Scattering of solitary waves in granular media

A detailed numerical study of the scattering of solitary waves by a barrier, in a granular media with Hertzian contact, shows the existence of secondary multipulse structures generated at the interface of two "sonic vacua", which have a similar structure as the one previously found by Nesterenko and coworkers.Comment: 4 pages, 9 figures (fig 5, replaced). Submitted to PR

Anomalous wave reflection from the interface of two strongly nonlinear granular media

Granular materials exhibit a strongly nonlinear behaviour affecting the propagation of information in the medium. Dynamically self-organized strongly nonlinear solitary waves are the main information carriers in granular chains. Here we report the first experimental observation of the dramatic change of reflectivity from the interface of two granular media triggered by a noncontact magnetically induced initial precompression. It may be appropriate to name this phenomenon the "acoustic diode" effect. Based on numerical simulations, we explain this effect by the high gradient of particle velocity near the interface.Comment: 14 pages, 3 figure

Delayed Scattering of Solitary Waves from Interfaces in a Granular Container

In granular media, the characterization of the behavior of solitary waves around interfaces is of importance in order to look for more applications of these systems. We study the behavior of solitary waves at both interfaces of a symmetric granular container, a class of systems that has received recent attention because it posses the feature of energy trapping. Hertzian contact is assumed. We have found that the scattering process is elastic at one interface, while at the other interface it is observed that the transmitted solitary wave has stopped its movement during a time that gets longer when the ratio between masses at the interfaces increases. The origin of this effect can be traced back to the phenomenon of gaps opening, recently observed experimentally.Comment: To appear in Physical Review E, vol 7

Strongly Nonlinear Waves in 3D Phononic Crystals

Three dimensional phononic crystal ("sonic vacuum" without prestress) was assembled from 137 vertical cavities arranged in hexagonal pattern in Silicone matrix filled with stainless steel spheres. This system has unique strongly nonlinear properties with respect to wave propagation inherited from nonlinear Hertz type elastic contact interaction. Trains of strongly nonlinear solitary waves excited by short duration impact were investigated. Solitary wave with speed below sound speed in the air and reflection from the boundary of two "sonic vacuums" were detected

Skyrme-Random-Phase-Approximation description of E1 strength in 92-100Mo

The isovector dipole E1 strength in Mo isotopes with A=92,94,96,98,100 is analyzed within the self-consistent separable random-phase approximation (SRPA) model with Skyrme forces SkT6, SkM*, SLy6, and SkI3. The special attention is paid to the low-energy region near the particle thresholds (4-12 MeV), which is important for understanding of astrophysical processes. We show that, due to a compensation effect, the influence of nuclear deformation on E1 strength below 10-12 MeV is quite modest. At the same time, in agreement with previous predictions, the deformation increases the strength at higher energy. At 4-8 MeV the strength is mainly determined by the tail of E1 giant resonance. The four Skyrme forces differ in description of the whole giant resonance but give rather similar results below 12 MeV.Comment: 12 pages, 7 figures, to be published in Int. J. Mod. Phys. (E) as contribution to Proceedings of 15th Nuclear Physics Workshop (Kazimierz, Poland, 2008

Energy trapping and shock disintegration in a composite granular medium

Granular materials demonstrate a strongly nonlinear behavior influencing the wave propagation in the medium. We report the first experimental observation of impulse energy confinement and the resultant disintegration of shock and solitary waves. The medium consists of alternating ensambles of high-modulus vs orders of magnitude lower modulus chains of different masses. The trapped energy is contained within the "softer" portions of the composite chain and is slowly released in the form of weak, separated pulses over an extended period of time. This effect is enhanced by using a specific group assembly and superimposed force.Comment: 15 pages, 2 figure

Observation of two-wave structure in strongly nonlinear dissipative granular chains

In a strongly nonlinear viscous granular chain under conditions of loading that exclude stationary waves (e.g., impact by a single grain) we observe a pulse that consists of two interconnected but distinct parts. One is a leading narrow "primary pulse" with properties similar to a solitary wave in a "sonic vacuum." It arises from strong nonlinearity and discreteness in the absence of dissipation, but now decays due to viscosity. The other is a broad, much more persistent shock-like "secondary pulse" trailing the primary pulse and caused by viscous dissipation. The medium behind the primary pulse is transformed from a "sonic vacuum" to a medium with finite sound speed. When the rapidly decaying primary pulse dies, the secondary pulse continues to propagate in the "sonic vacuum," with an oscillatory front if the viscosity is relatively small, until its eventual (but very slow) disintegration. Beyond a critical viscosity there is no separation of the two pulses, and the dissipation and nonlinearity dominate the shock-like attenuating pulse which now exhibits a nonoscillatory front

Strongly nonlinear waves in a chain of Teflon beads

One dimensional "sonic vacuum" type phononic crystals were assembled from a chain of Teflon spheres with different diameters in a Teflon holder. It was demonstrated for the first time that this polymer-based "sonic vacuum", with exceptionally low elastic modulus of particles, supports propagation of strongly nonlinear solitary waves with a very low speed.Comment: 33 pages, 6 figure

Experimental evidence of shock mitigation in a Hertzian tapered chain

We present an experimental study of the mechanical impulse propagation through a horizontal alignment of elastic spheres of progressively decreasing diameter $\phi_n$, namely a tapered chain. Experimentally, the diameters of spheres which interact via the Hertz potential are selected to keep as close as possible to an exponential decrease, $\phi_{n+1}=(1-q)\phi_n$, where the experimental tapering factor is either $q_1\simeq5.60$~% or $q_2\simeq8.27$~%. In agreement with recent numerical results, an impulse initiated in a monodisperse chain (a chain of identical beads) propagates without shape changes, and progressively transfer its energy and momentum to a propagating tail when it further travels in a tapered chain. As a result, the front pulse of this wave decreases in amplitude and accelerates. Both effects are satisfactorily described by the hard spheres approximation, and basically, the shock mitigation is due to partial transmissions, from one bead to the next, of momentum and energy of the front pulse. In addition when small dissipation is included, a better agreement with experiments is found. A close analysis of the loading part of the experimental pulses demonstrates that the front wave adopts itself a self similar solution as it propagates in the tapered chain. Finally, our results corroborate the capability of these chains to thermalize propagating impulses and thereby act as shock absorbing devices.Comment: ReVTeX, 7 pages with 6 eps, accepted for Phys. Rev. E (Related papers on http://www.supmeca.fr/perso/jobs/

Strongly Nonlinear Waves in Polymer Based Phononic Crystals

One dimensional "sonic vacuum"-type phononic crystals were assembled from chains of polytetrafluoroethylene (PTFE) beads and Parylene coated spheres with different diameters. It was demonstrated for the first time that these polymer-based granular system, with exceptionally low elastic modulus of particles, support the propagation of strongly nonlinear solitary waves with a very low speed. They can be described using classical nonlinear Hertz law despite the viscoelastic nature of the polymers and the high strain rate deformation of the contact area. Trains of strongly nonlinear solitary waves excited by an impact were investigated experimentally and were found to be in reasonable agreement with numerical calculations. Tunability of the signal shape and velocity was achieved through a non-contact magnetically induced precompression of the chains. This applied prestress allowed an increase of up to two times the solitary waves speed and significant delayed the signal splitting. Anomalous reflection at the interface of two "sonic vacua"-type systems was reported