arXiv subjects

Dirk Hennig

Publications and source records attributed to Dirk Hennig.

25 records · Page 2Linked to original sources

arXiv2014

Modulational instability and resonant wave modes act on the metastability of oscillator chains

We describe the emergence and interactions of breather modes and resonant wave modes within a two-dimensional ring-like oscillator chain in a microcanonical situation. Our analytical results identify different dynamical regimes characterized by the potential dominance of either type of mode. The chain is initially placed in a meta-stable state which it can leave by passing over the brim of the applied Mexican-hat-like potential. We elucidate the influence of the different wave modes on the mean-first passage time. A central finding is that also in this complex potential landscape a fast noise-free escape scenario solely relying on nonlinear cooperative effects is accomplishable even in a low energy setting.

nlin.CD↗

arXiv2014

Self-organized escape processes of linear chains in nonlinear potentials

An enhancement of localized nonlinear modes in coupled systems gives rise to a novel type of escape process. We study a spatially one dimensional set-up consisting of a linearly coupled oscillator chain of $N$ mass-points situated in a metastable nonlinear potential. The Hamilton-dynamics exhibits breather solutions as a result of modulational instability of the phonon states. These breathers localize energy by freezing other parts of the chain. Eventually this localised part of the chain grows in amplitude until it overcomes the critical elongation characterized by the transition state. Doing so, the breathers ignite an escape by pulling the remaining chain over the barrier. Even if the formation of singular breathers is insufficient for an escape, coalescence of moving breathers can result in the required concentration of energy. Compared to a chain system with linear damping and thermal fluctuations the breathers help the chain to overcome the barriers faster in the case of low damping. With larger damping, the decreasing life time of the breathers effectively inhibits the escape process.

nlin.AO↗

arXiv2013

Existence and non-existence of breather solutions in damped and driven nonlinear lattices

We investigate the existence of spatially localised solutions, in the form of discrete breathers, in general damped and driven nonlinear lattice systems of coupled oscillators. Conditions for the exponential decay of the difference between the maximal and minimal amplitudes of the oscillators are provided which proves that initial non-uniform spatial patterns representing breathers attain exponentially fast a spatially uniform state preventing the formation and/or preservation of any breather solution at all. Strikingly our results are generic in the sense that they hold for arbitrary dimension of the system, any attractive interaction, coupling strength and on-site potential and general driving fields. Furthermore, our rigorous quantitative results establish conditions under which discrete breathers in general damped and driven nonlinear lattices can exist at all and open the way for further research on the emergent dynamical scenarios, in particular features of pattern formation, localisation and synchronisation, in coupled cell networks.

nlin.PS↗

arXiv2013

The coupled dynamics of two particles with different limit sets

We consider a system of two coupled particles evolving in a periodic and spatially symmetric potential under the influence of external driving and damping. The particles are driven individually in such a way that in the uncoupled regime, one particle evolves on a chaotic attractor, while the other evolves on regular periodic attractors. Notably only the latter supports coherent particle transport. The influence of the coupling between the particles is explored, and in particular how it relates to the emergence of a directed current. We show that increasing the (weak) coupling strength subdues the current in a process, which in phase-space, is related to a merging crisis of attractors forming one large chaotic attractor in phase-space. Further, we demonstrate that complete current suppression coincides with a chaos-hyperchaos transition.

nlin.CD↗

arXiv2009

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

We consider 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 ratchet-like 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 current control in a wide temperature range.

cond-mat.stat-mech↗

arXiv2008

Directed transient long-range transport in a slowly driven Hamiltonian system of interacting particles

We study the Hamiltonian dynamics of a one-dimensional chain of linearly coupled particles in a spatially periodic potential which is subjected to a time-periodic mono-frequency external field. The average over time and space of the related force vanishes and hence, the system is effectively without bias which excludes any ratchet effect. We pay special attention to the escape of the entire chain when initially all of its units are distributed in a potential well. Moreover for an escaping chain we explore the possibility of the successive generation of a directed flow based on large accelerations. We find that for adiabatic slope-modulations due to the ac-field transient long-range transport dynamics arises whose direction is governed by the initial phase of the modulation. Most strikingly, that for the driven many particle Hamiltonian system directed collective motion is observed provides evidence for the existence of families of transporting invariant tori confining orbits in ballistic channels in the high dimensional phase spaces.

cond-mat.stat-mech↗

arXiv2004

Localization Properties of Electronic States in Polaron Model of poly(dG)-poly(dC) and poly(dA)-poly(dT) DNA polymers

We numerically investigate localization properties of electronic states in a static model of poly(dG)-poly(dC) and poly(dA)-poly(dT) DNA polymers with realistic parameters obtained by quantum-chemical calculation. The randomness in the on-site energies caused by the electron-phonon coupling are completely correlated to the off-diagonal parts. In the single electron model, the effect of the hydrogen-bond stretchings, the twist angles between the base pairs and the finite system size effects on the energy dependence of the localization length and on the Lyapunov exponent are given. The localization length is reduced by the influence of the fluctuations in the hydrogen bond stretchings. It is also shown that the helical twist angle affects the localization length in the poly(dG)-poly(dC) DNA polymer more strongly than in the poly(dA)-poly(dT) one. Furthermore, we show resonance structures in the energy dependence of the localization length when the system size is relatively small.

cond-mat.dis-nn↗