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Markus Bär

Publications and source records attributed to Markus Bär.

8 recordsLinked to original sources
PubMed2004

Dynamical model for chemically driven running droplets.

We propose coupled evolution equations for the thickness of a liquid film and the density of an adsorbate layer on a partially wetting solid substrate. Therein, running droplets are studied assuming a chemical reaction underneath the droplets that induces a wettability gradient on the substrate and provides the driving force for droplet motion. Two different regimes for moving droplets--reaction-limited and saturated regime--are described. They correspond to increasing and decreasing velocities with increasing reaction rates and droplet sizes, respectively. The existence of the two regimes offers a natural explanation of prior experimental observations.

Diffusion↗
PubMed2003

Doppler effect of nonlinear waves and superspirals in oscillatory media.

Nonlinear waves emitted from a moving source are studied. A meandering spiral in a reaction-diffusion medium provides an example in which waves originate from a source exhibiting a back-and-forth movement in a radial direction. The periodic motion of the source induces a Doppler effect that causes a modulation in wavelength and amplitude of the waves ("superspiral"). Using direct simulations as well as numerical nonlinear analysis within the complex Ginzburg-Landau equation, we show that waves subject to a convective Eckhaus instability can exhibit monotonic growth or decay as well as saturation of these modulations depending on the perturbation frequency. Our findings elucidate recent experimental observations concerning superspirals and their decay to spatiotemporal chaos.

Journal Article↗
PubMed2003

Bifurcation and stability analysis of rotating chemical spirals in circular domains: boundary-induced meandering and stabilization.

Recent experimental and model studies have revealed that the domain size may strongly influence the dynamics of rotating spirals in two-dimensional pattern forming chemical reactions. Hartmann et al. [Phys. Rev. Lett. 76, 1384 (1996)], report a frequency increase of spirals in circular domains with diameters substantially smaller than the spiral wavelength in a large domain for the catalytic NO+CO reaction on a microstructured platinum surface. Accompanying simulations with a simple reaction-diffusion system reproduced the behavior. Here, we supplement these studies by a numerical bifurcation and stability analysis of rotating spirals in a simple activator-inhibitor model. The problem is solved in a co-rotating frame of reference. No-flux conditions are imposed at the boundary of the circular domain. At large domain sizes, eigenvalues and eigenvectors very close to those corresponding to infinite medium translational invariance are observed. Upon decrease of domain size, we observe a simultaneous change in the rotation frequency and a deviation of these eigenvalues from being neutrally stable (zero real part). The latter phenomenon indicates that the translation symmetry of the spiral solution is appreciably broken due to the interaction with the (now nearby) wall. Various dynamical regimes are found: first, the spiral simply tries to avoid the boundary and its tip moves towards the center of the circular domain corresponding to a negative real part of the "translational" eigenvalues. This effect is noticeable at a domain radius of R<R(cr,1). The spiral subsequently exhibits an oscillatory instability: the tip trajectory displays a meandering motion, which may be characterized as boundary-induced spiral meandering. A systematic study of the spiral rotation as a function of a control parameter and the domain size reveals that the meandering instability in large domains becomes suppressed, and the spiral rotation becomes rigid, at a critical radius R(cr,0). Boundary-induced meandering arises below a second critical radius R(cr,2)<R(cr,0).

Journal Article↗
PubMed2002

Rippling patterns in aggregates of myxobacteria arise from cell-cell collisions.

Experiments with myxobacterial aggregates reveal standing waves called rippling patterns. Here these structures are modeled with a simple discrete model based on the interplay between migration and collisions of cells. Head-to-head collisions of cells result in cell reversals. To correctly reproduce the rippling patterns, a refractory phase after each cell reversal has to be assumed, during which further reversal is prohibited. The duration of this phase determines the wavelength and period of the ripple patterns as well as the reversal frequency of single cells.

Computer Simulation↗
PubMed2002

Dewetting of thin films on heterogeneous substrates: pinning versus coarsening.

We study a model for a thin liquid film dewetting from a periodic heterogeneous substrate (template). The amplitude and periodicity of a striped template heterogeneity necessary to obtain a stable periodic stripe pattern, i.e., pinning, are computed. This requires a stabilization of the longitudinal and transversal modes driving the typical coarsening dynamics during dewetting of a thin film on a homogeneous substrate. If the heterogeneity has a larger spatial period than that of the critical dewetting mode, weak heterogeneities are sufficient for pinning. Our results imply a large region of coexistence between coarsening dynamics and pinning.

Journal Article↗
PubMed2002

Drifting pattern domains in a reaction-diffusion system with nonlocal coupling.

Drifting pattern domains (DPDs), i.e., moving localized patches of traveling waves embedded in a stationary (Turing) pattern background and vice versa, are observed in simulations of a reaction-diffusion model with nonlocal coupling. Within this model, a region of bistability between Turing patterns and traveling waves arises from a codimension-2 Turing-wave bifurcation (TWB). DPDs are found within that region in a substantial distance from the TWB. We investigated the dynamics of single interfaces between Turing and wave patterns. It is found that DPDs exist due to a locking of the interface velocities, which is imposed by the absence of space-time defects near these interfaces.

Journal Article↗