arXiv subjects

Cecilia Vernia

Publications and source records attributed to Cecilia Vernia.

At least 19 recordsLinked to original sources

arXiv2026

Uphill transport in competitive drift-diffusion models with volume exclusion

This paper addresses uphill transport (defined as a regime in which particle flow is opposite to the prescriptions of Fick's diffusion) in drift-diffusion particle transport constrained by volume exclusion. Firstly, we show that the stationary hydrodynamic limit of a multispecies, weakly asymmetric exclusion process (SHDL) naturally predicts precisely characterized uphill regimes in the space of external drivings. Then, with specific reference to systems of oppositely charged particles, we identify well-defined model hypotheses and extensions whereby the SHDL converges to the modified Poisson-Nernst-Planck model, thus bridging the gap between exclusion-based particle models and continuum descriptions commonly used in engineering. The merits and limitations of the models in describing the particle fluxes and predicting uphill transport conditions are investigated in detail with respect to the adopted approximations and simplifications. The results demonstrate the persistence of uphill transport phenomena across modeling scales, clarify the conditions under which they occur, and suggest that uphill transport may play a significant role in nanoscale electrolytes, confined ionic and iontronic devices, and membrane-based technologies.

cond-mat.stat-mech↗

arXiv2025

Statistical Properties of the Rooted-Tree Encoding of $\mathbb{N}$

We prime-encode the natural numbers via recursive factorisation, iterated to the exponents, generating a corpus of planar rooted trees equivalently represented as Dyck words. This forms a deterministic text endowed with internal rules. Statistical analysis of the corpus reveals that the dictionary and the entropy grow sublinearly, compression shows non-monotonic trend, and the rank-frequency curves assume a stable parabolic form deviating from Zipf's law. Correlation analysis using mean-squared displacement reveals a transition from normal diffusion to superdiffusion in the associated walk. These findings characterise the tree-encoded sequence as a statistically structured text with long-range correlations grounded in its generative arithmetic law, providing an empirical basis for subsequent theoretical and learnability

math-ph↗

arXiv2024

A study of the Kuramoto model for synchronization phenomena based on degenerate Kolmogorov-Fokker-Planck equations

We study a nonlinear partial differential equation that arises when introducing inertial effects in the Kuramoto model. Based on the known theory of degenerate Kolmogorov operators, we prove existence, uniqueness and a priori estimates of the solution to the relevant Cauchy problem. Moreover, a stable numerical operator, which is consistent with the degenerate Kolmogorov operator, is introduced in order to produce numerical solutions. Finally, numerical experiments show how the synchronization phenomena depend on the parameters of the Kuramoto model with inertia.

math.AP↗

arXiv2023

Uphill in reaction-diffusion multi-species interacting particles systems

We study reaction-diffusion processes with multi-species of particles and hard-core interaction. We add boundary driving to the system by means of external reservoirs which inject and remove particles, thus creating stationary currents. We consider the condition that the time evolution of the average occupation evolves as the discretized version of a system of coupled diffusive equations with linear reactions. In particular, we identify a specific one-parameter family of such linear reaction-diffusion systems where the hydrodynamic limit behaviour can be obtained by means of a dual process. We show that partial uphill diffusion is possible for the discrete particle systems on the lattice, whereas it is lost in the hydrodynamic limit.

math-ph↗

arXiv2022

The inverse problem beyond two-body interaction: the cubic mean-field Ising model

In this paper we solve the inverse problem for the cubic mean-field Ising model. Starting from configuration data generated according to the distribution of the model we reconstruct the free parameters of the system. We test the robustness of this inversion procedure both in the region of uniqueness of the solutions and in the region where multiple thermodynamics phases are present.

cond-mat.stat-mech↗

arXiv2018

Finite-size corrections for the attractive mean-field monomer-dimer model

The finite volume correction for a mean-field monomer-dimer system with an attractive interaction are computed for the pressure density, the monomer density and the susceptibility. The results are obtained by introducing a two-dimensional integral representation for the partition function decoupling both the hard-core interaction and the attractive one. The next-to-leading terms for each of the mentioned quantities is explicitly derived as well as the value of their sign that is related to their monotonic convergence in the thermodynamic limit.

math-ph↗

arXiv2018

$O(N)$ fluctuations and lattice distortions in 1-dimensional systems

Statistical mechanics harmonizes mechanical and thermodynamical quantities, via the notion of local thermodynamic equilibrium (LTE). In absence of external drivings, LTE becomes equilibrium tout court, and states are characterized by several thermodynamic quantities, each of which is associated with negligibly fluctuating microscopic properties. Under small driving and LTE, locally conserved quantities are transported as prescribed by linear hydrodynamic laws, in which the local material properties of the system are represented by the transport coefficients. In 1-dimensional systems, on the other hand, the transport coefficients often appear to depend on the global state, rather than on the local state of the system at hand. We interpret these facts within the framework of boundary driven 1-dimensional Lennard-Jones chains of $N$ oscillators, observing that they experience non-negligible $O(N)$ lattice distortions and fluctuations. This implies that standard hydrodynamics and certain expressions of energy flow do not apply in these cases. One possible modification of the energy flow is considered.

cond-mat.stat-mech↗

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

Inverse problem for multi-species mean field models in the low temperature phase

In this paper we solve the inverse problem for a class of mean field models (Curie-Weiss model and its multi-species version) when multiple thermodynamic states are present, as in the low temperature phase where the phase space is clustered. The inverse problem consists in reconstructing the model parameters starting from configuration data generated according to the distribution of the model. We show that the application of the inversion procedure without taking into account the presence of many states produces very poor inference results. This problem is overcomed using the clustering algorithm. When the system has two symmetric states of positive and negative magnetization, the parameter reconstruction can be also obtained with smaller computational effort simply by flipping the sign of the magnetizations from positive to negative (or viceversa). The parameter reconstruction fails when the system is critical: in this case we give the correct inversion formulas for the Curie-Weiss model and we show that they can be used to measuring how much the system is close to criticality.

cond-mat.stat-mech↗

arXiv2016

Inverse problem for the mean-field monomer-dimer model with attractive interaction

The inverse problem method is tested for a class of monomer-dimer statistical mechanics models that contain also an attractive potential and display a mean-field critical point at a boundary of a coexistence line. The inversion is obtained by analytically identifying the parameters in terms of the correlation functions and via the maximum-likelihood method. The precision is tested in the whole phase space and, when close to the coexistence line, the algorithm is used together with a clustering method to take care of the underlying possible ambiguity of the inversion.

cond-mat.stat-mech↗

arXiv2014

Alienation in Italian cities. Social network fragmentation from collective data

We study the structure of a social network of strong ties (trust network) investigating its property of connectedness versus fragmentation. To this purpose we analyse an extensive set of census data, about marrying or having children with immigrants, collected by Italian national statistical institute for all Italian municipalities from 2001 to 2011. Not using neither obtaining personal local information but only average ones, our method fully complies with privacy and confidentiality. Our findings show that large cities display the behaviour of highly fragmented trust networks where individuals face possible phenomena of alienation. Smaller cities and villages instead behave like fully connected social systems with a rich tie structure, where isolation is rare or completely absent. While confirming classical sociological theories on alienation in large urban areas our approach provides a quantitative method to test them and a predictive tool for policy makers.

physics.soc-ph↗

arXiv2014

A stochastic approach for quantifying immigrant integration: the Spanish test case

We apply stochastic process theory to the analysis of immigrant integration. Using a unique and detailed data set from Spain, we study the relationship between local immigrant density and two social and two economic immigration quantifiers for the period 1999-2010. As opposed to the classic time-series approach, by letting immigrant density play the role of "time", and the quantifier the role of "space" it become possible to analyze the behavior of the quantifiers by means of continuous time random walks. Two classes of results are obtained. First we show that social integration quantifiers evolve following pure diffusion law, while the evolution of economic quantifiers exhibit ballistic dynamics. Second we make predictions of best and worst case scenarios taking into account large local fluctuations. Our stochastic process approach to integration lends itself to interesting forecasting scenarios which, in the hands of policy makers, have the potential to improve political responses to integration problems. For instance, estimating the standard first-passage time and maximum-span walk reveals local differences in integration performance for different immigration scenarios. Thus, by recognizing the importance of local fluctuations around national means, this research constitutes an important tool to assess the impact of immigration phenomena on municipal budgets and to set up solid multi-ethnic plans at the municipal level as immigration pressure build.

physics.soc-ph↗

arXiv2014

An analysis of a large dataset on immigrant integration in Spain. The Statistical Mechanics perspective on Social Action

How does immigrant integration in a country change with immigration density? Guided by a statistical mechanics perspective we propose a novel approach to this problem. The analysis focuses on classical integration quantifiers such as the percentage of jobs (temporary and permanent) given to immigrants, mixed marriages, and newborns with parents of mixed origin. We find that the average values of different quantifi?ers may exhibit either linear or non-linear growth on immigrant density and we suggest that social action, a concept identified by Max Weber, causes the observed non- linearity. Using the statistical mechanics notion of interaction to quantitatively emulate social action, a unified mathematical model for integration is proposed and it is shown to explain both growth behaviors observed. The linear theory instead, ignoring the possibility of interaction effects would underestimate the quantifiers up to 30% when immigrant densities are low, and overestimate them as much when densities are high. The capacity to quantitatively isolate different types of integration mechanisms makes our framework a suitable tool in the quest for more efficient integration policies.

physics.soc-ph↗

arXiv2010

Interface Energy in the Edwards-Anderson model

We numerically investigate the spin glass energy interface problem in three dimensions. We analyze the energy cost of changing the overlap from -1 to +1 at one boundary of two coupled systems (in the other boundary the overlap is kept fixed to +1). We implement a parallel tempering algorithm that simulate finite temperature systems and work with both cubic lattices and parallelepiped with fixed aspect ratio. We find results consistent with a lower critical dimension $D_c=2.5$. The results show a good agreement with the mean field theory predictions.

cond-mat.dis-nn↗

arXiv2009

On the structure of correlations in the three dimensional spin glasses

We investigate the low temperature phase of three-dimensional Edwards-Anderson model with Bernoulli random couplings. We show that at a fixed value $Q$ of the overlap the model fulfills the clustering property: the connected correlation functions between two local overlaps decay as a power whose exponent is independent of $Q$ for all $0\le |Q| < q_{EA}$. Our findings are in agreement with the RSB theory and show that the overlap is a good order parameter.

cond-mat.dis-nn↗

arXiv2008

Numerical study of ground state energy fluctuations in spin glasses

Using a stochastic algorithm introduced in a previous paper, we study the finite size volume corrections and the fluctuations of the ground state energy in the Sherrington-Kirkpatrick and the Edwards-Anderson models at zero temperature. The algorithm is based on a suitable annealing procedure coupled with a balanced greedy-reluctant strategy that drives the systems towards the deepest minimum of the energy function.

cond-mat.dis-nn↗

arXiv2008

Lack of monotonicity in spin glass correlation functions

We study the response of a spin glass system with respect to the rescaling of its interaction random variables and investigate numerically the behaviour of the correlation functions with respect to the volume. While for a ferromagnet the local energy correlation functions increase monotonically with the scale and, by consequence, with respect to the volume of the system we find that in a general spin glass model those monotonicities are violated.

cond-mat.dis-nn↗

arXiv2007

Comment on "Ultrametricity in the Edwards-Anderson Model"

In a recent interesting Letter Contucci {\it et al.} have investigated several properties of the three-dimensional (3d) Edwards-Anderson (EA) Ising spin glass. They claim to have found strong numerical evidence for the presence of a complex ultrametric structure similar to the one described by the replica symmetry breaking solution of the mean field model. We illustrate by numerical simulations that the relations used by Contucci {\it et al.} as evidence for an ultrametric structure in the 3d EA model are fulfilled to similar accuracy in the two-dimensional EA model, which is well-described by the droplet picture and has no spin glass phase at finite temperature. We conclude that the data presented in the Contucci {\it et al.} Letter is not sufficient to dismiss the possibility that, e.g., the droplet model might describe the behavior of the 3d EA model.

cond-mat.dis-nn↗