Dimer diffusion in a washboard potential

Diffusion enhancement and autoparametric resonance

The possibility of an autoparametric resonance in an isolated many-particle system induces a specific behavior of the particles in the presence of thermal noise. In particular, the variance associated with a resonant mode, and consequently that of the associated particles, is strongly increased compared to what it would have in the absence of parametric resonance. In this paper we consider a dimer submitted to a periodic potential for which there are only two modes, the center of mass motion and the internal vibration mode. This is the simplest system which is dynamically rich enough to exhibit an autoparametric excitation of the internal vibrations by the center of mass motion. The consequences of this autoparametric excitation on the particles diffusion will be discussed according to the stiffness of the interaction and to the initial energy of the dimer, the relevant parameters which characterize this dynamics.

Vortex motion and nonlinear response in coupled noisy phase oscillator lattices under shear stress

Vortex motion in coupled phase oscillator lattices is analogous to the dislocation motion in crystals. A single vortex exhibits a glide motion by force at the boundaries. Thermal fluctuations induce the glide motion even below the critical point corresponding to the Peierls stress. The random drift motion is approximated as a random walk in a tilted potential. If the temperature is high, vortices are spontaneously generated. A nonlinear response where the frequency profile is relatively flat in the central region and changes sharply near the boundaries is observed when the vortex density becomes large and nonuniform.

Internal energy and information flows mediate input and output power in bipartite molecular machines

Microscopic biological systems operate far from equilibrium, are subject to strong fluctuations, and are composed of many coupled components with interactions varying in nature and strength. Researchers are actively investigating the general design principles governing how biomolecular machines achieve effective free-energy transduction in light of these challenges. We use a model of two strongly coupled stochastic rotary motors to explore the effect of coupling strength between components of a molecular machine. We observe prominent thermodynamic characteristics at intermediate coupling strength, near that which maximizes output power: a maximum in power and information transduced from the upstream to the downstream system, and equal subsystem entropy production rates. These observations are unified through a bound on the machine's input and output power, which accounts for both the energy and information transduced between subsystems.

Enhancement of Brownian motion for a chain of particles in a periodic potential

The transport of particles in very confined channels in which single file diffusion occurs has been largely studied in systems where the transverse confining potential is smooth. However, in actual physical systems, this potential may exhibit both static corrugations and time fluctuations. Some recent results suggest the important role played by this nonsmoothness of the confining potential. In particular, quite surprisingly, an enhancement of the Brownian motion of the particles has been evidenced in these kinds of systems. We show that this enhancement results from the commensurate effects induced by the underlying potential on the vibrational spectra of the chain of particles, and from the effective temperature associated with its time fluctuations. We will restrict our derivation to the case of low temperatures for which the mean squared displacement of the particles remains smaller than the potential period.

Diffusion and mobility of anisotropic particles in tilted periodic structures

We numerically investigated the transport of anisotropic particles in tilted periodic structures. The diffusion and mobility of the particles demonstrate distinct behaviors dependence on the shape of the particles. In two-dimensional (2D) periodic potentials, we find that the mobility is influenced a little by the anisotropy of the particle, while the diffusion increases monotonically with the increasing of the particle anisotropy for large enough biased force. However, due to the sensitivity of the channels for the particle anisotropy, the transport in smooth channels is obviously different from that in energy potentials. The mobility decreases monotonically with the increasing of the particle anisotropy, while the diffusion can be a non-monotonic function of the particle anisotropy with a peak under appropriate biased force.

Tunable interactions between paramagnetic colloidal particles driven in a modulated ratchet potential

We study experimentally and theoretically the interactions between paramagnetic particles dispersed in water and driven above the surface of a stripe patterned magnetic garnet film. An external rotating magnetic field modulates the stray field of the garnet film and generates a translating potential landscape which induces directed particle motion. By varying the ellipticity of the rotating field, we tune the inter-particle interactions from net repulsive to net attractive. For attractive interactions, we show that pairs of particles can approach each other and form stable doublets which afterwards travel along the modulated landscape at a constant mean speed. We measure the strength of the attractive force between the moving particles and propose an analytically tractable model that explains the observations and is in quantitative agreement with experiment.

Molecular shape and the energetics of chemisorption: from simple to complex energy landscapes

We enumerate all local minima of the energy landscape for model rigid adsorbates characterized by three or four equivalent binding sites (e.g., thiol groups) on a close-packed (111) surface of a face-centered-cubic crystal. We show that the number of energy minima increases linearly with molecular size with a rate of increase that depends on the degree of registry between the molecule shape and the surface structure. The sparseness of energy minima and the large variations in the center-of-mass positions of these minima vs molecular size for molecules that are incommensurate with the surface suggests a strong coupling in these molecules between surface mobility and shape or size fluctuations resulting from molecular vibrations. We also find that the variation in the binding energy with respect to molecular size decreases more rapidly with molecular size for molecules with a higher degree of registry with the surface. This indicates that surface adsorption should be better able to distinguish molecules by size if the molecules are incommensurate with the surface.

Dimer motion on a periodic substrate: spontaneous symmetry breaking and absolute negative mobility

We consider two coupled particles moving along a periodic substrate potential with negligible inertia effects (overdamped limit). Even when the particles are identical and the substrate spatially symmetric, a sinusoidal external driving of appropriate amplitude and frequency may lead to spontaneous symmetry breaking in the form of a permanent directed motion of the dimer. Thermal noise restores ergodicity and thus zero net velocity, but entails arbitrarily fast diffusion of the dimer for sufficiently weak noise. Moreover, upon application of a static bias force, the dimer exhibits a motion opposite to that force (absolute negative mobility). The key requirement for all these effects is a nonconvex interaction potential of the two particles.

Two coupled Josephson junctions: dc voltage controlled by biharmonic current

We study transport properties of two Josephson junctions coupled by an external shunt resistance. One of the junctions (say, the first) is driven by an unbiased ac current consisting of two harmonics. The device can rectify the ac current yielding a dc voltage across the first junction. For some values of coupling strength, controlled by an external shunt resistance, a dc voltage across the second junction can be generated. By variation of system parameters such as the relative phase or frequency of two harmonics, one can conveniently manipulate both voltages with high efficiency, e.g. changing the dc voltages across the first and second junctions from positive to negative values and vice versa.

Exploring the dynamics of dimer crossing over a Kramers type potential

We explore the escape rate of a dimer crossing a potential barrier using both analytical and numerical approaches. We find that for small coupling strength k, the barrier hopping can be well approximated by a two step reaction scheme where one monomer hops over the barrier and is then followed by the other. In this regime the escape rate increases with k showing that the cooperativity between monomers enhances the crossing rate. However, in the limit of large coupling strength, applying the method of adiabatic elimination, we find that the escape rate is a decreasing function of k. Thus, we find that the escape rate is a non-monotonic function of the spring constant which is peaked at an optimal coupling strength. Furthermore, in the presence of a weak periodic signal, we show that the system response to the periodic signal is pronounced at a particular spring constant showing the dimer can be transported rapidly across the reaction coordinate in a half period.

From collective periodic running states to completely chaotic synchronised states in coupled particle dynamics

We consider the damped and driven dynamics of two interacting particles evolving in a symmetric and spatially periodic potential. The latter is exerted to a time-periodic modulation of its inclination. Our interest is twofold: First, we deal with the issue of chaotic motion in the higher-dimensional phase space. To this end, a homoclinic Melnikov analysis is utilised assuring the presence of transverse homoclinic orbits and homoclinic bifurcations for weak coupling allowing also for the emergence of hyperchaos. In contrast, we also prove that the time evolution of the two coupled particles attains a completely synchronised (chaotic) state for strong enough coupling between them. The resulting "freezing of dimensionality" rules out the occurrence of hyperchaos. Second, we address coherent collective particle transport provided by regular periodic motion. A subharmonic Melnikov analysis is utilised to investigate persistence of periodic orbits. For directed particle transport mediated by rotating periodic motion, we present exact results regarding the collective character of the running solutions entailing the emergence of a current. We show that coordinated energy exchange between the particles takes place in such a manner that they are enabled to overcome--one particle followed by the other--consecutive barriers of the periodic potential resulting in collective directed motion.

Particle diode: rectification of interacting Brownian ratchets

Transport of Brownian particles interacting with each other via the Morse potential is investigated in the presence of an ac driving force applied locally at one end of the chain. By using numerical simulations, we find that the system can behave as a particle diode for both overdamped and underdamped cases. For low frequencies, the transport from the free end to the ac acting end is prohibited, while the transport from the ac acting end to the free end is permitted. However, the polarity of the particle diode will reverse for medium frequencies. There exists an optimal value of the well depth of the interaction potential at which the average velocity takes its maximum. The average velocity υ decreases monotonically with the system size N by a power law υ ∝ N(-1).

Ratcheting of neutral elastic dimers on a charged filament

We consider an elastic neutral dimer formed by two bound equal masses carrying opposite charges and moving along an electrically active filament in one dimension. An ac electrical field drives the two dimer heads, when set free or bound together to form a rigid rod, to opposite directions, thus yielding a zero net dimer current for zero and infinite elastic constants. Under the same driving conditions, an elastically deformable dimer can get rectified and the ensuing net current maximized for an optimal value of dimer elastic constant. The dependence of the dimer current on the periodic charge distribution along the filament is analyzed in terms of global symmetries of the dimer dynamics.

Diffusion in a tilted periodic potential with entropic barriers

Diffusion of Brownian particles in a periodic channel is investigated in the presence of a tilted spatially periodic potential. Reduction of spatial dimensionality from two or three dimensions to an effective one-dimensional system entails the appearance of not only an entropic barrier but also an effective diffusion coefficient. It is found that diffusion exhibits striking features which are different from those observed in the previous cases. The interplay between the potential barriers and entropic barriers makes the phenomena richer. Remarkably, two temperature values exist at which the Peclet number takes its maximum.

Current control in a tilted washboard potential via time-delayed feedback

We consider the motion of an overdamped Brownian particle in a washboard potential exerted to a static tilting force. The bias yields directed net particle motion, i.e., a current. It is demonstrated that with an additional time-delayed feedback term, the particle current can be reversed against the direction of the bias. The control function induces a ratchetlike effect that hinders further current reversals and thus the particle moves against the direction of the static bias. Furthermore, varying the delay time allows also to continuously depreciate and even stop the transport in the washboard potential. We identify and characterize the underlying mechanism which applies to the current control in a wide temperature range.

Interaction-controlled Brownian motion in a tilted periodic potential

The drift and diffusion of a few interacting, overdamped Brownian particles in a tilted periodic potential are studied analytically and numerically. Both quantities exhibit a complex multipeaked structure as a function of the equilibrium interparticle separation. Upon variation of the interaction strength, both drift and diffusion may exhibit a nonmonotonic, resonancelike behavior.

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.

Resonancelike phenomena in the mobility of a chain of nonlinear coupled oscillators in a two-dimensional periodic potential

We study the Langevin dynamics of a two-dimensional discrete oscillator chain absorbed on a periodic substrate and subjected to an external localized point force. Going beyond the commonly used harmonic bead-spring model, we consider a nonlinear Morse interaction between the next-nearest neighbors. We focus interest on the activation of directed motion instigated by thermal fluctuations and the localized point force. In this context the local transition states are identified and the corresponding activation energies are calculated. It is found that the transport of the chain in point force direction is determined by stepwise escapes of a single unit or segments of the chain due to the existence of multiple locally stable attractors. The nonvanishing net current of the chain is quantitatively assessed by the value of the mobility of the center of mass. It turns out that the latter as a function of the ratio of the competing length scales of the system, that is the period of the substrate potential and the equilibrium distance between two chain units, shows a resonance behavior. More precisely there exists a set of optimal parameter values maximizing the mobility. Interestingly, the phenomenon of negative resistance is found, i.e., the mobility possesses a minimum at a finite value of the strength of the thermal fluctuations for a given overcritical external driving force.

Transition between locked and running states for dimer motion induced by periodic external driving

We study the motion of a dimer in a one-dimensional spatially periodic washboard potential. The tilt of the latter is time-periodically modulated by an ac field. We focus interest on the detrapping of the (static) ground state solution of the dimer caused by the ac field. Moreover, we demonstrate that slow tilt modulations not only induce a trapping-detrapping transition but drive the dimer dynamics into a regime of transient long-range running states. Most strikingly, the motion proceeds then unidirectionally, so that the dimer covers huge distances regardless of the fact that the bias force in the driven system vanishes on the average. We elucidate the underlying dynamics in phase space and associate long-lasting running states with the motion in ballistic channels occurring due to stickiness to invariant tori.

Diffusion of colloidal particles in a tilted periodic potential: theory versus experiment

We investigate the diffusion of a colloidal particle in a tilted periodic potential created by means of ten rotating optical tweezers arranged on a circle. Because of the viscous drag, the trap rotation leads to the onset of a tilting force in the corotating reference frame, so that in that frame the system can be described as an overdamped Brownian particle in a tilted periodic potential. The excellent agreement of the velocity and diffusion coefficient as a function of rotating frequency with theoretical predictions allowed us to extract the main parameters characterizing the system--the coefficient of free thermal diffusion and the potential corrugation depth--from the experimental results.