710 research outputs found

### Homogeneous nucleation of a non-critical phase near a continuous phase transition

Homogeneous nucleation of a new phase near a second, continuous, transition,
is considered. The continuous transition is in the metastable region associated
with the first-order phase transition, one of whose coexisting phases is
nucleating. Mean-field calculations show that as the continuous transition is
approached, the size of the nucleus varies as the response function of the
order parameter of the continuous transition. This response function diverges
at the continuous transition, as does the temperature derivative of the free
energy barrier to nucleation. This rapid drop of the barrier as the continuous
transition is approached means that the continuous transition acts to reduce
the barrier to nucleation at the first-order transition. This may be useful in
the crystallisation of globular proteins.Comment: 6 pages, 1 figur

### Nucleation Rate of Hadron Bubbles in Baryon-Free Quark-Gluon Plasma

We evaluate the factor $\kappa$ appearing in Langer's expression for the
nucleation rate extended to the case of hadron bubbles forming in zero baryon
number cooled quark-gluon plasma. We consider both the absence and presence of
viscosity and show that viscous effects introduce only small changes in the
value of $\kappa$Comment: 9 pages, revtex, no figures Full postscript version available at via
the WWW at http://nucth.physics.wisc.edu/preprints/ or by via from
ftp://nucth.physics.wisc.edu/pub/preprints/mad-nt-95-06.p

### Disjoining Potential and Spreading of Thin Liquid Layers in the Diffuse Interface Model Coupled to Hydrodynamics

The hydrodynamic phase field model is applied to the problem of film
spreading on a solid surface. The disjoining potential, responsible for
modification of the fluid properties near a three-phase contact line, is
computed from the solvability conditions of the density field equation with
appropriate boundary conditions imposed on the solid support. The equation
describing the motion of a spreading film are derived in the lubrication
approximation. In the case of quasi-equilibrium spreading, is shown that the
correct sharp-interface limit is obtained, and sample solutions are obtained by
numerical integration. It is further shown that evaporation or condensation may
strongly affect the dynamics near the contact line, and accounting for kinetic
retardation of the interphase transport is necessary to build up a consistent
theory.Comment: 14 pages, 5 figures, to appear in PR

### The Symplectic Penrose Kite

The purpose of this article is to view the Penrose kite from the perspective
of symplectic geometry.Comment: 24 pages, 7 figures, minor changes in last version, to appear in
Comm. Math. Phys

### Mesoscopic theory of the viscoelasticity of polymers

We have advanced our previous static theory of polymer entanglement involving
an extended Cahn-Hilliard functional, to include time-dependent dynamics. We go
beyond the Gaussian approximation, to the one-loop level, to compute the
frequency dependent storage and loss moduli of the system. The three parameters
in our theory are obtained by fitting to available experimental data on
polystyrene melts of various chain lengths. This provides a physical
representation of the parameters in terms of the chain length of the system. We
discuss the importance of the various terms in our energy functional with
respect to their contribution to the viscoelastic response of the polymeric
system.Comment: Submitted to Phys. Rev.

### Early stage scaling in phase ordering kinetics

A global analysis of the scaling behaviour of a system with a scalar order
parameter quenched to zero temperature is obtained by numerical simulation of
the Ginzburg-Landau equation with conserved and non conserved order parameter.
A rich structure emerges, characterized by early and asymptotic scaling
regimes, separated by a crossover. The interplay among different dynamical
behaviours is investigated by varying the parameters of the quench and can be
interpreted as due to the competition of different dynamical fixed points.Comment: 21 pages, latex, 7 figures available upon request from
[email protected]

### Layering in the Ising model

We consider the three-dimensional Ising model in a half-space with a boundary
field (no bulk field). We compute the low-temperature expansion of layering
transition lines

### FINE: Fisher Information Non-parametric Embedding

We consider the problems of clustering, classification, and visualization of
high-dimensional data when no straightforward Euclidean representation exists.
Typically, these tasks are performed by first reducing the high-dimensional
data to some lower dimensional Euclidean space, as many manifold learning
methods have been developed for this task. In many practical problems however,
the assumption of a Euclidean manifold cannot be justified. In these cases, a
more appropriate assumption would be that the data lies on a statistical
manifold, or a manifold of probability density functions (PDFs). In this paper
we propose using the properties of information geometry in order to define
similarities between data sets using the Fisher information metric. We will
show this metric can be approximated using entirely non-parametric methods, as
the parameterization of the manifold is generally unknown. Furthermore, by
using multi-dimensional scaling methods, we are able to embed the corresponding
PDFs into a low-dimensional Euclidean space. This not only allows for
classification of the data, but also visualization of the manifold. As a whole,
we refer to our framework as Fisher Information Non-parametric Embedding
(FINE), and illustrate its uses on a variety of practical problems, including
bio-medical applications and document classification.Comment: 30 pages, 21 figure

### Thermodynamics of non-local materials: extra fluxes and internal powers

The most usual formulation of the Laws of Thermodynamics turns out to be
suitable for local or simple materials, while for non-local systems there are
two different ways: either modify this usual formulation by introducing
suitable extra fluxes or express the Laws of Thermodynamics in terms of
internal powers directly, as we propose in this paper. The first choice is
subject to the criticism that the vector fluxes must be introduced a posteriori
in order to obtain the compatibility with the Laws of Thermodynamics. On the
contrary, the formulation in terms of internal powers is more general, because
it is a priori defined on the basis of the constitutive equations. Besides it
allows to highlight, without ambiguity, the contribution of the internal powers
in the variation of the thermodynamic potentials. Finally, in this paper, we
consider some examples of non-local materials and derive the proper expressions
of their internal powers from the power balance laws.Comment: 16 pages, in press on Continuum Mechanics and Thermodynamic

### Oscillatory wave fronts in chains of coupled nonlinear oscillators

Wave front pinning and propagation in damped chains of coupled oscillators
are studied. There are two important thresholds for an applied constant stress
$F$: for $|F|<F_{cd}$ (dynamic Peierls stress), wave fronts fail to propagate,
for $F_{cd} < |F| < F_{cs}$ stable static and moving wave fronts coexist, and
for $|F| > F_{cs}$ (static Peierls stress) there are only stable moving wave
fronts. For piecewise linear models, extending an exact method of Atkinson and
Cabrera's to chains with damped dynamics corroborates this description. For
smooth nonlinearities, an approximate analytical description is found by means
of the active point theory. Generically for small or zero damping, stable wave
front profiles are non-monotone and become wavy (oscillatory) in one of their
tails.Comment: 18 pages, 21 figures, 2 column revtex. To appear in Phys. Rev.

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