Biomedical subjects

S C Venkataramani

Publications and source records attributed to S C Venkataramani.

5 recordsLinked to original sources

PubMed2002

Trapping of vibrational energy in crumpled sheets.

We investigate the propagation of transverse elastic waves in crumpled media. We set up the wave equation for transverse waves on a generic curved, strained surface via a Langrangian formalism and use this to study the scaling behavior of the dispersion curves near the ridges and on the flat facets. This analysis suggests that ridges act as barriers to wave propagation and that modes in a certain frequency regime could be trapped in the facets. A simulation study of the wave propagation qualitatively supported our analysis and showed interesting effects of the ridges on wave propagation.

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PubMed2001

Singularities, structures, and scaling in deformed m-dimensional elastic manifolds.

The crumpling of a thin sheet can be understood as the condensation of elastic energy into a network of ridges that meet in vertices. Elastic energy condensation should occur in response to compressive strain in elastic objects of any dimension greater than 1. We study elastic energy condensation numerically in two-dimensional elastic sheets embedded in spatial dimensions three or four and three-dimensional elastic sheets embedded in spatial dimensions four and higher. We represent a sheet as a lattice of nodes with an appropriate energy functional to impart stretching and bending rigidity. Minimum energy configurations are found for several different sets of boundary conditions. We observe two distinct behaviors of local energy density falloff away from singular points, which we identify as cone scaling or ridge scaling. Using this analysis, we demonstrate that there are marked differences in the forms of energy condensation depending on the embedding dimension.

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PubMed2001

Front propagation of spatiotemporal chaos.

We study the dynamics of the front separating a spatiotemporally chaotic region from a stable steady region using a simple model applicable to periodically forced systems. In particular, we investigate both the coarsening of the front induced by the inherent "noise" of the chaotic region, and the long wavelength dynamics causing the front to develop cusps.

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PubMed2001

Pattern selection in extended periodically forced systems: a continuum coupled map approach.

We propose that a useful approach to the modeling of periodically forced extended systems is through continuum coupled map (CCM) models. CCM models are discrete time, continuous space models, mapping a continuous spatially varying field xi(n)(x) from time n to time n+1. The efficacy of CCM models is illustrated by an application to experiments of Umbanhowar, Melo, and Swinney [Nature 382, 793 (1996)] on vertically vibrated granular layers. Using a simple CCM model incorporating temporal period doubling and spatial patterning at a preferred length scale, we obtain results that bear remarkable similarities to the experimental observations. The fact that the model does not make use of physics specific to granular layers suggests that similar phenomena may be observed in other (nongranular) periodically forced, strongly dissipative systems. We also present a framework for the analysis of pattern selection in CCM models using a truncated modal expansion. Through the analysis, we predict scaling laws of various quantities, and these laws may be verifiable experimentally.

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PubMed1999

Noise stabilization of self-organized memories.

We investigate a nonlinear dynamical system which "remembers" preselected values of a system parameter. The deterministic version of the system can encode many parameter values during a transient period, but in the limit of long times, almost all of them are forgotten. Here we show that a certain type of stochastic noise can stabilize multiple memories, enabling many parameter values to be encoded permanently. We present analytic results that provide insight both into the memory formation and into the noise-induced memory stabilization. The relevance of our results to experiments on the charge-density wave material NbSe3 is discussed.

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