106 research outputs found
Mixing time of random walk on dynamical random cluster
We study the mixing time of a random walker who moves inside a dynamical
random cluster model on the d-dimensional torus of side-length n. In this
model, edges switch at rate \mu between open and closed, following a Glauber
dynamics for the random cluster model with parameters p,q. At the same time,
the walker jumps at rate 1 as a simple random walk on the torus, but is only
allowed to traverse open edges. We show that for small enough p the mixing time
of the random walker is of order n^2/\mu. In our proof we construct of a
non-Markovian coupling through a multi-scale analysis of the environment, which
we believe could be more widely applicable
Mixing time of random walk on dynamical random cluster
We study the mixing time of a random walker who moves inside a dynamical random cluster model on the d-dimensional torus of side-length n. In this model, edges switch at rate \mu between open and closed, following a Glauber dynamics for the random cluster model with parameters p,q. At the same time, the walker jumps at rate 1 as a simple random walk on the torus, but is only allowed to traverse open edges. We show that for small enough p the mixing time of the random walker is of order n^2/\mu. In our proof we construct of a non-Markovian coupling through a multi-scale analysis of the environment, which we believe could be more widely applicable
Mixing time of random walk on dynamical random cluster
We study the mixing time of a random walker who moves inside a dynamical
random cluster model on the d-dimensional torus of side-length n. In this
model, edges switch at rate \mu between open and closed, following a Glauber
dynamics for the random cluster model with parameters p,q. At the same time,
the walker jumps at rate 1 as a simple random walk on the torus, but is only
allowed to traverse open edges. We show that for small enough p the mixing time
of the random walker is of order n^2/\mu. In our proof we construct of a
non-Markovian coupling through a multi-scale analysis of the environment, which
we believe could be more widely applicable
Chemical etching of a disordered solid: from experiments to field theory
We present a two-dimensional theoretical model for the slow chemical
corrosion of a thin film of a disordered solid by suitable etching solutions.
This model explain different experimental results showing that the corrosion
stops spontaneously in a situation in which the concentration of the etchant is
still finite while the corrosion surface develops clear fractal features. We
show that these properties are strictly related to the percolation theory, and
in particular to its behavior around the critical point. This task is
accomplished both by a direct analysis in terms of a self-organized version of
the Gradient Percolation model and by field theoretical arguments.Comment: 7 pages, 3 figure
Non-equilibrium phase transition in negotiation dynamics
We introduce a model of negotiation dynamics whose aim is that of mimicking
the mechanisms leading to opinion and convention formation in a population of
individuals. The negotiation process, as opposed to ``herding-like'' or
``bounded confidence'' driven processes, is based on a microscopic dynamics
where memory and feedback play a central role. Our model displays a
non-equilibrium phase transition from an absorbing state in which all agents
reach a consensus to an active stationary state characterized either by
polarization or fragmentation in clusters of agents with different opinions. We
show the exystence of at least two different universality classes, one for the
case with two possible opinions and one for the case with an unlimited number
of opinions. The phase transition is studied analytically and numerically for
various topologies of the agents' interaction network. In both cases the
universality classes do not seem to depend on the specific interaction
topology, the only relevant feature being the total number of different
opinions ever present in the system.Comment: 4 pages, 4 figure
Theory of Boundary Effects in Invasion Percolation
We study the boundary effects in invasion percolation with and without
trapping. We find that the presence of boundaries introduces a new set of
surface critical exponents, as in the case of standard percolation. Numerical
simulations show a fractal dimension, for the region of the percolating cluster
near the boundary, remarkably different from the bulk one. We find a
logarithmic cross-over from surface to bulk fractal properties, as one would
expect from the finite-size theory of critical systems. The distribution of the
quenched variables on the growing interface near the boundary self-organises
into an asymptotic shape characterized by a discontinuity at a value ,
which coincides with the bulk critical threshold. The exponent of
the boundary avalanche distribution for IP without trapping is
; this value is very near to the bulk one. Then we
conclude that only the geometrical properties (fractal dimension) of the model
are affected by the presence of a boundary, while other statistical and
dynamical properties are unchanged. Furthermore, we are able to present a
theoretical computation of the relevant critical exponents near the boundary.
This analysis combines two recently introduced theoretical tools, the Fixed
Scale Transformation (FST) and the Run Time Statistics (RTS), which are
particularly suited for the study of irreversible self-organised growth models
with quenched disorder. Our theoretical results are in rather good agreement
with numerical data.Comment: 11 pages, 13 figures, revte
Opinion dynamics and synchronization in a network of scientific collaborations
In this paper we discuss opinion dynamics in the Opinion Changing Rate (OCR)
model, recently proposed (A.Pluchino, V.Latora and A.Rapisarda Int. J. Mod.
Phys. C, 16, No.4, 515-531 (2005)). The OCR model allows to study whether and
how a group of social agents, with a different intrinsic tendency rate to
change opinion, finds agreement. In particular, we implement the OCR model on a
small graph describing the topology of a real social system. The nodes of the
graph are scientists partecipating to the Tepoztlan conference, celebrating
Alberto Robledo's 60th birthday, and the links are based on coauthorship in
scientific papers. We study how opinions evolve in time according to the
frequency rates of the nodes, to the coupling term, and also to the presence of
group structures.Comment: 15 pages, 4 figures, Physica A (2006) in pres
The Search for Young Planetary Systems And the Evolution of Young Stars
The Space Interferometer Mission (SIM) will provide a census of planetary systems by con- ducting a broad survey of 2,000 stars that will be sensitive to the presence of planets with masses as small as approx. 15 Earth masses (1 Uranus mass) and a deep survey of approx. 250 of the nearest, stars with a mass limit of approx.3 Earth masses. The broad survey will include stars spanning a wide range of ages, spectral types, metallicity, and other important parameters. Within this larger context, the Young Stars and Planets Key Project will study approx. 200 stars with ages from 1 Myr to 100 Myr to understand the formation and dynamical evolution of gas giant planets. The SIM Young Stars and Planets Project will investigate both the frequency of giant planet formation and the early dynamical history of planetary systems. We will gain insight into how common the basic architecture of our solar system is compared with recently discovered systems with close-in giant planets by examining 200 of the nearest (less than 150 pc) and youngest (1-100 Myr) solar-type stars for planets. The sensitivity of the survey for stars located 140 pc away is shown in the planet mass-separation plane. We expect to find anywhere from 10 (assuming that only the presently known fraction of stars. 5-7%, has planets) to 200 (all young stars have planets) planetary systems. W-e have set our sensitivity threshold to ensure the detection of Jupiter-mass planets in the critical orbital range of 1 to 5 AU. These observations, when combined with the results of planetary searches of mature stars, will allow us to test theories of planetary formation and early solar system evolution. By searching for planets around pre-main sequence stars carefully selected to span an age range from 1 to 100 Myr, we will learn a t what epoch and with what frequency giant planets are found at the water-ice snowline where they are expected to form. This will provide insight into the physical mechanisms by which planets form and migrate from their place of birth, and about their survival rate. With these data in hand, we will provide data, for the first time, on such important questions as: What processes affect the formation and dynamical evolution of planets? When and where do planets form? What is initial mass distribution of planetary systems around young stars? How might planets be destroyed? What is the origin of the eccentricity of planetary orbits? What is the origin of the apparent dearth of companion objects between planets and brown dwarfs seen in mature stars? The observational strategy is a compromise between the desire to extend the planetary mass function as low as possible and the essential need to build up sufficient statistics on planetary occurrence. About half of the sample will be used to address the "where" and "when" of planet formation. We will study classical T Tauri stars (cTTs) which have massive accretion disks and post- accretion, weak-lined T Tauri stars (wTTs). Preliminary estimates suggest the sample will consist of approx. 30% cTTs and approx. 70% wTTs, driven in part by the difficulty of making accurate astrometric measurements toward objects with strong variability or prominent disks
Dynamic structure factor of the Ising model with purely relaxational dynamics
We compute the dynamic structure factor for the Ising model with a purely
relaxational dynamics (model A). We perform a perturbative calculation in the
expansion, at two loops in the high-temperature phase and at one
loop in the temperature magnetic-field plane, and a Monte Carlo simulation in
the high-temperature phase. We find that the dynamic structure factor is very
well approximated by its mean-field Gaussian form up to moderately large values
of the frequency and momentum . In the region we can investigate,
, , where is the correlation
length and the zero-momentum autocorrelation time, deviations are at
most of a few percent.Comment: 21 pages, 3 figure
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