Topological defects in 1D elastic waves

It has been recently shown theoretically that a topological defect in a 1D periodic potential may give rise to two localized states within the energy gaps. In this work we present an experimental realization of this effect for the case of torsional waves in elastic rods. We also show numerically that three, or even more, localized states can be present if the parameters characterizing the topological defect are suitably varied.Comment: 3 pages, 4 figures, accepted in Physica

Ratchet behavior in nonlinear Klein-Gordon systems with point-like inhomogeneities

We investigate the ratchet dynamics of nonlinear Klein-Gordon kinks in a periodic, asymmetric lattice of point-like inhomogeneities. We explain the underlying rectification mechanism within a collective coordinate framework, which shows that such system behaves as a rocking ratchet for point particles. Careful attention is given to the kink width dynamics and its role in the transport. We also analyze the robustness of our kink rocking ratchet in the presence of noise. We show that the noise activates unidirectional motion in a parameter range where such motion is not observed in the noiseless case. This is subsequently corroborated by the collective variable theory. An explanation for this new phenomenom is given

Anderson Localization in Disordered Vibrating Rods

We study, both experimentally and numerically, the Anderson localization phenomenon in torsional waves of a disordered elastic rod, which consists of a cylinder with randomly spaced notches. We find that the normal-mode wave amplitudes are exponentially localized as occurs in disordered solids. The localization length is measured using these wave amplitudes and it is shown to decrease as a function of frequency. The normal-mode spectrum is also measured as well as computed, so its level statistics can be analyzed. Fitting the nearest-neighbor spacing distribution a level repulsion parameter is defined that also varies with frequency. The localization length can then be expressed as a function of the repulsion parameter. There exists a range in which the localization length is a linear function of the repulsion parameter, which is consistent with Random Matrix Theory. However, at low values of the repulsion parameter the linear dependence does not hold.Comment: 10 pages, 6 figure

Estudio clínico morfológico de la deformación del borde dorsal del cuello en caballos cruzados de carruaje en Sevilla y Córdoba (Andalucía, España)

The aim of this study was to a clinical, morphological of deformation dorsal neck edge on in horse of carriage in Seville and Cordoba, Andalusia, Spain. We studied a total of 110 horses. Clinical examination was performed and morphological considering weight and body condition was measured cervical perimeter. Deformation of the dorsal edge of the neck in all cases studied was evident. Morphological study to consider the deformation of the dorsal edge of the neck taking into account the ridge of the neck (score of 1 to 5) evidenced: for score 0: 33.6%; score 1: 51.8%; Rankings 2: 10%; Rated: 4.5 % for score 4 and 5 no horse was observed in these categories. The average diameter of the neck was 92.54cm, the average neck length was 92.46 cm and the weight was 3.92kg. The statistical result of the degree of deformation of the neck with the weight was 0.465 and the correlation between the degrees of deformation with weight was 0.652. The degree of correlation between neck circumference and body condition was 0.634. In conclusion deformation dorsal edge of the collar in horses used for carriage crossed in Cordoba and Seville, Spain, was observed a prevalence of 66%.Se plantea como objetivo un estudio clínico morfológico de la deformación del borde dorsal del cuello en caballos de carruaje en Sevilla y Córdoba, Andalucía-España. Fueron estudiados un total de 110 caballos. Se practicó un examen clínico y morfológico considerando condición corporal peso y se midió el perímetro cervical. El estudio morfológico para considerar la deformación del borde dorsal del cuello tomando en cuenta la cresta de la nuca (puntuación del 1 al 5) evidencio: para la puntuación 0: 33.6%; puntuación 1: 51.8%; puntuación 2: 10%; puntuación: 4.5%, para la puntuación 4 y 5 ningún caballo se observó en estas categorías. El promedio del diámetro del cuello fue de 92.54cm, el promedio de la longitud del cuello fue de 92.46 cm y el peso fue de 3.92Kg. Los resultados estadísticos del grado de deformación del cuello con el peso fue de 0.465 y la correlación entre el grado de deformación con el peso fue de 0.652. El grado de correlación entre el perímetro cervical y la condición corporal fue de 0.634. En conclusión se observó la deformación del borde dorsal del cuello en caballos cruzados empleados para carruajes en Córdoba y Sevilla, España, con una prevalencia puntual de 66%

Soliton ratchets in homogeneous nonlinear Klein-Gordon systems

We study in detail the ratchet-like dynamics of topological solitons in homogeneous nonlinear Klein-Gordon systems driven by a bi-harmonic force. By using a collective coordinate approach with two degrees of freedom, namely the center of the soliton, $X(t)$, and its width, $l(t)$, we show, first, that energy is inhomogeneously pumped into the system, generating as result a directed motion; and, second, that the breaking of the time shift symmetry gives rise to a resonance mechanism that takes place whenever the width $l(t)$ oscillates with at least one frequency of the external ac force. In addition, we show that for the appearance of soliton ratchets, it is also necesary to break the time-reversal symmetry. We analyze in detail the effects of dissipation in the system, calculating the average velocity of the soliton as a function of the ac force and the damping. We find current reversal phenomena depending on the parameter choice and discuss the important role played by the phases of the ac force. Our analytical calculations are confirmed by numerical simulations of the full partial differential equations of the sine-Gordon and $\phi^4$ systems, which are seen to exhibit the same qualitative behavior. Our results are in agreement with recent experimental work on dissipation induced symmetry breaking.Comment: Minor corrections, several references added, accepted for publication in Chao

Optimization of soliton ratchets in inhomogeneous sine-Gordon systems

Unidirectional motion of solitons can take place, although the applied force has zero average in time, when the spatial symmetry is broken by introducing a potential $V(x)$, which consists of periodically repeated cells with each cell containing an asymmetric array of strongly localized inhomogeneities at positions $x_{i}$. A collective coordinate approach shows that the positions, heights and widths of the inhomogeneities (in that order) are the crucial parameters so as to obtain an optimal effective potential $U_{opt}$ that yields a maximal average soliton velocity. $U_{opt}$ essentially exhibits two features: double peaks consisting of a positive and a negative peak, and long flat regions between the double peaks. Such a potential can be obtained by choosing inhomogeneities with opposite signs (e.g., microresistors and microshorts in the case of long Josephson junctions) that are positioned close to each other, while the distance between each peak pair is rather large. These results of the collective variables theory are confirmed by full simulations for the inhomogeneous sine-Gordon system

Internal mode mechanism for collective energy transport in extended systems

We study directed energy transport in homogeneous nonlinear extended systems in the presence of homogeneous ac forces and dissipation. We show that the mechanism responsible for unidirectional motion of topological excitations is the coupling of their internal and translation degrees of freedom. Our results lead to a selection rule for the existence of such motion based on resonances that explains earlier symmetry analysis of this phenomenon. The direction of motion is found to depend both on the initial and the relative phases of the two harmonic drivings, even in the presence of noise.Comment: Final version, to appear in Physical Review Letter