115 research outputs found
Examination of the Necessity of Complete Wetting near Critical Points in Systems with Long-Range Forces
Cahn’s general argument for complete wetting in the vicinity of critical points is critically reviewed. Critical-point wetting does occur in systems with short-range (exponentially decaying) forces. Whenever short-range forces favor wetting, while at the same time there is a tendency towards drying due to weak long-range (algebraically decaying) forces, neither critical-point wetting nor drying takes place. In this case the thickness of the partial wetting layer diverges as the bulk correlation length upon approach of the critical point
Effect of Criticality on Wetting Layers
We study wetting phenomena in which the wetting layer is (nearly) critical and intrudes between two noncritical phases. Finite-size scaling theory predicts an interaction, identical in range to that due to the van der Waals forces, between the interfaces bounding the wetting layer. This finite-size interaction leads to new wetting phenomena near critical end points, e.g., in ternary mixtures. The interaction amplitude and its possible universality can be observed directly in experiment
Effects of confinement and surface enhancement on superconductivity
Within the Ginzburg-Landau approach a theoretical study is performed of the
effects of confinement on the transition to superconductivity for type-I and
type-II materials with surface enhancement. The superconducting order parameter
is characterized by a negative surface extrapolation length . This leads to
an increase of the critical field and to a surface critical
temperature in zero field, , which exceeds the bulk . When the
sample is {\em mesoscopic} of linear size the surface induces
superconductivity in the interior for .
In analogy with adsorbed fluids, superconductivity in thin films of type-I
materials is akin to {\em capillary condensation} and competes with the
interface delocalization or "wetting" transition. The finite-size scaling
properties of capillary condensation in superconductors are scrutinized in the
limit that the ratio of magnetic penetration depth to superconducting coherence
length, , goes to zero, using analytic
calculations. While standard finite-size scaling holds for the transition in
non-zero magnetic field , an anomalous critical-point shift is found for
H=0. The increase of for H=0 is calculated for mesoscopic films,
cylindrical wires, and spherical grains of type-I and type-II materials.
Surface curvature is shown to induce a significant increase of ,
characterized by a shift inversely proportional to the
radius .Comment: 37 pages, 5 figures, accepted for PR
Multi-interaction mean-field renormalization group
We present an extension of the previously proposed mean-field renormalization
method to model Hamiltonians which are characterized by more than just one type
of interaction. The method rests on scaling assumptions about the magnetization
of different sublattices of the given lattice and it generates as many flow
equations as coupling constants without arbitrary truncations on the
renormalized Hamiltonian. We obtain good results for the test case of Ising
systems with an additional second-neighbor coupling in two and three
dimensions. An application of the method is also done to a morphological model
of interacting surfaces introduced recenlty by Likos, Mecke and Wagner [J.
Chem. Phys. {\bf{102}}, 9350 (1995)].
PACS: 64.60.Ak, 64.60.Fr, 05.70.JkComment: Tex file and three macros appended at the end. Five figures available
upon request to: [email protected], Fax: [+]39-40-224-60
Heterogeneous nucleation near a metastable vapour-liquid transition: the effect of wetting transitions
Phase transformations such as freezing typically start with heterogeneous
nucleation. Heterogeneous nucleation near a wetting transition, of a
crystalline phase is studied. The wetting transition occurs at or near a
vapour-liquid transition which occurs in a metastable fluid. The fluid is
metastable with respect to crystallisation, and it is the crystallisation of
this fluid phase that we are interested in. At a wetting transition a thick
layer of a liquid phase forms at a surface in contact with the vapour phase.
The crystalline nucleus is then immersed in this liquid layer, which reduces
the free energy barrier to nucleation and so dramatically increases the
nucleation rate. The variation in the rate of heterogeneous nucleation close to
wetting transitions is calculated for systems in which the longest-range forces
are dispersion forces.Comment: 11 pages including 3 figure
Finite-Size Interaction Amplitudes and their Universality: Exact, Mean-Field, and Renormalization-Group Results
We discuss the interaction between interfaces that is mediated by critical fluctuations, and in particular the universality of the corresponding finite-size amplitudes. In the case of the two-dimensional Ising model we address the universality with respect to anisotropy. For this purpose we derive the exact free energy of a finite, anisotropic triangular lattice on a cylinder. For the rectangular Ising model we verify universality also with respect to the magnitude of the boundary fields. In mean-field theory we display the mechanism for this universality and for that with respect to the surface coupling enhancement. Numerical results, which are of experimental relevance, are obtained employing a renormalization-group approximation for three-dimensional systems
Liquid drop in a cone - line tension effects
The shape of a liquid drop placed in a cone is analyzed macroscopically.
Depending on the values of the cone opening angle, the Young angle and the line
tension four different interfacial configurations may be realized. The phase
diagram in these variables is constructed and discussed; it contains both the
first- and the second-order transition lines. In particular, the tricritical
point is found and the value of the critical exponent characterizing the
behaviour of the system along the line of the first-order transitions in the
neighbourhood of this point is determined.Comment: 11 pages, 4 figure
Trading interactions for topology in scale-free networks
Scale-free networks with topology-dependent interactions are studied. It is
shown that the universality classes of critical behavior, which conventionally
depend only on topology, can also be explored by tuning the interactions. A
mapping, , describes how a shift of the
standard exponent of the degree distribution can absorb the
effect of degree-dependent pair interactions .
Replica technique, cavity method and Monte Carlo simulation support the
physical picture suggested by Landau theory for the critical exponents and by
the Bethe-Peierls approximation for the critical temperature. The equivalence
of topology and interaction holds for equilibrium and non-equilibrium systems,
and is illustrated with interdisciplinary applications.Comment: 4 pages, 5 figure
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