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Phase-field-crystal models for condensed matter dynamics on atomic length and diffusive time scales: an overview
Here, we review the basic concepts and applications of the
phase-field-crystal (PFC) method, which is one of the latest simulation
methodologies in materials science for problems, where atomic- and microscales
are tightly coupled. The PFC method operates on atomic length and diffusive
time scales, and thus constitutes a computationally efficient alternative to
molecular simulation methods. Its intense development in materials science
started fairly recently following the work by Elder et al. [Phys. Rev. Lett. 88
(2002), p. 245701]. Since these initial studies, dynamical density functional
theory and thermodynamic concepts have been linked to the PFC approach to serve
as further theoretical fundaments for the latter. In this review, we summarize
these methodological development steps as well as the most important
applications of the PFC method with a special focus on the interaction of
development steps taken in hard and soft matter physics, respectively. Doing
so, we hope to present today's state of the art in PFC modelling as well as the
potential, which might still arise from this method in physics and materials
science in the nearby future.Comment: 95 pages, 48 figure
Phase field modelling of surfactants in multi-phase flow
A diffuse interface model for surfactants in multi-phase flow with three or
more fluids is derived. A system of Cahn-Hilliard equations is coupled with a
Navier-Stokes system and an advection-diffusion equation for the surfactant
ensuring thermodynamic consistency. By an asymptotic analysis the model can be
related to a moving boundary problem in the sharp interface limit, which is
derived from first principles. Results from numerical simulations support the
theoretical findings. The main novelties are centred around the conditions in
the triple junctions where three fluids meet. Specifically the case of local
chemical equilibrium with respect to the surfactant is considered, which allows
for interfacial surfactant flow through the triple junctions
Phase-field-crystal models for condensed matter dynamics on atomic length and diffusive time scales: an overview
Here we review the basic concepts and applications of the phase-field-crystal (PFC) method,
which is one of the latest simulation methodologies in materials science for problems, where
atomic- and microscales are tightly coupled. The PFC method operates on atomic length and
diffusive time scales, and thus constitutes a computationally efficient alternative to molecular
simulation methods. Its intense development in materials science started fairly recently following
the work by Elder et al. [Phys. Rev. Lett. 88 (2002), p. 245701]. Since these initial
studies, dynamical density functional theory and thermodynamic concepts have been linked to
the PFC approach to serve as further theoretical fundamentals for the latter. In this review, we
summarize these methodological development steps as well as the most important applications
of the PFC method with a special focus on the interaction of development steps taken in hard
and soft matter physics, respectively. Doing so, we hope to present today’s state of the art in
PFC modelling as well as the potential, which might still arise from this method in physics and
materials science in the nearby future
A Soluble Phase Field Model
The kinetics of an initially undercooled solid-liquid melt is studied by
means of a generalized Phase Field model, which describes the dynamics of an
ordering non-conserved field phi (e.g. solid-liquid order parameter) coupled to
a conserved field (e.g. thermal field). After obtaining the rules governing the
evolution process, by means of analytical arguments, we present a discussion of
the asymptotic time-dependent solutions. The full solutions of the exact
self-consistent equations for the model are also obtained and compared with
computer simulation results. In addition, in order to check the validity of the
present model we confronted its predictions against those of the standard Phase
field model and found reasonable agreement. Interestingly, we find that the
system relaxes towards a mixed phase, depending on the average value of the
conserved field, i.e. on the initial condition. Such a phase is characterized
by large fluctuations of the phi field.Comment: 13 pages, 8 figures, RevTeX 3.1, submitted to Physical Review
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