arXiv subjects

Matteo Colangeli

Publications and source records attributed to Matteo Colangeli.

At least 19 recordsLinked to original sources

arXiv2025

Dynamics of stochastic oscillator chains with harmonic and FPUT potentials

Inspired by recent studies on deterministic oscillator models, we introduce a stochastic one-dimensional model for a chain of interacting particles. The model consists of $N$ oscillators performing continuous-time random walks on the integer lattice $\mathbb{Z}$ with exponentially distributed waiting times. The oscillators are bound by confining forces to two particles that do not move, placed at positions $x_0$ and $x_{N+1}$, respectively, and they feel the presence of baths with given inverse temperatures: $\beta_L$ to the left, $\beta_B$ in the middle, and $\beta_R$ to the right. Each particle has an index and interacts with its nearest neighbors in index space through either a quadratic potential or a Fermi-Pasta-Ulam-Tsingou type coupling. This local interaction in index space can give rise to effective long-range interactions on the spatial lattice, depending on the instantaneous configuration. Particle hopping rates are governed either by the Metropolis rule or by a modified version that breaks detailed balance at the interfaces between regions with different baths.

cond-mat.stat-mech↗

arXiv2025

Dynamics of the Kac Ring Model with switching scatterers

We introduce a generalized version of the Kac ring model in which particles are of two types, black and white. Black particles modify the environment through which all particles move, thereby inducing indirect and potentially long-range interactions among them. Unlike the inert scatterers of Kac's original model, the scatterers in our setting possess internal states that change upon interaction with black particles and can be interpreted as energy levels of the environment. This makes the model self-consistent, as it incorporates a form of particle interactions, mediated by the environment, that drives the system toward some kind of stationary state. Although indirect and long-range interactions do not necessarily promote thermodynamic states, interactions are necessary for energy to be shared among the elementary constituents of matter, enabling the establishment of equipartition, which is a prerequisite for defining temperature. Therefore, our model is one step forward in this direction, elucidating the role of interactions and energy exchange. We prove that any initial state of the system converges to a time periodic state (i.e. a phase space orbit) and describe basins of attraction for some of such asymptotic periodic states.

cond-mat.stat-mech↗

arXiv2025

Dissipation functions and Brownian oscillators

We develop a general framework for response theory in diffusion processes governed by Fokker-Planck equations, based on the notion of the Dissipation Function. Using the analytically solvable Brownian oscillator model, we derive exact response formulae for both overdamped and underdamped dynamics of harmonically bound Brownian particles. We also demonstrate that for certain observables and under suitable time scaling, the operations of model reduction and response formula extraction commute.

cond-mat.stat-mech↗

arXiv2024

A hybrid approach to model reduction of Generalized Langevin Dynamics

We consider a classical model of non-equilibrium statistical mechanics accounting for non-Markovian effects, which is referred to as the Generalized Langevin Equation in the literature. We derive reduced Markovian descriptions obtained through the neglection of inertial terms and/or heat bath variables. The adopted reduction scheme relies on the framework of the Invariant Manifold method, which allows to retain the slow degrees of freedom from a multiscale dynamical system. Our approach is also rooted on the Fluctuation-Dissipation Theorem, which helps preserve the proper dissipative structure of the reduced dynamics. We highlight the appropriate time scalings introduced within our procedure, and also prove the commutativity of selected reduction paths.

cond-mat.stat-mech↗

arXiv2024

Detecting Phase Transitions through Nonequilibrium Work Fluctuations

We show how averages of exponential functions of path dependent quantities, such as those of Work Fluctuation Theorems, detect phase transitions in deterministic and stochastic systems. State space truncation -- the restriction of the observations to a subset of state space with prescribed probability -- is introduced to obtain that result. Two stochastic processes undergoing first-order phase transitions are analyzed both analytically and numerically: the Ehrenfest urn model and the 2D Ising model subject to a magnetic field. In presence of phase transitions, we prove that even minimal state space truncation makes averages of exponentials of path dependent variables sensibly deviate from full state space values. Specifically, in the case of discontinuous phase transitions, this approach is strikingly effective in locating the critical transition value of the control parameter. As this approach works even with variables different from those of fluctuation theorems, it provides a new recipe to identify order parameters in the study of nonequilibrium phase transitions, profiting from the often incomplete statistics that are available.

cond-mat.stat-mech↗

arXiv2023

Finite reservoirs and irreversibility corrections to Hamiltonian systems statistics

We consider several Hamiltonian systems perturbed by external agents, that preserve their Hamiltonian structure. We investigate the corrections to the canonical statistics resulting from coupling such systems with possibly large but finite reservoirs, and from the onset of processes breaking the time reversal symmetry. We analyze exactly solvable oscillators systems, and perform simulations of relatively more complex ones. This indicates that the standard statistical mechanical formalism needs to be adjusted, in the ever more investigated nano-scale science and technology. In particular, the hypothesis that heat reservoirs be considered infinite and be described by the classical ensembles is found to be critical when exponential quantities are considered, since the large size limit may not coincide with the infinite size canonical result. Furthermore, process-dependent emergent irreversibility affects ensemble averages, effectively frustrating, on a statistical level, the time reversal invariance of Hamiltonian dynamics, that is used to obtain numerous results.

cond-mat.stat-mech↗

arXiv2022

A reduction scheme for coupled Brownian harmonic oscillators

We propose a reduction scheme for a system constituted by two coupled harmonically-bound Brownian oscillators. We reduce the description by constructing a lower dimensional model which inherits some of the basic features of the original dynamics and is written in terms of suitable transport coefficients. The proposed procedure is twofold: while the deterministic component of the dynamics is obtained by a direct application of the invariant manifold method, the diffusion terms are determined via the Fluctuation-Dissipation Theorem. We highlight the behavior of the coefficients up to a critical value of the coupling parameter, which marks the endpoint of the interval in which a contracted description is available. The study of the weak coupling regime is addressed and the commutativity of alternative reduction paths is also discussed.

cond-mat.stat-mech↗

arXiv2021

Reduced Markovian Descriptions of Brownian Dynamics: Toward an Exact Theory

We outline a reduction scheme for a class of Brownian dynamics which leads to meaningful corrections to the Smoluchowski equation in the overdamped regime. The mobility coefficient of the reduced dynamics is obtained by exploiting the Dynamic Invariance principle, whereas the diffusion coefficient fulfils the Fluctuation-Dissipation theorem. Explicit calculations are carried out in the case of a harmonically bound particle. A quantitative pointwise representation of the reduction error is also provided and connections to both the Maximum Entropy method and the linear response theory are highlighted. Our study paves the way to the development of reduction procedures applicable to a wider class of diffusion processes.

cond-mat.stat-mech↗

arXiv2021

Exact Response Theory and Kuramoto dynamics

The dynamics of Kuramoto oscillators is investigated in terms of the exact response theory based on the Dissipation Function, which has been introduced in the field of nonequilibrium molecular dynamics. While linear response theory is a cornerstone of nonequilibrium statistical mechanics, it does not apply, in general, to systems undergoing phase transitions. Indeed, even a small perturbation may in that case result in a large modification of the state. An exact theory is instead expected to handle such situations. The Kuramoto dynamics, which undergoes synchronization transitions, is thus investigated as a testbed for the exact theory mentioned above. A comparison between the two approaches shows how the linear theory fails, while the exact theory yields the correct response.

cond-mat.stat-mech↗

arXiv2021

A Mesoscopic Lattice Model for Morphology Formation in Ternary Mixtures with Evaporation

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 other components are dissolved, as a model for a 2-component coating solution that is drying on a substrate. We propose a 3-spins dynamics to describe the evolution of the three interacting species. As main tool, we use a Monte Carlo Metropolis-based algorithm, with the possibility of varying the system's temperature, mixture composition, interaction strengths, and evaporation kinetics. The main novelty is the structure of the mesoscopic model -- a bi-dimensional lattice with periodic boundary conditions and divided in square cells to encode a mesoscopic range interaction among the units. We investigate the effect of the model parameters on the structure of the resulting morphologies. Finally, we compare the results obtained with the mesoscopic model with corresponding ones based on an analogous lattice model with a short range interaction among the units, i.e. when the mesoscopic length scale coincides with the microscopic length scale of the lattice.

cond-mat.stat-mech↗

arXiv2021

Towards a quantitative reduction of the SIR epidemiological model

Motivated by our intention to use SIR-type epidemiological models in the context of dynamic networks as provided by large-scale highly interacting inhomogeneous human crowds, we investigate in this framework possibilities to reduce the classical SIR model to a representative evolution model for a suitably chosen observable. For selected scenarios, we provide practical {\em a priori} error bounds between the approximate and the original observables. Finally, we illustrate numerically the behavior of the reduced models compared to the original ones.

cond-mat.stat-mech↗

arXiv2021

Deterministic model of battery, uphill currents and non-equilibrium phase transitions

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 horizontal velocity, as if colliding with vertical walls. The second channel is divided in two halves parallel to the first, but located in the opposite sides of the cavities. In the second channel, motion is free. We show that, suitably tuning the sizes of cavities, of the channels and of $T$, non--equilibrium phase transitions take place in the $N\rightarrow \infty$ limit. This induces a stationary current in the circuit, thus modeling a kind of battery, although our model is deterministic, conservative, and time reversal invariant.

cond-mat.stat-mech↗

arXiv2020

Deterministic reversible model of non-equilibrium phase transitions and stochastic counterpart

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 those in a channel that are moving away from a cavity invert their motion (rebound), if their number exceeds a given threshold T. When the geometrical parameters of the billiard table are fixed, this mechanism gives rise to non--equilibrium phase transitions in the large N limit: letting T/N decrease, the homogeneous particle distribution abruptly turns into a stationary inhomogeneous one. The equivalence with a modified Ehrenfest two urn model, motivated by the ergodicity of the billiard with no rebound, allows us to obtain analytical results that accurately describe the numerical billiard simulation results. Thus, a stochastic exactly solvable model that exhibits non-equilibrium phase transitions is also introduced.

cond-mat.stat-mech↗

arXiv2020

When diffusion faces drift: consequences of exclusion processes for bi--directional pedestrian flows

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 is passive -- being unaware of the local environment; particles belonging to this group perform a symmetric random walk. The other population has information on the local geometry in the sense that as soon as particles enter a visibility zone, a drift activates them. Their self-propulsion leads them towards the exit. This second type of species is referred here as active. The assumed crowdedness corresponds to a near--jammed scenario. The main question we ask in this paper is: Can we induce modifications of the dynamics of the active particles to improve the outgoing current of the passive particles? To address this question, we compute occupation number profiles and currents for both populations in selected parameter ranges. Besides observing the more classical faster--is--slower effect, new features appear as prominent like the non--monotonicity of currents, self--induced phase separation within the active population, as well as acceleration of passive particles for large--drift regimes of active particles.

cond-mat.stat-mech↗

arXiv2020

A combinatorial representation for the invariant measure of diffusion processes on metric graphs

We give a generalization to a continuous setting of the classic Markov chain tree Theorem. In particular, we consider an irreducible diffusion process on a metric graph. The unique invariant measure has an atomic component on the vertices and an absolutely continuous part on the edges. We show that the corresponding density at $x$ can be represented by a normalized superposition of the weights associated to metric arborescences oriented toward the point $x$. The weight of each oriented metric arborescence is obtained by the exponential of integrals of the form $\int\frac{b}{\sigma^2}$ along the oriented edges time a weight for each node determined by the local orientation of the arborescence around the node time the inverse of the diffusion coefficient at $x$. The metric arborescences are obtained cutting the original metric graph along some edges.

math.PR↗

arXiv2019

Uniqueness and stability with respect to parameters of solutions to a fluid-like driven system for active-passive pedestrian dynamics

We study a system of parabolic equations consisting of a double nonlinear parabolic equations of Forchheimer type coupled with a semilinear parabolic equations. The system describes a fluid-like driven system for active-passive pedestrian dynamics. The structure of the nonlinearity of the coupling allows us to prove the uniqueness of solutions. We provide also stability estimates of solutions with respect to selected parameters.

math.AP↗

arXiv2019

Weak solvability a fluid-like driven system for active-passive pedestrian dynamics

We study the question of weak solvability for a nonlinear coupled parabolic system that models the evolution of a complex pedestrian flow. The main feature is that the flow is composed of a mix of densities of active and passive pedestrians that are moving with different velocities. We rely on special energy estimates and on the use a Schauder's fixed point argument to tackle the existence of solutions to our evolution problem.

math.AP↗

arXiv2019

A lattice model for active--passive pedestrian dynamics: a quest for drafting effects

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 geometry of the corridor and of the location of the exit. We provide numerical evidence that, in spite of the hard core interaction between particles -- namely, there can be at most one particle of any species per site, -- adding a fraction of active particles in the system enhances the evacuation rate of all particles from the corridor. A similar effect is also observed when looking at the outgoing particle flux, when the system is in contact with an external particle reservoir that induces the onset of a steady state. We interpret this phenomenon as a discrete space counterpart of the drafting effect typically observed in a continuum set--up as the aerodynamic drag experienced by pelotons of competing cyclists.

physics.soc-ph↗