arXiv subjects

Emilio N. M. Cirillo

Publications and source records attributed to Emilio N. M. Cirillo.

At least 19 recordsLinked to original sources

arXiv2026

Boundary-Driven Anisotropic Coarsening in Conserved Phase Separation

Universal scaling in phase separation is typically assumed to be isotropic in systems with conserved dynamics. Here we show that boundary forcing alone can break this dynamical scaling symmetry, leading to anisotropic coarsening, with different effective global growth laws observed parallel and perpendicular to the boundary. We consider a ternary mixture with two conserved components and a passive species undergoing surface evaporation, which provides a simple setting to investigate this effect. In this case, evaporation leads to a progressive mass loss and to the formation of macroscopic concentration gradients, which, in turn, drive anisotropic coarsening, with different effective growth laws observed parallel and perpendicular to the boundary. At the same time, bulk regions appear to retain the standard Model B scaling, suggesting that the observed anisotropy is mainly induced by boundary fluxes rather than by changes in the intrinsic dynamics. Our results indicate that boundary conditions can play an important role in breaking scaling symmetry and may offer a way to influence coarsening behavior in nonequilibrium phase separation.

cond-mat.stat-mech↗

arXiv2026

Inefficiency of the block approximation in diploid Probabilistic Cellular Automata

We study a probabilistic cellular automaton obtained as a mixture of the additive elementary rules 60 and 102. We prove that, for any finite periodic lattice and for mixing parameter $λ=1/2$, the system almost surely reaches the absorbing all-zero configuration in finitely many steps. In addition, Monte Carlo simulations indicate as well the presence of a zero-density stationary state in a finite interval around $λ=1/2$. Despite this absorbing behavior, both mean-field and block approximation schemes predict a stationary state with non-zero density. This failure, traced to the additive and mirror symmetries of the deterministic components, highlights a fundamental limitation of finite-block approximation in capturing the global dynamics of probabilistic cellular automata.

nlin.CG↗

arXiv2026

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: $β_L$ to the left, $β_B$ in the middle, and $β_R$ 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↗

arXiv2026

Serial vs parallel recall in the Blume-Every-Griffiths neural networks

Fully connected Blume-Emery-Griffiths neural networks performing pattern recognition and associative memory have been heuristically studied in the past (mainly via the replica trick and under the replica symmetric assumption) as generalization of the standard Hopfield reference. In these notes, at first, by relying upon Guerra interpolation, we re-obtain the existing picture rigorously. Next we show that, due to dilution in the patterns, these networks are able to switch from serial recall (where one pattern is retrieved per time) to parallel recall (where several patterns are retrieved at once) and the larger the dilution, the stronger this emerging multi-tasking capability. In particular, we inspect the regimes of mild dilution (where solely a low storage of pattern can be enabled) and extreme dilution (where a medium storage of patterns can be sustained) separately as they give rise to different outcomes: the former displays hierarchical recall (distributing the amplitudes of the retrieved signals with different amplitudes), the latter -- instead -- performs a equal-strength recall (where a O(1) fraction of all the patterns is simultaneously retrieved with the same amplitude per pattern). Finally, in order to implement graded responses in the neurons, variations on theme obtained by enlarging the possible values of neural activity these neurons may sustain are also discussed generalizing the Ghatak-Sherrington model for inverse freezing in Hebbian terms.

cond-mat.dis-nn↗

arXiv2025

Optimal strategies for the growth of dual-seeded lattice structures

Optimal growth of structures governed by spatially stochastic dynamics arises in many scientific settings, for example in processes such as solution-based crystallization and the formation of microbial biofilms on patterned substrates or microfluidic networks. In this work, we investigate lattice growth using a two-dimensional, zero-temperature stochastic model of short-range spin interactions. Our goal is to determine how external perturbations can be optimized to steer the system efficiently toward the uniformly positive state, starting from two initial clusters of positive sites. To achieve this, we cast the problem as a Markov decision process adapted for a two-dimensional Ising model with zero-temperature dynamics. Within this framework, we compare alternative growth geometries and identify the structure of optimal strategies across three representative regimes.

math.OC↗

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

Guerra interpolation for inverse freezing

In these short notes, we adapt and systematically apply Guerra's interpolation techniques on a class of disordered mean-field spin glasses equipped with crystal fields and multi-value spin variables. These models undergo the phenomenon of inverse melting or inverse freezing. In particular, we focus on the Ghatak-Sherrington model, its extension provided by Katayama and Horiguchi, and the disordered Blume-Emery-Griffiths-Capel model in the mean-field limit, deepened by Crisanti and Leuzzi and by Schupper and Shnerb. Once shown how all these models can be retrieved as particular limits of a unique broader Hamiltonian, we study their free energies. We provide explicit expressions of their annealed and quenched expectations, inspecting the cases of replica symmetry and (first-step) broken replica symmetry. We recover several results previously obtained via heuristic approaches (mainly the replica trick) to prove full agreement with the existing literature. As a sideline, we also inspect the onset of replica symmetry breaking by providing analytically the expression of the de Almeida-Thouless instability line for a replica symmetric description: in this general setting, the latter is new also from a physical viewpoint.

cond-mat.dis-nn↗

arXiv2025

3D morphology formation in a mixture of three differently averse components

Film formation from solvent evaporation in polymer ternary solutions is relevant for several technological applications, such as the fabrication of organic solar cells. The performance of the final device will strongly depend on the internal morphology of the obtained film, which, in turn, is affected by the processing conditions. We are interested in modeling morphology formation in 3D for ternary mixtures using both a lattice model and its continuous counterpart in the absence of evaporation. In our previous works, we found that, in 2D, both models predict the existence of two distinct regimes: (i) a low-solvent regime, characterized by two interpenetrated domains of the two polymers, and (ii) a high-solvent regime, where isolated polymer domains are dispersed in the solvent background. In the significantly more intriguing 3D case, we observe a comparable scenario both for the discrete and the continuous model. The lattice model reveals its ability to describe morphology formation even in the high solvent content 3D case, in which the three-dimensional nature of space could have prevented cluster formation.

cond-mat.soft↗

arXiv2024

Pattern formation in three-state systems: Towards understanding morphology formation in the presence of evaporation

Inspired by experimental evidence collected when processing thin films from ternary solutions made of two solutes, typically polymers, and one solvent, we computationally study the morphology formation of domains obtained in three-state systems using both a lattice model and a continuum counterpart. The lattice-based approach relies on the Blume-Capel nearest neighbor model with bulk conservative Kawasaki dynamics, whereas as continuum system we consider a coupled system of evolution equations that is derived as hydrodynamic limit when replacing the nearest neighbor interaction in the lattice case by a suitable Kac potential. We explore how the obtained morphology depends on the solvent content in the mixture. In particular, we study how these scenarios change when the solvent is allowed to evaporate.

cond-mat.stat-mech↗

arXiv2023

Phase separation and morphology formation in interacting ternary mixtures under evaporation: Well-posedness and numerical simulation of a non-local evolution system

We study a nonlinear coupled parabolic system with non-local drift terms modeling at the continuum level the inter-species interaction within a ternary mixture that allows the evaporation of one of the species. In the absence of evaporation, the proposed system coincides with the hydrodynamic limit of a stochastic interacting particle system of Blume-Capel-type driven by the Kawasaki dynamics. Similar governing dynamics are found in models used to study morphology formation in the design of organic solar cells, thin adhesive bands, and other applications. We investigate the well-posedness of the target system and present preliminary numerical simulations which incorporate evaporation into the model. We employ a finite volumes scheme to construct approximations of the weak solution and illustrate how the evaporation process can affect the shape and connectivity of the evolving-in-time morphologies.

math.AP↗

arXiv2023

Homogenization of a reaction-diffusion problem with large nonlinear drift and Robin boundary data

We study the periodic homogenization of a reaction-diffusion problem with large nonlinear drift and Robin boundary condition posed in an unbounded perforated domain. The nonlinear problem is associated with the hydrodynamic limit of a totally asymmetric simple exclusion process (TASEP) governing a population of interacting particles crossing a domain with obstacle. We are interested in deriving rigorously the upscaled model equations and the corresponding effective coefficients for the case when the microscopic dynamics are linked to a particular choice of characteristic length and time scales that lead to an exploding nonlinear drift. The main mathematical difficulty lies in proving the two-scale compactness and strong convergence results needed for the passage to the homogenization limit. To cope with the situation, we use the concept of two-scale compactness with drift, which is similar to the more classical two-scale compactness result but it is defined now in moving coordinates. We provide as well a strong convergence result for the corrector function, starting this way the search for the order of the convergence rate of the homogenization process for our target nonlinear drift problem.

math.AP↗

arXiv2023

Homogeneous and heterogeneous nucleation in the three--state Blume--Capel model

The metastable behavior of the stochastic Blume--Capel model with Glauber dynamics is studied when zero-boundary conditions are considered. The presence of zero-boundary conditions changes drastically the metastability scenarios of the model: \emph{heterogeneous nucleation} will be proven in the region of the parameter space where the chemical potential is larger than the external magnetic field.

math-ph↗

arXiv2023

Learning models for classifying Raman spectra of genomic DNA from tumor subtypes

An early detection of different tumor subtypes is crucial for an effective guidance to personalized therapy. While much efforts focus on decoding the sequence of DNA basis to detect the genetic mutations related to cancer, it is becoming clear that physical properties, including structural conformation, stiffness, and shape, as well as biological processes, such as methylation, can be pivotal to recognize DNA modifications. Here we exploit the Surface Enhanced Raman Scattering (SERS) platform, based on disordered silver coated--silicon nanowires, to investigate genomic DNA from subtypes of melanoma and colon cancers and to efficiently discriminate tumor and healthy cells, as well as the different tumor subtypes. The diagnostic information is obtained by performing label--free Raman maps of the dried drops of DNA solutions onto the Ag/NWs mat, and leveraging the classification ability of learning models to reveal the specific and distinct interaction of healthy and tumor DNA molecules with nanowires.

stat.AP↗

arXiv2022

A Continuum Model for Morphology Formation from Interacting Ternary Mixtures: Simulation Study of the Formation and Growth of Patterns

Our interest lies in exploring the ability of a coupled nonlocal system of two quasilinear parabolic partial differential equations to produce phase separation patterns. The obtained patterns are referred here as morphologies. Our target system is derived in the literature as the rigorous hydrodynamic limit of a suitably scaled interacting particle system of Blume--Capel--type driven by Kawasaki dynamics. The system describes in a rather implicit way the interaction within a ternary mixture that is the macroscopic counterpart of a mix of two populations of interacting solutes in the presence of a background solvent. Our discussion is based on the qualitative behavior of numerical simulations of finite volume approximations of smooth solutions to our system and their quantitative postprocessing in terms of two indicators (correlation and structure factor calculations). Our results show many similar features compared to what one knows at the level of the stochastic Blume--Capel dynamics with three interacting species. The properties of the obtained morphologies (shape, connectivity, and so on) can play a key role in, e.g., the design of the active layer for efficient organic solar cells.

cond-mat.stat-mech↗

arXiv2022

Metastability of synchronous and asynchronous dynamics

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 the mean field Curie--Weiss model was approached by means of stochastic techniques, this topic has been largely studied by the scientific community. Several papers and books have been published in which many different spin models were studied and different approaches were developed. In this review we focus on the comparison between the metastable behavior of synchronous and asynchronous dynamics, namely, stochastic processes in discrete time in which at each time either all the spins or one single spin are updated. In particular we discuss how the two different stochastic implementation of the very same Hamiltonian give rise to different metastable behaviors.

cond-mat.stat-mech↗

arXiv2022

Upscaling of a reaction-diffusion-convection problem with exploding non-linear drift

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 imposed large drift scaling, this nonlinearity is expected to explode in the limit of a vanishing scaling parameter. As main working techniques, we employ two-scale formal homogenization asymptotics with drift to derive the corresponding upscaled model equations as well as the structure of the effective transport tensors. Finally, we use Schauder's fixed point theorem as well as monotonicity arguments to study the weak solvability of the upscaled model posed in an unbounded domain. This study wants to contribute with theoretical understanding needed when designing thin composite materials that are resistant to high velocity impacts.

math.AP↗

arXiv2022

Statistical classification for Raman spectra of tumoral genomic DNA

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 approaches, one based on the Principal Component Analysis of spectral data and one based on the computation of the $\ell^2$ distance between spectra. Both methods prove to be highly efficient and we test their accuracy via the so-called Cohen's $κ$ statistics. We show that the synergistic combination of the SERS spectroscopy and the statistical analysis methods leads to efficient and fast cancer diagnostic applications allowing a rapid and unexpansive discrimination between healthy and tumoral genomic DNA alternative to the more complex and expensive DNA sequencing.

q-bio.QM↗

arXiv2021

Scaling effects on the periodic homogenization of a reaction-diffusion-convection problem posed in homogeneous domains connected by a thin composite layer

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 population of interacting particles crossing a domain with obstacle. Using energy-type estimates as well as concepts like thin-layer convergence and two-scale convergence, we derive the homogenized evolution equation and the corresponding effective model parameters for a regularized problem. Special attention is paid to the derivation of the effective transmission conditions across the separating limit interface in essentially two different situations: (i) finitely thin layer and (ii) infinitely thin layer. This study should be seen as a preliminary step needed for the investigation of averaging fast non-linear drifts across material interfaces -- a topic with direct applications in the design of thin composite materials meant to be impenetrable to high-velocity impacts.

math.AP↗