Uniform convergence of basic Fourier-Bessel series on a -linear grid.

We study Fourier-Bessel series on a -linear grid, defined as expansions in complete -orthogonal systems constructed with the third Jackson -Bessel function, and obtain sufficient conditions for uniform convergence. The convergence results are illustrated with specific examples of expansions in -Fourier-Bessel series.

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 kink moves 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.

General approach for dealing with dynamical systems with spatiotemporal periodicities.

Dynamical systems often contain oscillatory forces or depend on periodic potentials. Time or space periodicity is reflected in the properties of these systems through a dependence on the parameters of their periodic terms. In this paper we provide a general theoretical framework for dealing with these kinds of systems, regardless of whether they are classical or quantum, stochastic or deterministic, dissipative or nondissipative, linear or nonlinear, etc.

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.

Comment on "Ratchet universality in the presence of thermal noise".

A recent paper [P. J. Martínez and R.

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.

Symmetries shape the current in ratchets induced by a biharmonic driving force.

Equations describing the evolution of particles, solitons, or localized structures, driven by a zero-average, periodic, external force, and invariant under time reversal and a half-period time shift, exhibit a ratchet current when the driving force breaks these symmetries. The biharmonic force f(t)=1 cos(qomegat+phi1)+2 cospomegat+phi2) does it for almost any choice of vphi1 and phi2, provided p and q are two coprime integers such that p+q is odd. It has been widely observed, in experiments in semiconductors, in Josephson junctions, photonic crystals, etc.

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 lambda 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.