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

New analytic running coupling in QCD: higher loop levels

The properties of the new analytic running coupling are investigated at the higher loop levels. The expression for this invariant charge, independent of the normalization point, is obtained by invoking the asymptotic freedom condition. It is shown that at any loop level the relevant $\beta$ function has the universal behaviors at small and large values of the invariant charge. Due to this feature the new analytic running coupling possesses the universal asymptotics both in the ultraviolet and infrared regions irrespective of the loop level. The consistency of the model considered with the general definition of the QCD invariant charge is shown.Comment: LaTeX 2.09, 12 pages with 5 EPS figures, uses mpla1.sty; enlarged version is accepted for publication in Mod. Phys. Lett.

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

Highly nonlinear pulse splitting and recombination in a two-dimensional granular network

The propagation of highly nonlinear signals in a branched two-dimensional granular system was investigated experimentally and numerically for a system composed of chains of spherical beads of different materials. The system studied consists of a double Y-shaped guide in which high- and low-modulus/mass chains of spheres are arranged in various geometries. We observed the transformation of a single or a train of solitary pulses crossing the interface between branches. We report fast splitting of the initial pulse, rapid chaotization of the signal and impulse redirection and bending. Pulse and energy trapping was also observed in the branches. Numerical analysis based on Hertzian interaction between the particles and the side walls of the guide was found in agreement with the experimental data, except for nonsymmetric arrangements of particles excited by a large mass striker

Boundary conditions at spatial infinity for fields in Casimir calculations

The importance of imposing proper boundary conditions for fields at spatial infinity in the Casimir calculations is elucidated.Comment: 8 pages, 1 figure, submitted to the Proceedings of The Seventh Workshop QFEXT'05 (Barcelona, September 5-9, 2005

Mechanisms of fragmentation of Al-W granular composites under dynamic loading

Numerical simulations of Aluminum (Al) and Tungsten (W) granular composite rings under various dynamic loading conditions caused by explosive loading were examined. Three competing mechanisms of fragmentation were observed: a continuum level mechanism generating large macrocracks described by the Grady-Kipp fragmentation mechanism, a mesoscale mechanism generating voids and microcracks near the initially unbonded Al/W interfaces due to tensile strains, and a mesoscale jetting due to the development of large velocity gradients between the W particles and adjacent Al. These mesoscale mechanisms can be used to tailor the size of the fragments by selecting an appropriate initial mesostructure for a given loading condition.Comment: 10 pages, 3 figures, submitted to AP

How Hertzian solitary waves interact with boundaries in a 1-D 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 preconstrain. 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.Comment: Proof corrections, ReVTeX, 11 pages, 3 eps (Focus and related papers on http://www.supmeca.fr/perso/jobs/

Self-Consistent Separable Rpa Approach for Skyrme Forces: Axial Nuclei

The self-consistent separable RPA (random phase approximation) method is formulated for Skyrme forces with pairing. The method is based on a general self-consistent procedure for factorization of the two-body interaction. It is relevant for various density- and current-dependent functionals. The contributions of the time-even and time-odd Skyrme terms as well as of the Coulomb and pairing terms to the residual interaction are taken self-consistently into account. Most of the expression have a transparent analytical form, which makes the method convenient for the treatment and analysis. The separable character of the residual interaction allows to avoid diagonalization of high-rank RPA matrices and thus to minimize the calculation effort. The previous studies have demonstrated high numerical accuracy and efficiency of the method for spherical nuclei. In this contribution, the method is specified for axial nuclei. We provide systematic and detailed presentation of formalism and discuss different aspects of the model.Comment: 42 page

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/