Driven and damped double sine-Gordon equation: The influence of internal modes on the soliton ratchet mobility

This work studies the damped double sine-Gordon equation driven by a biharmonic force, where a parameter λ controls the existence and the frequency of an internal mode. The role of internal oscillations of the kink width in ratchet dynamics of kink is investigated within the framework of collective coordinate theories. It is found that the ratchet velocity of the kink, when an internal mode appears in this system, decreases contrary to what was expected. It is also shown that the kink exhibits a higher mobility in the double sine-Gordon without internal mode, but with a quasilocalized first phonon mode.Ministerio de Educación y Ciencia (España) MTM2006-13000-C03-01Ministerio de Ciencia e Innovación (España) FIS2008-02380/FISJunta de Andalucía. Consejería de Innovación, Ciencia y Empresas FQM262Universidad de Granada FQM207Junta de Andalucía P06-FQM-0173

Factorization method for difference equations of hypergeometric type on nonuniform lattices

We study the factorization of the hypergeometric-type difference equation of Nikiforov and Uvarov on nonuniform lattices. An explicit form of the raising and lowering operators is derived and some relevant examples are given.Comment: 21 page

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.)

Propulsion efficiency of a dynamic self-assembled helical ribbon

We study the dynamic self-assembly and propulsion of a ribbon formed from paramagnetic colloids in a dynamic magnetic field. The sedimented ribbon assembles due to time averaged dipolar interactions between the beads. The time dependence of the dipolar interactions together with hydrodynamic interactions cause a twisted ribbon conformation. Domain walls of high twist connect domains of nearly constant orientation and negligible twist and travel through the ribbon. The particular form of the domain walls can be controlled via the frequency and the eccentricity of the modulation. The flux of twist walls—a true ribbon property absent in slender bodies—provides the thrust onto the surrounding liquid that propels this biomimetic flagellum into the opposite direction. The propulsion efficiency increases with frequency and ceases abruptly at a critical frequency where the conformation changes discontinuously to a flat standing ribbon conformation

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

The Hahn Quantum Variational Calculus

We introduce the Hahn quantum variational calculus. Necessary and sufficient optimality conditions for the basic, isoperimetric, and Hahn quantum Lagrange problems, are studied. We also show the validity of Leitmann's direct method for the Hahn quantum variational calculus, and give explicit solutions to some concrete problems. To illustrate the results, we provide several examples and discuss a quantum version of the well known Ramsey model of economics.Comment: Submitted: 3/March/2010; 4th revision: 9/June/2010; accepted: 18/June/2010; for publication in Journal of Optimization Theory and Application

Asymptotics and zeros of Sobolev orthogonal polynomials on unbounded supports

In this paper we present a survey about analytic properties of polynomials orthogonal with respect to a weighted Sobolev inner product such that the vector of measures has an unbounded support. In particular, we are focused in the study of the asymptotic behaviour of such polynomials as well as in the distribution of their zeros. Some open problems as well as some new directions for a future research are formulated.Comment: Changed content; 34 pages, 41 reference

Somatic growth dynamics of West Atlantic hawksbill sea turtles: a spatio-temporal perspective

This is the final version of the article. Available from the publisher via the DOI in this record.Somatic growth dynamics are an integrated response to environmental conditions. Hawksbill sea turtles (Eretmochelys imbricata) are long-lived, major consumers in coral reef habitats that move over broad geographic areas (hundreds to thousands of kilometers). We evaluated spatio-temporal effects on hawksbill growth dynamics over a 33-yr period and 24 study sites throughout the West Atlantic and explored relationships between growth dynamics and climate indices. We compiled the largest ever data set on somatic growth rates for hawksbills – 3541 growth increments from 1980 to 2013. Using generalized additive mixed model analyses, we evaluated 10 covariates, including spatial and temporal variation, that could affect growth rates. Growth rates throughout the region responded similarly over space and time. The lack of a spatial effect or spatio-temporal interaction and the very strong temporal effect reveal that growth rates in West Atlantic hawksbills are likely driven by region-wide forces. Between 1997 and 2013, mean growth rates declined significantly and steadily by 18%. Regional climate indices have significant relationships with annual growth rates with 0- or 1-yr lags: positive with the Multivariate El Niño Southern Oscillation Index (correlation = 0.99) and negative with Caribbean sea surface temperature (correlation = −0.85). Declines in growth rates between 1997 and 2013 throughout the West Atlantic most likely resulted from warming waters through indirect negative effects on foraging resources of hawksbills. These climatic influences are complex. With increasing temperatures, trajectories of decline of coral cover and availability in reef habitats of major prey species of hawksbills are not parallel. Knowledge of how choice of foraging habitats, prey selection, and prey abundance are affected by warming water temperatures is needed to understand how climate change will affect productivity of consumers that live in association with coral reefs