15,879 research outputs found
Finite size effects on the phase diagram of a binary mixture confined between competing walls
A symmetrical binary mixture AB that exhibits a critical temperature T_{cb}
of phase separation into an A-rich and a B-rich phase in the bulk is considered
in a geometry confined between two parallel plates a distance D apart. It is
assumed that one wall preferentially attracts A while the other wall
preferentially attracts B with the same strength (''competing walls''). In the
limit , one then may have a wetting transition of first order at a
temperature T_{w}, from which prewetting lines extend into the one phase region
both of the A-rich and the B-rich phase. It is discussed how this phase diagram
gets distorted due to the finiteness of D% : the phase transition at T_{cb}
immediately disappears for D<\infty due to finite size rounding, and the phase
diagram instead exhibit two two-phase coexistence regions in a temperature
range T_{trip}<T<T_{c1}=T_{c2}. In the limit D\to \infty T_{c1},T_{c2} become
the prewetting critical points and T_{trip}\to T_{w}.
For small enough D it may occur that at a tricritical value D_{t} the
temperatures T_{c1}=T_{c2} and T_{trip} merge, and then for D<D_{t} there is a
single unmixing critical point as in the bulk but with T_{c}(D) near T_{w}. As
an example, for the experimentally relevant case of a polymer mixture a phase
diagram with two unmixing critical points is calculated explicitly from
self-consistent field methods
Wetting and Capillary Condensation in Symmetric Polymer Blends: A comparison between Monte Carlo Simulations and Self-Consistent Field Calculations
We present a quantitative comparison between extensive Monte Carlo
simulations and self-consistent field calculations on the phase diagram and
wetting behavior of a symmetric, binary (AB) polymer blend confined into a
film. The flat walls attract one component via a short range interaction. The
critical point of the confined blend is shifted to lower temperatures and
higher concentrations of the component with the lower surface free energy. The
binodals close the the critical point are flattened compared to the bulk and
exhibit a convex curvature at intermediate temperatures -- a signature of the
wetting transition in the semi-infinite system. Investigating the spectrum of
capillary fluctuation of the interface bound to the wall, we find evidence for
a position dependence of the interfacial tension. This goes along with a
distortion of the interfacial profile from its bulk shape. Using an extended
ensemble in which the monomer-wall interaction is a stochastic variable, we
accurately measure the difference between the surface energies of the
components, and determine the location of the wetting transition via the Young
equation. The Flory-Huggins parameter at which the strong first order wetting
transition occurs is independent of chain length and grows quadratically with
the integrated wall-monomer interaction strength. We estimate the location of
the prewetting line. The prewetting manifests itself in a triple point in the
phase diagram of very thick films and causes spinodal dewetting of ultrathin
layers slightly above the wetting transition. We investigate the early stage of
dewetting via dynamic Monte Carlo simulations.Comment: to appear in Macromolecule
Second-Order Dynamics in the Collective Evolution of Coupled Maps and Automata
We review recent numerical studies and the phenomenology of spatially
synchronized collective states in many-body dynamical systems. These states
exhibit thermodynamic noise superimposed on the collective, quasiperiodic order
parameter evolution with typically one basic irrational frequency. We
concentrate on the description of the global temporal properties in terms of
second-order difference equations.Comment: 11 pages (plain TeX), 4 figures (PostScript), preprint OUTP-92-51
On computational complexity of Siegel Julia sets
It has been previously shown by two of the authors that some polynomial Julia
sets are algorithmically impossible to draw with arbitrary magnification. On
the other hand, for a large class of examples the problem of drawing a picture
has polynomial complexity. In this paper we demonstrate the existence of
computable quadratic Julia sets whose computational complexity is arbitrarily
high.Comment: Updated version, to appear in Commun. Math. Phy
A model for a non-minimally coupled scalar field interacting with dark matter
In this work we investigate the evolution of a Universe consisted of a scalar
field, a dark matter field and non-interacting baryonic matter and radiation.
The scalar field, which plays the role of dark energy, is non-minimally coupled
to space-time curvature, and drives the Universe to a present accelerated
expansion. The non-relativistic dark matter field interacts directly with the
dark energy and has a pressure which follows from a thermodynamic theory. We
show that this model can reproduce the expected behavior of the density
parameters, deceleration parameter and luminosity distance.Comment: 3 pages, 4 figures. To appear in Brazilian Journal of Physic
Gravitational Clustering: A Simple, Robust and Adaptive Approach for Distributed Networks
Distributed signal processing for wireless sensor networks enables that
different devices cooperate to solve different signal processing tasks. A
crucial first step is to answer the question: who observes what? Recently,
several distributed algorithms have been proposed, which frame the
signal/object labelling problem in terms of cluster analysis after extracting
source-specific features, however, the number of clusters is assumed to be
known. We propose a new method called Gravitational Clustering (GC) to
adaptively estimate the time-varying number of clusters based on a set of
feature vectors. The key idea is to exploit the physical principle of
gravitational force between mass units: streaming-in feature vectors are
considered as mass units of fixed position in the feature space, around which
mobile mass units are injected at each time instant. The cluster enumeration
exploits the fact that the highest attraction on the mobile mass units is
exerted by regions with a high density of feature vectors, i.e., gravitational
clusters. By sharing estimates among neighboring nodes via a
diffusion-adaptation scheme, cooperative and distributed cluster enumeration is
achieved. Numerical experiments concerning robustness against outliers,
convergence and computational complexity are conducted. The application in a
distributed cooperative multi-view camera network illustrates the applicability
to real-world problems.Comment: 12 pages, 9 figure
Life-Cycle Models and Cross-Country Analysis of Saving
This paper develops a rational expectations life-cycle model designed as a framework for the cross-country analysis of (private) saving decisions. It is shown that a broad range of life-cycle models that have been used in the literature to study aggregate time series on consumption and saving fail to deliver plausible predictions for the purpose of analyzing saving decisions across countries as they imply that the level of saving has a constant mean and that the long-run saving rate may tend to zero. Introducing a utility specification that ties the long-run evolution of consumers' aspired consumption paths to that of aggregate labor income, an analytically tractable life-cycle model is proposed that has plausible long-run properties, including the implication that the net asset-labor income ratio, the saving rate, and the consumption-labor income ratio have meaningful long-run distributions. The moments of the long-run saving rate are shown to depend in a precise way on various characteristics of consumers' preferences, the real rate of interest, the growth rate and volatility of labor income, the government consumption-labor income ratio, and the government debt-labor income ratio. Employing a data set on saving rates and asset holdings across OECD economies and using techniques for the estimation of dynamic heterogeneous panels, the paper will also adduce empirical evidence assessing the model's ability to explain differences in the saving patterns across these economies.
Phase diagram of polymer blends in confined geometry
Within self-consistent field theory we study the phase behavior of a
symmetrical 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 localization/delocalization 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. Only below a triple point there is
a single two phase coexistence region. The crossover between these
qualitatively different limiting behaviors occurs gradually, however, the
critical temperature and the critical composition exhibit a non-monotonic
dependence on the surface field. The dependence of the phase behavior for
antisymmetric boundaries is studied as a function of the film thickness and the
strength of the surface interactions. Upon reducing the film thickness or
decreasing the strength of the surface interactions we can change the order of
the interface localization/delocalization transition from first to second. The
role of fluctuations is explored via Monte Carlo simulations of a coarse
grained lattice model. Close to the (prewetting) critical points we observe 2D
Ising critical behavior. At lower temperatures capillary waves of the AB
interface lead to a pronounced dependence of the effective interface potential
on the lateral system size.Comment: submitted to the Journal of Molecular Liquids and Condensed Matter
Physic
Estimation and Inference in Short Panel Vector Autoregressions with Unit Roots and Cointegration
This paper considers estimation and inference in panel vector autoregressions (PVARs) with fixed effects when the time dimension of the panel is finite, and the cross-sectional dimension is large. A Maximum Likelihood (ML) estimator based on a transformed likelihood function is proposed and shown to be consistent and asymptotically normally distributed irrespective of the unit root and cointegrating properties of the underlying PVAR model. The transformed likelihood framework is also used to derive unit root and cointegration tests in panels with short time dimension; these tests have the attractive feature that they are based on standard chi-squared and normal distributed statistics. Examining Generalised Method of Moments (GMM) estimation as an alternative to our proposed ML estimator, it is shown that conventional GMM estimators based on standard orthogonality conditions break down if the underlying time series contain unit roots.Panel vector autoregressions, Fixed effects, Unit roots, Cointegration
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