arXiv subjects

Matteo Colangeli

Publications and source records attributed to Matteo Colangeli.

At least 37 records · Page 2Linked to original sources

arXiv2019

Uphill migration in coupled driven particle systems

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 independent random walkers on a pair of rings, one of which features biased hopping rates, in which this phenomenon is observed and fully explained.

cond-mat.stat-mech↗

arXiv2019

Transport in quantum multi-barrier systems as random walks on a lattice

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 probabilities of the particles moving on the lattice and with the injection rates from external particle reservoirs. Analytical and numerical results prove that the stationary density profile of the particle system overlaps with the quantum mass density profile of the stationary Schrodinger equation, when the parameters of the two models are suitably matched. The equivalence between the quantum model and a stochastic particle system would mainly be fruitful in a disordered setup. Indeed, we also show, here, that this connection, analytically proven to hold for periodic barriers, holds even when the width of the barriers and the distance between barriers are randomly chosen.

cond-mat.stat-mech↗

arXiv2018

A lattice model approach to the morphology formation from ternary mixtures during the evaporation of one component

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 the case in the fabrication of thin films from solution for organic photovoltaics. We use, as a tool, a generalized version of the Potts and Blume-Capel models in 2D, with the Monte Carlo Kawasaki-Metropolis algorithm, to simulate the phase behaviour of a ternary mixture upon evaporation of one of its components. The components with spin $+1$, $-1$ and $0$ in the Blume-Capel dynamics correspond to the electron--acceptor, electron--donor and solvent molecules, respectively, in a ternary mixture used in the preparation of the active layer films in an organic solar cell. Further, we introduce parameters that account for the relative composition of the mixture, temperature, and interaction between the species in the system. We identify the parameter regions that are prone to facilitate the phase separation. Furthermore, we study qualitatively the types of formed configurations. We show that even a relatively simple model, as the present one, can generate key morphological features, similar to those observed in experiments, which proves the method valuable for the study of complex systems.

cond-mat.stat-mech↗

arXiv2018

Fick and Fokker--Planck diffusion law in inhomogeneous media

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 diffusive scaling that gives, as a macroscopic evolution equation, the Fokker--Planck equation corresponding to the evolution of the probability distribution of a reversible spatially inhomogeneous diffusion process. The geometric macroscopic counterpart of reversibility is encoded into a tensor metrics and a positive function. The Fick's law with inhomogeneous diffusion matrix is obtained in the case when the spatial inhomogeneity is associated exclusively with the edge weights. We discuss also some related properties of the systems like a non-homogeneous Einstein relation and the possibility of uphill diffusion.

cond-mat.stat-mech↗

arXiv2018

Modelling interactions between active and passive agents moving through heterogeneous environments

We study the dynamics of interacting agents from two distinct inter-mixed populations: One population includes active agents that follow a predetermined velocity field, while the second population contains exclusively passive agents, i.e. agents that have no preferred direction of motion. The orientation of their local velocity is affected by repulsive interactions with the neighboring agents and environment. We present two models that allow for a qualitative analysis of these mixed systems. We show that the residence times of this type of systems containing mixed populations is strongly affected by the interplay between these two populations. After showing our modeling and simulation results, we conclude with a couple of mathematical aspects concerning the well-posedness of our models.

math.NA↗

arXiv2017

Non-equilibrium 2D Ising model with stationary uphill diffusion

Usually, in a non-equilibrium setting, a current brings mass from the highest density regions to the lowest density ones. Although rare, the opposite phenomenon (known as "uphill diffusion") has also been observed in multicomponent systems, where it appears as an artificial effect of the interaction among components. We show here that uphill diffusion can be a substantial effect, i.e. it may occur even in single component systems as a consequence of some external work. To this aim we consider the 2D ferromagnetic Ising model in contact with two reservoirs that fix, at the left and the right boundaries, magnetizations of the same magnitude but of opposite signs. We provide numerical evidence that a class of non-equilibrium steady states exists in which, by tuning the reservoir magnetizations, the current in the system changes from "downhill" to "uphill". Moreover, we also show that, in such non-equilibrium set-up, the current vanishes precisely when the reservoir magnetizations equal the magnetization of the corresponding equilibrium dynamics, thus establishing a novel relation between equilibrium and non-equilibrium properties.

cond-mat.stat-mech↗

arXiv2017

Stationary uphill currents in locally perturbed Zero Range Processes

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 asymmetry in the hopping rates on a single site at the center of the lattice. For fixed injection rates at the boundaries, we prove that a suitable tuning of the asymmetry in the bulk may induce uphill diffusion at arbitrarily large, finite volumes. We also deduce heuristically the hydrodynamic behavior of the model and connect the local asymmetry characterizing the ZRP dynamics to a matching condition relevant for the macroscopic problem.

cond-mat.stat-mech↗

arXiv2017

Microscopic models for uphill diffusion

We study a system of particles which jump on the sites of the interval $[1,L]$ of $\mathbb Z$. The density at the boundaries is kept fixed to simulate the action of mass reservoirs. The evolution depends on two parameters $λ'\ge 0$ and $λ"\ge 0$ which are the strength of an external potential and respectively of an attractive potential among the particles. When $λ'=λ"= 0$ the system behaves diffusively and the density profile of the final stationary state is linear, Fick's law is satisfied. When $λ'> 0$ and $λ"= 0$ the system models the diffusion of carbon in the presence of silicon as in the Darken experiment: the final state of the system is in qualitative agreement with the experimental one and uphill diffusion is present at the weld. Finally if $λ'=0$ and $λ">0$ is suitably large, the system simulates a vapor-liquid phase transition and we have a surprising phenomenon. Namely when the densities in the reservoirs correspond respectively to metastable vapor and metastable liquid we find a final stationary current which goes uphill from the reservoir with smaller density (vapor) to that with larger density (liquid). Our results are mainly numerical, we have convincing theoretical explanations yet we miss a complete mathematical proof.

cond-mat.stat-mech↗

arXiv2017

Trapping in bottlenecks: interplay between microscopic dynamics and large scale effects

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 proportional to the local occupation numbers. The bottleneck is modelled by a particular site of the lattice where the updating rate saturates to a constant value as soon as the local occupation number exceeds a fixed threshold. We show that, for any finite value of such threshold, the stationary particle current saturates to the limiting bottleneck rate when the total particle density in the system exceeds the bottleneck rate itself.

cond-mat.stat-mech↗

arXiv2017

Stochastic Parameterization: Towards a new view of Weather and Climate Models

The last decade has seen the success of stochastic parameterizations in short-term, medium-range and seasonal forecasts: operational weather centers now routinely use stochastic parameterization schemes to better represent model inadequacy and improve the quantification of forecast uncertainty. Developed initially for numerical weather prediction, the inclusion of stochastic parameterizations not only provides better estimates of uncertainty, but it is also extremely promising for reducing longstanding climate biases and relevant for determining the climate response to external forcing. This article highlights recent developments from different research groups which show that the stochastic representation of unresolved processes in the atmosphere, oceans, land surface and cryosphere of comprehensive weather and climate models (a) gives rise to more reliable probabilistic forecasts of weather and climate and (b) reduces systematic model bias. We make a case that the use of mathematically stringent methods for the derivation of stochastic dynamic equations will lead to substantial improvements in our ability to accurately simulate weather and climate at all scales. Recent work in mathematics, statistical mechanics and turbulence is reviewed, its relevance for the climate problem demonstrated, and future research directions outlined.

physics.ao-ph↗

arXiv2017

Particle models with self sustained current

We present some computer simulations run on a stochastic CA (cellular automaton). The CA simulates a gas of particles which are in a channel, the interval $[1,L]$ in $\mathbb Z$, but also in "reservoirs" $\mathcal R_1$ and $\mathcal R_2$. The evolution in the channel simulates a lattice gas with Kawasaki dynamics with attractive Kac interactions, the temperature is chosen smaller than the mean field critical one. There are also exchanges of particles between the channel and the reservoirs and among reservoirs. When the rate of exchanges among reservoirs is in a suitable interval the CA reaches an apparently stationary state with a non zero current, for different choices of the initial condition the current changes sign. We have a quite satisfactory theory of the phenomenon but we miss a full mathematical proof.

cond-mat.stat-mech↗

arXiv2016

Blockage induced condensation controlled by a local reaction

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 characterized by two non--analyticity points.

cond-mat.stat-mech↗

arXiv2016

Latent heat and the Fourier law

We present computer simulations run with a stochastic cellular automaton which describes $d=1$ particle systems connected to reservoirs which keep two different densities at the endpoints. We fix the parameters so that there is a phase transition (of the van der Waals type) and observe that if the densities at the boundaries are metastable then, after a transient, the system reaches an apparently stationary regime where the current flows from the reservoir with smaller density to the one with larger density.

cond-mat.stat-mech↗

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↗

arXiv2015

Highly anisotropic scaling limits

We consider a highly anisotropic $d=2$ Ising spin model whose precise definition can be found at the beginning of Section 2. In this model the spins on a same horizontal line (layer) interact via a $d=1$ Kac potential while the vertical interaction is between nearest neighbors, both interactions being ferromagnetic. The temperature is set equal to 1 which is the mean field critical value, so that the mean field limit for the Kac potential alone does not have a spontaneous magnetization. We compute the phase diagram of the full system in the Lebowitz-Penrose limit showing that due to the vertical interaction it has a spontaneous magnetization. The result is not covered by the Lebowitz-Penrose theory because our Kac potential has support on regions of positive codimension.

math-ph↗

arXiv2014

A continuum limit for the Kronig-Penney model

We investigate the transmission properties of a quantum one-dimensional periodic system of fixed length $L$, with $N$ barriers of constant height $V$ and width $λ$, and $N$ wells of width $δ$. In particular, we study the behaviour of the transmission coefficient in the limit $N\to \infty$, with $L$ fixed. This is achieved by letting $δ$ and $λ$ both scale as $1/N$, in such a way that their ratio $γ= λ/δ$ is a fixed parameter characterizing the model. In this continuum limit the multi-barrier system behaves as it were constituted by a unique barrier of constant height $E_o=(γV)/(1+γ)$. The analysis of the dispersion relation of the model shows the presence of forbidden energy bands at any finite $N$.

math-ph↗

arXiv2014

Role of Ergodicity in the Transient Fluctuation Relation and a New Relation for a Dissipative Non-Chaotic Map

Deterministic dynamical systems such as the baker maps are useful to shed light on some of the conditions verified by deterministic models in non-equilibrium statistical physics. We investigate a 2D dynamical system, enjoying a weak form of reversibility, with peculiar basins of attraction and steady states. In particular, we test the conditions required for the validity of the Transient Fluctuation Relation. Our analysis illustrates by means of concrete examples why ergodicity of the equilibrium dynamics seems to be a necessary condition for the Transient Fluctuation Relation to hold. This investigation then leads to the numerical verification of a kind of transient relation which, differently from the usual Transient Fluctuation Relation (FR), holds only asymptotically. At the same time, it is not a steady state fluctuation relation, because no fluctuations are present in the steady state.

math.DS↗