Emilio N. M. Cirillo

Sapienza University of Rome | la sapienza · Department of Basic and Applied Sciences for Engineering

We study the deterministic dynamics of N point particles moving at constant speed in a 2D table made of two polygonal urns connected by an active rectangular channel, which applies a feedback-control on the particles, inverting the horizontal component of their velocities, when their number in the channel exceeds a fixed threshold. Such a bounce--b...

We study a reaction-diffusion-convection problem with nonlinear drift posed in a domain with periodically arranged obstacles. The non-linearity in the drift is linked to the hydrodynamic limit of a totally asymmetric simple exclusion process (TASEP) governing a population of interacting particles crossing a domain with obstacle. Because of the impo...

We perform a quantitative analysis of Monte-Carlo simulations results of phase separation in ternary blends upon evaporation of one component. Specifically, we calculate the average domain size and plot it as a function of simulation time to compute the exponent of the obtained power-law. We compare and discuss results obtained by two different met...

Metastability is a ubiquitous phenomenon in nature, which interests several fields of natural sciences. Since metastability is a genuine non-equilibrium phenomenon, its description in the framework of thermodynamics and statistical mechanics has progressed slowly for a long time. Since the publication of the first seminal paper in which the metasta...

We exploit Surface-Enhanced Raman Scattering (SERS) to investigate aqueous droplets of genomic DNA deposited onto silver-coated silicon nanowires and we show that it is possible to efficiently discriminate between spectra of tumoral and healthy cells. To assess the robustness of the proposed technique, we develop two different statistical approache...

Metastability is an ubiquitous phenomenon in nature, which interests several fields of natural sciences. Its description in the framework of thermodynamics and statistical mechanics has been a taboo for long time since it is a genuine non--equilibrium phenomenon. Since the publication of the first seminal paper in which the metastable behavior of t...

We study the question of periodic homogenization of a variably scaled reaction-diffusion problem with non-linear drift posed for a domain crossed by a flat composite thin layer. The structure of the non-linearity in the drift was obtained in earlier works as hydrodynamic limit of a totally asymmetric simple exclusion process (TASEP) for a populatio...

We discuss the properties of the residence time in presence of moving defects or obstacles for a particle performing a one dimensional random walk. More precisely, for a particle conditioned to exit through the right endpoint, we measure the typical time needed to cross the entire lattice in presence of defects. We find explicit formulae for the re...

We study the question of periodic homogenization of a variably scaled reaction-diffusion problem with non-linear drift posed for a domain crossed by a flat composite thin layer. The structure of the non-linearity in the drift was obtained in earlier works as hydrodynamic limit of a totally asymmetric simple exclusion process (TASEP) process for a p...

Diffusion in inhomogeneous materials can be described by both the Fick and Fokker–Planck diffusion equations. Here, we study a mixed Fick and Fokker–Planck diffusion problem with coefficients rapidly oscillating both in space and time. We obtain macroscopic models performing the homogenization limit by means of the unfolding technique.

We develop a mesoscopic lattice model to study the morphology formation in interacting ternary mixtures with evaporation of one component. As concrete application of our model, we wish to capture morphologies as they are typically arising during fabrication of organic solar cells. In this context, we consider an evaporating solvent into which two o...

We consider point particles in a table made of two circular cavities connected by two rectangular channels, forming a closed loop under periodic boundary conditions. In the first channel, a bounce-back mechanism acts when the number of particles flowing in one direction exceeds a given threshold T. In that case, the particles invert their horizonta...

We investigate one–dimensional probabilistic cellular automata, called Diploid Elementary Cellular Automata (DECA), obtained as random mixtures of two different elementary cellular automata rules. All the cells are updated synchronously and the probability for one cell to be 0 or 1 at time t depends only on the value of the same cell and that of it...

We consider point particles in a table made of two circular cavities connected by two rectangular channels, forming a closed loop under periodic boundary conditions. In the first channel, a bounce--back mechanism acts when the number of particles flowing in one direction exceeds a given threshold $T$. In that case, the particles invert their horizo...

We investigate one-dimensional Probabilistic Cellular Automata, called Diploid Elementary Cellular Automata (DECA), obtained as random mixture of two different Elementary Cellular Automata rules. All the cells are updated synchronously and the probability for one cell to be $0$ or $1$ at time $t$ depends only on the value of the same cell and that...

We show that residence time measure can be used to identify the geometrical and transmission properties of a defect along a path. The model we study is based on a one--dimensional simple random walk. The sites of the lattice are regular, i.e., the jumping probabilities are the same in each site, except for a site, called \emph{defect}, where the ju...

We study the upscaling of a system of many interacting particles through a heterogenous thin elongated obstacle as modeled via a two-dimensional diffusion problem with a one-directional nonlinear convective drift. Assuming that the obstacle can be described well by a thin composite strip with periodically placed microstructures, we aim at deriving...

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 assume the stiffness to be a positive function of the field and we discuss the stability of the stationary solutions proving both linear and local non–linear stability.

Stochastic particle–based models are useful tools for describing the collective movement of large crowds of pedestrians in crowded confined environments. Using descriptions based on the simple exclusion process, two populations of particles, mimicking pedestrians walking in a built environment, enter a room from two opposite sides. One population i...

N point particles move within a billiard table made of two circular cavities connected by a straight channel. The usual billiard dynamics is modified so that it remains deterministic, phase space volumes preserving and time reversal invariant. Particles move in straight lines and are elastically reflected at the boundary of the table, as usual, but...

N point particles move within a billiard table made of two circular cavities connected by a straight channel. The usual billiard dynamics is modified so that it remains deterministic, phase space volumes preserving and time reversal invariant. Particles move in straight lines and are elastically reflected at the boundary of the table, as usual, but...

Diffusion in inhomogeneous materials can be described by both the Fick and Fokker--Planck diffusion equations. Here, we study a mixed Fick and Fokker-Planck diffusion problem with coefficients rapidly oscillating both in space and time. We obtain macroscopic models performing the homogenization limit by means of the unfolding technique.

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 assume the stiffness to be a positive function of the field and we discuss the stability of the stationary solutions proving both linear and local non-linear stability.

Stochastic particle--based models are useful tools for describing the collective movement of large crowds of pedestrians in crowded confined environments. Using descriptions based on the simple exclusion process, two populations of particles, mimicking pedestrians walking in a built environment, enter a room from two opposite sides. One population...

Human crowds base most of their behavioral decisions upon anticipated states of their walking environment. We explore a minimal version of a lattice model to study lanes formation in pedestrian counterflow. Using the concept of horizon depth, our simulation results suggest that the anticipation effect together with the presence of a small backgroun...

We study the pedestrian escape from an obscure room using a lattice gas model with two species of particles. One species, called passive, performs a symmetric random walk on the lattice, whereas the second species, called active, is subject to a drift guiding the particles towards the exit. The drift mimics the awareness of some pedestrians of the...

A quantum finite multi-barrier system, with a periodic potential, is considered and exact expressions for its plane wave amplitudes are obtained using the Transfer Matrix method (Colangeli et al. in J Stat Mech Theor Exp 6:P06006, 2015). This quantum model is then associated with a stochastic process of independent random walks on a lattice, by pro...

We study the pedestrian escape from an obscure corridor using a lattice gas model with two species of particles. One species, called passive, performs a symmetric random walk on the lattice, whereas the second species, called active, is subject to a drift guiding the particles towards the exit. The drift mimics the awareness of some pedestrians of...

The effect of space inhomogeneities on a diffusing particle is studied in the framework of the 1D random walk. The typical time needed by a particle to cross a one-dimensional finite lane, the so-called residence time, is computed possibly in presence of a drift. A local inhomogeneity is introduced as a single defect site with jumping probabilities...

Stimulated by experimental evidence in the field of solution-born thin films, we study the morphology formation in a three state lattice system subjected to the evaporation of one component. The practical problem that we address is the understanding of the parameters that govern morphology formation from a ternary mixture upon evaporation, as is th...

In particle systems subject to a nonuniform drive, particle migration is observed from the driven to the non-driven region and vice-versa, depending on details of the hopping dynamics, leading to apparent violations of Fick's law and of steady-state thermodynamics. We propose and discuss a very basic model in the framework of the zero-range process...

We discuss particle diffusion in a spatially inhomogeneous medium. From the microscopic viewpoint we consider independent particles randomly evolving on a lattice. We show that the reversibility condition has a discrete geometric interpretation in terms of weights associated to un–oriented edges and vertices. We consider the hydrodynamic diffusive...

A quantum finite multi-barrier system, with a periodic potential, is considered and exact expressions for its plane wave amplitudes are obtained using the Transfer Matrix method [10]. This quantum model is then associated with a stochastic process of independent random walks on a lattice, by properly relating the wave amplitudes with the hopping pr...

Stimulated by experimental evidence in the field of solution--born thin films, we study the morphology formation in a three state lattice system subjected to the evaporation of one component. The practical problem that we address is the understanding of the parameters that govern morphology formation from a ternary mixture upon evaporation, as is t...

The effect of space inhomogeneities on a diffusing particle is studied in the framework of the 1D random walk. The typical time needed by a particle to cross a one--dimensional finite lane, the so--called residence time, is computed possibly in presence of a drift. A local inhomogeneity is introduced as a single defect site with jumping probabiliti...

We discuss diffusion of particles in a spatially inhomogeneous medium. From the microscopic viewpoint we consider independent particles randomly evolving on a lattice. We show that the reversibility condition has a discrete geometric interpretation in terms of weights associated to un--oriented edges and vertices. We consider the hydrodynamic diffu...

We present modeling strategies that describe the motion and interaction of groups of pedestrians in obscured spaces. We start off with an approach based on balance equations in terms of measures and then we exploit the descriptive power of a probabilistic cellular automaton model. Based on a variation of the simple symmetric random walk on the squa...

Diffusion of particles through an heterogenous obstacle line is modeled as a two-dimensional diffusion problem with a one-directional nonlinear convective drift and is examined using two-scale asymptotic analysis. At the scale where the structure of heterogeneities is observable the obstacle line has an inherent thickness. Assuming the heterogeneit...

Diffusion of particles through an heterogenous obstacle line is modeled as a two-dimensional diffusion problem with a one-directional nonlinear convective drift and is examined using two-scale asymptotic analysis. At the scale where the structure of heterogeneities is observable the obstacle line has an inherent thickness. Assuming the heterogeneit...

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 parallel char...

We present modeling strategies that describe the motion and interaction of groups of pedestrians in obscured spaces. We start off with an approach based on balance equations in terms of measures and then we exploit the descriptive power of a probabilistic cellular automaton model. Based on a variation of the simple symmetric random walk on the squa...

We study the effect of a large obstacle on the so called residence time, i.e., the time that a particle performing a symmetric random walk in a rectangular (2D) domain needs to cross the strip. We observe a complex behavior, that is we find out that the residence time does not depend monotonically on the geometric properties of the obstacle, such a...

Uphill currents are observed when mass diffuses in the direction of the density gradient. We study this phenomenon in stationary conditions in the framework of locally perturbed one-dimensional zero range processes (ZRPs). We show that the onset of currents flowing from the reservoir with smaller density to the one with larger density can be caused...

Uphill currents are observed when mass diffuses in the direction of the density gradient. We study this phenomenon in stationary conditions in the framework of locally perturbed 1D Zero Range Processes (ZRP). We show that the onset of currents flowing from the reservoir with smaller density to the one with larger density can be caused by a local as...

The presence of obstacles modify the way in which particles diffuse. In cells, for instance, it is observed that, due to the presence of macromolecules playing the role of obstacles, the mean square displacement ofbiomolecules scales as a power law with exponent smaller than one. On the other hand, different situations in grain and pedestrian dynam...

We investigate the appearance of trapping states in pedestrian flows through bottlenecks as a result of the interplay between the geometry of the system and the microscopic stochastic dynamics. We model the flow trough a bottleneck via a Zero Range Process on a one dimensional periodic lattice. Particle are removed from the lattice sites with rates...

We consider the set-up of stationary Zero Range models and discuss the onset of condensation induced by a local blockage on the lattice. We show that the introduction of a local feedback on the hopping rates allows to control the particle fraction in the condensed phase. This phenomenon results in a current vs. blockage parameter curve characterize...

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{para...

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...

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 s...

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 her...

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...

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 fr...

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...

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 dri...

Large arrays of aligned carbon nanotubes (CNTs), open at one end, could be used as target material for the directional detection of weakly interacting dark matter particles (WIMPs). As a result of a WIMP elastic scattering on a CNT, a carbon ion might be injected in the body of the array and propagate through multiple collisions within the lattice....

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 her...

We study the motion of pedestrians through an obscure tunnel where the lack of visibility hides the exits. Using a lattice model, we explore the effects of communication on the effective transport properties of the crowd of pedestrians. More precisely, we study the effect of two thresholds on the structure of the effective nonlinear diffusion coeff...

We propose a simple model of columnar growth through diffusion limited aggregation (DLA). Consider a graph $G_N\times \mathbb N$, where the basis has $N$ vertices $G_N:=\{1,\dots,N\}$, and two vertices $(x,h)$ and $(x',h')$ are adjacent if $|h-h'|\le 1$. Consider there a simple random walk coming from infinity which deposits on a growing cluster as...

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 l...

We study a zero range process characterized by the presence of a threshold switching the particle dynamics from the independent particle model to the simple exclusion process. The setting is relevant to pedestrian dynamics in obscured corridors. We investigate the hydrodynamic limit of the model considering both symmetric and asymmetric jump probab...

We propose a detailed analysis of the so-called volume transition phenomenon in hydrogels establishing the ranges of both temperature and traction which allow for the coexistence of two different phases, the swollen and the shrunk one. Within the framework of continuum mechanics and considering in particular a one dimensional problem} we show that...

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 associa...

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 anisotr...

We investigate the outflux of ions through the channels in a cell membrane. The channels undergo an open/close cycle according to a periodic schedule. Our study is based both on theoretical considerations relying on homogenization theory, and on Monte Carlo numerical simulations. We examine the onset of a limiting boundary behavior characterized by...

We study the effect of intracellular ion diffusion on ionic currents permeating through the cell membrane. Ion flux across the cell membrane is mediated by special proteins forming specific channels. The structure of potassium channels have been widely studied in recent years with remarkable results: very precise measurements of the true current ac...

The occurrence of heterogeneous perturbations of fluid mass density and solid elastic strain of a porous continuum, as a consequence of its undrained response is a very important topic in theoretical and applied poromechanics. The classical Mandel--Cryer effect provides an explanation of fluid overpressure in the central region of a porous sample,...

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{pa...

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...

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-e...

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...

We present two conceptually new modeling approaches aimed at describing the motion of pedestrians in obscured corridors: (i) a Becker-Döring-type dynamics and (ii) 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 p...

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 tha...