Biomedical subjects

Surajit Sen

Publications and source records attributed to Surajit Sen.

7 recordsLinked to original sources

PubMed2006

Decorated, tapered, and highly nonlinear granular chain.

It has been seen that inertial mismatches in 1D granular chains lead to remarkable energy absorption which increases with the number of spheres, N, and tapering, q. Short chains, however, are limited in that regard, and we therefore present one solution which greatly improves performance for any size chain. These strongly nonlinear and scalable systems feature surprisingly complicated dynamics and are inadequately represented by a hard-sphere approximation. Additionally, such systems have shock absorption capacities that vary as a function of position along the chain. In this Letter, we present results in the form of normalized kinetic energy diagrams to illustrate the impressive mitigation capability of both original and improved tapered chains.

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PubMed2005

Impulse absorption by tapered horizontal alignments of elastic spheres.

We present an analytical and numerical study of the problem of mechanical impulse propagation through a horizontal alignment of progressively shrinking (tapered) elastic spheres that are placed between two rigid end walls. The studies are confined to cases where initial loading between the spheres is zero (i.e., in the "sonic vacuum" region). The spheres are assumed to interact via the Hertz potential. Force and energy as a function of time for selected grains that comprise the solitary wave are provided and shed light on the system's behavior. Propagation of energy is analytically studied in the hard-sphere approximation and phase diagrams plotting normalized kinetic energy of the smallest grain at the tapered end are developed for various chain lengths and tapering factors. These details are then compared to kinetic energy phase diagrams obtained via extensive dynamical simulations. Our figures indicate that the ratios of the kinetic energies of the smallest to largest grains possess a Gaussian dependence on tapering and an exponential decay when the number of grains increases. The conclusions are independent of system size, thus being applicable to tapered alignments of micron-sized spheres as well as those that are macroscopic and more easily realizable in the laboratory. Results demonstrate the capabililty of these chains to thermalize propagating impulses and thereby act as potential shock absorbing devices.

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PubMed2005

How hertzian solitary waves interact with boundaries in a 1D granular medium.

We perform measurements, numerical simulations, and quantitative comparisons with available theory on solitary wave propagation in a linear chain of beads without static preconstraint. By designing a nonintrusive force sensor to measure the impulse as it propagates along the chain, we study the solitary wave reflection at a wall. We show that the main features of solitary wave reflection depend on wall mechanical properties. Since previous studies on solitary waves have been performed at walls without these considerations, our experiment provides a more reliable tool to characterize solitary wave propagation. We find, for the first time, precise quantitative agreements.

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PubMed2004

Impulse penetration into idealized granular beds: behavior of cumulative surface kinetic energy.

We report a particle dynamics based simulational study of the propagation of delta function mechanical impulses in idealized three-dimensional hexagonal close packed lattices of monosized Hertz spheres. This paper presents five key results on the kinetic energy of grains at the surface of a granular bed after the generation of a normal impulse into the bed. (i) We find that the time integrated or cumulative average kinetic energy per surface grain, kappa, drops as an impulse penetrates into the bed. The minimum value of kappa, say kappa(0), is reached at some time t=tau after the impulse has been generated. (ii) This value, kappa(0), depends upon the restitutional losses at the grain contacts and kappa(0) increases as restitutional losses at granular contacts increase in magnitude. (iii) The asymptotic value of kappa is denoted by kappa(final) . Our data show that increasing the area across which an impulse is generated, A, leads to kappa(final) proportional to A(-1/2) . (iv) If we assign random masses to our monosized grains, kappa(final) grows quadratically as a function of the range of mass variation about a mean mass. We find that at large times, i.e., t>>tau , kappa proportional to (1-exp [k (1-t/tau)]) , where the constant k is roughly independent of restitution for the typical values of restitution encountered. (v) Our data suggest that at early times, the backscattering process carries signatures of ballistic propagation of the mechanical energy while at late times, the backscattering process is reminiscent of vibrations of an essentially ergodic system. Given the ballisticlike propagation of mechanical energy into granular beds, we conclude that a wave equation based description of mechanical energy propagation into granular beds may not always be appropriate.

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PubMed2003

Impulse backscattering in granular beds: introducing a toy model.

Impulses efficiently propagate into nominally dry granular beds and backscatter from buried inclusions in such beds may be potentially exploited to image shallow buried objects (SBOs). However, reliable imaging of SBOs requires "cleaning up" of surface vibrations, and, in addition to three-dimensional (3D) particle dynamics simulations, a phenomenological model to parametrize the bed surface may be useful for field applications. We introduce a 1D mean-field-like toy model with two parameters, which allows one to model surface vibrations, is consistent with experiments in a granular bed, and can help estimate the approximate signal transmission properties of the bed.

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PubMed2002

Secondary solitary wave formation in systems with generalized Hertz interactions.

We consider a chain of monodisperse elastic grains of radius R where the grains are barely in contact. The grains repel upon contact via the Hertz-type potential, V proportional to delta(n), n > 2, where delta > or = 0, is the grain-grain overlap, delta identical with 2R-(u(i+1)-u(i)), where u(i) denotes the displacement of grain i from its original equilibrium position. This being a computational study, we consider n to be arbitrary. Our dynamical simulations build on several earlier studies by Nesterenko, Coste, and Sen and co-workers that have shown that an impulse propagates as a solitary wave of fixed spatial extent, infinity < L(n) < 1, through a chain of grains. Here, we develop on a recent study by Manciu, Sen, and Hurd [Phys. Rev. E 63, 016614 (2001)] that shows that colliding solitary waves in the chains of interest spawn a well-defined hierarchy of multiple secondary solitary waves (SSWs) that carry approximately 0.5% or less of the energy of the original solitary waves. We show that the emergence of SSWs is a complex process where nonlinear forces and the discreteness of the grains lead to the partitioning of the available energy into hierarchies of SSWs. The process of formation of SSWs involves length scales and time scales that are controlled by the strength of the nonlinearity in the system. To the best of our knowledge, there is no formal theory that describes the dynamics associated with the formation of SSWs. Calculations for cases where the Hertz-type potential can be symmetric in the overlap parameter delta, i.e., where delta can be both positive and negative, suggest that the formation of secondary solitary waves may be a fundamental property of certain discrete, nonlinear systems.

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PubMed2000

Dynamics of a gravitationally loaded chain of elastic beads.

Elastic beads repel in a highly nonlinear fashion, as described by Hertz law, when they are compressed against one another. Vertical stacking results in significant compressions of beads at finite distances from the surface of the stack due to gravity. Analytic studies that have been reported in the literature assume acoustic excitations upon weak perturbation [J. Hong et al., Phys. Rev. Lett. 82, 3058 (1999)] and soliton-like excitations upon strong perturbation [V. Nesterenko, J. Appl. Mech. Tech. Phys. 5, 733 (1983); S. Sen and M. Manciu, Physica A 268, 644 (1999)]. The present study probes the position, velocity and acceleration and selected two-point temporal correlations and their power spectra for individual beads for cases in which the system has been (i) weakly, (ii) strongly, and (iii) moderately perturbed at the surface in the sense specified in the text. Our studies reveal the existence of distinctly different dynamical behavior of the tagged beads, in contrast to conventional acoustic response, as the strength of the perturbation is varied at fixed gravitational loading. We also comment on the effects of polydispersity on system dynamics and probe the relaxation of isolated light and heavy beads in the chain. (c) 2000 American Institute of Physics.

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