Physica A-statistical Mechanics and Its Applications, 2002
We give an overview of our studies of spiral turbulence and spatiotemporal chaos in partialdi ere... more We give an overview of our studies of spiral turbulence and spatiotemporal chaos in partialdi erential-equation models for two excitable media: (a) the oxidation of carbon monoxide on Pt(1 1 0); and (b) ventricular ÿbrillation in mammalian hearts. Our characterization of spiral turbulence and spatiotemporal chaos in these models leads us to an e cient scheme for controlling such chaos. We discuss this scheme and its application for electrical deÿbrillation.
We show that different ways of extracting time scales from time-dependent velocity structure func... more 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.
Every sixth death in industrialised countries occurs because of cardiac arrhythmias like ventricu... more Every sixth death in industrialised countries occurs because of cardiac arrhythmias like ventricular tachycardia (VT) and ventricular fibrillation (VF). There is growing consensus that VT is associated with an unbroken spiral wave of electrical activation on cardiac tissue but VF with broken waves, spiral turbulence, spatiotemporal chaos and rapid, irregular activation. Thus spiral-wave activity in cardiac tissue has been studied extensively. Nevertheless many aspects of such spiral dynamics remain elusive because of the intrinsically high-dimensional nature of the cardiac-dynamical system. In particular, the role of tissue heterogeneities in the stability of cardiac spiral waves is still being investigated. Experiments with conduction blocks in cardiac tissue yield a variety of results: some suggest that blocks can eliminate VF partially or completely, leading to VT or quiescence, but others show that VF is unaffected by obstacles. We propose theoretically that this variety of results is a natural manifestation of a fractal boundary that must separate the basins of the attractors associated, respectively, with VF and VT. We substantiate this with extensive numerical studies of Panfilov and Luo-Rudy I models, where we show that the suppression of VF depends sensitively on the position, size, and nature of the inhomogeneity.
Ventricular fibrillation, the major reason behind sudden cardiac death, is turbulent cardiac elec... more 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 make 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.
We review some advances in the theory of homogeneous, isotropic turbulence. Our emphasis is on th... more We review some advances in the theory of homogeneous, isotropic turbulence. Our emphasis is on the new insights that have been gained from recent numerical studies of the three-dimensional Navier Stokes equation and simpler shell models for turbulence. In particular, we examine the status of multiscaling corrections to Kolmogorov scaling, extended self similarity, generalized extended self similarity, and non-Gaussian probability distributions for velocity differences and related quantities. We recount our recent proposal of a wave-vector-space version of generalized extended self similarity and show how it allows us to explore an intriguing and apparently universal crossover from inertial- to dissipation-range asymptotics.
We propose and verify a wave-vector-space version of generalized extended self similarity and bro... more 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 $4 \times 10^{4} \leq Re_{\lambda} \leq 3 \times 10^{6}\/$, we find that the inertial-range exponents ($\zeta_{p}\/$) of the order - $p\/$ structure functions do not approach their Kolmogorov value $p/3\/$ as $Re_{\lambda}\/$ increases.
We present a pseudospectral study of the randomly forced Navier-Stokes equation (RFNSE) stirred b... more We present a pseudospectral study of the randomly forced Navier-Stokes equation (RFNSE) stirred by a stochastic force with zero mean and a variance ϳk 42d2y , with k the wave vector and the dimension d 3. We provide the first evidence for multiscaling of velocity structure functions for y $ 4. We extract the multiscaling exponent ratios z p ͞z 2 by using extended self-similarity, examine their dependence on y, and show that, if y 4, they are in agreement with those obtained for the Navier-Stokes equation forced at large spatial scales (3DNSE). Also well-defined vortex filaments, which appear clearly in studies of the 3DNSE, are absent in the RFNSE. [S0031-9007(98)07657-1]
Physica A-statistical Mechanics and Its Applications, 2002
We give an overview of our studies of spiral turbulence and spatiotemporal chaos in partialdi ere... more We give an overview of our studies of spiral turbulence and spatiotemporal chaos in partialdi erential-equation models for two excitable media: (a) the oxidation of carbon monoxide on Pt(1 1 0); and (b) ventricular ÿbrillation in mammalian hearts. Our characterization of spiral turbulence and spatiotemporal chaos in these models leads us to an e cient scheme for controlling such chaos. We discuss this scheme and its application for electrical deÿbrillation.
We show that different ways of extracting time scales from time-dependent velocity structure func... more 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.
Every sixth death in industrialised countries occurs because of cardiac arrhythmias like ventricu... more Every sixth death in industrialised countries occurs because of cardiac arrhythmias like ventricular tachycardia (VT) and ventricular fibrillation (VF). There is growing consensus that VT is associated with an unbroken spiral wave of electrical activation on cardiac tissue but VF with broken waves, spiral turbulence, spatiotemporal chaos and rapid, irregular activation. Thus spiral-wave activity in cardiac tissue has been studied extensively. Nevertheless many aspects of such spiral dynamics remain elusive because of the intrinsically high-dimensional nature of the cardiac-dynamical system. In particular, the role of tissue heterogeneities in the stability of cardiac spiral waves is still being investigated. Experiments with conduction blocks in cardiac tissue yield a variety of results: some suggest that blocks can eliminate VF partially or completely, leading to VT or quiescence, but others show that VF is unaffected by obstacles. We propose theoretically that this variety of results is a natural manifestation of a fractal boundary that must separate the basins of the attractors associated, respectively, with VF and VT. We substantiate this with extensive numerical studies of Panfilov and Luo-Rudy I models, where we show that the suppression of VF depends sensitively on the position, size, and nature of the inhomogeneity.
Ventricular fibrillation, the major reason behind sudden cardiac death, is turbulent cardiac elec... more 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 make 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.
We review some advances in the theory of homogeneous, isotropic turbulence. Our emphasis is on th... more We review some advances in the theory of homogeneous, isotropic turbulence. Our emphasis is on the new insights that have been gained from recent numerical studies of the three-dimensional Navier Stokes equation and simpler shell models for turbulence. In particular, we examine the status of multiscaling corrections to Kolmogorov scaling, extended self similarity, generalized extended self similarity, and non-Gaussian probability distributions for velocity differences and related quantities. We recount our recent proposal of a wave-vector-space version of generalized extended self similarity and show how it allows us to explore an intriguing and apparently universal crossover from inertial- to dissipation-range asymptotics.
We propose and verify a wave-vector-space version of generalized extended self similarity and bro... more 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 $4 \times 10^{4} \leq Re_{\lambda} \leq 3 \times 10^{6}\/$, we find that the inertial-range exponents ($\zeta_{p}\/$) of the order - $p\/$ structure functions do not approach their Kolmogorov value $p/3\/$ as $Re_{\lambda}\/$ increases.
We present a pseudospectral study of the randomly forced Navier-Stokes equation (RFNSE) stirred b... more We present a pseudospectral study of the randomly forced Navier-Stokes equation (RFNSE) stirred by a stochastic force with zero mean and a variance ϳk 42d2y , with k the wave vector and the dimension d 3. We provide the first evidence for multiscaling of velocity structure functions for y $ 4. We extract the multiscaling exponent ratios z p ͞z 2 by using extended self-similarity, examine their dependence on y, and show that, if y 4, they are in agreement with those obtained for the Navier-Stokes equation forced at large spatial scales (3DNSE). Also well-defined vortex filaments, which appear clearly in studies of the 3DNSE, are absent in the RFNSE. [S0031-9007(98)07657-1]
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Papers by Rahul Pandit