arXiv subjects

S. Martens

Publications and source records attributed to S. Martens.

23 records · Page 2Linked to original sources

arXiv2014

Front propagation in three-dimensional corrugated reaction-diffusion media

Propagation of traveling fronts in three-dimensional reaction-diffusion media with spatially modulated cross-section is studied using the Schlögl model as a representative example. Applying appropriate perturbation techniques leads first to a reduction of dimensionality in which the spatially dependent Neumann boundary condition translate into a boundary-induced advection term and, secondly, to an equation of motion for the traveling wave position in weakly corrugated confinements. Comparisons with numerical simulations demonstrate that our analytical results properly predicts the nonlinear dependence of the propagation velocity on ratio of the spatial period of the confinement to the intrinsic width of the front; including the peculiarity of propagation failure. Based on the eikonal equation, we obtain an analytical estimate for the finite interval of propagation failure. Lastly, we demonstrate that the front velocity is determined by the suppressed diffusivity of the reactants if the intrinsic width of the front is much larger than the spatial variation of the medium.

nlin.PS↗

arXiv2013

How entropy and hydrodynamics cooperate in rectifying particle transport

Using the analytical Fick-Jacobs approximation formalism and extensive Brownian dynamics simulations we study particle transport through two-dimensional periodic channels with triangularly shaped walls. Directed motion is caused by the interplay of constant bias acting along the channel axis and a pressure-driven flow. In particular, we analyze the particle mobility and the effective diffusion coefficient. The mechanisms of entropic rectification is revealed in channels with a broken spatial reflection symmetry in presence of hydrodynamically enforced entropic trapping. Due to the combined action of the forcing and the pressure-driven flow field, efficient rectification with a drastically reduced diffusivity is achieved.

cond-mat.stat-mech↗

arXiv2012

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.

cond-mat.stat-mech↗

arXiv2011

Driven Brownian transport through arrays of symmetric obstacles

We numerically investigate the transport of a suspended overdamped Brownian particle which is driven through a two-dimensional rectangular array of circular obstacles with finite radius. Two limiting cases are considered in detail, namely, when the constant drive is parallel to the principal or the diagonal array axes. This corresponds to studying the Brownian transport in periodic channels with reflecting walls of different topologies. The mobility and diffusivity of the transported particles in such channels are determined as functions of the drive and the array geometric parameters. Prominent transport features, like negative differential mobilities, excess diffusion peaks, and unconventional asymptotic behaviors, are explained in terms of two distinct lengths, the size of single obstacles (trapping length) and the lattice constant of the array (local correlation length). Local correlation effects are further analyzed by continuously rotating the drive between the two limiting orientations.

physics.chem-ph↗

arXiv2008

Resonance-like phenomena of 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. As a novel feature 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 non-vanishing 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 exist 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.

nlin.AO↗