30 research outputs found
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
Continuation for thin film hydrodynamics and related scalar problems
This chapter illustrates how to apply continuation techniques in the analysis
of a particular class of nonlinear kinetic equations that describe the time
evolution through transport equations for a single scalar field like a
densities or interface profiles of various types. We first systematically
introduce these equations as gradient dynamics combining mass-conserving and
nonmass-conserving fluxes followed by a discussion of nonvariational amendmends
and a brief introduction to their analysis by numerical continuation. The
approach is first applied to a number of common examples of variational
equations, namely, Allen-Cahn- and Cahn-Hilliard-type equations including
certain thin-film equations for partially wetting liquids on homogeneous and
heterogeneous substrates as well as Swift-Hohenberg and Phase-Field-Crystal
equations. Second we consider nonvariational examples as the
Kuramoto-Sivashinsky equation, convective Allen-Cahn and Cahn-Hilliard
equations and thin-film equations describing stationary sliding drops and a
transversal front instability in a dip-coating. Through the different examples
we illustrate how to employ the numerical tools provided by the packages
auto07p and pde2path to determine steady, stationary and time-periodic
solutions in one and two dimensions and the resulting bifurcation diagrams. The
incorporation of boundary conditions and integral side conditions is also
discussed as well as problem-specific implementation issues
Inclusive Production Cross Sections from 920 GeV Fixed Target Proton-Nucleus Collisions
Inclusive differential cross sections and
for the production of \kzeros, \lambdazero, and
\antilambda particles are measured at HERA in proton-induced reactions on C,
Al, Ti, and W targets. The incident beam energy is 920 GeV, corresponding to
GeV in the proton-nucleon system. The ratios of differential
cross sections \rklpa and \rllpa are measured to be and , respectively, for \xf . No significant dependence upon the
target material is observed. Within errors, the slopes of the transverse
momentum distributions also show no significant
dependence upon the target material. The dependence of the extrapolated total
cross sections on the atomic mass of the target material is
discussed, and the deduced cross sections per nucleon are
compared with results obtained at other energies.Comment: 17 pages, 7 figures, 5 table
The QCD transition temperature: results with physical masses in the continuum limit II.
We extend our previous study [Phys. Lett. B643 (2006) 46] of the cross-over
temperatures (T_c) of QCD. We improve our zero temperature analysis by using
physical quark masses and finer lattices. In addition to the kaon decay
constant used for scale setting we determine four quantities (masses of the
\Omega baryon, K^*(892) and \phi(1020) mesons and the pion decay constant)
which are found to agree with experiment. This implies that --independently of
which of these quantities is used to set the overall scale-- the same results
are obtained within a few percent. At finite temperature we use finer lattices
down to a <= 0.1 fm (N_t=12 and N_t=16 at one point). Our new results confirm
completely our previous findings. We compare the results with those of the
'hotQCD' collaboration.Comment: 19 pages, 8 figures, 3 table
Verfahren zur Kennzeichnung und zur Identifikation von Halbleiterscheiben
The invention relates to a process for the recognition and identification of a semiconductor wafer (1) by means of a code (2) applied to the surface of the semiconductor wafer (1), said code being decodable by means of a scanning system (3), whereby the code (2) in the edge area of the semiconductor wafer (1) is applied as the result of code symbols (4) formed as recesses