arXiv subjects

Rahul Pandit

Publications and source records attributed to Rahul Pandit.

At least 73 records · Page 4Linked to original sources

arXiv2019

The formation of compact objects at finite temperatures in a dark-matter-candidate self-gravitating bosonic system

We study self-gravitating bosonic systems, candidates for dark-matter halos, by carrying out a suite of direct numerical simulations (DNSs) designed to investigate the formation of finitetemperature, compact objects in the three-dimensional (3D) Fourier-truncated Gross-Pitaevskii-Poisson equation (GPPE). This truncation allows us to explore the collapse and fluctuations of compact objects, which form at both zero temperature and finite temperature. We show that the statistically steady state of the GPPE, in the large-time limit and for the system sizes we study, can also be obtained efficiently by tuning the temperature in an auxiliary stochastic Ginzburg-Landau-Poisson equation (SGLPE). We show that, over a wide range of model parameters, this system undergoes a thermally driven first-order transition from a collapsed, compact, Bose-Einstein condensate (BEC) to a tenuous Bose gas without condensation. By a suitable choice of initial conditions in the GPPE, we also obtain a binary condensate that comprises a pair of collapsed objects rotating around their center of mass.

cond-mat.quant-gas↗

arXiv2019

The one-dimensional Kardar-Parisi-Zhang and Kuramoto-Sivashinsky universality class: limit distributions

Tracy-Widom and Baik-Rains distributions appear as universal limit distributions for height fluctuations in the one-dimensional Kardar-Parisi-Zhang (KPZ) \textit{stochastic} partial differential equation (PDE). We obtain the same universal distributions in the spatiotemporally chaotic, nonequilibrium, but statistically steady state (NESS) of the one-dimensional Kuramoto-Sivashinsky (KS) \textit{deterministic} PDE, by carrying out extensive pseudospectral direct numerical simulations to obtain the spatiotemporal evolution of the KS height profile $h(x,t)$ for different initial conditions. We establish, therefore, that the statistical properties of the 1D KS PDE in this state are in the 1D KPZ universality class.

cond-mat.stat-mech↗

arXiv2019

Deep-learning-assisted detection and termination of spiral- and broken-spiral waves in mathematical models for cardiac tissue

Unbroken and broken spiral waves, in partial-differential-equation (PDE) models for cardiac tissue, are the mathematical analogs of life-threatening cardiac arrhythmias, namely, ventricular tachycardia (VT) and ventricular-fibrillation (VF). We develop a (a) deep-learning method for the detection of unbroken and broken spiral waves and (b) the elimination of such waves, e.g., by the application of low-amplitude control currents in the cardiac-tissue context. Our method is based on a convolutional neural network (CNN) that we train to distinguish between patterns with spiral waves S and without spiral waves NS. We obtain these patterns by carrying out extensive direct numerical simulations (DNS) of PDE models for cardiac tissue in which the transmembrane potential V, when portrayed via pseudocolor plots, displays patterns of electrical activation of types S and NS. We then utilize our trained CNN to obtain, for a given pseudocolor image of V, a heat map that has high intensity in the regions where this image shows the cores of spiral waves. Given this heat map, we show how to apply low-amplitude Gaussian current pulses to eliminate spiral waves efficiently. Our in silico results are of direct relevance to the detection and elimination of these arrhythmias because our elimination of unbroken or broken spiral waves is the mathematical analog of low-amplitude defibrillation.

physics.bio-ph↗

arXiv2019

Two-dimensional magnetohydrodynamic turbulence with large and small energy-injection length scales

Two-dimensional magnetohydrodynamics (2D MHD), forced at (a) large length scales or (b) small length scales, displays turbulent, but statistically steady, states with widely different statistical properties. We present a systematic, comparative study of these two cases (a) and (b) by using direct numerical simulations (DNSs). We find that, in case (a), there is energy equipartition between the magnetic and velocity fields, whereas, in case (b), such equipartition does not exist. By computing various probability distribution functions (PDFs), we show that case (a) displays extreme events that are much less common in case (b).

physics.flu-dyn↗

arXiv2018

Comparisons of wave dynamics in Hodgkin-Huxley and Markov-state formalisms for the Sodium (Na) channel in some mathematical models for human cardiac tissue

We compare and contrast spiral- and scroll-wave dynamics in five different mathematical models for cardiac tissue. The first is the TP06 model, due to ten Tusscher and Panfilov, which is based on the Hodgkin-Huxley formalism; the remaining four are Markov-state models, MM1 WT and MM2 WT, for the wild-type (WT) Na channel, and MM1 MUT and MM2 MUT, for the mutant Na channel. Our results are based on extensive direct numerical simulations of waves of electrical activation in these models, in two- and three-dimensional (2D and 3D) homogeneous simulation domains and also in domains with localised heterogeneities, either obstacles with randomly distributed inexcitable regions or mutant cells in a wild-type background. Our study brings out the sensitive dependence of spiral- and scroll-wave dynamics on these five models and the parameters that define them. We also explore the control of spiral-wave turbulence in these models.

physics.bio-ph↗

arXiv2018

Transport, multifractality, and the breakdown of single-parameter scaling at the localization transition in quasiperiodic systems

There has been a revival of interest in localization phenomena in quasiperiodic systems with a view to examining how they differ fundamentally from such phenomena in random systems. Mo- tivated by this, we study transport in the quasiperiodic, one-dimentional (1d) Aubry-Andre model and its generalizations to 2d and 3d. We study the conductance of open systems, connected to leads, as well as the Thouless conductance, which measures the response of a closed system to boundary perturbations. We find that these conductances show signatures of a metal-insulator transition from an insulator, with localized states, to a metal, with extended states having (a) ballistic transport (1d), (b) superdiffusive transport (2d), or (c) diffusive transport (3d); precisely at the transition, the system displays sub-diffusive critical states. We calculate the beta function $β(g) = dln(g)/dln(L)$ and show that, in 1d and 2d, single-parameter scaling is unable to describe the transition. Further- more, the conductances show strong non-monotonic variations with L and an intricate structure of resonant peaks and subpeaks. In 1d the positions of these peaks can be related precisely to the prop- erties of the number that characterizes the quasiperiodicity of the potential; and the L-dependence of the Thouless conductance is multifractal. We find that, as d increases, this non-monotonic de- pendence of g on L decreases and, in 3d, our results for $β(g)$ are reasonably well approximated by single-parameter scaling.

cond-mat.dis-nn↗

arXiv2018

Ionic-heterogeneity-induced spiral- and scroll-wave turbulence in mathematical models of cardiac tissue

Spatial variations in the electrical properties of cardiac tissue can occur because of cardiac diseases. We introduce such gradients into mathematical models for cardiac tissue and then study, by extensive numerical simulations, their effects on reentrant electrical waves and their stability in both two and three dimensions. We explain the mechanism of spiral- and scroll-wave instability, which entails anisotropic thinning in the wavelength of the waves because of anisotropic variation in its electrical properties.

physics.bio-ph↗

arXiv2018

Exotic Multifractal Conductance Fluctuations in Graphene

In quantum systems, signatures of multifractality are rare. They have been found only in the multiscaling of eigenfunctions at critical points. Here we demonstrate multifractality in the magnetic-field-induced universal conductance fluctuations of the conductance in a quantum condensed-matter system, namely, high-mobility single-layer graphene field-effect transistors. This multifractality decreases as the temperature increases or as doping moves the system away from the Dirac point. Our measurements and analysis present evidence for an incipient Anderson-localization near the Dirac point as the most plausible cause for this multifractality. Our experiments suggest that multifractality in the scaling behaviour of local eigenfunctions are reflected in macroscopic transport coefficients. We conjecture that an incipient Anderson-localization transition may be the origin of this multifractality. It is possible that multifractality is ubiquitous in transport properties of low-dimensional systems. Indeed, our work suggests that we should look for multifractality in transport in other low-dimensional quantum condensed-matter systems.

cond-mat.mes-hall↗

arXiv2017

Heavy inertial particles in turbulent flows gain energy slowly but lose it rapidly

We present an extensive numerical study of the time irreversibility of the dynamics of heavy inertial particles in three-dimensional, statistically homogeneous and isotropic turbulent flows. We show that the probability density function (PDF) of the increment, $W(τ)$, of a particle's energy over a time-scale $τ$ is non-Gaussian, and skewed towards negative values. This implies that, on average, particles gain energy over a period of time that is longer than the duration over which they lose energy. We call this $\textit{slow gain}$ and $\textit{fast loss}$. We find that the third moment of $W(τ)$ scales as $τ^3$, for small values of $τ$. We show that the PDF of power-input $p$ is negatively skewed too; we use this skewness ${\rm Ir}$ as a measure of the time-irreversibility and we demonstrate that it increases sharply with the Stokes number ${\rm St}$, for small ${\rm St}$; this increase slows down at ${\rm St} \simeq 1$. Furthermore, we obtain the PDFs of $t^+$ and $t^-$, the times over which $p$ has, respectively, positive or negative signs, i.e., the particle gains or loses energy. We obtain from these PDFs a direct and natural quantification of the the slow-gain and fast-loss of the particles, because these PDFs possess exponential tails, whence we infer the characteristic loss and gain times $t_{\rm loss}$ and $t_{\rm gain}$, respectively; and we obtain $t_{\rm loss} < t_{\rm gain}$, for all the cases we have considered. Finally, we show that the slow-gain in energy of the particles is equally likely in vortical or strain-dominated regions of the flow; in contrast, the fast-loss of energy occurs with greater probability in the latter than in the former.

physics.flu-dyn↗

arXiv2017

The role of BKM-type theorems in $3D$ Euler, Navier-Stokes and Cahn-Hilliard-Navier-Stokes analysis

The Beale-Kato-Majda theorem contains a single criterion that controls the behaviour of solutions of the $3D$ incompressible Euler equations. Versions of this theorem are discussed in terms of the regularity issues surrounding the $3D$ incompressible Euler and Navier-Stokes equations together with a phase-field model for the statistical mechanics of binary mixtures called the $3D$ Cahn-Hilliard-Navier-Stokes (CHNS) equations. A theorem of BKM-type is established for the CHNS equations for the full parameter range. Moreover, for this latter set, it is shown that there exists a Reynolds number and a bound on the energy-dissipation rate that, remarkably, reproduces the $Re^{3/4}$ upper bound on the inverse Kolmogorov length normally associated with the Navier-Stokes equations alone. An alternative length-scale is introduced and discussed, together with a set of pseudo-spectral computations on a $128^{3}$ grid.

nlin.CD↗

arXiv2017

Particles and Fields in Superfluids: Insights from the Two-dimensional Gross-Pitaevskii Equation

We carry out extensive direct numerical simulations (DNSs) to investigate the interaction of active particles and fields in the two-dimensional (2D) Gross-Pitaevskii (GP) superfluid, in both simple and turbulent flows. The particles are active in the sense that they affect the superfluid even as they are affected by it. We tune the mass of the particles, which is an important control parameter. At the one-particle level, we show how light, neutral, and heavy particles move in the superfluid, when a constant external force acts on them; in particular, beyond a critical velocity, at which a vortex-antivortex pair is emitted, particle motion can be periodic or chaotic. We demonstrate that the interaction of a particle with vortices leads to dynamics that depends sensitively on the particle characteristics. We also demonstrate that assemblies of particles and vortices can have rich, and often turbulent spatiotemporal evolution. In particular, we consider the dynamics of the following illustrative initial configurations: (a) one particle placed in front of a translating vortex-antivortex pair; (b) two particles placed in front of a translating vortex-antivortex pair; (c) a single particle moving in the presence of counter-rotating vortex clusters; and (d) four particles in the presence of counter-rotating vortex clusters. We compare our work with earlier studies and examine its implications for recent experimental studies in superfluid Helium and Bose-Einstein condensates.

cond-mat.quant-gas↗

arXiv2017

The statistical properties of spiral- and scroll-wave turbulence in cardiac tissue

Disorganized electrical activity in the heart leads to sudden cardiac death. To what extent can this electrical turbulence be viewed as classical fluid turbulence,which is an important central problem in modern physics? We investigate,for the first time,via extensive DNSs,the statistical properties of spiral-and scroll-wave turbulence in two- and three-dimensional excitable media by using approaches employed in studies of classical turbulence. We use the Panfilov and the Aliev-Panfilov mathematical models for cardiac tissue. We show that once electrical-wave turbulence has been initiated,there is a forward cascade,in which spirals or scrolls form,interact,and break to yield a turbulent state that is statistically steady and,far away from boundaries,is statistically homogeneous and isotropic. For the transmembrane potential $V$ and the slow recovery variable $g$,which define our models,we define $E_V(k)$ and $E_g(k)$,the electrical-wave analogs of the fluid energy spectrum $E(k)$ in fluid turbulence. We show that $E_V(k)$ and $E_g(k)$ are spread out over several decades in $k$. Thus spiral- and scroll-wave turbulence involves a wide range of spatial scales. $E_V(k)$ and $E_g(k)$ show approximate power laws,in some range of $k$, however,their exponents cannot be determined as accurately as their fluid-turbulence counterparts. The dimensionless ratio $L/λ$ is a convenient control parameter like the Reynolds number for fluid turbulence,where $L$ is the linear size of the domain and $λ$ the wavelength of a plane wave in the medium. By comparing several other statistical properties for spiral- and scroll-wave turbulence with their fluid-turbulence counterparts,we show that,although spiral- and scroll-wave turbulence have some statistical properties like those of fluid turbulence,overall these types of turbulence are special and differ in important ways from fluid turbulence.

physics.bio-ph↗

arXiv2017

Melting of a nonequilibrium vortex crystal in a fluid film with polymers : elastic versus fluid turbulence

We perform a direct numerical simulation (DNS) of the forced, incompressible two-dimensional Navier-Stokes equation coupled with the FENE-P equations for the polymer-conformation tensor. The forcing is such that, without polymers and at low Reynolds numbers $\mbox{Re}$, the film attains a steady state that is a square lattice of vortices and anti-vortices. We find that, as we increase the Weissenberg number $\mbox{Wi}$, a sequence of nonequilibrium phase transitions transforms this lattice, first to spatially distorted, but temporally steady, crystals and then to a sequence of crystals that oscillate in time, periodically, at low $\mbox{Wi}$, and quasiperiodically, for slightly larger $\mbox{Wi}$. Finally, the system becomes disordered and displays spatiotemporal chaos and elastic turbulence. We then obtain the nonequilibrium phase diagram for this system, in the $\mbox{Wi} - Ω$ plane, where $Ω\propto {\mbox{Re}}$, and show that (a) the boundary between the crystalline and turbulent phases has a complicated, fractal-type character and (b) the Okubo-Weiss parameter $Λ$ provides us with a natural measure for characterizing the phases and transitions in this diagram.

physics.flu-dyn↗

arXiv2016

A regularity criterion for solutions of the three-dimensional Cahn-Hilliard-Navier-Stokes equations and associated computations

We consider the 3D Cahn-Hilliard equations coupled to, and driven by, the forced, incompressible 3D Navier-Stokes equations. The combination, known as the Cahn-Hilliard-Navier-Stokes (CHNS) equations, is used in statistical mechanics to model the motion of a binary fluid. The potential development of singularities (blow-up) in the contours of the order parameter $ϕ$ is an open problem. To address this we have proved a theorem that closely mimics the Beale-Kato-Majda theorem for the $3D$ incompressible Euler equations [Beale et al. Commun. Math. Phys., Commun. Math. Phys., ${\rm 94}$, $ 61-66 ({\rm 1984})$]. By taking an $L^{\infty}$ norm of the energy of the full binary system, designated as $E_{\infty}$, we have shown that $\int_{0}^{t}E_{\infty}(τ)\,dτ$ governs the regularity of solutions of the full 3D system. Our direct numerical simulations (DNSs), of the 3D CHNS equations, for (a) a gravity-driven Rayleigh Taylor instability and (b) a constant-energy-injection forcing, with $128^3$ to $512^3$ collocation points and over the duration of our DNSs, confirm that $E_{\infty}$ remains bounded as far as our computations allow.

physics.flu-dyn↗

arXiv2016

Two-dimensional, homogeneous, isotropic fluid turbulence with polymer additives

We present the most extensive direct numerical simulations, attempted so far, of statistically steady, homogeneous, isotropic turbulence in two-dimensional fluid films with air-drag-induced friction and with polymer additives. Our study reveals that the polymers (a) reduce the total fluid energy, enstrophy, and palinstrophy, (b) modify the fluid energy spectrum both in inverse- and forward-cascade regimes, (c) reduce small-scale intermittency, (d) suppress regions of large vorticity and strain rate, and (e) stretch in strain-dominated regions. We compare our results with earlier experimental studies; and we propose new experiments.

physics.flu-dyn↗

arXiv2016

Binary-Fluid Turbulence: Signatures of Multifractal Droplet Dynamics and Dissipation Reduction

We present an extensive direct numerical simulation of statistically steady, homogeneous, isotropic turbulence in two-dimensional, binary-fluid mixtures with air-drag-induced friction by using the Cahn-Hilliard-Navier-Stokes equations. We choose parameters, e.g., the surface tension, such that we have a droplet of the minority phase moving inside a turbulent background of the majority phase. We characterize the deformation of the droplet and show that it displays multifractal dynamics. The probability distribution functions of the components of the acceleration of the center of mass of the droplet exhibit wide, non-Gaussian tails. Our study reveals that the droplet enhances the energy spectrum $E(k)$ when the wavenumber $k$ is large; this enhancement leads to dissipation reduction.

physics.flu-dyn↗

arXiv2016

Dynamic multiscaling in magnetohydrodynamic turbulence

We present the first study of the multiscaling of time-dependent velocity and magnetic-field structure functions in homogeneous, isotropic magnetohydrodynamic (MHD) turbulence in three dimensions. We generalize the formalism that has been developed for analogous studies of time-dependent structure functions in fluid turbulence to MHD. By carrying out detailed numerical studies of such time-dependent structure functions in a shell model for three-dimensional MHD turbulence, we obtain both equal-time and dynamic scaling exponents.

physics.flu-dyn↗

arXiv2016

Instability of spiral and scroll waves in the presence of a gradient in the fibroblast density: the effects of fibroblast-myocyte coupling

Fibroblast-myocyte coupling can modulate electrical-wave dynamics in cardiac tissue. In diseased hearts, the distribution of fibroblasts is heterogeneous, so there can be gradients in the fibroblast density (henceforth we call this GFD) especially from highly injured regions, like infarcted or ischemic zones, to less-wounded regions of the tissue. Fibrotic hearts are known to be prone to arrhythmias, so it is important to understand the effects of GFD in the formation and sustenance of arrhythmic re- entrant waves, like spiral or scroll waves. Therefore, we investigate the effects of GFD on the stability of spiral and scroll waves of electrical activation in a state-of-the- art mathematical model for cardiac tissue in which we also include fibroblasts. By introducing GFD in controlled ways, we show that spiral and scroll waves can be unstable in the presence of GFDs because of regions with varying spiral or scroll-wave frequency ω, induced by the GFD. We examine the effects of the resting membrane potential of the fibroblast and the number of fibroblasts attached to the myocytes on the stability of these waves. Finally, we show that the presence of GFDs can lead to the formation of spiral waves at high-frequency pacing.

physics.bio-ph↗