Complex oscillation modes in the Belousov-Zhabotinsky reaction by weak diffusive coupling.

We study the diffusive coupling of oscillating or excitable Belousov-Zhabotinsky reaction units arranged in a square lattice array and show that for certain sizes of the units and for certain distances between the units, complex oscillation modes of individual spots occur, which manifest themselves in multi-periodic, amplitude-modulated, and multi-mode oscillations. This experimental finding can be reproduced in simulations of the FitzHugh-Nagumo model mimicking the experimental setup, suggesting that it is a generic phenomenon in systems of coupled excitable units such as excitable cell tissues or coupled oscillators such as neurons. Further analysis let us conclude that the complex oscillation modes occur close to the transition from quiescent to coupling-induced oscillations states if this transition is taking place at weak coupling strength.

Growth kinetics of racemic heptahelicene-2-carboxylic acid nanowires on calcite (104).

Molecular self-assembly of racemic heptahelicene-2-carboxylic acid on a dielectric substrate at room temperature can be used to generate wire-like organic nanostructures consisting of single and double molecular rows. By means of non-contact atomic force microscopy, we investigate the growth of the wire-like pattern after deposition by experimental and theoretical means. From analyzing the time dependence of the mean row length, two distinct regimes were found. At the early post-deposition stage, the mean length grows in time. Subsequently, a crossover to a second regime is observed, where the mean row length remains nearly constant. We explain these findings by a mean-field rate equation approach providing a comprehensive picture of the growth kinetics. As a result, we demonstrate that the crossover between the two distinct regimes is accomplished by vanishing of the homochiral single rows. At later stages only heterochiral double row structures remain.

Maximum efficiency of state-space models of nanoscale energy conversion devices.

The performance of nano-scale energy conversion devices is studied in the framework of state-space models where a device is described by a graph comprising states and transitions between them represented by nodes and links, respectively. Particular segments of this network represent input (driving) and output processes whose properly chosen flux ratio provides the energy conversion efficiency. Simple cyclical graphs yield Carnot efficiency for the maximum conversion yield. We give general proof that opening a link that separate between the two driving segments always leads to reduced efficiency. We illustrate these general result with simple models of a thermoelectric nanodevice and an organic photovoltaic cell. In the latter an intersecting link of the above type corresponds to non-radiative carriers recombination and the reduced maximum efficiency is manifested as a smaller open-circuit voltage.

Initiation of atrial fibrillation by interaction of pacemakers with geometrical constraints.

Atrial fibrillation (AF) is the most common arrhythmia of the heart in industrialized countries. Its generation and the transitory behavior of paroxysmal AF are still not well understood. In this work we examine the interaction of two activation sources via an isthmus as possible cause for the initiation of fibrillation episodes. For this study, the electrophysiological model of Bueno-Orovio, Cherry and Fenton is adapted to atrial electrophysiology, both for physiological and electrophysiologically remodeled conditions due to AF. We show that the interaction of the pacemakers, combined with the geometrical constraints of the isthmus, can produce fibrillatory-type irregularities, which we quantify by the loss of spatial phase coherence in the transmembrane voltage. Transitions to irregular behavior occur when the frequencies of the pacemakers exceed certain thresholds, suggesting that AF episodes are initiated by frequency changes of the activating sources (sinus node, ectopic focus).

Phase transitions in Brownian pumps.

We study stochastic particle transport between two reservoirs along a channel, where the particles are pumped against a bias by a traveling wave potential. It is shown that phase transitions of period-averaged densities or currents occur inside the channel when exclusion interactions between the particles are taken into account. These transitions reflect those known for the asymmetric simple exclusion process. We argue that their occurrence is a generic feature of Brownian motors operating in open systems.

One-dimensional transport of interacting particles: currents, density profiles, phase diagrams, and symmetries.

Driven lattice gases serve as canonical models for investigating collective transport phenomena and properties of nonequilibrium steady states. Here we study one-dimensional transport with nearest-neighbor interactions both in closed bulk systems and in open channels coupled to two particle reservoirs at the ends of the channel. For the widely employed Glauber rates we derive an exact current-density relation in the bulk for unidirectional hopping. An approach based on time-dependent density functional theory provides a good description of the kinetics. For open systems, the system-reservoir couplings are shown to have a striking influence on boundary-induced phase diagrams. The role of particle-hole symmetry is discussed, and its consequence for the topology of the phase diagrams. It is furthermore demonstrated that systems with weak bias can be mapped onto systems with unidirectional hopping.

Irregular excitation patterns in reaction-diffusion systems due to perturbation by secondary pacemakers.

Spatiotemporal excitation patterns in the FitzHugh-Nagumo model are studied, which result from the disturbance of a primary pacemaker by a secondary pacemaker. The primary and secondary pacemakers generate regular waves with frequencies f(pace) and f(pert), respectively. The pacemakers are spatially separated, but waves emanating from them encounter each other via a small bridge. This leads to three different types I-III of irregular excitation patterns in disjunct domains of the f(pace)-f(pert) plane. Types I and II are caused by detachments of waves coming from the two pacemakers at corners of the bridge. Type III irregularities are confined to a boundary region of the system and originate from a partial penetration of the primary waves into a space, where circular wave fronts from the secondary pacemaker prevail. For this type, local frequencies can significantly exceed f(pace) and f(pert). The degree of irregularity found for the three different types is quantified by the entropy of the local frequency distribution and an order parameter for phase coherence.

Classical driven transport in open systems with particle interactions and general couplings to reservoirs.

We study nonequilibrium steady states of lattice gases with nearest-neighbor interactions that are driven between two reservoirs. Density profiles in these systems exhibit oscillations close to the reservoirs. We demonstrate that an approach based on time-dependent density functional theory copes with these oscillations and predicts phase diagrams of bulk densities to a good approximation under arbitrary boundary-reservoir couplings. The minimum or maximum current principles can be applied only for specific bulk-adapted couplings. We show that they generally fail to give the correct topology of phase diagrams but can still be useful for getting insight into the mutual arrangement of different phases.

Second-layer induced island morphologies in thin-film growth of fullerenes.

Deposition of fullerenes on the CaF(2)(111) surface yields peculiar island morphologies with close similarities to previous findings for (100) surfaces of other ionic crystals. By means of noncontact atomic force microscopy we find a smooth transition from compact, triangular islands to branched hexagonal islands upon lowering the temperature. While triangular islands are two monolayers high, hexagonal islands have a base of one monolayer and exhibit a complicated structure with a second-layer outer rim and trenches oriented towards the interior. By developing a kinetic growth model we unravel the microscopic mechanisms of the structure formation.

Unidirectional hopping transport of interacting particles on a finite chain.

Particle transport through an open, discrete one-dimensional channel against a mechanical or chemical bias is analyzed within a master equation approach. The channel, externally driven by time-dependent site energies, allows multiple occupation due to the coupling to reservoirs. Performance criteria and optimization of active transport in a two-site channel are discussed as a function of reservoir chemical potentials, the load potential, interparticle interaction strength, driving mode, and driving period. Our results, derived from exact rate equations, are used in addition to test a previously developed time-dependent density functional theory, suggesting a wider applicability of that method in investigations of many particle systems far from equilibrium.

Nonlinear hopping transport in ring systems and open channels.

We study the nonlinear hopping transport in one-dimensional rings and open channels. Analytical results are derived for the stationary current response to a constant bias without assuming any specific coupling of the rates to the external fields. It is shown that anomalous large effective jump lengths, as observed in recent experiments by taking the ratio of the third-order nonlinear and the linear conductivity, can occur already in ordered systems. Rectification effects due to site energy disorder in ring systems are expected to become irrelevant for large system sizes. In open channels, in contrast, rectification effects occur already for disorder in the jump barriers and do not vanish in the thermodynamic limit. Numerical solutions for a sinusoidal bias show that the ring system provides a good description for the transport behavior in the open channel for intermediate and high frequencies. For low frequencies temporal variations in the mean particle number have to be taken into account in the open channel, which cannot be captured in the more simple ring model.

Work distributions for Ising chains in a time-dependent magnetic field.

Master equations can be conveniently used to investigate many particle systems driven out of equilibrium by time-dependent external fields. This topic is of vital interest in connection with fluctuation theorems and the associated microscopic work and heat distributions. We present an exact Monte Carlo simulation algorithm, which allows us to study interaction effects on these distributions. The method is applied to an Ising chain with Glauber dynamics. We find that the distributions are characterized by delta and step functions with a smooth part in between. With decreasing sweeping rate of the external field or decreasing interaction strength, the singular part becomes less dominant and the Gaussian fluctuation regime is approached.

Scaling of island densities in submonolayer growth of binary alloys.

We study the nucleation kinetics of binary alloys formed by codeposition of A and B atoms onto a planar substrate with fluxes F(alpha) (alpha=A, B). Based on a generalization of mean-field rate equations, we derive scaling relations for the dependence of the number density of stable islands on the ratios D(alpha)/F(alpha), where D(alpha) are the diffusion coefficients of two types of adatoms. Novel scaling laws are predicted for different situations of cluster stabilities with respect to their size and composition. The predictions are validated by kinetic Monte Carlo simulations and can be tested in experiments.

Friction and second-order phase transitions.

A microscopic model is studied numerically to describe wearless dry friction without thermal fluctuations between atomically flat contact interfaces. The analysis is based on a double-chain model with a Lennard-Jones interaction between the chains which are the respective upper flexible monolayers of the rigid bulk systems. Whereas below a critical interaction strength epsilon(c) the system exhibits a frictionless state, it offers static friction above epsilon(c) . Introducing an appropriate order parameter function we demonstrate the analogy of the critical behavior to a phase transition of second order. The order parameter is related to a hull function describing uniquely the incommensurate ground state of the model. The breakdown of analyticity of the hull function is identified with the phase transition. Critical exponents are calculated and the validity of finite-size scaling is displayed.