Biomedical subjects

M Bestehorn

Publications and source records attributed to M Bestehorn.

13 recordsLinked to original sources

PubMed2004

Spatiotemporal structures in a model with delay and diffusion.

Pattern formation described by differential-difference equations with diffusion is investigated. It is shown that an arbitrarily small diffusion induces space-time turbulence just at the instability threshold of the homogeneous stationary solution. We prove this property by deriving a complex Ginzburg-Landau equation on the basis of normal form analysis. Well above threshold, such turbulent structures give way to synchronized states ordered by spirals and targets. This secondary instability can be understood with an asymptotic method representing the system as a cellular automaton network.

Biophysics↗

PubMed2003

Modelling thin-film dewetting on structured substrates and templates: bifurcation analysis and numerical simulations.

We study the dewetting process of a thin liquid film on a chemically patterned solid substrate (template) by means of a thin-film evolution equation incorporating a space-dependent disjoining pressure. Dewetting of a thin film on a homogeneous substrate leads to fluid patterns with a typical length scale, that increases monotonously in time (coarsening). Conditions are identified for the amplitude and periodicity of the heterogeneity that allow to transfer the template pattern onto the liquid structure ("pinning") emerging from the dewetting process. A bifurcation and stability analysis of the possible liquid ridge solutions on a periodically striped substrate reveal parameter ranges where pinning or coarsening ultimately prevail. We obtain an extended parameter range of multistability of the pinning and coarsening morphologies. In this regime, the selected pattern depends sensitively on the initial conditions and potential finite perturbations (noise) in the system as we illustrate with numerical integrations in time. Finally, we discuss the instability to transversal modes leading to a decay of the ridges into rows of drops and show that it may diminish the size of the parameter range where the pinning of the thin film to the template is successful.

Biomedical Engineering↗

PubMed2001

Sliding drops in the diffuse interface model coupled to hydrodynamics.

Using a film thickness evolution equation derived recently combining long-wave approximation and diffuse interface theory [L. M. Pismen and Y. Pomeau, Phys. Rev. E 62, 2480 (2000)] we study one-dimensional surface profiles for a thin film on an inclined plane. We discuss stationary flat film and periodic solutions including their linear stability. Flat sliding drops are identified as universal profiles, whose main properties do not depend on mean film thickness. The flat drops are analyzed in detail, especially how their velocity, advancing and receding dynamic contact angles and plateau thicknesses depend on the inclination of the plane. A study of nonuniversal drops shows the existence of a dynamical wetting transition with hysteresis between droplike solutions and a flat film with small amplitude nonlinear waves.

Journal Article↗

PubMed2001

Surface patterns of laterally extended thin liquid films in three dimensions.

We examine the fully nonlinear behavior of a thin liquid film in three spatial dimension for a large lateral extension. A partial differential equation is used for the spatiotemporal evolution of the height of the film. To take intermolecular forces in the liquid into account, we concentrate on a recently formulated model of Pismen and Pomeau, who derived an expression for the disjoining pressure only from the wetting properties of the fluid. Finally, the motion of a falling film on an inclined plane is studied within this model.

Journal Article↗

PubMed1996