9 research outputs found
Chiral perturbation theory for three-flavour lattice QCD with isospin splitting
An important tool for the analysis of results of numerical simulations of
lattice QCD is chiral perturbation theory. In Wilson chiral perturbation theory
the effects of the finite lattice spacing are taken into account. In recent
years the effects of isospin splitting on the masses of hadrons have been
investigated in Monte Carlo simulations. Correspondingly, in this article we
derive the expansions of the masses of the pseudoscalar mesons in chiral
perturbation theory at next-to-leading order for twisted mass lattice QCD with
three light quark flavours, taking the mass difference between the up and down
quarks into account. The results include terms up to orders in the
quark masses, in the mass splitting between up- and down quarks,
and in the lattice spacing, respectively.Comment: 12 pages, revised version, as publishe
The collective behaviour of ensembles of condensing liquid drops on heterogeneous inclined substrates
Employing a long-wave mesoscopic hydrodynamic model for the film height
evolution we study ensembles of pinned and sliding drops of a volatile liquid
that continuously condense onto a chemically heterogeneous inclined substrate.
Our analysis combines, on the one hand, path continuation techniques to
determine bifurcation diagrams for the depinning of single drops of nonvolatile
liquid on single hydrophilic spots on a partially wettable substrate and, on
the other hand, time simulations of growth and depinning of individual
condensing drops as well as of the long-time behaviour of large ensembles of
such drops. Pinned drops grow on the hydrophilic spots, depin and slide along
the substrate while merging with other pinned drops and smaller drops that
slide more slowly, and possibly undergo a pearling instability. As a result,
the collective behaviour converges to a stationary state where condensation and
outflow balance. The main features of the emerging drop size distribution can
then be related to single-drop bifurcation diagrams
The collective behaviour of ensembles of condensing liquid drops on heterogeneous inclined substrates
First order phase transitions and the thermodynamic limit
We consider simple mean field continuum models for first order liquid–liquid demixing and solid–liquid phase transitions and show how the Maxwell construction at phase coexistence emerges on going from finite-size closed systems to the thermodynamic limit. The theories considered are the Cahn–Hilliard model of phase separation, which is also a model for the liquid-gas transition, and the phase field crystal model of the solid–liquid transition. Our results show that states comprising the Maxwell line depend strongly on the mean density with spatially localized structures playing a key role in the approach to the thermodynamic limit