219 research outputs found
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: . 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
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