ADVANCES IN PHYSICS

 Advances in Physics, Volume 57, Issue 1, 2008
~
	Original Articles
LA eng
AU Heike Emmerich
TE Advances of and by phase-field modelling in condensed-matter
   physics
RE Phase-field modelling is still a young discipline in
   condensed-matter physics, which established itself for the class
   of systems that can be characterised by domains of different
   phases separated by a distinct interface. Driven out of
   equilibrium, their dynamics result in the evolution of those
   interfaces which might develop into well defined-structures with
   characteristic length scales at the nano-, micro- or meso-scale.
   Since the material properties of such systems are to a large
   extent determined by those small-scale structures, acquiring a
   precise understanding of the mechanisms that drive the
   interfacial dynamics is a great challenge for scientists in this
   field. Phase-field modelling is an approach that allows this
   challenge to be tackled in a simulation-based manner. This
   review provides a critical overview of the conceptual background
   of the phase-field method, the most relevant fields of
   condensed-matter physics that have been approached using
   phase-field modelling, as well as the respective model
   formulations and the insight gained so far via their simulation
   and analysis. Moreover, we discuss directions of further
   development and the quality of the scientific contributions to
   be expected from those.
KE Keywords: phase-field modelling; thermodynamic consistency;
   asymptotic analysis; phase diagrams; nucleation energetics;
   growth kinetics
PP 1-87
$$
LA eng
AU Zolta'n Eisler, Imre Bartos, Ja'nos Kerte'sz
TE Fluctuation scaling in complex systems: Taylor's law and beyond
RE [Dedicated to the memory of L.R.Taylor (1924-2007)].
   Complex systems consist of many interacting elements which
   participate in some dynamical process. The activity of various
   elements is often different and the fluctuation in the activity
   of an element grows monotonically with the average activity.
   This relationship is often of the form
   "fluctuations-constant-average^{alpha}", where the exponent
   alpha is predominantly in the range [1/2,1]. This power law has
   been observed in a very wide range of disciplines, ranging from
   population dynamics through the Internet to the stock market and
   it is often treated under the names Taylor's law or fluctuation
   scaling. This review attempts to show how general the above
   scaling relationship is by surveying the literature, as well as
   by reporting some new empirical data and model calculations. We
   also show some basic principles that can underlie the generality
   of the phenomenon. This is followed by a mean-field framework
   based on sums of random variables. In this context the emergence
   of fluctuation scaling is equivalent to some corresponding limit
   theorems. In certain physical systems fluctuation scaling can be
   related to finite size scaling.
KE Keywords: fluctuation scaling; Taylor's law; complex systems;
   scaling
PP 89-142
$$