Nonlinear response of a linear chain to weak driving

We study the escape of a chain of coupled units over the barrier of a metastable potential. It is demonstrated that a very weak external driving field with suitably chosen frequency suffices to accomplish speedy escape. The latter requires the passage through a transition state the formation of which is triggered by permanent feeding of energy from a phonon background into humps of localised energy and elastic interaction of the arising breather solutions. In fact, cooperativity between the units of the chain entailing coordinated energy transfer is shown to be crucial for enhancing the rate of escape in an extremely effective and low-energy cost way where the effect of entropic localisation and breather coalescence conspire

Frequency and Phase Synchronization in Stochastic Systems

The phenomenon of frequency and phase synchronization in stochastic systems requires a revision of concepts originally phrased in the context of purely deterministic systems. Various definitions of an instantaneous phase are presented and compared with each other with special attention payed to their robustness with respect to noise. We review the results of an analytic approach describing noise-induced phase synchronization in a thermal two-state system. In this context exact expressions for the mean frequency and the phase diffusivity are obtained that together determine the average length of locking episodes. A recently proposed method to quantify frequency synchronization in noisy potential systems is presented and exemplified by applying it to the periodically driven noisy harmonic oscillator. Since this method is based on a threshold crossing rate pioneered by S.O. Rice the related phase velocity is termed Rice frequency. Finally, we discuss the relation between the phenomenon of stochastic resonance and noise-enhanced phase coherence by applying the developed concepts to the periodically driven bistable Kramers oscillator.Comment: to appear in the Chaos focus issue on "Control, communication, and synchronization in chaotic dynamical systems

Zigzag transitions and nonequilibrium pattern formation in colloidal chains

Paramagnetic colloidal particles that are optically trapped in a linear array can form a zigzag pattern when an external magnetic field induces repulsive interparticle interactions. When the traps are abruptly turned off, the particles form a nonequilibrium expanding pattern with a zigzag symmetry, even when the strength of the magnetic interaction is weaker than that required to break the linear symmetry of the equilibrium state. We show that the transition to the equilibrium zigzag state is always potentially possible for purely harmonic traps. For anharmonic traps that have a finite height, the equilibrium zigzag state becomes unstable above a critical anharmonicity. A normal mode analysis of the equilibrium line configuration demonstrates that increasing the magnetic field leads to a hardening and softening of the spring constants in the longitudinal and transverse directions, respectively. The mode that first becomes unstable is the mode with the zigzag symmetry, which explains the symmetry of nonequilibrium patterns. Our analytically tractable models help to give further insight into the way that the interplay of such factors as the length of the chain, hydrodynamic interactions, thermal fluctuations affect the formation and evolution of the experimentally observed nonequilibrium patterns.Comment: 16 pages, 8 figures; to appear in the Journal of Chemical Physic

Giant enhancement of hydrodynamically enforced entropic trapping in thin channels

Using our generalized Fick-Jacobs approach [Martens et al., PRL 110, 010601 (2013); Martens et al., Eur. Phys. J. Spec. Topics 222, 2453-2463 (2013)] and extensive Brownian dynamics simulations, we study particle transport through three-dimensional periodic channels of different height. Directed motion is caused by the interplay of constant bias acting along the channel axis and a pressure-driven flow. The tremendous change of the flow profile shape in channel direction with the channel height is reflected in a crucial dependence of the mean particle velocity and the effective diffusion coefficient on the channel height. In particular, we observe a giant suppression of the effective diffusivity in thin channels; four orders of magnitude compared to the bulk value.Comment: 16 pages, 8 figure

Hydrodynamically enforced entropic trapping of Brownian particles

We study the transport of Brownian particles through a corrugated channel caused by a force field containing curl-free (scalar potential) and divergence-free (vector potential) parts. We develop a generalized Fick-Jacobs approach leading to an effective one-dimensional description involving the potential of mean force. As an application, the interplay of a pressure-driven flow and an oppositely oriented constant bias is considered. We show that for certain parameters, the particle diffusion is significantly suppressed via the property of hyrodynamically enforced entropic particle trapping.Comment: 5 pages, 4 figures, in press with Physical Review Letter

Cooperative behavior between oscillatory and excitable units: the peculiar role of positive coupling-frequency correlations

We study the collective dynamics of noise-driven excitable elements, so-called active rotators. Crucially here, the natural frequencies and the individual coupling strengths are drawn from some joint probability distribution. Combining a mean-field treatment with a Gaussian approximation allows us to find examples where the infinite-dimensional system is reduced to a few ordinary differential equations. Our focus lies in the cooperative behavior in a population consisting of two parts, where one is composed of excitable elements, while the other one contains only self-oscillatory units. Surprisingly, excitable behavior in the whole system sets in only if the excitable elements have a smaller coupling strength than the self-oscillating units. In this way positive local correlations between natural frequencies and couplings shape the global behavior of mixed populations of excitable and oscillatory elements.Comment: 10 pages, 6 figures, published in Eur. Phys. J.