11,934 research outputs found
Do crossover functions depend on the shape of the interaction profile?
We examine the crossover from classical to non-classical critical behaviour
in two-dimensional systems with a one-component order parameter. Since the
degree of universality of the corresponding crossover functions is still
subject to debate, we try to induce non-universal effects by adding
interactions with a second length scale. Although the crossover functions
clearly depend on the range of the interactions, they turn out to be remarkably
robust against further variation of the interaction profile. In particular, we
find that the earlier observed non-monotonic crossover of the effective
susceptibility exponent occurs for several qualitatively different shapes of
this profile.Comment: 7 pages + 4 PostScript figures. Accepted for publication in
Europhysics Letters. Also available as PDF file at
http://www.cond-mat.physik.uni-mainz.de/~luijten/erikpubs.htm
Symmetric Diblock Copolymers in Thin Films (I): Phase stability in Self-Consistent Field Calculations and Monte Carlo Simulations
We investigate the phase behavior of symmetric AB diblock copolymers confined
into a thin film. The film boundaries are parallel, impenetrable and attract
the A component of the diblock copolymer. Using a self-consistent field
technique [M.W. Matsen, J.Chem.Phys. {\bf 106}, 7781 (1997)], we study the
ordered phases as a function of incompatibility and film thickness in
the framework of the Gaussian chain model. For large film thickness and small
incompatibility, we find first order transitions between phases with different
number of lamellae which are parallel oriented to the film boundaries. At high
incompatibility or small film thickness, transitions between parallel oriented
and perpendicular oriented lamellae occur. We compare the self-consistent field
calculations to Monte Carlo simulations of the bond fluctuation model for chain
length N=32. In the simulations we quench several systems from to
and monitor the morphology into which the diblock copolymers
assemble. Three film thicknesses are investigated, corresponding to parallel
oriented lamellae with 2 and 4 interfaces and a perpendicular oriented
morphology. Good agreement between self-consistent field calculations and Monte
Carlo simulations is found.Comment: to appear in J.Chem.Phy
Coupled Fluctuations near Critical Wetting
Recent work on the complete wetting transition has emphasized the role played
by the coupling of fluctuations of the order parameter at the wall and at the
depinning fluid interface. Extending this approach to the wetting transition
itself we predict a novel crossover effect associated with the decoupling of
fluctuations as the temperature is lowered towards the transition temperature
T_W. Using this we are able to reanalyse recent Monte-Carlo simulation studies
and extract a value \omega(T_W)=0.8 at T_W=0.9T_C in very good agreement with
long standing theoretical predictions.Comment: 4 pages, LaTex, 1 postscript figur
Alternating steady state in one-dimensional flocking
We study flocking in one dimension, introducing a lattice model in which
particles can move either left or right. We find that the model exhibits a
continuous nonequilibrium phase transition from a condensed phase, in which a
single `flock' contains a finite fraction of the particles, to a homogeneous
phase; we study the transition using numerical finite-size scaling.
Surprisingly, in the condensed phase the steady state is alternating, with the
mean direction of motion of particles reversing stochastically on a timescale
proportional to the logarithm of the system size. We present a simple argument
to explain this logarithmic dependence. We argue that the reversals are
essential to the survival of the condensate. Thus, the discrete directional
symmetry is not spontaneously broken.Comment: 8 pages LaTeX2e, 5 figures. Uses epsfig and IOP style. Submitted to
J. Phys. A (Math. Gen.
Non-monotonous crossover between capillary condensation and interface localisation/delocalisation transition in binary polymer blends
Within self-consistent field theory we study the phase behaviour of a
symmetric binary AB polymer blend confined into a thin film. The film surfaces
interact with the monomers via short range potentials. One surface attracts the
A component and the corresponding semi-infinite system exhibits a first order
wetting transition. The surface interaction of the opposite surface is varied
as to study the crossover from capillary condensation for symmetric surface
fields to the interface localisation/delocalisation transition for
antisymmetric surface fields. In the former case the phase diagram has a single
critical point close to the bulk critical point. In the latter case the phase
diagram exhibits two critical points which correspond to the prewetting
critical points of the semi-infinite system. The crossover between these
qualitatively different limiting behaviours occurs gradually, however, the
critical temperature and the critical composition exhibit a non-monotonic
dependence on the surface field.Comment: to appear in Europhys.Let
Polymer Brushes in Cylindrical Pores: Simulation versus Scaling Theory
The structure of flexible polymers endgrafted in cylindrical pores of
diameter D is studied as a function of chain length N and grafting density
\sigma, assuming good solvent conditions. A phenomenological scaling theory,
describing the variation of the linear dimensions of the chains with \sigma, is
developed and tested by Molecular Dynamics simulations of a bead-spring model.Comment: 35 pages, 38 figure
Domain Growth in Ising Systems with Quenched Disorder
We present results from extensive Monte Carlo (MC) simulations of domain
growth in ferromagnets and binary mixtures with quenched disorder. These are
modeled by the "random-bond Ising model" and the "dilute Ising model" with
either nonconserved (Glauber) spin-flip kinetics or conserved (Kawasaki)
spin-exchange kinetics. In all cases, our MC results are consistent with
power-law growth with an exponent which depends on the
quench temperature and the disorder amplitude . Such exponents
arise naturally when the coarsening domains are trapped by energy barriers
which grow logarithmically with the domain size. Our MC results show excellent
agreement with the predicted dependence of .Comment: 11 pages, 15 figure
On the Symmetry of Universal Finite-Size Scaling Functions in Anisotropic Systems
In this work a symmetry of universal finite-size scaling functions under a
certain anisotropic scale transformation is postulated. This transformation
connects the properties of a finite two-dimensional system at criticality with
generalized aspect ratio to a system with . The symmetry
is formulated within a finite-size scaling theory, and expressions for several
universal amplitude ratios are derived. The predictions are confirmed within
the exactly solvable weakly anisotropic two-dimensional Ising model and are
checked within the two-dimensional dipolar in-plane Ising model using Monte
Carlo simulations. This model shows a strongly anisotropic phase transition
with different correlation length exponents parallel
and perpendicular to the spin axis.Comment: RevTeX4, 4 pages, 3 figure
Extended Defects in the Potts-Percolation Model of a Solid: Renormalization Group and Monte Carlo Analysis
We extend the model of a 2 solid to include a line of defects. Neighboring
atoms on the defect line are connected by ?springs? of different strength and
different cohesive energy with respect to the rest of the system. Using the
Migdal-Kadanoff renormalization group we show that the elastic energy is an
irrelevant field at the bulk critical point. For zero elastic energy this model
reduces to the Potts model. By using Monte Carlo simulations of the 3- and
4-state Potts model on a square lattice with a line of defects, we confirm the
renormalization-group prediction that for a defect interaction larger than the
bulk interaction the order parameter of the defect line changes discontinuously
while the defect energy varies continuously as a function of temperature at the
bulk critical temperature.Comment: 13 figures, 17 page
Macroeconometric Modelling with a Global Perspective
This paper provides a synthesis and further development of a global modelling approach introduced in Pesaran, Schuermann and Weiner (2004), where country specific models in the form of VARX* structures are estimated relating a vector of domestic variables to their foreign counterparts and then consistently combined to form a Global VAR (GVAR). It is shown that VARX* models can be derived as the solution to a dynamic stochastic general equilibrium (DSGE) model where over-identifying long-run theoretical relations can be tested and imposed if acceptable. Similarly, short-run over-identifying theoretical restrictions can be tested and imposed if accepted. The assumption of the weak exogeneity of the foreign variables for the long-run parameters can be tested, where foreign variables can be interpreted as proxies for global factors. Rather than using deviations from ad hoc statistical trends, the equilibrium values of the variables reflecting the long-run theory embodied in the model can be calculated
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