Controlled nanochannel lattice formation utilizing prepatterned substrates

Solid substrates can be endued with self-organized regular stripe patterns of nanoscopic lengthscale by Langmuir-Blodgett transfer of organic monolayers. Here we consider the effect of periodically prepatterned substrates on this process of pattern formation. It leads to a time periodic forcing of the oscillatory behavior at the meniscus. Utilizing higher order synchronization with this forcing, complex periodic patterns of predefined wavelength can be created. The dependence of the synchronization on the amplitude and the wavelength of the wetting contrast is investigated in one and two spatial dimensions and the resulting patterns are discussed. Furthermore, the effect of prepatterned substrates on the pattern selection process is investigated

Dynamics of a thin liquid film with surface rigidity and spontaneous curvature

The effect of rigid surfaces on the dynamics of thin liquid films which are amenable to the lubrication approximation is considered. It is shown that the Helfrich energy of the layer gives rise to additional terms in the time-evolution equations of the liquid film. The dynamics is found to depend on the absolute value of the spontaneous curvature, irrespective of its sign. Due to the additional terms, a novel finite wavelength instability of flat rigid interfaces can be observed. Furthermore, the dependence of the shape of a droplet on the bending rigidity as well as on the spontaneous curvature is discussed.Comment: 4 pages, 5 figure

On the strange vector form factors of the nucleon in the NJL soliton model

Within the Nambu--Jona--Lasinio model strange degrees of freedom are incorporated into the soliton picture using the collective approach of Yabu and Ando. The form factors of the nucleon associated with the nonet vector current are extracted. The numerical results provide limits for the strange magnetic moment: $-0.05\le\mu_s\le0.25$. For the strange magnetic form factor of the nucleon the valence quark and vacuum contributions add coherently while there are significant cancellations for the strange electric form factor.Comment: 9 pages, one figure, postscript file submitted as uuencoded compressed fil

The Newsvendor problem: analysis of the cost structure under normally distributed demand

We briefly review selected mathematical models that describe the dynamics of pattern formation phenomena in dip-coating and Langmuir-Blodgett transfer experiments, where solutions or suspensions are transferred onto a substrate producing patterned deposit layers with structure length from hundreds of nanometres to tens of micrometres. The models are presented with a focus on their gradient dynamics formulations that clearly shows how the dynamics is governed by particular free energy functionals and facilitates the comparison of the models. In particular, we include a discussion of models based on long-wave hydrodynamics as well as of more phenomenological models that focus on the pattern formation processes in such systems. The models and their relations are elucidated and examples of resulting patterns are discussed before we conclude with a discussion of implications of the gradient dynamics formulation and of some related open issues

Thin film dynamics with surfactant phase transition

A thin liquid film covered with an insoluble surfactant in the vicinity of a first-order phase transition is discussed. Within the lubrication approximation we derive two coupled equations to describe the height profile of the film and the surfactant density. Thermodynamics of the surfactant is incorporated via a Cahn-Hilliard type free-energy functional which can be chosen to describe a transition between two stable phases of different surfactant density. Within this model, a linear stability analysis of stationary homogeneous solutions is performed, and drop formation in a film covered with surfactant in the lower density phase is investigated numerically in one and two spatial dimensions