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

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

Regularizing Property of the Maximal Acceleration Principle in Quantum Field Theory

It is shown that the introduction of an upper limit to the proper acceleration of a particle can smooth the problem of ultraviolet divergencies in local quantum field theory. For this aim, the classical model of a relativistic particle with maximal proper acceleration is quantized canonically by making use of the generalized Hamiltonian formalism developed by Dirac. The equations for the wave function are treated as the dynamical equations for the corresponding quantum field. Using the Green's function connected to these wave equations as propagators in the Feynman integrals leads to an essential improvement of their convergence properties.Comment: 9 pages, REVTeX, no figures, no table

Frenet-Serret dynamics

We consider the motion of a particle described by an action that is a functional of the Frenet-Serret [FS] curvatures associated with the embedding of its worldline in Minkowski space. We develop a theory of deformations tailored to the FS frame. Both the Euler-Lagrange equations and the physical invariants of the motion associated with the Poincar\'e symmetry of Minkowski space, the mass and the spin of the particle, are expressed in a simple way in terms of these curvatures. The simplest non-trivial model of this form, with the lagrangian depending on the first FS (or geodesic) curvature, is integrable. We show how this integrability can be deduced from the Poincar\'e invariants of the motion. We go on to explore the structure of these invariants in higher-order models. In particular, the integrability of the model described by a lagrangian that is a function of the second FS curvature (or torsion) is established in a three dimensional ambient spacetime.Comment: 20 pages, no figures - replaced with version to appear in Class. Quant. Grav. - minor changes, added Conclusions sectio

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/

An elementary proof of the irrationality of Tschakaloff series

We present a new proof of the irrationality of values of the series $T_q(z)=\sum_{n=0}^\infty z^nq^{-n(n-1)/2}$ in both qualitative and quantitative forms. The proof is based on a hypergeometric construction of rational approximations to $T_q(z)$.Comment: 5 pages, AMSTe

Quark mass correction to the string potential

A consistent method for calculating the interquark potential generated by the relativistic string with massive ends is proposed. In this approach the interquark potential in the model of the Nambu--Goto string with point--like masses at its ends is calculated. At first the calculation is done in the one--loop approximation and then the variational estimation is performed. The quark mass correction results in decreasing the critical distance (deconfinement radius). When quark mass decreases the critical distance also decreases. For obtaining a finite result under summation over eigenfrequencies of the Nambu--Goto string with massive ends a suitable mode--by--mode subtraction is proposed. This renormalization procedure proves to be completely unique. In the framework of the developed approach the one--loop interquark potential in the model of the relativistic string with rigidity is also calculated.Comment: 34 pages, LATE