168 research outputs found
A local limit theorem for triple connections in subcritical Bernoulli percolation
We prove a local limit theorem for the probability of a site to be connected
by disjoint paths to three points in subcritical Bernoulli percolation on
in the limit where their distances tend to infinity.Comment: 31 page
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
Thermodynamic instabilities in one dimensional particle lattices: a finite-size scaling approach
One-dimensional thermodynamic instabilities are phase transitions not
prohibited by Landau's argument, because the energy of the domain wall (DW)
which separates the two phases is infinite. Whether they actually occur in a
given system of particles must be demonstrated on a case-by-case basis by
examining the (non-) analyticity properties of the corresponding transfer
integral (TI) equation. The present note deals with the generic Peyrard-Bishop
model of DNA denaturation. In the absence of exact statements about the
spectrum of the singular TI equation, I use Gauss-Hermite quadratures to
achieve a single-parameter-controlled approach to rounding effects; this allows
me to employ finite-size scaling concepts in order to demonstrate that a phase
transition occurs and to derive the critical exponents.Comment: 5 pages, 6 figures, subm. to Phys. Rev.
Molecular ordering of precursor films during spreading of tiny liquid droplets
In this work we address a novel feature of spreading dynamics of tiny liquid
droplets on solid surfaces, namely the case where the ends of the molecules
feel different interactions to the surface. We consider a simple model of
dimers and short chain--like molecules which cannot form chemical bonds with
the surface. We study the spreading dynamics by Molecular Dynamics techniques.
In particular, we examine the microscopic structure of the time--dependent
precursor film and find that in some cases it can exhibit a high degree of
local order. This order persists even for flexible chains. Our results suggest
the possibility of extracting information about molecular interactions from the
structure of the precursor film.Comment: 4 pages, revtex, no figures, complete file available from
ftp://rock.helsinki.fi/pub/preprints/tft/ or at
http://www.physics.helsinki.fi/tft/tft_preprints.html (to appear in Phys.
Rev. E Rapid Comm.
Exact time-dependent correlation functions for the symmetric exclusion process with open boundary
As a simple model for single-file diffusion of hard core particles we
investigate the one-dimensional symmetric exclusion process. We consider an
open semi-infinite system where one end is coupled to an external reservoir of
constant density and which initially is in an non-equilibrium state
with bulk density . We calculate the exact time-dependent two-point
density correlation function and the mean and variance of the integrated average net flux
of particles that have entered (or left) the system up to time .
We find that the boundary region of the semi-infinite relaxing system is in a
state similar to the bulk state of a finite stationary system driven by a
boundary gradient. The symmetric exclusion model provides a rare example where
such behavior can be proved rigorously on the level of equal-time two-point
correlation functions. Some implications for the relaxational dynamics of
entangled polymers and for single-file diffusion in colloidal systems are
discussed.Comment: 11 pages, uses REVTEX, 2 figures. Minor typos corrected and reference
17 adde
A Soluble Phase Field Model
The kinetics of an initially undercooled solid-liquid melt is studied by
means of a generalized Phase Field model, which describes the dynamics of an
ordering non-conserved field phi (e.g. solid-liquid order parameter) coupled to
a conserved field (e.g. thermal field). After obtaining the rules governing the
evolution process, by means of analytical arguments, we present a discussion of
the asymptotic time-dependent solutions. The full solutions of the exact
self-consistent equations for the model are also obtained and compared with
computer simulation results. In addition, in order to check the validity of the
present model we confronted its predictions against those of the standard Phase
field model and found reasonable agreement. Interestingly, we find that the
system relaxes towards a mixed phase, depending on the average value of the
conserved field, i.e. on the initial condition. Such a phase is characterized
by large fluctuations of the phi field.Comment: 13 pages, 8 figures, RevTeX 3.1, submitted to Physical Review
Nonequilibrium wetting
When a nonequilibrium growing interface in the presence of a wall is
considered a nonequilibrium wetting transition may take place. This transition
can be studied trough Langevin equations or discrete growth models. In the
first case, the Kardar-Parisi-Zhang equation, which defines a very robust
universality class for nonequilibrium moving interfaces, with a soft-wall
potential is considered. While in the second, microscopic models, in the
corresponding universality class, with evaporation and deposition of particles
in the presence of hard-wall are studied. Equilibrium wetting is related to a
particular case of the problem, it corresponds to the Edwards-Wilkinson
equation with a potential in the continuum approach or to the fulfillment of
detailed balance in the microscopic models. In this review we present the
analytical and numerical methods used to investigate the problem and the very
rich behavior that is observed with them.Comment: Review, 36 pages, 16 figure
Surface and capillary transitions in an associating binary mixture model
We investigate the phase diagram of a two-component associating fluid mixture
in the presence of selectively adsorbing substrates. The mixture is
characterized by a bulk phase diagram which displays peculiar features such as
closed loops of immiscibility. The presence of the substrates may interfere the
physical mechanism involved in the appearance of these phase diagrams, leading
to an enhanced tendency to phase separate below the lower critical solution
point. Three different cases are considered: a planar solid surface in contact
with a bulk fluid, while the other two represent two models of porous systems,
namely a slit and an array on infinitely long parallel cylinders. We confirm
that surface transitions, as well as capillary transitions for a large
area/volume ratio, are stabilized in the one-phase region. Applicability of our
results to experiments reported in the literature is discussed.Comment: 12 two-column pages, 12 figures, accepted for publication in Physical
Review E; corrected versio
Observational constraints on holographic dark energy with varying gravitational constant
We use observational data from Type Ia Supernovae (SN), Baryon Acoustic
Oscillations (BAO), Cosmic Microwave Background (CMB) and observational Hubble
data (OHD), and the Markov Chain Monte Carlo (MCMC) method, to constrain the
cosmological scenario of holographic dark energy with varying gravitational
constant. We consider both flat and non-flat background geometry, and we
present the corresponding constraints and contour-plots of the model
parameters. We conclude that the scenario is compatible with observations. In
1 we find ,
, and
, while for the present value
of the dark energy equation-of-state parameter we obtain
.Comment: 12 pages, 2 figures, version published in JCA
Optimal designs for rational function regression
We consider optimal non-sequential designs for a large class of (linear and
nonlinear) regression models involving polynomials and rational functions with
heteroscedastic noise also given by a polynomial or rational weight function.
The proposed method treats D-, E-, A-, and -optimal designs in a
unified manner, and generates a polynomial whose zeros are the support points
of the optimal approximate design, generalizing a number of previously known
results of the same flavor. The method is based on a mathematical optimization
model that can incorporate various criteria of optimality and can be solved
efficiently by well established numerical optimization methods. In contrast to
previous optimization-based methods proposed for similar design problems, it
also has theoretical guarantee of its algorithmic efficiency; in fact, the
running times of all numerical examples considered in the paper are negligible.
The stability of the method is demonstrated in an example involving high degree
polynomials. After discussing linear models, applications for finding locally
optimal designs for nonlinear regression models involving rational functions
are presented, then extensions to robust regression designs, and trigonometric
regression are shown. As a corollary, an upper bound on the size of the support
set of the minimally-supported optimal designs is also found. The method is of
considerable practical importance, with the potential for instance to impact
design software development. Further study of the optimality conditions of the
main optimization model might also yield new theoretical insights.Comment: 25 pages. Previous version updated with more details in the theory
and additional example
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