Collective Coordinates Theory for Discrete Soliton Ratchets in the sine-Gordon Model

A collective coordinate theory is develop for soliton ratchets in the damped discrete sine-Gordon model driven by a biharmonic force. An ansatz with two collective coordinates, namely the center and the width of the soliton, is assumed as an approximated solution of the discrete non-linear equation. The evolution of these two collective coordinates, obtained by means of the Generalized Travelling Wave Method, explains the mechanism underlying the soliton ratchet and captures qualitatively all the main features of this phenomenon. The theory accounts for the existence of a non-zero depinning threshold, the non-sinusoidal behaviour of the average velocity as a function of the difference phase between the harmonics of the driver, the non-monotonic dependence of the average velocity on the damping and the existence of non-transporting regimes beyond the depinning threshold. In particular it provides a good description of the intriguing and complex pattern of subspaces corresponding to different dynamical regimes in parameter space

Energy Flow Puzzle of Soliton Ratchets

We study the mechanism of directed energy transport for soliton ratchets. The energy flow appears due to the progressive motion of a soliton (kink) which is an energy carrier. However, the energy current formed by internal system deformations (the total field momentum) is zero. We solve the underlying puzzle by showing that the energy flow is realized via an {\it inhomogeneous} energy exchange between the system and the external ac driving. Internal kink modes are unambiguously shown to be crucial for that transport process to take place. We also discuss effects of spatial discretization and combination of ac and dc external drivings.Comment: 4 pages, 3 figures, submitted to PR

On the existence of internal modes of sine-Gordon kinks

We study whether or not sine-Gordon kinks exhibit internal modes or ``quasimodes.'' By considering the response of the kinks to ac forces and initial distortions, we show that neither intrinsic internal modes nor ``quasimodes'' exist in contrast to previous reports. However, we do identify a different kind of internal mode bifurcating from the bottom edge of the phonon band which arises from the discretization of the system in the numerical simulations, thus confirming recent predictions.Comment: 4 pages, 2 figures, REVTeX, to appear as a Rapid Communication in Phys Rev E (July 1st

Anomalous resonance phenomena of solitary waves with internal modes

We investigate the non-parametric, pure ac driven dynamics of nonlinear Klein-Gordon solitary waves having an internal mode of frequency $\Omega_i$. We show that the strongest resonance arises when the driving frequency $\delta=\Omega_i/2$, whereas when $\delta=\Omega_i$ the resonance is weaker, disappearing for nonzero damping. At resonance, the dynamics of the kink center of mass becomes chaotic. As we identify the resonance mechanism as an {\em indirect} coupling to the internal mode due to its symmetry, we expect similar results for other systems.Comment: 4 pages, 4 figures, to appear in Phys Rev Let

Paramagnetic colloidal ribbons in a precessing magnetic field

We investigate the dynamics of a kink in a damped parametrically driven nonlinear Klein-Gordon equation.We show by using a method of averaging that, in the high-frequency limit, the kinkmoves in an effective potential and is driven by an effective constant force. We demonstrate that the shape of the solitary wave can be controlled via the frequency and the eccentricity of the modulation. This is in accordance with the experimental results reported in a recent paper [Casic et al., Phys. Rev. Lett. 110, 168302 (2013)], where the dynamic self-assembly and propulsion of a ribbon formed from paramagnetic colloids in a time-dependent magnetic field has been studied.Ministerio de Economía y Competitividad MTM2012-36732-C03-03 (R.A.N.)Ministerio de Economía y Competitividad FIS2011-24540 (N.R.Q.)Junta de Andalucía FQM262 (R.A.N.)Junta de Andalucía FQM207 (N.R.Q.)Junta de Andalucía FQM-7276Junta de Andalucía P09-FQM-4643 (N.R.Q., R.A.N.)Alexander von Humboldt Foundation (Germany) through Research Fellowship for Experienced Researchers SPA 1146358 STP (N.R.Q.)

Kink topology control by high-frequency external forces in nonlinear Klein-Gordon models

A method of averaging is applied to study the dynamics of a kink in the damped double sine-Gordon equation driven by both external (nonparametric) and parametric periodic forces at high frequencies. This theoretical approach leads to the study of a double sine-Gordon equation with an effective potential and an effective additive force. Direct numerical simulations show how the appearance of two connected π kinks and of an individual π kink can be controlled via the frequency. An anomalous negative mobility phenomenon is also predicted by theory and confirmed by simulations of the original equation.Ministerio de Economía y Competitividad (España) MTM2012-36732-C03-03 FIS2011-24540Junta de Andalucía (España) FQM262 FQM207 FQM-7276 P09-FQM-4643Humboldt Foundation through the Research Fellowship for Experienced Researchers SPA 1146358 ST

An instrument to measure mechanical up-conversion phenomena in metals in the elastic regime

Crystalline materials, such as metals, are known to exhibit deviation from a simple linear relation between strain and stress when the latter exceeds the yield stress. In addition, it has been shown that metals respond to varying external stress in a discontinuous way in this regime, exhibiting discrete releases of energy. This crackling noise has been extensively studied both experimentally and theoretically when the metals are operating in the plastic regime. In our study, we focus on the behavior of metals in the elastic regime, where the stresses are well below the yield stress. We describe an instrument that aims to characterize non-linear mechanical noise in metals when stressed in the elastic regime. In macroscopic systems, this phenomenon is expected to manifest as a non-stationary noise modulated by external disturbances applied to the material, a form of mechanical up-conversion of noise. The main motivation for this work is for the case of maraging steel components (cantilevers and wires) in the suspension systems of terrestrial gravitational wave detectors. Such instruments are planned to reach very ambitious displacement sensitivities, and therefore mechanical noise in the cantilevers could prove to be a limiting factor for the detectors’ final sensitivities, mainly due to non-linear up-conversion of low frequency residual seismic motion to the frequencies of interest for the gravitational wave observations. We describe here the experimental setup, with a target sensitivity of 10^(−15) m/√Hz in the frequency range of 10–1000 Hz, a simple phenomenological model of the non-linear mechanical noise, and the analysis method that is inspired by this model

Validación de la escala latinoamericana y caribeña de seguridad alimentaria en gestantes adolescentes

Objetivo Realizar validación estadística de  la Escala Latinoamericana y Caribeña de Seguridad Alimentaria (ELCSA), que había sido adaptada lingüísticamente para Colombia en el año 2008 por la Escuela de Nutrición de la Universidad de Antioquia. Métodos Estudio descriptivo. Con un 95 % de nivel de confianza, se aplicó la escala ELCSA a una muestra representativa de 150 hogares de gestantes adolescentes, procedentes de población pobre y vulnerable, consultantes de la ESE Salud Pereira, entre abril y junio de 2009. Se capacitaron cuatro entrevistadores, profesionales de enfermería, sobre el objeto de cada una de las preguntas. Se encuestaron 32 hogares de sólo adultos y 118 hogares con adultos, jóvenes y niños. El análisis estadístico se realizó con SPSS. Se utilizó alfa de Cronbach,  análisis factorial y de componentes múltiples. Resultados La ELCSA mostró excelente confiabilidad aplicada tanto en hogares de sólo adultos (Cronbach=0,927), como en hogares con adultos, jóvenes y niños (Cronbach=0,953). El análisis factorial utilizando la medida de Kaiser-Meyer-Olkin, presentó alta correlación entre los ítems, tanto en hogares de solo adultos (p=0.889), como en hogares con adultos, jóvenes y niños (p=0,895). La capacidad predictiva de la escala fue de 75 % en los tres componentes identificados: calidad y cantidad de alimentos, acceso o disponibilidad de alimentos, y medios socialmente no aceptables de adquisición y distribución. Conclusiones Los resultados  validaron la escala ELCSA como un instrumento confiable para medir la seguridad alimentaria en los hogares colombianos