Showing papers by "Ramakrishna Ramaswamy published in 1999"
TL;DR: These densities, which are used to characterize the nonuniform spatial organization on chaotic attractors, are robust to noise and can, therefore, be measured from experimental data.
Abstract: We study the probability densities of finite-time or local Lyapunov exponents in low-dimensional chaotic systems. While the multifractal formalism describes how these densities behave in the asymptotic or long-time limit, there are significant finite-size corrections, which are coordinate dependent. Depending on the nature of the dynamical state, the distribution of local Lyapunov exponents has a characteristic shape. For intermittent dynamics, and at crises, dynamical correlations lead to distributions with stretched exponential tails, while for fully developed chaos the probability density has a cusp. Exact results are presented for the logistic map, $\stackrel{\ensuremath{\rightarrow}}{x}4x(1\ensuremath{-}x).$ At intermittency the density is markedly asymmetric, while for ``typical'' chaos, it is known that the central limit theorem obtains and a Gaussian density results. Local analysis provides information on the variation of predictability on dynamical attractors. These densities, which are used to characterize the nonuniform spatial organization on chaotic attractors, are robust to noise and can, therefore, be measured from experimental data.
74 citations
TL;DR: In this article, it was shown that the Lyapunov exponent is non-positive and symmetry breaking associated with the creation of SNAs are robust and occur in a large class of systems.
Abstract: Strange nonchaotic attractors (SNAs) can be created due to the collision of an invariant curve with itself. This novel "homoclinic" transition to SNAs occurs in quasiperiodically driven maps which derive from the discrete Schrodinger equation for a particle in a quasiperiodic potential. In the classical dynamics, there is a transition from torus attractors to SNAs, which, in the quantum system, is manifest as the localization transition. This equivalence provides new insight into a variety of properties of SNAs, including its fractal measure. Further, there is a symmetry breaking associated with the creation of SNAs which rigorously shows that the Lyapunov exponent is nonpositive. We show that these characteristics associated with the appearance of SNA are robust and occur in a large class of systems.
50 citations
TL;DR: In this article, the behavior of granular material is controlled by the interplay of two factors (levitation due to upward airflow and sliding back due to gravity) in a shallow fluidized bed.
Abstract: The results of the experimental study of the dynamics of a shallow fluidized bed are reported. The behavior of granular material is controlled by the interplay of two factors--levitation due to the upward airflow, and sliding back due to gravity. Near the threshold of instability, the system shows critical behavior with remarkably long transient dynamics. The experimental observations are compared with a simple cellular automata model. (c) 1999 The American Physical Society.
10 citations
TL;DR: In this article, the structural and dynamical aspects of 13-atom binary rare-gas clusters of Ar and Xe were studied using constant energy molecular dynamics simulations and the ground state geometry for Ar n Xe 13−n, n=1−12, remains near-icosahedral, with an Ar atom occupying the central position.
Abstract: We study the structural and dynamical aspects of 13–atom binary rare-gas clusters of Ar and Xe using constant–energy molecular dynamics simulations. The ground state geometry for Ar n Xe 13−n , n=1−12, remains near-icosahedral, with an Ar atom occupying the central position. The thermodynamic properties of these clusters are significantly different from the pure 13-atom Ar or Xe clusters and for Xe–dominated compositions, melting is preceded by a surface–melting stage. Slow oscillations of the short-time-averaged (STA) temperature are observed both for surface–melting and complete melting stage, suggesting dynamical coexistence between different phases. At the complete melting stage, the oscillations in the STA temperature and the species of the central atom are correlated.
2 citations
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TL;DR: In this article, the invariant measure on the attractor is modified to make chaotic motion in low-dimensional dynamical systems non-positive, i.e., the largest Lyapunov exponent can be made nonpositive.
Abstract: Upon addition of noise, chaotic motion in low-dimensional dynamical systems can sometimes be transformed into nonchaotic dynamics: namely, the largest Lyapunov exponent can be made nonpositive. We study this phenomenon in model systems with a view to understanding the circumstances when such behaviour is possible. This technique for inducing ``order'' through stochastic driving works by modifying the invariant measure on the attractor: by appropriately increasing measure on those portions of the attractor where the dynamics is contracting, the overall dynamics can be made nonchaotic, however {\it not} a strange nonchaotic attractor. Alternately, by decreasing measure on contracting regions, the largest Lyapunov exponent can be enhanced. A number of different chaos control and anticontrol techniques are known to function on this paradigm.