arXiv subjects

Rahul Pandit

Publications and source records attributed to Rahul Pandit.

122 records · Page 7Linked to original sources

arXiv2005

Drag Reduction by Polymer Additives in Decaying Turbulence

We present results from a systematic numerical study of decaying turbulence in a dilute polymer solution by using a shell-model version of the FENE-P equations. Our study leads to an appealing definition of drag reduction for the case of decaying turbulence. We exhibit several new results, such as the potential-energy spectrum of the polymer, hitherto unobserved features in the temporal evolution of the kinetic-energy spectrum, and characterize intermittency in such systems. We compare our results with the GOY shell model for fluid turbulence.

cond-mat.stat-mech↗

arXiv2005

Is Multiscaling an Artifact in the Stochastically Forced Burgers Equation?

We study turbulence in the one-dimensional Burgers equation with a white-in-time, Gaussian random force that has a Fourier-space spectrum $\sim 1/k$, where $k$ is the wave number. From very-high-resolution numerical simulations, in the limit of vanishing viscosity, we find evidence for multiscaling of velocity structure functions which cannot be falsified by standard tests. We find a new artifact in which logarithmic corrections can appear disguised as anomalous scaling and conclude that bifractal scaling is likely.

nlin.CD↗

arXiv2004

Superfluid, Mott-Insulator, and Mass-Density-Wave Phases in the One-Dimensional Extended Bose-Hubbard Model

We use the finite-size density-matrix-renormalization-group (FSDMRG) method to obtain the phase diagram of the one-dimensional ($d = 1$) extended Bose-Hubbard model for density $ρ= 1$ in the $U-V$ plane, where $U$ and $V$ are, respectively, onsite and nearest-neighbor interactions. The phase diagram comprises three phases: Superfluid (SF), Mott Insulator (MI) and Mass Density Wave (MDW). For small values of $U$ and $V$, we get a reentrant SF-MI-SF phase transition. For intermediate values of interactions the SF phase is sandwiched between MI and MDW phases with continuous SF-MI and SF-MDW transitions. We show, by a detailed finite-size scaling analysis, that the MI-SF transition is of Kosterlitz-Thouless (KT) type whereas the MDW-SF transition has both KT and two-dimensional-Ising characters. For large values of $U$ and $V$ we get a direct, first-order, MI-MDW transition. The MI-SF, MDW-SF and MI-MDW phase boundaries join at a bicritical point at ($U, V) = (8.5 \pm 0.05, 4.75 \pm 0.05)$.

cond-mat.supr-con↗

arXiv2004

The Decay of Magnetohydrodynamic Turbulence from Power-Law Initial Conditions

We derive relations for the decay of the kinetic and magnetic energies and the growth of the Taylor and integral scales in unforced, incompressible, homogeneous and isotropic three-dimensional magnetohydrodynamic (3DMHD) turbulence with power-law initial energy spectra. We also derive bounds for the decay of the cross- and magnetic helicities. We then present results from systematic numerical studies of such decay both within the context of an MHD shell model and direct numerical simulations (DNS) of 3DMHD. We show explicitly that our results about the power-law decay of the energies hold for times $t<t_*$, where $t_*$ is the time at which the integral scales become comparable to the system size. For $t<t_*$, our numerical results are consistent with those predicted by the principle of `permanence of large eddies'.

cond-mat.stat-mech↗

arXiv2003

The Varieties of Dynamic Multiscaling in Fluid Turbulence

We show that different ways of extracting time scales from time-dependent velocity structure functions lead to different dynamic-multiscaling exponents in fluid turbulence. These exponents are related to equal-time multiscaling exponents by different classes of bridge relations which we derive. We check this explicitly by detailed numerical simulations of the GOY shell model for fluid turbulence. Our results can be generalized to any system in which both equal-time and time-dependent structure functions show multiscaling.

nlin.CD↗

arXiv2003

Noise Correlations in Shear Flows

We consider the effects of a shear on velocity fluctuations in a flow. The shear gives rise to a transient amplification that not only influences the amplitude of perturbations but also their time correlations. We show that, in the presence of white noise, time correlations of transversal velocity components are exponential and that correlations of the longitudinal components are exponential with an algebraic prefactor. Cross correlations between transversal and downstream components are strongly asymmetric and provide a clear indication of non-normal amplification. We suggest experimental tests of our predictions.

nlin.CD↗

arXiv2001

Defibrillation via the Elimination of Spiral Turbulence in a Model for Ventricular Fibrillation

Ventricular fibrillation, the major reason behind sudden cardiac death, is turbulent cardiac electrical activity in which rapid, irregular disturbances in the spatiotemporal electrical activation of the heart makes it incapable of any concerted pumping action. Methods of controlling ventricular fibrillation include electrical defibrillation as well as injected medication. Electrical defibrillation, though widely used, involves subjecting the whole heart to massive, and often counterproductive, electrical shocks. We propose a defibrillation method that uses a very-low-amplitude shock (of order mV) applied for a brief duration (of order 100 ms) and over a coarse mesh of lines on our model ventricle.

nlin.CD↗

arXiv2000

Spiral Turbulence: From the Oxidation of CO on Pt(110) to Ventricular Fibrillation

We give a brief overview of systems that show spiral patterns and spatiotemporally chaotic states. We concentrate on two physical systems: (1) the oxidation of CO on Pt(110) and (2) ventricular fibrillation in hearts. The equations that have been suggested as simple models for these two different systems are closely related for they are both {\it excitable media}. We present these equations and give a short summary of the phenomena they yield.}

nlin.CD↗

arXiv1999

Inequivalence of Dynamical Ensembles in a Generalised Driven Diffusive Lattice Gas

We generalise the Driven Diffusive Lattice Gas (DDLG) model by using a combination of Kawasaki and Glauber dynamics. We find via Monte Carlo simulations and perturbation studies that the simplest possible generalisation of the equivalence of the canonical and grand-canonical ensembles, which holds in equilibrium, does not apply for this class of nonequilibrium systems.

cond-mat↗

arXiv1997

Turbulence and Multiscaling in the Randomly Forced Navier Stokes Equation

We present an extensive pseudospectral study of the randomly forced Navier-Stokes equation (RFNSE) stirred by a stochastic force with zero mean and a variance $\sim k^{4-d-y}$, where $k$ is the wavevector and the dimension $d = 3$. We present the first evidence for multiscaling of velocity structure functions in this model for $y \geq 4$. We extract the multiscaling exponent ratios $ζ_p/ζ_2$ by using extended self similarity (ESS), examine their dependence on $y$, and show that, if $y = 4$, they are in agreement with those obtained for the deterministically forced Navier-Stokes equation ($3d$NSE). We also show that well-defined vortex filaments, which appear clearly in studies of the $3d$NSE, are absent in the RFNSE.

chao-dyn↗

arXiv1997

Multiscaling in Models of Magnetohydrodynamic Turbulence

From a direct numerical simulation of the MHD equations we show, for the first time, that velocity and magnetic-field structure functions exhibit multiscaling, extended self similarity (ESS), and generalized extended self similarity (GESS). We also propose a new shell model for homogeneous and isotropic MHD turbulence, which preserves all the invariants of ideal MHD, reduces to a well-known shell model for fluid turbulence for zero magnetic field, has no adjustable parameters apart from Reynolds numbers, and exhibits the same multiscaling, ESS, and GESS as the MHD equations. We also study dissipation-range asymptotics and the inertial- to dissipation-range crossover.

chao-dyn↗

arXiv1996

Inertial- and Dissipation-Range Asymptotics in Fluid Turbulence

We propose and verify a wave-vector-space version of generalized extended self similarity and broaden its applicability to uncover intriguing, universal scaling in the far dissipation range by computing high-order ($\leq 20\/$) structure functions numerically for: (1) the three-dimensional, incompressible Navier Stokes equation (with and without hyperviscosity); and (2) the GOY shell model for turbulence. Also, in case (2), with Taylor-microscale Reynolds numbers $4 \times 10^{4} \leq Re_λ \leq 3 \times 10^{6}\/$, we find that the inertial-range exponents ($ζ_{p}\/$) of the order - $p\/$ structure functions do not approach their Kolmogorov value $p/3\/$ as $Re_λ\/$ increases.

chao-dyn↗

arXiv1996

The Exotic Barium Bismuthates

We review the remarkable properties, including superconductivity, charge-density-wave ordering, and metal-insulator transitions, of lead- and potassium-doped barium bismuthate. We discuss some of the early theoretical studies of these systems. Our recent theoretical work, on the negative-$U\/$, extended-Hubbard model for these systems, is also described. Both the large- and intermediate-$U\/$ regimes of this model are examined, using mean-field and random-phase approximations, particularly with a view to fitting various experimental properties of these bismuthates. On the basis of our studies, we point out possibilities for exotic physics in these systems. We also emphasize the different consequences of electronic and phonon-mediated mechanisms for the negative $U.\/$ We show that, for an electronic mechanism, the \secin \,\,phases of these bismuthates must be unique, with their transport properties {\it dominated by charge $\pm 2e$ Cooperon bound states}. This can explain the observed difference between the optical and transport gaps. We propose other experimental tests for this novel mechanism of charge transport and comment on the effects of disorder.

cond-mat↗

arXiv1994

Nonequilibrium Phase Transitions in a Driven Sandpile Model

We construct a driven sandpile slope model and study it by numerical simulations in one dimension. The model is specified by a threshold slope $σ_c\/$, a parameter $α\/$, governing the local current-slope relation (beyond threshold), and $j_{\rm in}$, the mean input current of sand. A nonequilibrium phase diagram is obtained in the $α\, -\, j_{\rm in}\/$ plane. We find an infinity of phases, characterized by different mean slopes and separated by continuous or first-order boundaries, some of which we obtain analytically. Extensions to two dimensions are discussed.

cond-mat↗