arXiv subjects

Emilio N. M. Cirillo

Publications and source records attributed to Emilio N. M. Cirillo.

At least 55 records · Page 3Linked to original sources

arXiv2016

Sum of exit times in a series of two metastable states

We consider the problem of non degenerate in energy metastable states forming a series in the framework of reversible finite state space Markov chains. We assume that starting from the state at higher energy the system necessarily visits the second one before reaching the stable state. In this framework, we give a sharp estimate of the exit time from the metastable state at higher energy and, on the proper exponential time scale, we prove an addition rule. As an application of the theory, we study the Blume-Capel model in the zero chemical potential case.

math-ph↗

arXiv2016

Basic Ideas to Approach Metastability in Probabilistic Cellular Automata

Cellular Automata are discrete--time dynamical systems on a spatially extended discrete space which provide paradigmatic examples of nonlinear phenomena. Their stochastic generalizations, i.e., Probabilistic Cellular Automata, are discrete time Markov chains on lattice with finite single--cell states whose distinguishing feature is the \textit{parallel} character of the updating rule. We review some of the results obtained about the metastable behavior of Probabilistic Cellular Automata and we try to point out difficulties and peculiarities with respect to standard Statistical Mechanics Lattice models.

cond-mat.stat-mech↗

arXiv2016

Sum of exit times in series of metastable states in Probabilistic Cellular Automata

Reversible Probabilistic Cellular Automata are a special class of automata whose stationary behavior is described by Gibbs-like measures. For those models the dynamics can be trapped for a very long time in states which are very different from the ones typical of stationarity. This phenomenon can be recasted in the framework of metastability theory which is typical of Statistical Mechanics. In this paper we consider a model presenting two not degenerate in energy metastable states which form a series, in the sense that, when the dynamics is started at one of them, before reaching stationarity, the system must necessarily visit the second one. We discuss a rule for combining the exit times from each of the metastable states.

math-ph↗

arXiv2016

Stationary currents in particle systems with constrained hopping rates

We study the effect on the stationary currents of constraints affecting the hopping rates in stochastic particle systems. In the framework of Zero Range Processes with drift within a finite volume, we discuss how the current is reduced by the presence of the constraint and deduce exact formulae, fully explicit in some cases. The model discussed here has been introduced in Ref. [1] and is relevant for the description of pedestrian motion in elongated dark corridors, where the constraint on the hopping rates can be related to limitations on the interaction distance among pedestrians.

cond-mat.stat-mech↗

arXiv2016

Effects of communication efficiency and exit capacity on fundamental diagrams for pedestrian motion in an obscure tunnel - a particle system approach

Fundamental diagrams describing the relation between pedestrians speed and density are key points in understanding pedestrian dynamics. Experimental data evidence the onset of complex behaviors in which the velocity decreases with the density and different logistic regimes are identified. This paper addresses the issue of pedestrians transport and of fundamental diagrams for a scenario involving the motion of pedestrians escaping from an obscure tunnel. We capture the effects of the communication efficiency and the exit capacity by means of two thresholds controlling the rate at which particles (walkers, pedestrians) move on the lattice. Using a particle system model, we show that in absence of limitation in communication among pedestrians we reproduce with good accuracy the standard fundamental diagrams, whose basic behaviors can be interpreted in terms of the exit capacity limitation. When the effect of a limited communication ability is considered, then interesting non-intuitive phenomena occur. Particularly, we shed light on the loss of monotonicity of the typical speed--density curves, revealing the existence of a pedestrians density optimizing the escape. We study both the discrete particle dynamics as well as the corresponding hydrodynamic limit (a porous medium equation and a transport (continuity) equation). We also point out the dependence of the effective transport coefficients on the two thresholds - the essence of the microstructure information.

cond-mat.stat-mech↗

arXiv2016

Compacton formation under Allen--Cahn dynamics

We study the solutions of a generalized Allen-Cahn equation deduced from a Landau energy functional, endowed with a non-constant higher order stiffness. We analytically solve the stationary problem and deduce the existence of so-called compactons, namely, connections on a finite interval between the two phases. The dynamics problem is numerically solved and compacton formation is described.

nlin.PS↗

arXiv2016

A lattice model of reduced jamming by barrier

We study an asymmetric simple exclusion process in a strip in the presence of a solid impenetrable barrier. We focus on the effect of the barrier on the residence time of the particles, namely, the typical time needed by the particles to cross the whole strip. We explore the conditions for reduced jamming when varying the environment (different drifts, reservoir densities, horizontal diffusion walks, etc.). Particularly, we discover an interesting non--monotonic behavior of the residence time as a function of the barrier length. Besides recovering by means of both the lattice dynamics and mean-field model well-known aspects like faster-is-slower effect and the intermittence of the flow, we propose also a birth-and-death process and a reduced one-dimensional model with variable barrier permeability to capture qualitatively the behavior of the residence time with respect to the parameters. We report our first steps towards the understanding to which extent the presence of obstacles can fluidize pedestrian and biological transport in crowded heterogeneous environments.

cond-mat.stat-mech↗

arXiv2016

Temperature-driven volume transition in hydrogels: phase--coexistence and interface localization

We study volume transition phenomenon in hydrogels within the framework of Flory-Rehner thermodynamic modelling; we show that starting from different models for the Flory parameter different conclusions can be achieved, in terms of admissible coexisting equilibria of the system. In particular, with explicit reference to a one-dimensional problem we establish the ranges of both temperature and traction which allow for the coexistence of a swollen and a shrunk phase. Through consideration of an augmented Flory-Rehner free-energy, which also accounts for the gradient of volume changes, we determine the position of the interface between the coexisting phases, and capture the connection profile between them.

cond-mat.soft↗

arXiv2015

Residence time estimates for asymmetric simple exclusion dynamics on stripes

The target of our study is to approximate numerically and, in some particular physically relevant cases, also analytically, the residence time of particles undergoing an asymmetric simple exclusion dynamics on a stripe. The source of asymmetry is twofold: (i) the choice of boundary conditions (different reservoir levels) and (ii) the strong anisotropy from a nonlinear drift with prescribed directionality. We focus on the effect of the choice of anisotropy in the flux on the asymptotic behavior of the residence time with respect to the length of the stripe. The topic is relevant for situations occurring in pedestrian flows or biological transport in crowded environments, where lateral displacements of the particles occur predominantly affecting therefore in an essentially way the efficiency of the overall transport mechanism.

nlin.CG↗

arXiv2014

A comparison between different cycle decompositions for Metropolis dynamics

In the last decades the problem of metastability has been attacked on rigorous grounds via many different approaches and techniques which are briefly reviewed in this paper. It is then useful to understand connections between different point of views. In view of this we consider irreducible, aperiodic and reversible Markov chains with exponentially small transition probabilities in the framework of Metropolis dynamics. We compare two different cycle decompositions and prove their equivalence.

math.PR↗

arXiv2013

Effect of self-interaction on the phase diagram of a Gibbs-like measure derived by a reversible Probabilistic Cellular Automata

Cellular Automata are discrete-time dynamical systems on a spatially extended discrete space which provide paradigmatic examples of nonlinear phenomena. Their stochastic generalizations, i.e., Probabilistic Cellular Automata (PCA), are discrete time Markov chains on lattice with finite single-cell states whose distinguishing feature is the \emph{parallel} character of the updating rule. We study the ground states of the Hamiltonian and the low-temperature phase diagram of the related Gibbs measure naturally associated with a class of reversible PCA, called the \textit{cross PCA}. In such a model the updating rule of a cell depends indeed only on the status of the five cells forming a cross centered at the original cell itself. In particular, it depends on the value of the center spin (\textit{self-interaction}). The goal of the paper is that of investigating the role played by the self-interaction parameter in connection with the ground states of the Hamiltonian and the low-temperature phase diagram of the Gibbs measure associated with this particular PCA.

cond-mat.stat-mech↗

arXiv2013

Flux through a time-periodic gate: Monte Carlo test of a homogenization result

We investigate via Monte Carlo numerical simulations and theoretical considerations the outflux of random walkers moving in an interval bounded by an interface exhibiting channels (pores, doors) which undergo an open/close cycle according to a periodic schedule. We examine the onset of a limiting boundary behavior characterized by a constant ratio between the outflux and the local density, in the thermodynamic limit. We compare such a limit with the predictions of a theoretical model already obtained in the literature as the homogenization limit of a suitable diffusion problem.

math-ph↗

arXiv2013

Pedestrians moving in dark: Balancing measures and playing games on lattices

We present two conceptually new modeling approaches aimed at describing the motion of pedestrians in obscured corridors: * a Becker-Döring-type dynamics * a probabilistic cellular automaton model. In both models the group formation is affected by a threshold. The pedestrians are supposed to have very limited knowledge about their current position and their neighborhood; they can form groups up to a certain size and they can leave them. Their main goal is to find the exit of the corridor. Although being of mathematically different character, the discussion of both models shows that it seems to be a disadvantage for the individual to adhere to larger groups. We illustrate this effect numerically by solving both model systems. Finally we list some of our main open questions and conjectures.

physics.soc-ph↗

arXiv2012

Kink Localization under Asymmetric Double-Well Potential

We study diffuse phase interfaces under asymmetric double-well potential energies with degenerate minima and demonstrate that the limiting sharp profile, for small interface energy cost, on a finite space interval is in general not symmetric and its position depends exclusively on the second derivatives of the potential energy at the two minima (phases). We discuss an application of the general result to porous media in the regime of solid-fluid segregation under an applied pressure and describe the interface between a fluid-rich and a fluid-poor phase. Asymmetric double-well potential energies are also relevant in a very different field of physics as that of Brownian motors. An intriguing analogy between our result and the direction of the dc soliton current in asymmetric substrate driven Brownian motors is pointed out.

math-ph↗

arXiv2012

Can cooperation slow down emergency evacuations?

We study the motion of pedestrians through obscure corridors where the lack of visibility hides the precise position of the exits. Using a lattice model, we explore the effects of cooperation on the overall exit flux (evacuation rate). More precisely, we study the effect of the buddying threshold (of no--exclusion per site) on the dynamics of the crowd. In some cases, we note that if the evacuees tend to cooperate and act altruistically, then their collective action tends to favor the occurrence of disasters.

physics.soc-ph↗

arXiv2012

Allen-Cahn and Cahn-Hilliard-like equations for dissipative dynamics of saturated porous media

We consider a saturated porous medium in the regime of solid-fluid segregation under an applied pressure on the solid constituent. We prove that, depending on the dissipation mechanism, the dynamics is described either by a Cahn-Hilliard or by an Allen-Cahn-like equation. More precisely, when the dissipation is modeled via the Darcy law we find that, for small deformation of the solid and small variations of the fluid density, the evolution equation is very similar to the Cahn-Hilliard equation. On the other hand, when only the Stokes dissipation term is considered, we find that the evolution is governed by an Allen-Cahn-like equation. We use this theory to describe the formation of interfaces inside porous media. We consider a recently developed model proposed to study the solid-liquid segregation in consolidation and we are able to fully describe the formation of an interface between the fluid-rich and the fluid-poor phase.

cond-mat.mtrl-sci↗

arXiv2012

Relaxation Height in Energy Landscapes: an Application to Multiple Metastable States

The study of systems with multiple (not necessarily degenerate) metastable states presents subtle difficulties from the mathematical point of view related to the variational problem that has to be solved in these cases. We introduce the notion of relaxation height in a general energy landscape and we prove sufficient conditions which are valid even in presence of multiple metastable states. We show how these results can be used to approach the problem of multiple metastable states via the use of the modern theories of metastability. We finally apply these general results to the Blume--Capel model for a particular choice of the parameters ensuring the existence of two multiple, and not degenerate in energy, metastable states.

math-ph↗

arXiv2012

Folding transitions in three-dimensional space with defects

A model describing the three-dimensional folding of the triangular lattice on the face-centered cubic lattice is generalized allowing the presence of defects corresponding to cuts in the two-dimensional network. The model can be expressed in terms of Ising-like variables with nearest-neighbor and plaquette interactions in the hexagonal lattice; its phase diagram is determined by the Cluster Variation Method. The results found by varying the curvature and defect energy show that the introduction of defects turns the first-order crumpling transitions of the model without defects into continuous transitions. New phases also appear by decreasing the energy cost of defects and the behavior of their densities has been analyzed.

cond-mat.stat-mech↗