23,320 research outputs found
Critical properties of an aperiodic model for interacting polymers
We investigate the effects of aperiodic interactions on the critical behavior
of an interacting two-polymer model on hierarchical lattices (equivalent to the
Migadal-Kadanoff approximation for the model on Bravais lattices), via
renormalization-group and tranfer-matrix calculations. The exact
renormalization-group recursion relations always present a symmetric fixed
point, associated with the critical behavior of the underlying uniform model.
If the aperiodic interactions, defined by s ubstitution rules, lead to relevant
geometric fluctuations, this fixed point becomes fully unstable, giving rise to
novel attractors of different nature. We present an explicit example in which
this new attractor is a two-cycle, with critical indices different from the
uniform model. In case of the four-letter Rudin-Shapiro substitution rule, we
find a surprising closed curve whose points are attractors of period two,
associated with a marginal operator. Nevertheless, a scaling analysis indicates
that this attractor may lead to a new critical universality class. In order to
provide an independent confirmation of the scaling results, we turn to a direct
thermodynamic calculation of the specific-heat exponent. The thermodynamic free
energy is obtained from a transfer matrix formalism, which had been previously
introduced for spin systems, and is now extended to the two-polymer model with
aperiodic interactions.Comment: 19 pages, 6 eps figures, to appear in J. Phys A: Math. Ge
Critical Behavior of a Three-State Potts Model on a Voronoi Lattice
We use the single-histogram technique to study the critical behavior of the
three-state Potts model on a (random) Voronoi-Delaunay lattice with size
ranging from 250 to 8000 sites. We consider the effect of an exponential decay
of the interactions with the distance,, with , and
observe that this system seems to have critical exponents and
which are different from the respective exponents of the three-state Potts
model on a regular square lattice. However, the ratio remains
essentially the same. We find numerical evidences (although not conclusive, due
to the small range of system size) that the specific heat on this random system
behaves as a power-law for and as a logarithmic divergence for
and Comment: 3 pages, 5 figure
Deblocking of interacting particle assemblies: from pinning to jamming
A wide variety of interacting particle assemblies driven by an external force
are characterized by a transition between a blocked and a moving phase. The
origin of this deblocking transition can be traced back to the presence of
either external quenched disorder, or of internal constraints. The first case
belongs to the realm of the depinning transition, which, for example, is
relevant for flux-lines in type II superconductors and other elastic systems
moving in a random medium. The second case is usually included within the
so-called jamming scenario observed, for instance, in many glassy materials as
well as in plastically deforming crystals. Here we review some aspects of the
rich phenomenology observed in interacting particle models. In particular, we
discuss front depinning, observed when particles are injected inside a random
medium from the boundary, elastic and plastic depinning in particle assemblies
driven by external forces, and the rheology of systems close to the jamming
transition. We emphasize similarities and differences in these phenomena.Comment: 20 pages, 8 figures, submitted for a special issue of the Brazilian
Journal of Physics entitled: Statistical Mechanics of Irreversible Stochastic
Models - I
Fundraising and vote distribution: a non-equilibrium statistical approach
The number of votes correlates strongly with the money spent in a campaign,
but the relation between the two is not straightforward. Among other factors,
the output of a ballot depends on the number of candidates, voters, and
available resources. Here, we develop a conceptual framework based on Shannon
entropy maximization and Superstatistics to establish a relation between the
distributions of money spent by candidates and their votes. By establishing
such a relation, we provide a tool to predict the outcome of a ballot and to
alert for possible misconduct either in the report of fundraising and spending
of campaigns or on vote counting. As an example, we consider real data from a
proportional election with candidates, where a detailed data
verification is virtually impossible, and show that the number of potential
misconducting candidates to audit can be reduced to only nine
Qualitative Analysis of Polycycles in Filippov Systems
In this paper, we are concerned about the qualitative behaviour of planar
Filippov systems around some typical minimal sets, namely, polycycles. In the
smooth context, a polycycle is a simple closed curve composed by a collection
of singularities and regular orbits, inducing a first return map. Here, this
concept is extended to Filippov systems by allowing typical singularities lying
on the switching manifold. Our main goal consists in developing a method to
investigate the unfolding of polycycles in Filippov systems. In addition, we
applied this method to describe bifurcation diagrams of Filippov systems around
certain polycycles
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