Enm Emilio Cirillo

Dynamics of pedestrians in regions with no visibility : a lattice model without exclusion

We investigate the motion of pedestrians through obscure corridors where the lack of visibility (due to smoke, fog, darkness, etc.) hides the precise position of the exits. We focus our attention on a set of basic mechanisms, which we assume to be governing the dynamics at the individual level. Using a lattice model, we explore the effects of non-exclusion 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 and investigate to which extent our model confirms the following pattern revealed by investigations on real emergencies: If the evacuees tend to cooperate and act altruistically, then their collective action tends to favor the occurrence of disasters. The research reported here opens many fundamental questions and should be seen therefore as a preliminary investigation of the very complex behavior of the people and their motion in dark regions.

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.

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 prove sufficient conditions to identify multiple metastable states. Since this analysis typically involves non-trivial technical issues, we give different conditions that can be chosen appropriately depending on the specific model under study. We show how these results can be used to attack the problem of multiple metastable states via the use of the modern approaches to metastability. We finally apply these general results to the Blume–Capel model for a particular choice of the parameters for which the model happens to have two multiple not degenerate in energy metastable states. We estimate in probability the time for the transition from the metastable states to the stable state. Moreover we identify the set of critical configurations that represent the minimal gate for the transition.

Competitive nucleation in reversible probabilistic cellular automata

The problem of competitive nucleation in the framework of probabilistic cellular automata is studied from the dynamical point of view. The dependence of the metastability scenario on the self-interaction is discussed. An intermediate metastable phase, made of two flip-flopping chessboard configurations, shows up depending on the ratio between the magnetic field and the self-interaction. A behavior similar to the one of the stochastic Blume-Capel model with Glauber dynamics is found.

Metastability for general dynamics with rare transitions : escape time and critical configurations

Metastability is a physical phenomenon ubiquitous in first order phase transitions. A fruitful mathematical way to approach this phenomenon is the study of rare transitions Markov chains. For Metropolis chains associated with statistical mechanics systems, this phenomenon has been described in an elegant way in terms of the energy landscape associated to the Hamiltonian of the system. In this paper, we provide a similar description in the general rare transitions setup. Beside their theoretical content, we believe that our results are a useful tool to approach metastability for non-Metropolis systems such as Probabilistic Cellular Automata.

Residence time estimates for asymmetric simple exclusion dynamics on strips

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 two-dimensional vertical strip. The sources of asymmetry are twofold: (i) the choice of boundary conditions (different reservoir levels) and (ii) the strong anisotropy from a drift nonlinear in density with prescribed directionality. We focus on the effect of the choice of anisotropy on residence time. We analyze our results by means of two theoretical models, a Mean Field and a one-dimensional Birth and Death one. For positive drift we find a striking agreement between Monte Carlo and theoretical results. In the zero drift case we still find agreement as long as particles can freely escape the strip through the bottom boundary. Otherwise, the two models give different predictions and their ability to reproduce numerical results depends on the horizontal displacement probability. 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.

Sum of exit times in a series of two metastable states

Abstract The problem of not degenerate in energy metastable states forming a series in the framework of reversible finite state space Markov chains is considered. Metastability has been widely studied both in the mathematical and physical literature. Metastable states arises close to a first order phase transition, when the system can be trapped for a long time (exponentially long with respect to the inverse of the temperature) before switching to the thermodynamically stable phase. In this paper, under rather general conditions, we give a sharp estimate of the exit time from a metastable state in a presence of a second metastable state that must be necessarily visited by the system before eventually reaching the stable phase. 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.

Lattice model of reduced jamming by a 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.). In particular, we discover an interesting nonmonotonic behavior of the residence time as a function of the barrier length. Besides recovering by means of both the lattice dynamics and the mean-field model well-known aspects like the faster-is-slower effect and the intermittence of the flow, we propose also a birth-and-death process and a reduced one-dimensional (1D) model with variable barrier permeability to capture the behavior of the residence time with respect to the parameters.

Weak solutions to Allen–Cahn-like equations modelling consolidation of porous media

We study the weak solvability of a system of coupled Allen-Cahn-like equations resembling cross-diffusion which is arising as a model for the consolidation of saturated porous media. Besides using energy like estimates, we cast the special structure of the system in the framework of the Leray-Schauder fixed point principle and ensure this way the local existence of strong solutions to a regularised version of our system. Furthermore, weak convergence techniques ensure the existence of weak solutions to the original consolidation problem. The uniqueness of global-in-time solutions is guaranteed in a particular case. Moreover, we use a finite difference scheme to show the negativity of the vector of solutions.

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.