625 research outputs found
Phase Transition with the Berezinskii--Kosterlitz--Thouless Singularity in the Ising Model on a Growing Network
We consider the ferromagnetic Ising model on a highly inhomogeneous network
created by a growth process. We find that the phase transition in this system
is characterised by the Berezinskii--Kosterlitz--Thouless singularity, although
critical fluctuations are absent, and the mean-field description is exact.
Below this infinite order transition, the magnetization behaves as
. We show that the critical point separates the phase
with the power-law distribution of the linear response to a local field and the
phase where this distribution rapidly decreases. We suggest that this phase
transition occurs in a wide range of cooperative models with a strong
infinite-range inhomogeneity. {\em Note added}.--After this paper had been
published, we have learnt that the infinite order phase transition in the
effective model we arrived at was discovered by O. Costin, R.D. Costin and C.P.
Grunfeld in 1990. This phase transition was considered in the papers: [1] O.
Costin, R.D. Costin and C.P. Grunfeld, J. Stat. Phys. 59, 1531 (1990); [2] O.
Costin and R.D. Costin, J. Stat. Phys. 64, 193 (1991); [3] M. Bundaru and C.P.
Grunfeld, J. Phys. A 32, 875 (1999); [4] S. Romano, Mod. Phys. Lett. B 9, 1447
(1995). We would like to note that Costin, Costin and Grunfeld treated this
model as a one-dimensional inhomogeneous system. We have arrived at the same
model as a one-replica ansatz for a random growing network where expected to
find a phase transition of this sort based on earlier results for random
networks (see the text). We have also obtained the distribution of the linear
response to a local field, which characterises correlations in this system. We
thank O. Costin and S. Romano for indicating these publications of 90s.Comment: 5 pages, 2 figures. We have added a note indicating that the infinite
order phase transition in the effective model we arrived at was discovered in
the work: O. Costin, R.D. Costin and C.P. Grunfeld, J. Stat. Phys. 59, 1531
(1990). Appropriate references to the papers of 90s have been adde
No directed fractal percolation in zero area
We show that fractal (or "Mandelbrot") percolation in two dimensions produces
a set containing no directed paths, when the set produced has zero area. This
improves a similar result by the first author in the case of constant retention
probabilities to the case of retention probabilities approaching 1
Duality and perfect probability spaces
Abstract. Given probability spaces (Xi, Ai,Pi),i =1,2,let M(P1,P2)denote the set of all probabilities on the product space with marginals P1 and P2 and let h be a measurable function on (X1 × X2, A1 ⊗A2). Continuous versions of linear programming stemming from the works of Monge (1781) and Kantorovich-Rubinˇstein (1958) for the case of compact metric spaces are concerned with the validity of the duality sup { hdP:P∈M(P1,P2)
Regulatory Dynamics on Random Networks: Asymptotic Periodicity and Modularity
We study the dynamics of discrete-time regulatory networks on random
digraphs. For this we define ensembles of deterministic orbits of random
regulatory networks, and introduce some statistical indicators related to the
long-term dynamics of the system. We prove that, in a random regulatory
network, initial conditions converge almost surely to a periodic attractor. We
study the subnetworks, which we call modules, where the periodic asymptotic
oscillations are concentrated. We proof that those modules are dynamically
equivalent to independent regulatory networks.Comment: 23 pages, 3 figure
Population Dynamics in Spatially Heterogeneous Systems with Drift: the generalized contact process
We investigate the time evolution and stationary states of a stochastic,
spatially discrete, population model (contact process) with spatial
heterogeneity and imposed drift (wind) in one- and two-dimensions. We consider
in particular a situation in which space is divided into two regions: an oasis
and a desert (low and high death rates). Carrying out computer simulations we
find that the population in the (quasi) stationary state will be zero,
localized, or delocalized, depending on the values of the drift and other
parameters. The phase diagram is similar to that obtained by Nelson and
coworkers from a deterministic, spatially continuous model of a bacterial
population undergoing convection in a heterogeneous medium.Comment: 8 papes, 12 figure
Dependence of paracentric inversion rate on tract length
BACKGROUND: We develop a Bayesian method based on MCMC for estimating the relative rates of pericentric and paracentric inversions from marker data from two species. The method also allows estimation of the distribution of inversion tract lengths. RESULTS: We apply the method to data from Drosophila melanogaster and D. yakuba. We find that pericentric inversions occur at a much lower rate compared to paracentric inversions. The average paracentric inversion tract length is approx. 4.8 Mb with small inversions being more frequent than large inversions. If the two breakpoints defining a paracentric inversion tract are uniformly and independently distributed over chromosome arms there will be more short tract-length inversions than long; we find an even greater preponderance of short tract lengths than this would predict. Thus there appears to be a correlation between the positions of breakpoints which favors shorter tract lengths. CONCLUSION: The method developed in this paper provides the first statistical estimator for estimating the distribution of inversion tract lengths from marker data. Application of this method for a number of data sets may help elucidate the relationship between the length of an inversion and the chance that it will get accepted
Force distributions in a triangular lattice of rigid bars
We study the uniformly weighted ensemble of force balanced configurations on
a triangular network of nontensile contact forces. For periodic boundary
conditions corresponding to isotropic compressive stress, we find that the
probability distribution for single-contact forces decays faster than
exponentially. This super-exponential decay persists in lattices diluted to the
rigidity percolation threshold. On the other hand, for anisotropic imposed
stresses, a broader tail emerges in the force distribution, becoming a pure
exponential in the limit of infinite lattice size and infinitely strong
anisotropy.Comment: 11 pages, 17 figures Minor text revisions; added references and
acknowledgmen
Roughening Transition in a One-Dimensional Growth Process
A class of nonequilibrium models with short-range interactions and sequential
updates is presented. The models describe one dimensional growth processes
which display a roughening transition between a smooth and a rough phase. This
transition is accompanied by spontaneous symmetry breaking, which is described
by an order parameter whose dynamics is non-conserving. Some aspects of models
in this class are related to directed percolation in 1+1 dimensions, although
unlike directed percolation the models have no absorbing states. Scaling
relations are derived and compared with Monte Carlo simulations.Comment: 4 pages, 3 Postscript figures, 1 Postscript formula, uses RevTe
Evolution of the most recent common ancestor of a population with no selection
We consider the evolution of a population of fixed size with no selection.
The number of generations to reach the first common ancestor evolves in
time. This evolution can be described by a simple Markov process which allows
one to calculate several characteristics of the time dependence of . We also
study how is correlated to the genetic diversity.Comment: 21 pages, 10 figures, uses RevTex4 and feynmf.sty Corrections :
introduction and conclusion rewritten, references adde
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