XVII NATIONAL CONFERENCE ON STATISTICAL PHYSICS AND COMPLEX SYSTEMS

with a special session devoted to

*The physics of quasi-fluids and quasi-solids: the dynamics of active and granular matter*

Wednesday 20 - Friday 22 June 2012, University of Parma

poster session

Pietro Coletti - Università di Roma *Roma Tre*

Out of equilibrium properties of the Potts Model

The Potts model is a generalization of the Ising model, with q possible
states for every
lattice site. Whereas for q<5 the system has a second order transition as
the Ising model, for
q ≥ 5 the Potts model exhibits a first order phase transition.
Moreover,
the system has q
degenerate ground state to collapse in, and the competition between these
ground states can
inhibit the condensation into a single phase.
We study the out of equilibrium properties of the Potts model. We show
some preliminary
results of numerical simulation on a square lattice regarding how the
system evolves after a
quench to a subcritical temperature. A special focus is on the domain
growth law, whose
characteristics are analyzed as a function of the initial correlation
length (finite vs infinite)
and whose early stage presents peculiar behaviour. The Ising case (q=2) is
shown for
comparison and used as a starting point for the analysis.

Aldo Di Biasio - Università degli Studi di Parma

Cooperativity and anticooperativity in chemical kinetics through
mean-field models

We consider cooperative reactions and we study the effects of the
interaction strength among the system components on the reaction rate,
hence realizing a connection between microscopic and macroscopic
observables. Our approach is based on statistical mechanics models and it
is developed analytically via mean-field techniques.
We show that cooperative and anticooperative behaviors naturally emerge
from the model when the coupling strength is set to be respectively
positive and negative,
so that varying a simple effective parameter a plethora of different
phenomena are recovered.

Davide Galli - Università di Milano

We present a study of submonolayer He adsorbed on two derivatives of
graphene: graphene-fluoride (GF) and graphane (GH). A semiempirical
interaction with the
substrate is used in state of the art quantum simulations. We predict that
both isotopes
^{3}He and ^{4}He
form anisotropic fluid states at low
coverage. The commensurate
state analogous to
the standard √×√ R30°
phase that preempts fluid states on graphite
turns out to be
unstable relative to a fluid state. The commensurate insulating ground
state on GF and GH is
disfavored by the much smaller inter-site distance (below 1.5 Å)
compared
to graphite (2.46 Å)
implying a large energy penalty for localizing He atoms. The 4He
ground state on both
substrates is a self-bound anisotropic superfluid with anisotropic roton
excitations and with a
superfluid density
ρ_{s}
reduced from 100% due to the corrugation of the
adsorption potential. In
the case of GF such corrugation is so large that
ρ_{s} = 57%
at T=0K and the
superfluid is
essentially restricted to move in a multiconnected space, along the bonds
of a honeycomb
lattice. We predict a superfluid transition temperature
T ≈
0.25(1.1)K for
4He on GF (GH). At
higher coverages we find two kinds of solids, an incommensurate triangular
one as well as a
novel commensurate state at filling factor 2/7 with 4 atoms in the unit
cell. We have evidence
that this 2/7 state is supersolid. We conclude that these new platforms
for adsorption studies
offer the possibility of studying novel phases of quantum condensed matter
like an anisotropic
Fermi fluid, possibly superfluid, an anisotropic Bose superfluid and a
commensurate
supersolid.

Stefano Iubini, Università di Firenze

The nonequilibrium discrete nonlinear Schroedinger equation

I will present the main features of
nonequilibrium steady states of the one-dimensional discrete nonlinear
Schroedinger (DNLS) equation.
Such equation has important applications in many domains of
physics. A classical example is electronic transport in biomolecules.
In the context of optics or
acoustics it describes the propagation of nonlinear waves
in a layered photonic or phononic system. On the other hand, in
the realm of the physics of cold atomic gases, the model
is an approximate semiclassical description of bosons
trapped in periodic optical lattices.
While a vast literature has been devoted to the dynamical
behavior of the DNLS equation, much less is known about finite-temperature
properties and almost nothing about nonequilibrium properties.
Due to the presence of two conserved quantities,
energy and norm (or number of particles), the model displays coupled
transport
in the sense of linear irreversible thermodynamics.
Suitable models of thermostat
are implemented to impose a given temperature and chemical potential at
the
chain ends. As a result, we find that the system exhibits normal
transport,
ruled by the Fourier law.
However, for large differences between the thermostat parameters, density
and
temperature profiles may display an unusual nonmonotonic shape. This is
due to
the strong dependence of the transport coefficients on the thermodynamic
variables.

Stefano Luccioli - CNR ISC Firenze

Collective dynamics, extensivity and non-additivity in sparse networks

The dynamics of sparse networks is investigated both at the microscopic
and macroscopic level, upon varying the connectivity. In all cases
(chaotic maps, Stuart-Landau oscillators, and leaky integrate-and-fire
neuron models), we find that a few tens of random connections are
sufficient to sustain a nontrivial (and possibly irregular) collective
dynamics. At the same time, the microscopic evolution turns out to be
extensive, both in the presence and absence of a macroscopic evolution.
This result is quite remarkable, considered the non-additivity of the
underlying dynamical rule.

Ref: S. Luccioli, S. Olmi, A. Politi and A. Torcini, "Collective dynamics in sparse networks", submitted to Phys. Rev. Lett.

Ref: S. Luccioli, S. Olmi, A. Politi and A. Torcini, "Collective dynamics in sparse networks", submitted to Phys. Rev. Lett.

Simona Olmi - CNR ISC Firenze

Stability of the splay state in networks of pulse-coupled neurons

The stability of the dynamical states characterised by a uniform
firing rate
("splay states") is analysed in a network of N globally
pulse-coupled
rotators (neurons) subjected to a generic velocity field. This is
done by reducing the set of differential equations to an event
driven map that is investigated in the limit of large network size.
We show that the Floquet spectrum characterising the stability of
the
splay state can be decomposed in two components: (i) a
long-wavelength component
which is the only one usually considered in mean-field analysis
[Abbott-van Vreesvijk, 1993]; (ii) a short-wavelenght component
measuring the instability of ``finite-frequency" modes.
By developing a perturbative technique, we have found analytically
that, in the limit of large N, the short-wavelenght spectrum scales
as 1/N^2 for generic discontinuous velocity fields.
Moreover, the stability of this component is determined by the sign
of
the jump at the discontinuity. Altogether, the form of the spectrum
depends on the pulse shape but is independent of the velocity
field.
Furthermore, numerical results indicate that in the case of
continuous
velocity fields, the Floquet exponents scale faster than 1/N^2
(namely, as 1/N^4) and we even find strictly neutral directions in
a wider class than the sinusoidal velocity fields considered by
Watanabe and Strogatz in Physica D 74 (1994) 197-253.

References

R. Zillmer, R. Livi, A. Politi, and A. Torcini, Phys. Rev. E 76 (2007) 046102 M. Calamai, A. Politi, and A. Torcini, Phys. Rev. E 80, 036209 (2009)

S. Olmi, A.Politi, and A. Torcini, "Stability of the splay state in networks of pulse-coupled neurons", submitted to J. Mathematical Neuroscience (2012)

References

R. Zillmer, R. Livi, A. Politi, and A. Torcini, Phys. Rev. E 76 (2007) 046102 M. Calamai, A. Politi, and A. Torcini, Phys. Rev. E 80, 036209 (2009)

S. Olmi, A.Politi, and A. Torcini, "Stability of the splay state in networks of pulse-coupled neurons", submitted to J. Mathematical Neuroscience (2012)

Matteo Polettini - INFN Bologna

State-Dependent Diffusion from General Covariance

The form of the correct equations describing brownian motion
with state-dependent diffusion is subject to long-standing debates. In
this poster I discuss one proposal which is founded on the principle of
general covariance, by which I mean: Covariance under coordinate
transformations; Invariance under internal "gauge" transformations. I
derive a generally covariant Langevin equation from first principles; the
overdamping limit yields a first-oder SDE which is neither Ito,
Straonovich, Klimontovich nor else. The corresponding Fokker-Planck
equation affords an equilibrium (detailed-balanced) steady state,
differing from other proposals. Among the experimentally testable
consequences of the theory, the spatial density of the steady state is not
uniform, dispensing with the equal-a-priori postulate.

Marco Pretti, CNR-ISC @ Politecnico di Torino

Chemically-controlled denaturation of a RNA-like polymer model

We consider a lattice polymer model of the 2-tolerant type (i.e., a random
walk allowed to visit lattice bonds at most twice), in which
doubly-visited bonds yield an attractive energy term (pairing energy).
Such a model has been previously proposed as a rough, non-specific
description of the RNA folding mechanism. In fact, the model predicts,
besides the usual theta-collapse, an extra transition to a low-temperature
fully-paired state.
In the current work, we propose an extension of the model, in which an
additional (micromolecular) chemical species can bind the polymer and
locally forbid base-pairing. This special kind of interaction is meant to
mimic a generic mechanism by which micro-RNA molecules could hamper
messenger RNA folding, and ultimately
exert their down-regulating effect within a gene-expression network. We
investigate equilibrium thermodynamics in the grand-canonical picture, at
the level of a Bethe approximation, which is, a refined mean-field
technique, equivalent to the exact solution on a random-regular graph.
The general trend we observe is that expected from the mechanism
implemented in the model (increasing micro-RNA concentration favors
denaturation and lowers the folding temperature), but the resulting phase
diagram turns out to be unexpectedly interesting and rich.

Francesco Santamaria, Università di Torino

Stokes' Drift for inertial particles

In this work we study the effects of waves on the motion of inertial
particles in an incompressible fluid.
We performed analytical calculations, using also multiple-scale
techniques, to predict the
behaviour of such a particle, firstly in deep water waves and then in an
arbitrarily deep regime.
All these analytical results were checked by numerical simulations of the
problem.
We found that the presence of inertia leads to corrections to the
well-known Stokes Drift. These
corrections become relevant in certain ranges of the parameters of the
system.
Furthermore, with the same methods, we observed that, even in the absence
of gravity (g = 0),
inertial particles drift downwards.

Guido Uguzzoni - Università degli Studi di Parma

The true reinforced random walk with bias

Stochastic processes with memory are a common way to model systems
ranging from physics to ecology and biology.

In particular, self-attracting and self-avoiding random walks provide basic, yet non trivial, examples.

Here, we first review the main definitions of random walks with memory and then we focus on the case of (true) reinforced random walk where memory effects are implemented at each time step, differently from the static case, where memory effects are accounted for globally.

We investigate the model in dimension $d=1$, also accounting for the presence of a field of strength $s$, which biases the walker toward a target site.

We analyze in details the asymptotic long-time behavior of the walker through the main statistical quantities (e.g. distinct sites visited, end-to-end distance) and we discuss a possible mapping between such dynamic self-attracting model and the trapping problem for a simple random walk, in analogy with the static model. Moreover, we find that, for any $s>0$, the random walk behavior switches to ballistic and that field effects always prevail on memory effects without any singularity, already in $d=1$; this is in contrast with the behavior observed in the static model.

In particular, self-attracting and self-avoiding random walks provide basic, yet non trivial, examples.

Here, we first review the main definitions of random walks with memory and then we focus on the case of (true) reinforced random walk where memory effects are implemented at each time step, differently from the static case, where memory effects are accounted for globally.

We investigate the model in dimension $d=1$, also accounting for the presence of a field of strength $s$, which biases the walker toward a target site.

We analyze in details the asymptotic long-time behavior of the walker through the main statistical quantities (e.g. distinct sites visited, end-to-end distance) and we discuss a possible mapping between such dynamic self-attracting model and the trapping problem for a simple random walk, in analogy with the static model. Moreover, we find that, for any $s>0$, the random walk behavior switches to ballistic and that field effects always prevail on memory effects without any singularity, already in $d=1$; this is in contrast with the behavior observed in the static model.