Scattering of Elastic Waves in a Quasi-one-dimensional Cavity: Theory and Experiment

We study the scattering of torsional waves through a quasi-one-dimensional cavity both, from the experimental and theoretical points of view. The experiment consists of an elastic rod with square cross section. In order to form a cavity, a notch at a certain distance of one end of the rod was grooved. To absorb the waves, at the other side of the rod, a wedge, covered by an absorbing foam, was machined. In the theoretical description, the scattering matrix S of the torsional waves was obtained. The distribution of S is given by Poisson's kernel. The theoretical predictions show an excellent agreement with the experimental results. This experiment corresponds, in quantum mechanics, to the scattering by a delta potential, in one dimension, located at a certain distance from an impenetrable wall

Electromagnetic prompt response in an elastic wave cavity

A rapid, or prompt response, of an electromagnetic nature, is found in an elastic wave scattering experiment. The experiment is performed with torsional elastic waves in a quasi-one-dimensional cavity with one port, formed by a notch grooved at a certain distance from the free end of a beam. The stationary patterns are diminished using a passive vibration isolation system at the other end of the beam. The measurement of the resonances is performed with non-contact electromagnetic-acoustic transducers outside the cavity. In the Argand plane, each resonance describes a circle over a base impedance curve which comes from the electromagnetic components of the equipment. A model, based on a variation of Poisson's kernel is developed. Excellent agreement between theory and experiment is obtained.Comment: 4 pages, 5 figure

Cellular automaton supercolliders

Gliders in one-dimensional cellular automata are compact groups of non-quiescent and non-ether patterns (ether represents a periodic background) translating along automaton lattice. They are cellular-automaton analogous of localizations or quasi-local collective excitations travelling in a spatially extended non-linear medium. They can be considered as binary strings or symbols travelling along a one-dimensional ring, interacting with each other and changing their states, or symbolic values, as a result of interactions. We analyse what types of interaction occur between gliders travelling on a cellular automaton `cyclotron' and build a catalog of the most common reactions. We demonstrate that collisions between gliders emulate the basic types of interaction that occur between localizations in non-linear media: fusion, elastic collision, and soliton-like collision. Computational outcomes of a swarm of gliders circling on a one-dimensional torus are analysed via implementation of cyclic tag systems

Dalitz plot slope parameters for K→πππK \to \pi\pi\pi decays and two particle interference

We study the possible distortion of phase-space in the decays $K \to \pi \pi \pi$, which may result from final state interference among the decay products. Such distortion may influence the values of slope parameters extracted from the Dalitz plot distribution of these decays. We comment on the consequences on the magnitude of violation of the $\mid \Delta I \mid = 1/2$ rule in these decays.Comment: 17 pages, LaTex2e, 6 figures, v2 authors' affiliation modified, to appear in Mod. Phys. Lett.

Linearization of nonlinear connections on vector and affine bundles, and some applications

A linear connection is associated to a nonlinear connection on a vector bundle by a linearization procedure. Our definition is intrinsic in terms of vector fields on the bundle. For a connection on an affine bundle our procedure can be applied after homogenization and restriction. Several applications in Classical Mechanics are provided

Absorption and Direct Processes in Chaotic Wave Scattering

Recent results on the scattering of waves by chaotic systems with losses and direct processes are discussed. We start by showing the results without direct processes nor absorption. We then discuss systems with direct processes and lossy systems separately. Finally the discussion of systems with both direct processes and loses is given. We will see how the regimes of strong and weak absorption are modified by the presence of the direct processes.Comment: 8 pages, 4 figures, Condensed Matter Physics (IV Mexican Meeting on Mathematical and Experimental Physics), Edited by M. Martinez-Mares and J. A. Moreno-Raz