Internal mode mechanism for collective energy transport in extended systems

Soliton ratchet induced by random transitions among symmetric sine-Gordon potentials

The generation of net soliton motion induced by random transitions among N symmetric phase-shifted sine-Gordon potentials is investigated, in the absence of any external force and without any thermal noise. The phase shifts of the potentials and the damping coefficients depend on a stationary Markov process. Necessary conditions for the existence of transport are obtained by an exhaustive study of the symmetries of the stochastic system and of the soliton velocity. It is shown that transport is generated by unequal transfer rates among the phase-shifted potentials or by unequal friction coefficients or by a properly devised combination of potentials (N>2). Net motion and inversions of the currents, predicted by the symmetry analysis, are observed in simulations as well as in the solutions of a collective coordinate theory. A model with high efficient soliton motion is designed by using multistate phase-shifted potentials and by breaking the symmetries with unequal transfer rates.

Symmetry breaking: Abnormal transport induced by mass modulation

Here, we investigate transport of an inertial particle in a symmetric periodic potential and subjected to an external signal, such that mass of the particle is modulated sinusoidally. Our numerical results indicate that the mass modulation can induce abnormal transport in the system, whereas no current appears in the case of constant mass. In the absence of external bias, direction of mean velocity of the particle changes several times as amplitude and frequency of the mass modulation are varied, i.e., a multiple current reversals (CR) phenomenon. The multiple CRs result from temporal symmetry breaking of the system. In the presence of external bias, multiple absolute negative mobilities (ANM) take place in the system. Intrinsic physical mechanisms responsible for the occurrence of the multiple ANMs are analyzed in detail.

Spectroscopy and Directed Transport of Topological Solitons in Crystals of Trapped Ions

We study experimentally and theoretically discrete solitons in crystalline structures consisting of several tens of laser-cooled ions confined in a radio frequency trap. Resonantly exciting localized, spectrally gapped vibrational modes of the soliton, a nonlinear mechanism leads to a nonequilibrium steady state of the continuously cooled crystal. We find that the propagation and the escape of the soliton out of its quasi-one-dimensional channel can be described as a thermal activation mechanism. We control the effective temperature of the soliton's collective coordinate by the amplitude of the external excitation. Furthermore, the global trapping potential permits controlling the soliton dynamics and realizing directed transport depending on its topological charge.

Multiple absolute negative mobilities

In this paper, we investigate transport of an inertial particle in a spatially symmetric potential and subjected to two harmonic signals with different frequencies in both deterministic and stochastic cases. Numerical results indicate that: (i) In the deterministic case, the two harmonic signals can induce many (up to six) segments of negative slopes in the curve of mean velocity vs. external constant force, i.e., a multiple absolute negative mobilities (ANMs) effect. But the occurrence of the effect depends on their frequencies and amplitudes. (ii) For the stochastic case, the multiple ANMs relay on stable index and symmetry parameter of the Lévy noise. In the case of symmetric noise, appropriate stable index makes the multiple ANMs be the strongest. Our further investigations indicate that an indispensable condition for the multiple ANMs to occur in the system is the temporal symmetry breaking by one multiplicative periodic signal and one additive periodic signal.

Kink ratchet induced by a time-dependent symmetric field potential

The ratchet effect of a sine-Gordon kink is investigated in the absence of any external force while the symmetry of the field potential at every time instant is maintained. The directed motion appears by a time shift of the sine-Gordon potential through a time-dependent additional phase. A symmetry analysis provides the necessary conditions for the existence of net motion. It is also shown analytically, by using a collective coordinate theory, that the novel physical mechanism responsible for the appearance of the ratchet effect is the coupled dynamics of the kink width with the background field. Biharmonic and dichotomic periodic variations of the additional phase of the sine-Gordon potential are considered. The predictions established by the symmetry analysis and the collective coordinate theory are verified by means of numerical simulations. Inversion and maximization of the resulting current as a function of the system parameters are investigated.

Collective coordinates theory for discrete soliton ratchets in the sine-Gordon model

A collective coordinate theory is developed 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 nonlinear equation. The dynamical equations of these two collective coordinates, obtained by means of the generalized travelling wave method, explain the mechanism underlying the soliton ratchet and capture qualitatively all the main features of this phenomenon. The numerical simulation of these equations accounts for the existence of a nonzero depinning threshold, the nonsinusoidal behavior of the average velocity as a function of the relative phase between the harmonics of the driver, the nonmonotonic dependence of the average velocity on the damping, and the existence of nontransporting 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.

Asymmetric ac fluxon depinning in a Josephson junction array: a highly discrete limit

Directed motion and depinning of topological solitons in a strongly discrete damped and biharmonically ac-driven array of Josephson junctions is studied. The mechanism of the depinning transition is investigated in detail. We show that the depinning process takes place through chaotization of an initially standing fluxon periodic orbit. Detailed investigation of the Floquet multipliers of these orbits shows that, depending on the depinning parameters (either the driving amplitude or the phase shift between harmonics), the chaotization process can take place either along the period-doubling scenario or due to the type I intermittency.

Refined empirical stability criterion for nonlinear Schrödinger solitons under spatiotemporal forcing

We investigate the dynamics of traveling oscillating solitons of the cubic nonlinear Schrödinger (NLS) equation under an external spatiotemporal forcing of the form f(x,t)=aexp[iK(t)x]. For the case of time-independent forcing, a stability criterion for these solitons, which is based on a collective coordinate theory, was recently conjectured. We show that the proposed criterion has a limited applicability and present a refined criterion which is generally applicable, as confirmed by direct simulations. This includes more general situations where K(t) is harmonic or biharmonic, with or without a damping term in the NLS equation. The refined criterion states that the soliton will be unstable if the "stability curve" p(v), where p(t) and v(t) are the normalized momentum and the velocity of the soliton, has a section with a negative slope. In the case of a constant K and zero damping, we use the collective coordinate solutions to compute a "phase portrait" of the soliton where its dynamics is represented by two-dimensional projections of its trajectories in the four-dimensional space of collective coordinates. We conjecture, and confirm by simulations, that the soliton is unstable if a section of the resulting closed curve on the portrait has a negative sense of rotation.

Generalized traveling-wave method, variational approach, and modified conserved quantities for the perturbed nonlinear Schrödinger equation

The generalized traveling wave method (GTWM) is developed for the nonlinear Schrödinger equation (NLSE) with general perturbations in order to obtain the equations of motion for an arbitrary number of collective coordinates. Regardless of the particular ansatz that is used, it is shown that this alternative approach is equivalent to the Lagrangian formalism, but has the advantage that only the Hamiltonian of the unperturbed system is required, instead of the Lagrangian for the perturbed system. As an explicit example, we take 4 collective coordinates, namely the position, velocity, amplitude and phase of the soliton, and show that the GTWM yields the same equations of motion as the perturbation theory based on the Inverse Scattering Transform and as the time variation of the norm, first moment of the norm, momentum, and energy for the perturbed NLSE.

Regular and chaotic transport of discrete solitons in asymmetric potentials

Ratchet dynamics of topological solitons of the forced and damped discrete double sine-Gordon system are studied. Directed transport occurring both in regular and in chaotic regions of the phase space and its dependence on damping, amplitude, and frequency of the driving, asymmetry parameter, and coupling constant, has been extensively investigated. We show that the passage from ratchet phase-locked regime to chaotic ratchets occurs via a period doubling route to chaos and that, quite surprisingly, pinned states can exist inside phase locking and chaotic transport regions for intermediate values of the coupling constant. The possibility to control chaotic discrete soliton ratchets by means of both small subharmonic signals and more general periodic drivings, has also been investigated.

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., as well as in simulations, that the ratchet current induced by this force has the shape v proportional, variant1p2q cos(pphi1-qphi2+theta0) for small amplitudes, where theta0 depends on the damping ( theta0=pi/2 if there is no damping, and theta0=0 for overdamped systems). We rigorously prove that this precise shape can be obtained solely from the broken symmetries of the system and is independent of the details of the equation describing the system.

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. 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.

Soliton ratchets in sine-Gordon systems with additive inhomogeneities

We investigate the ratchet dynamics of solitons of a sine-Gordon system with additive inhomogeneities. We show by means of a collective coordinate approach that the soliton moves like a particle in an effective potential which is a result of the inhomogeneities. Different degrees of freedom of the soliton are used as collective coordinates in order to study their influence on the motion of the soliton. The collective coordinates considered are the soliton position, its width and offset, and the height of the spikes that appear on the soliton. The results of the theory are compared with numerical simulations of the full system.

Chaotic transport in deterministic sine-Gordon soliton ratchets

We investigate homogeneous and inhomogeneous sine-Gordon ratchet systems in which a temporal symmetry and the spatial symmetry, respectively, are broken. We demonstrate that in the inhomogeneous systems with ac driving the soliton dynamics is chaotic in certain parameter regions, although the soliton motion is unidirectional. This is qualitatively explained by a one-collective-coordinate theory which yields an equation of motion for the soliton that is identical to the equation of motion for a single particle ratchet which is known to exhibit chaotic transport in its underdamped regime. For a quantitative comparison with our simulations we use a two-collective-coordinate (2CC) theory. In contrast to this, homogeneous sine-Gordon ratchets with biharmonic driving, which breaks a temporal shift symmetry, do not exhibit chaos. This is explained by a 2CC theory which yields two ODEs: one is linear, the other one describes a parametrically driven oscillator which does not exhibit chaos. The latter ODE can be solved by a perturbation theory which yields a hierarchy of linear equations that can be solved exactly order by order. The results agree very well with the simulations.

Phase synchronization in tilted inertial ratchets as chaotic rotators

The phenomenon of phase synchronization for a particle in a periodic ratchet potential is studied. We consider the deterministic dynamics in the underdamped case where the inertia plays an important role since the dynamics can become chaotic. The ratchet potential is tilted due to a constant external force and is rocking by an external periodic forcing. This potential has to be tilted in order to obtain a rotator or self-sustained nonlinear oscillator in the absence of the external periodic forcing; this oscillator then acquires an intrinsic frequency that can be locked with the frequency of the external driving. We introduced an instantaneous linear phase, using a set of discrete time markers, and the associated average frequency, and show that this frequency can be synchronized with the frequency of the driving. We calculate Arnold tongues in a two-dimensional parameter space and discuss their implications for the chaotic transport in ratchets. We show that the local maxima in the current correspond to the borders of these Arnold tongues; in this way we established a link between optimal transport in ratchets and phase synchronization.

Rectified oscillatory motion of the self-ordered front under zero-mean ac force: role of symmetry of the rate function

The rectified oscillatory motion of the "bistable" fronts (BFs) joining two states of the different stability in a spatially extended system with two stable equilibria is studied by use of the macroscopic kinetic equation of the reaction-diffusion type. The adiabatic approximation is used: We assume that the period of the ac force acting on the front in the system significantly exceeds the characteristic relaxation time of the system. By using the arguments based on the symmetry properties of the rate function in the governing equation of the ac driven front, we show that a close corelation (one-to-one correspondence) between the rate functions of the different symmetry, the symmetrical and asymmetrical ones, and the response functions performing the "input-output" conversion between the oscillatory forcing (input) function and the speed (output) function, which describes the temporal oscillations of the moment velocity of the ac driven BF, exists. Making use of the symmetry analysis we are able to show that the average characteristics of the ratchetlike transport of the ac driven BFs derivable by the symmetrical and asymmetrical rate functions radically differ. In particular, we find that depending on the symmetry of the rate function used, either symmetrical or asymmetrical one, the complete ensemble of the forward and backward running fronts propagating at the different initial velocities in the ac driven system remains either permanently at rest on average or it travels at some fixed nonzero velocity. We confirm our predictions being derived with the rate function of the general form by the direct calculations carried out by use of the cubic polynomial rate function and its piecewise linear emulations satisfying the different symmetry properties.

Sine-Gordon ratchets with general periodic, additive, and parametric driving forces

We study the soliton ratchets in the damped sine-Gordon equation with periodic nonsinusoidal, additive, and parametric driving forces. By means of symmetry analysis of this system we show that the net motion of the kink is not possible if the frequencies of both forces satisfy a certain relationship. Using a collective coordinate theory with two degrees of freedom, we show that the ratchet motion of kinks appears as a consequence of a resonance between the oscillations of the momentum and the width of the kink. We show that the equations of motion that fulfill these collective coordinates follow from the corresponding symmetry properties of the original systems. As a further application of the collective coordinate technique we obtain another relationship between the frequencies of the parametric and additive drivers that suppresses the ratchetlike motion of the kink. We check all these results by means of numerical simulations of the original system and the numerical solutions of the collective coordinate equations.

Controlling the ratchet effect through the symmetries of the systems: Application to molecular motors

We discuss a novel generic mechanism for controlling the ratchet effect through the breaking of relevant symmetries. We review previous works on ratchets where directed transport is induced by the breaking of standard temporal symmetries f(t)=-f(t+T/2) and f(t)=f(-t) (or f(t)=-f(-t)). We find that in seemingly unrelated systems the average velocity (or the current) of particles (or solitons) exhibits common features. We show that, as a consequence of Curie's symmetry principle, the average velocity (or the current) is related to the breaking of the symmetries of the system. This relationship allows us to control the transport in a systematic way. The qualitative agreement between the present analytical predictions and previous experimental, numerical, and theoretical results leads us to suggest that for the given breaking of the temporal symmetries there is an optimal wave form for a given time-periodic force. Also, we comment on how this mechanism can be applied to the case where a ratchet effect is induced by breaking of spatial symmetries. Finally, we conjecture that the ratchet potential underlying biological motor proteins might be optimized according to the breaking of the relevant symmetries.

Moving and colliding pulses in the subcritical Ginzburg-Landau model with a standing-wave drive

We show the existence of steadily moving solitary pulses (SPs) in the complex Ginzburg-Landau equation, which includes the cubic-quintic nonlinearity and a conservative linear driving term, whose amplitude is a standing wave with wave number k and frequency omega, the motion of the SPs being possible at resonant velocities +/-omega/k, which provide for locking to the drive. The model may be realized in terms of traveling-wave convection in a narrow channel with a standing wave excited in its bottom (or on the surface). An analytical approximation is developed, based on an effective equation of motion for the SP coordinate. Direct simulations demonstrate that the effective equation accurately predicts characteristics of the driven motion of pulses, such as a threshold value of the drive's amplitude. Collisions between two solitons traveling in opposite directions are studied by means of direct simulations, which reveal that they restore their original shapes and velocity after the collision.

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 xi. 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 Uopt that yields a maximal average soliton velocity. Uopt 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 variable theory are confirmed by full simulations for the inhomogeneous sine-Gordon system.

Ratchet effect in a damped sine-Gordon system with additive and parametric ac driving forces

We study in detail the damped sine-Gordon equation, driven by two ac forces (one is added as a parametric perturbation and the other one in an additive way), as an example of soliton ratchets. By means of a collective coordinate approach we derive an analytical expression for the average velocity of the soliton, which allows us to show that this mechanism of transport requires certain relationships both between the frequencies and between the initial phases of the two ac forces. The control of the velocity by the damping coefficient and parameters of the ac forces is also presented and discussed. All these results are subsequently checked by means of simulations for the driven and damped sine-Gordon equation that we have studied.

Domain wall dynamics in expanding spaces

We study the effects on the dynamics of kinks due to expansions and contractions of the space. We show that the propagation velocity of the kink can be adiabatically tuned through slow expansions and/or contractions, while its width is given as a function of the velocity. We also analyze the case of fast expansions and/or contractions, where we are no longer on the adiabatic regime. In this case the kink moves more slowly after an expansion-contraction cycle as a consequence of the loss of energy through radiation. All these effects are numerically studied in the nonlinear Klein-Gordon equations (both for the sine-Gordon and for the potential), and they are also studied within the framework of the collective coordinate evolution equations for the width and the center of mass of the kink. These collective coordinate evolution equations are obtained with a procedure that allows us to consider even the case of large expansions and/or contractions.

Discrete soliton ratchets driven by biharmonic fields

Directed motion of topological solitons (kinks or antikinks) in the damped and ac-driven discrete sine-Gordon system is investigated. We show that if the driving field breaks certain time-space symmetries, the soliton can perform unidirectional motion. The phenomenon resembles the well known effects of ratchet transport and nonlinear harmonic mixing. Direction of the motion and its velocity depends on the shape of the ac drive. Necessary conditions for the occurrence of the effect are formulated. In comparison with the previously studied continuum case, the discrete case shows a number of new features: nonzero depinning threshold for the driving amplitude, locking to the rational fractions of the driving frequency, and diffusive ratchet motion in the case of weak intersite coupling.

Energy flow of moving dissipative topological solitons

We study the energy flow due to the motion of topological solitons in nonlinear extended systems in the presence of damping and driving. The total field momentum contribution to the energy flux, which reduces the soliton motion to that of a point particle, is insufficient. We identify an additional exchange energy flux channel mediated by the spatial and temporal inhomogeneity of the system state. In the well-known case of a dc external force the corresponding exchange current is shown to be small but nonzero. For the case of ac driving forces, which lead to a soliton ratchet, the exchange energy flux mediates the complete energy flow of the system. We also consider the case of combination of ac and dc external forces, as well as spatial discretization effects.

Inhomogeneous soliton ratchets under two ac forces

We extend our previous work on soliton ratchet devices [L. Morales-Molina, Eur. Phys. J. B 37, 79 (2004)] to consider the joint effect of two ac forces including nonharmonic drivings, as proposed for particle ratchets by Savele'v [Europhys. Lett. 67, 179 (2004); Phys. Rev. E 70, 066109 (2004)]. Current reversals due to the interplay between the phases, frequencies, and amplitudes of the harmonics are obtained. An analysis of the effect of the damping coefficient on the dynamics is presented. We show that solitons give rise to nontrivial differences in the phenomenology reported for particle systems that arise from their extended character. A comparison with soliton ratchets in homogeneous systems with biharmonic forces is also presented. This ratchet device may be an ideal candidate for Josephson junction ratchets with intrinsic large damping.

Soliton ratchets in homogeneous nonlinear Klein-Gordon systems

We study in detail the ratchetlike dynamics of topological solitons in homogeneous nonlinear Klein-Gordon systems driven by a biharmonic 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 necessary 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 phi4 systems, which are seen to exhibit the same qualitative behavior. Our results show features similar to those obtained in recent experimental work on dissipation induced symmetry breaking.

Vibrational ratchets

Transport in one-dimensional symmetric devices can be activated by the combination of thermal noise and a biharmonic drive. For the study case of an overdamped Brownian particle diffusing on a periodic one-dimensional substrate, we distinguish two apparently different biharmonic regimes: (i) Harmonic mixing, where the two drive frequencies are commensurate and of the order of some intrinsic relaxation rate. Earlier predictions based on perturbation expansions seem inadequate to interpret our simulation results; (ii) Vibrational mixing, where one harmonic drive component is characterized by high frequency but finite amplitude-to-frequency ratio. Its effect on the device response to either a static or a low-frequency additional input signal is accurately reproduced by rescaling each spatial Fourier component of the substrate potential, separately. Contrary to common wisdom, based on the linear response theory, we show that extremely high-frequency modulations can indeed influence the response of slowly (or dc) operated devices, with potential applications in sensor technology and cellular physiology. Finally, the mixing of two high-frequency beating signal is also investigated both numerically and analytically.

Transport by bi-harmonic drives: from harmonic to vibrational mixing

Transport in a one-dimensional symmetric device can be activated by the combination of thermal noise and a bi-harmonic drive. The results of extensive simulations allow us to distinguish between two apparently different bi-harmonic regimes: (i) harmonic mixing, where the two drive frequencies are commensurate but not too high; (ii) vibrational mixing, where one harmonic drive component possesses a high frequency but finite amplitude-to-frequency ratio. A comparison with the earlier theoretical predictions shows that at present the analytical understanding of nonlinear frequency mixing is still not satisfactory.

Comment on "Soliton ratchets induced by excitation of internal modes"

Very recently Willis [Phys. Rev. E 69, 056612 (2004)] have used a collective variable theory to explain the appearance of a nonzero energy current in an ac-driven, damped sine-Gordon equation. In this Comment, we prove rigorously that the time-averaged energy current in an ac-driven nonlinear Klein-Gordon system is strictly zero.

Ratchet behavior in nonlinear Klein-Gordon systems with pointlike inhomogeneities

We investigate the ratchet dynamics of nonlinear Klein-Gordon kinks in a periodic, asymmetric lattice of pointlike inhomogeneities. We explain the underlying rectification mechanism within a collective coordinate framework, which shows that such a 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 phenomenon is given.

Analytical approach to soliton ratchets in asymmetric potentials

We use soliton perturbation theory and collective coordinate ansatz to investigate the mechanism of soliton ratchets in a driven and damped asymmetric double sine-Gordon equation. We show that, at the second order of the perturbation scheme, the soliton internal vibrations can couple effectively, in presence of damping, to the motion of the center of mass, giving rise to transport. An analytical expression for the mean velocity of the soliton is derived. The results of our analysis confirm the internal mode mechanism of soliton ratchets proposed in [Phys. Rev. E 65, 025602(R) (2002)].

Noise-assisted transport on symmetric periodic substrates

The rectification of a massive Brownian particle moving on a periodic substrate can be achieved in the absence of spatial asymmetry, by having recourse to (at least) two periodic, zero-mean input signals. We determine the relevant drift current under diverse operation conditions, namely, additive and multiplicative couplings, adiabatic and fast oscillating drives, and propagating substrate modulations. Distinct rectification mechanisms result from the interplay of noise and commensuration of the input frequencies, mediated through the nonlinearity of the substrate. These mechanisms are then extended to characterize soliton transport along a directed multistable chain. As the side-wise soliton diffusion is ultimately responsible for the transverse diffusion of such chains, our approach provides a full account of the Brownian motion of both pointlike and linear objects on a periodic substrate.

Length scale competition in nonlinear Klein-Gordon models: a collective coordinate approach

Working within the framework of nonlinear Klein-Gordon models as a paradigmatic example, we show that length scale competition, an instability of solitons subjected to perturbations of an specific length, can be understood by means of a collective coordinate approach in terms of soliton position and width. As a consequence, we provide a natural explanation of the phenomenon in much simpler terms than any previous treatment of the problem. Our technique allows us to study the existence of length scale competition in most soliton bearing nonlinear models and can be extended to coherent structures with more degrees of freedom.

Mode-locking of mobile discrete breathers

We study numerically synchronization phenomena of mobile discrete breathers in dissipative nonlinear lattices periodically forced. When varying the driving intensity, the breather velocity generically locks at rational multiples of the driving frequency. In most cases, the locking plateau coincides with the linear stability domain of the resonant mobile breather and desynchronization occurs by the regular appearance of type-I intermittencies. However, some plateaus also show chaotic mobile breathers with locked velocity in the locking region. The addition of a small subharmonic driving tames the locked chaotic solution and enhances the stability of resonant mobile breathers.

Unidirectional drift of bistable front under asymmetrically oscillating zero-mean force

The unidirectional drift of bistable fronts (BFs) that separate two stable uniform states of a bistable system under the action of an asymmetrically oscillating zero-mean force (driver) is considered within the "pseudolinear" (piecewise-linear) model of the system. The particular case of the symmetrical (symmetrically shaped) rate functions is studied. To perform a rigorous analytic treatment for arbitrary strengths of the driving force we assume that the applied ac force is quasistatically slow. Both cases of the initially static and the initially propagating BFs are examined; various types of the "unforced" dc motion are found. We show that the unforced transport of BF takes place in any case of the asymmetric driver, whether Maxwellian construction of the rate function was balanced or not. In particular, progressive (accelerated) dc drift of the initially static BFs occurred. In contrast, both progressive and regressive (decelerated) types of unforced dc drift of the initially propagating BFs take place. Moreover, reversal of the directed motion of the initially propagating BF occurred, if the deviation of Maxwellian construction from the strictly balanced situation was relatively small; by tuning the strength of the driving force the dc drift of BF exhibits the reversal. The symmetry properties of the biharmonic driver are discussed. The biharmonic ac force consisting of a superposition of the fundamental mode and its even (odd) superharmonics is an asymmetrically (symmetrically) oscillating one. The reversal type of the unforced dc drift occurred only in the case of the even superharmonic "mixing," when the superharmonic mode of the biharmonic driver was even.

Transport via nonlinear signal mixing in ratchet devices

The nonlinear signal mixing of two driving forces is used to control transport in overdamped ratchet devices. The interplay between the relative phase and the frequency ratio of the two driving forces is sufficient to generate an intriguing transport action that can be put to work to optimize shuttling and separation of particles in a variety of physical and technological applications. Analytic results for a striking multiple current reversal behavior including prominent, spikelike current features are obtained for doubly rocked and rocked-pulsated Brownian ratchets. This tunable signal mixing is readily implementable and exhibits even richer behaviors than those realized by the hard-to-implement modifiable-ratchet profiles.