysically realistic mathematical models for human ventricular myocytes

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 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 and the HuVEC15 model, at the levels of single myocytes, one- and two-dimensional (1D and 2D) tissue, and anatomically realistic bi-ventricular domains. By using continuation analysis, we uncover steady- to oscillatory-state transitions in the Ca\textsuperscript{2+} concentrations and show that they lead to DADs. We demonstrate that the Sarco/endoplasmic reticulum Ca\textsuperscript{2+}-ATPase (SERCA) pump uptake rate and the Ca\textsuperscript{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. 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 for different types of DADs. We demonstrate that the Na\textsuperscript{+}/Ca\textsuperscript{2+} exchanger plays a protective role by suppressing DADs in the TP06 model. We present tissue simulations to illustrate how arrhythmogenic premature ventricular complexes (PVCs) emerge from patches of DAD cells when we pace the tissue. We discuss the implications of our results for some DAD-induced ventricular arrhythmias, which we examine in detail in the companion Paper II.

q-bio.TO↗
arXiv2023

Inertial Particles in Superfluid Turbulence: Coflow and Counterflow

We use pseudospectral direct numerical simulations (DNSs) to solve the three-dimensional (3D) Hall-Vinen-Bekharevich-Khalatnikov (HVBK) model of superfluid Helium. We then explore the statistical properties of inertial particles, in both coflow and counterflow superfluid turbulence (ST) in the 3D HVBK system; particle motion is governed by a generalization of the Maxey-Riley-Gatignol equations. We first characterize the anisotropy of counterflow ST by showing that there exist large vortical columns. The light particles show confined motion as they are attracted towards these columns and they form large clusters; by contrast, heavy particles are expelled from these vortical regions. We characterise the statistics of such inertial particles in 3D HVBK ST: (1) The mean angle $Θ(τ)$, between particle positions, separated by the time lag $τ$, exhibits two different scaling regions in (a) dissipation and (b) inertial ranges, for different values of the parameters in our model; in particular, the value of $Θ(τ)$, at large $τ$, depends on the magnitude of ${\bf U}_{ns}$. (2) The irreversibility of 3D HVBK turbulence is quantified by computing the statistics of energy increments for inertial particles. (3) The probability distribution function (PDF) of energy increments is of direct relevance to recent experimental studies of irreversibility in superfluid turbulence; we find, in agreement with these experiments, that, for counterflow ST, the skewness of this PDF is less pronounced than its counterparts for coflow ST or for classical-fluid turbulence.

physics.flu-dyn↗