arXiv subjects

Alberto Petri

Publications and source records attributed to Alberto Petri.

At least 19 recordsLinked to original sources

arXiv2025

Universalities in the Avalanche Dynamics of Novelties and Non-Novelties and some Notes on the Heaps law

Unprecedented events intertwine with the repetition of the past in natural phenomena and human activities. Key statistical patterns, such as Heaps' and Taylor's laws and Zipf's law, have been identified as characterizing the dynamical processes that govern the emergence of novelties and the abundance of repeated elements. Observing these statistical regularities has been pivotal in motivating the search for modeling schemes that can explain them and clarify key mechanisms underlying the appearance of new elements and their subsequent recurrence. In this study, we analyze sequences of novel and non-novel elements, referred to as avalanches, in real-world systems. We show that avalanche statistics provide a complementary characterization of innovation dynamics, extending beyond the three fundamental laws mentioned above. Although arising from collective dynamics, some systems behave as a single instance of a stochastic process. Others, such as natural language, exhibit features that we can only explain by a superposition of different dynamics. This distinction is not apparent when considering Heaps' law alone, while it clearly emerges in the avalanche statistics. By interpreting these empirical observations, we also advance the theoretical understanding of urn-based models that successfully reproduce the observed behaviors associated with Heaps', Zipf's, and Taylor's laws. We derive analytical expressions that accurately describe the probability distributions of avalanches and the Heaps law beyond its asymptotic regime. Building on these results, we derive a scaling relation that we show also holds in real-world systems, indicating a form of universality in the dynamics of novelty.

physics.soc-ph↗

arXiv2024

Control of friction: shortcuts and optimization for the rate- and state-variable equation

Frictional forces are a key ingredient of any physical description of the macroscopic world, as they account for the phenomena causing transformation of mechanical energy into heat. They are ubiquitous in nature, and a wide range of practical applications involve the manipulation of physical systems where friction plays a crucial role. In this paper, we apply control theory to dynamics governed by the paradigmatic rate- and state-variable law for solid-on-solid friction. Several control problems are considered for the case of a slider dragged on a surface by an elastic spring. By using swift state-to-state protocols, we show how to drive the system between two arbitrary stationary states characterized by different constant sliding velocities in a given time. Remarkably, this task proves to be feasible even when specific constraints are imposed on the dynamics, such as preventing the instantaneous sliding velocity or the frictional force from exceeding a prescribed bound. The derived driving protocols also allow to avoid a stick-slip instability, which instead occurs when velocity is suddenly switched. By exploiting variational methods, we also address the functional minimization problem of finding the optimal protocol that connects two steady states in a specified time, while minimizing the work done by the friction. We find that the optimal strategy can change qualitatively depending on the time imposed for the duration of the process. Our results mark a significant step forward in establishing a theoretical framework for control problems in the presence of friction and naturally pave the way for future experiments.

cond-mat.soft↗

arXiv2024

Earthquake dynamics constrained from laboratory experiments: new insights from granular materials

The traction evolution is a fundamental ingredient to model the dynamics of an earthquake rupture which ultimately controls, during the coseismic phase, the energy release, the stress redistribution and the consequent excitation of seismic waves. In the present paper we explore the use of the friction behavior derived from laboratory shear experiments performed on granular materials at low normal stress. We find that the rheological properties emerging from these laboratory experiments can not be described in terms of preexisting governing models already presented in literature; our results indicate that neither rate-and state-dependent friction laws nor nonlinear slip-dependent models, commonly adopted for modeling earthquake ruptures, are able to capture all the features of the experimental data. Then, by exploiting a novel numerical approach, we directly incorporate the laboratory data into a code to simulate the fully dynamic propagation of a 3-D slip failure. We demonstrate that the rheology of the granular material, imposed as fault boundary condition, is dynamically consistent. Indeed, it is able to reproduce the basic features of a crustal earthquake, spontaneously accelerating up to some terminal rupture speed, both sub- and supershear.

physics.geo-ph↗

arXiv2024

Shear profile in a dense packing of large grains

We investigate the shear of a dense bed of refracting supermillimetric grains confined within a transparent horizontal annular cell with a rotating top. The local time correlation functions of interferometric images allow to characterize the shear profile close to the wall, with a spatial resolution well below the grain diameter. For increasing shear, we observe a transition in the system response and the manifestations of anisotropies in the force chains. The employed technique is of easy implementation and is especially suitable for the study of stationary processes.

cond-mat.soft↗

arXiv2023

A Markovian approach to the Prandtl-Tomlinson frictional model

We consider the Prandtl-Tomlinson model in the case of a constant driving force and in the presence of thermal fluctuations. We show that the system dynamics is well reproduced by a simplified description obtained through a Markov process, even in the case of potentials with several minima. After estimating the chain parameters by numerical simulation, we compute the average velocity and friction at varying driving force and temperature. Then we take advantage of this approach for calculating the entropy produced by the system and, in the case of a single minimum potential, to derive its explicit relation with the external force and the mobility at low temperatures. We observe that the coefficient relating the entropy production to the force is not a monotonic function of the temperature.

cond-mat.stat-mech↗

arXiv2023

Rescaling invariance and anomalous energy transport in a small vertical column of grains

It is well known that energy dissipation and finite size can deeply affect the dynamics of granular matter, often making usual hydrodynamic approaches problematic. Here we report on the experi-mental investigation of a small model system, made of ten beads constrained into a 1-d geometry by a narrow vertical pipe and shaken at the base by a piston excited by a periodic wave. Recording the beads motion with high frame rate camera allows to investigate in detail the microscopic dynamics and test hydrodynamic and kinetic models. Varying the energy we explore different regimes from fully fluidized to the edge of condensation, observing good hydrodynamic behavior down to the edge of fluidization, despite the small system size. Density and temperature fields for different system energies can be collapsed by suitable space and time rescaling, and the expected constitutive equation holds very well when the particle diameter is considered. At the same time the balance between dissipated and fed energy is not well described by commonly adopted dependence, due to the up-down symmetry breaking. Our observations, supported by the measured particle velocity distributions, show a different phenomenological temperature dependence, which yields equation solutions in agreement with experimental results.

cond-mat.soft↗

arXiv2023

Hard-needle elastomer in one spatial dimension

We perform exact Statistical Mechanics calculations for a system of elongated objects (hard needles) that are restricted to translate along a line and rotate within a plane, and that interact via both excluded-volume steric repulsion and harmonic elastic forces between neighbors. This system represents a one-dimensional model of a liquid crystal elastomer, and has a zero-tension critical point that we describe using the transfer-matrix method. In the absence of elastic interactions, we build on previous results by Kantor and Kardar, and find that the nematic order parameter $Q$ decays linearly with tension $\sigma$. In the presence of elastic interactions, the system exhibits a standard universal scaling form, with $Q / |\sigma|$ being a function of the rescaled elastic energy constant $k / |\sigma|^\Delta$, where $\Delta$ is a critical exponent equal to $2$ for this model. At zero tension, simple scaling arguments lead to the asymptotic behavior $Q \sim k^{1/\Delta}$, which does not depend on the equilibrium distance of the springs in this model.

cond-mat.stat-mech↗

arXiv2022

The trickle down from environmental innovation to productive complexity

We study the empirical relationship between green technologies and industrial production at very fine-grained levels by employing Economic Complexity techniques. Firstly, we use patent data on green technology domains as a proxy for competitive green innovation and data on exported products as a proxy for competitive industrial production. Secondly, with the aim of observing how green technological development trickles down into industrial production, we build a bipartite directed network linking single green technologies at time $t_1$ to single products at time $t_2 \ge t_1$ on the basis of their time-lagged co-occurrences in the technological and industrial specialization profiles of countries. Thirdly we filter the links in the network by employing a maximum entropy null-model. In particular, we find that the industrial sectors most connected to green technologies are related to the processing of raw materials, which we know to be crucial for the development of clean energy innovations. Furthermore, by looking at the evolution of the network over time, we observe that more complex green technological know-how requires more time to be transmitted to industrial production, and is also linked to more complex products.

econ.GN↗

arXiv2018

Breakdown of Scaling and Friction Weakening in the Critical Granular Flow

The way granular materials response to an applied shear stress is of the utmost relevance to both human activities and natural environment. One of the their most intriguing and less understood behavior, is the stick-instability, whose most dramatic manifestation are earthquakes, ultimately governed by the dynamics of rocks and debris jammed within the fault gauge. Many of the features of earthquakes, i.e. intermittency, broad times and energy scale involved, are mimicked by a very simple experimental set-up, where small beads of glass under load are slowly sheared by an elastic medium. Analyzing data from long lasting experiments, we identify a critical dynamical regime, that can be related to known theoretical models used for "crackling-noise" phenomena. In particular, we focus on the average shape of the slip velocity, observing a "breakdown of scaling": while small slips show a self-similar shape, large does not, in a way that suggests the presence of subtle inertial effects within the granular system. In order to characterise the crossover between the two regimes, we investigate the frictional response of the system, which we trat as a stochastic quantity. Computing different averages, we evidence a weakening effect, whose Stribeck threshold velocity can be related to the aforementioned breaking of scaling.

cond-mat.soft↗

arXiv2017

Uniaxial and biaxial structures in the elastic Maier-Saupe model

We perform statistical mechanics calculations to analyze the global phase diagram of a fully-connected version of a Maier-Saupe-Zwanzig lattice model with the inclusion of couplings to an elastic strain field. We point out the presence of uniaxial and biaxial nematic structures, depending on temperature $T$ and on the applied stress $σ$. Under uniaxial extensive tension, applied stress favors uniaxial orientation, and we obtain a first-order boundary, along which there is a coexistence of two uniaxial paranematic phases, and which ends at a simple critical point. Under uniaxial compressive tension, stress favors biaxial orientation; for small values of the coupling parameters, the first-order boundary ends at a tricritical point, beyond which there is a continuous transition between a paranematic and a biaxially ordered structure. For some representative choices of the model parameters, we obtain a number of analytic results, including the location of critical and tricritical points and the line of stability of the biaxial phase.

cond-mat.soft↗

arXiv2015

How log-normal is your country? An analysis of the statistical distribution of the exported volumes of products

We have considered the statistical distributions of the volumes of the different products exported by 148 countries. We have found that the form of these distributions is not unique but heavily depends on the level of development of the nation, as expressed by macroeconomic indicators like GDP, GDP per capita, total export and a recently introduced measure for countries' economic complexity called fitness. We have identified three major classes: a) an incomplete log-normal shape, truncated on the left side, for the less developed countries, b) a complete log-normal, with a wider range of volumes, for nations characterized by intermediate economy, and c) a strongly asymmetric shape for countries with a high degree of development. The ranking curves of the exported volumes from each country seldom cross each other, showing a clear hierarchy of export volumes. Finally, the log-normality hypothesis has been checked for the distributions of all the 148 countries through different tests, Kolmogorov-Smirnov and Cramer-Von Mises, confirming that it cannot be rejected only for the countries of intermediate economy.

econ.GN↗

arXiv2014

Anomalous metastability in a temperature-driven transition

Langer theory of metastability provides a description of the lifetime and properties of the metastable phase of the Ising model field-driven transition, describing the magnetic field-driven transition in ferromagnets and the chemical potential-driven transition of fluids. An immediate further step is to apply it to the study of a transition driven by the temperature, as the one underwent by the two-dimensional Potts model. For this model a study based on the analytical continuation of the free energy (Meunier, Morel 2000) predicts the anomalous vanishing of the metastable temperature range in the limit of large system size, an issue that has been controversial since the eighties. With a parallel-GPU algorithm we compare the Monte Carlo dynamics with the theory, obtaining agreement and characterizing the anomalous system size dependence. We discuss the microscopic origin of these metastable phenomena, essentially different with respect to the Ising case.

cond-mat.stat-mech↗

arXiv2014

Dynamic metastability in the two-dimensional Potts ferromagnet

We investigate the non-equilibrium dynamics of the 2D Potts model on the square lattice after a quench below the discontinuous transition point. By means of numerical simulations of systems with q =12,24 and 48 we observe the onset of a stationary regime below the temperature-driven transition, in a temperature interval decreasing with the system size and increasing with q. These results obtained dynamically agree with those obtained from the analytical continuation of the free energy (Meunier and Morel, 2000), from which metastability in the 2D Potts model results to be a finite size effect.

cond-mat.stat-mech↗

arXiv2013

Non-equilibrium fluctuations in frictional granular motor: experiments and kinetic theory

We report the study of a new experimental granular Brownian motor, inspired to the one published in [Phys. Rev. Lett. 104, 248001 (2010)], but different in some ingredients. As in that previous work, the motor is constituted by a rotating pawl whose surfaces break the rotation-inversion symmetry through alternated patches of different inelasticity, immersed in a gas of granular particles. The main novelty of our experimental setup is in the orientation of the main axis, which is parallel to the (vertical) direction of shaking of the granular fluid, guaranteeing an isotropic distribution for the velocities of colliding grains, characterized by a variance $v_0^2$. We also keep the granular system diluted, in order to compare with Boltzmann-equation-based kinetic theory. In agreement with theory, we observe for the first time the crucial role of Coulomb friction which induces two main regimes: (i) rare collisions (RC), with an average drift $\ < ω\ > \sim v_0^3$, and (ii) frequent collisions (FC), with $\ < ω\ > \sim v_0$. We also study the fluctuations of the angle spanned in a large time interval, $Δθ$, which in the FC regime is proportional to the work done upon the motor. We observe that the Fluctuation Relation is satisfied with a slope which weakly depends on the relative collision frequency.

cond-mat.stat-mech↗

arXiv2010

Random neighbour model for yielding

We introduce a model for yielding, inspired by fracture models and the failure of a sheared granular medium in which the applied shear is resisted by self-organized force chains. The force chains in the granular medium (GM) are considered as a bundle of fibres of finite strength amongst which stress is randomly redistributed after any other fibre breaks under excessive load. The model provides an exponential distribution of the internal stress and a log-normal shaped distribution of failure stress, in agreement with experimental observations. The model displays critical behaviour which approaches mean field as the number of random neighbours $k$ becomes large and also displays a failure strength which remains finite in the limit of infinite size. From comparison with different models it is argued that this is an effect of uncorrelation. All these macroscopic properties appear statistically stable with respect to the choice of the chains' initial strength distribution. The investigated model is relevant for all systems in which some generic external load or pressure is borne by a number of units, independent of one another except when failure of a unit causes load transfer to some random choice of neighbouring units.

cond-mat.stat-mech↗

arXiv2009

Brownian motor in a granular medium

In this work we experimentally study the behavior of a freely-rotating asymmetric probe immersed in a vibrated granular medium. For a wide variety of vibration conditions the probe exhibits a steady rotation whose direction is constant with respect to the asymmetry. By changing the vibration amplitude and by filtering the noise in different frequency bands we show that the velocity of rotation does not depend only on the RMS acceleration $Γ$, but also on the amount of energy provided to two separate frequency bands which are revealed to be important for the dynamics of the granular medium: the first band governs the transfer of energy from the grains to the probe, and the second affects the dynamics by altering the viscosity of the vibro-fluidized material.

cond-mat.soft↗

arXiv2008

Stochastic dynamics of a sheared granular medium

We experimentally investigate the response of a sheared granular medium in a Couette geometry. The apparatus exhibits the expected stick-slip motion and we probe it in the very intermittent regime resulting from low driving. Statistical analysis of the dynamic fluctuations reveals notable regularities. We observe a possible stability property for the torque distribution, reminiscent of the stability of Gaussian independent variables. In this case, however, the variables are correlated and the distribution is skewed. Moreover, the whole dynamical intermittent regime can be described with a simple stochastic model, finding good quantitative agreement with the experimental data. Interestingly, a similar model has been previously introduced in the study of magnetic domain wall motion, a source of Barkhausen noise. Our study suggests interesting connections between different complex phenomena and reveals some unexpected features that remain to be explained.

cond-mat.stat-mech↗

arXiv2008

Ordering dynamics in the presence of multiple phases

The dynamics of the 2D Potts ferromagnet when quenched below the transition temperature is investigated in the case of discontinuous phase transition, which is interesting for understandingthe non equilibrium dynamics of systems with many competing equivalent low temperature phases, that appears to be not much explored. After briefly reviewing some recent findings, we focus on the numerical study of quenches just below the transition temperature on square lattices. We show that, up to a certain time, metastable states can be observed for which energy stays constant above the equilibrium energy and the self-correlation function displays a fast decay.

cond-mat.stat-mech↗