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Cecilia VERNIA

Professore Ordinario presso: Dipartimento di Scienze Fisiche, Informatiche e Matematiche sede ex-Matematica


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Pubblicazioni

2020 - On a Statistical Mechanics Approach to Some Problems of the Social Sciences [Articolo su rivista]
Contucci, P.; Vernia, C.
abstract

This work is a survey of some results on a statistical mechanics approach to the social sciences emerged in the last two decades. The pioneering work of Daniel McFadden, known as discrete choice theory, is interpreted in terms of a non-interacting model and extended along the lines of the Brock and Durlauf interacting systems. The generalization to the multi-populated model is presented and two specific case studies are reviewed with their phenomenological and theoretical analysis.


2019 - Emergence of stationary uphill currents in 2D Ising models: the role of reservoirs and boundary conditions [Articolo su rivista]
Colangeli, Matteo; Giberti, Claudio; Vernia, Cecilia; Kröger, Martin
abstract

We investigate the dynamics of a 2D Ising model on a square lattice with conservative Kawasaki dynamics in the bulk, coupled with two external reservoirs that pull the dynamics out of equilibrium. Two different mechanisms for the action of the reservoirs are considered. In the first, called ISF, the condition of local equilibrium between reservoir and the lattice is not satisfied. The second mechanism, called detailed balance (DB), implements a DB condition, thus satisfying the local equilibrium property. We provide numerical evidence that, for a suitable choice of the temperature (i.e. below the critical temperature of the equilibrium 2D Ising model) and the reservoir magnetizations, in the long time limit the ISF model undergoes a ferromagnetic phase transition and gives rise to stationary uphill currents, namely positive spins diffuse from the reservoir with lower magnetization to the reservoir with higher magnetization. The same phenomenon does not occur for DB dynamics with properly chosen boundary conditions. Our analysis extends the results reported in Colangeli et al. [Phys. Rev. E 97, 030103(R) (2018)], shedding also light on the effect of temperature and the role of different boundary conditions for this model. These issues may be relevant in a variety of situations (e.g. mesoscopic systems) in which the violation of the local equilibrium condition produces unexpected phenomena that seem to contradict the standard laws of transport.


2019 - Finite-size corrections for the attractive mean-field monomer-dimer model [Articolo su rivista]
Alberici, Diego; Contucci, Pierluigi; Luzi, Rachele; Vernia, Cecilia
abstract

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 are explicitly derived as well as the value of their sign that is related to their monotonic convergence in the thermodynamic limit.


2019 - Meccanica Statistica e problemi di interesse biomedico: adesione alle campagne di screening. [Abstract in Atti di Convegno]
Vernia, Cecilia
abstract

Screening campaigns have been adopted by National Health Systems to detect anticipatory signs of serious illnesses by preliminary tests. The success and the sustainability of these programs strongly depend on the level of adhesion, still in many countries under the acceptable values indicated by International Health organizations. The idea of the project is to study the collective behavior in the participation to the screening, by using methods and models from statistical mechanics. Through the solution of the model, we can derive forecasts of different strategies to improve participation.


2019 - O(N) Fluctuations and Lattice Distortions in 1-Dimensional Systems [Articolo su rivista]
Giberti, C.; Rondoni, L.; Vernia, C.
abstract

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, various anomalies are reported, such as the dependence of the heat conductivity on the global state, rather than on the local state. Such deductions, that rely on the existence of thermodynamic quantities like temperature and heat, are here interpreted within the framework of boundary driven 1-dimensional Lennard-Jones chains of N oscillators. It is found that these chains experience non-negligible O(N) lattice distortions, resulting in strongly inhomogeneous systems, and O(N) position fluctuations, that are in contrast with the requirements of LTE.


2019 - Temperature and correlations in 1-dimensional systems [Articolo su rivista]
Giberti, Claudio; Rondoni, Lamberto; Vernia, Cecilia
abstract

Local thermodynamic equilibrium(LTE) plays a crucial role in statistical mechanics and thermodynamics. Under small driving and LTE, locally conserved quantities are transported as prescribed by linear hydrodynamic laws, in which the local material properties of the systems at hand are represented by the transport coefficients. The robustness and universality of equilibrium properties is not guaranteed in nonequilibrium states, in which different microscopic quantities may behave differently, even if they coincide at equilibrium. We investigate these issues considering 1-dimensional chains of N oscillators. We observe that non-negligible fluctuations, and persistence of correlations frustrate the onset of LTE, hence the existence of thermodynamic fields, such as temperature.


2018 - Nonequilibrium two-dimensional Ising model with stationary uphill diffusion [Articolo su rivista]
Colangeli, Matteo; Giardinà, Cristian; Giberti, Claudio; Vernia, Cecilia
abstract

Usually, in a nonequilibrium 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 two-dimensional 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 nonequilibrium 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 nonequilibrium setup, the current vanishes when the reservoir magnetization attains a value approaching, in the large volume limit, the magnetization of the equilibrium dynamics, thus establishing a relation between equilibrium and nonequilibrium properties.


2018 - Social interaction effects on immigrant integration [Articolo su rivista]
Agliari, Elena; Barra, Adriano; Contucci, Pierluigi; Pizzoferrato, Andrea; Vernia, Cecilia
abstract

In recent years Italy has been involved in massive migration flows and, consequently, migrant integration is becoming a urgent political, economic and social issue. In this paper we apply quantitative methods, based on probability theory and statistical mechanics, to study the relative integration of migrants in Italy. In particular, we focus on the probability distribution of a classical quantifier that social scientists use to measure migrant integration, that is, the fraction of mixed (natives and immigrants) married couples, and we study, in particular, how it changes with respect to the migrant density. The analysed dataset collected yearly by ISTAT (Italian National Institute of Statistics), from 2002 to 2010, provides information on marriages and population compositions for all Italian municipalities. Our findings show that there are strong differences according to the size of the municipality. In fact, in large cities the occurrence of mixed marriages grows, on average, linearly with respect to the migrant density and its fluctuations are always Gaussian; conversely, in small cities, growth follows a square-root law and the fluctuations, which have a much larger scale, approach an exponential quartic distribution at very small densities. Following a quantitative approach, whose origins trace back to the probability theory of interacting systems, we argue that the difference depends on how connected the social tissue is in the two cases: large cities present a highly fragmented social network made of very small isolated components while villages behave as percolated systems with a rich tie structure where isolation is rare or completely absent. Our findings are potentially useful for policy makers; for instance, the incentives towards a smooth integration of migrants or the size of nativist movements should be predicted based on the size of the targeted population.


2017 - Inverse problem for multispecies ferromagneticlike mean-field models in phase space with many states [Articolo su rivista]
Fedele, Micaela; Vernia, Cecilia
abstract

In this paper we solve the inverse problem for the Curie-Weiss model and its multispecies version when multiple thermodynamic states are present as in the low temperature phase where the phase space is clustered. The inverse problem consists of reconstructing the model parameters starting from configuration data generated according to the distribution of the model. We demonstrate that, without taking into account the presence of many states, the application of the inversion procedure produces very poor inference results. To overcome this problem, we use the clustering algorithm. When the system has two symmetric states of positive and negative magnetizations, the parameter reconstruction can also be obtained with smaller computational effort simply by flipping the sign of the magnetizations from positive to negative (or vice versa). The parameter reconstruction fails when the system undergoes a phase transition: In that case we give the correct inversion formulas for the Curie-Weiss model and we show that they can be used to measure how close the system gets to being critical.


2017 - Inverse problem for the mean-field monomer-dimer model with attractive interaction [Articolo su rivista]
Contucci, Pierluigi; Luzi, Rachele; Vernia, Cecilia
abstract

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.


2015 - Enhancing participation to health screening campaigns by group interactions [Articolo su rivista]
Burioni, Raffaella; Contucci, Pierluigi; Fedele, Micaela; Vernia, Cecilia; Vezzani, Alessandro
abstract

Improving the prevention efficacy of health screening campaigns by increasing their attendance rate represents a challenge that calls for new strategies. This paper analyzes the response to a Pap test screening campaign of 155,000 women over the last decade. Using a mathematical model of statistical physics origins we derive a quantitative estimate of the mutual influence between participating groups. Different scenarios and possible actions are studied from the cost-benefit perspective. The performance of alternative strategies to improve participation are forecasted and compared. The results show that the standard strategies with incentives concentrated toward the low participating groups are outperformed by those toward pivotal groups with higher influence power. Our method provides a flexible tool useful to support policy maker decisions while complying with ethical regulations on privacy and confidentiality.


2014 - A Statistical Mechanics Approach to Immigrant Integration in Emilia Romagna (Italy) [Relazione in Atti di Convegno]
DE PRETIS, Francesco; Vernia, Cecilia
abstract

Integration phenomena are social processes among human beings that take place every day when an autochthone population is experiencing the arrival of new immigrants. Although being a rising phenomenon (involving now over one billion people according to United Nations) which questions societies and policy-makers all over the world, numerical measurements capable to give robust insights over the way immigrant integration occurs are still far from what is usually considered an affordable standard in mathematical and physical sciences. Basing our analysis on previous seminal works, we follow here a statistical physics approach to the analysis of immigrant integration. In specific, we consider a large dataset collected by the Emilia Romagna region office of statistics (Italy), containing information over all marriages occurred amid the regional population during a sixteen years span, from 1995 to 2010. We define as quantifier of integration the percentage of marriages with spouses of mixed origin and we perform several analyses over the dataset, including binning and data fitting. The final outcome consists in an emerging pattern: quantifier’s average measurements align around a square root fit when considered with respect to a suitable function of the immigrant density. The theoretical interpretation we offer is that such result agrees with a suitable version of the Curie-Weiss model used in statistical mechanics to describe ferromagnetisms. More explicitly, immigrants living in Emilia Romagna municipalities seem to present mainly imitative behavior’s phenomena in making social actions for integration. The result emerged with Emilia Romagna data complies with previous works concerning similar data coming from Spain.


2014 - A stochastic approach for quantifying immigrant integration: the Spanish test case. [Articolo su rivista]
E., Agliari; A., Barra; P., Contucci; R., Sandell; Vernia, Cecilia
abstract

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 becomes possible to analyse the behavior of the quantifiers by means of continuous time random walks. Two classes of results are then obtained. First, we show that social integration quantifiers evolve following diffusion law, while the evolution of economic quantifiers exhibits 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 pressures build.


2014 - An analysis of a large dataset on immigrant integration in Spain. The Statistical Mechanics perspective on Social Action [Articolo su rivista]
A., Barra; P., Contucci; R., Sandell; Vernia, Cecilia
abstract

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 quantifiers 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.


2013 - Inverse problem robustness for multi-species mean-field spin models [Articolo su rivista]
M., Fedele; Vernia, Cecilia; P., Contucci
abstract

The inverse problem method is tested for a class of mean-field statistical mechanics models representing a mixture of particles of different species. The robustness of the inversion is investigated for different values of the physical parameters, system sizes and independent samples. We show how to reconstruct the parameter values with a precision of a few per cent.


2011 - Interface Energy in the Edwards-Anderson Model [Articolo su rivista]
Pierluigi, Contucci; Giardina', Cristian; Giberti, Claudio; Giorgio, Parisi; Vernia, Cecilia
abstract

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 simulates finite temperature systems and works 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.


2011 - Meccanica Razionale per Ingegneria [Monografia/Trattato scientifico]
Franceschini, Valter; Vernia, Cecilia
abstract

Il testo si propone come supporto per l'insegnamento della Meccanica Razionale presso i corsi di laurea in Ingegneria dell'Università di Modena e Reggio Emilia. Gli obiettivi specifici che ci si è posti sono quelli di introdurre gli elementi di base della Meccanica Classica e di fornire gli strumenti matematici essenziali per la costruzione e lo studio dei modelli che descrivono i fenomeni meccanici.Il testo è suddiviso in due parti: teoria ed esercizi. La teoria è organizzata in nove capitoli: i primi sei con lenozioni necessarie, a parere degli autori, per un corso di Meccanica Razionale di base; gli ultimi tre per unsecondo corso più avanzato, che tratti anche eventuali argomenti dei primi sei capitoli tralasciati in precedenza. Gli esercizi, tutti svolti in dettaglio, fanno riferimento ai primi sei capitoli della teoria, con l'aggiunta negli esercizi di Meccanica dei sistemi di alcune applicazioni riguardanti le equazioni di Lagrange, le piccole oscillazioni e lo studio qualitativo del moto.


2010 - Modelling Complex Systems with Statistical Mechanics: The Computational Approach [Articolo su rivista]
P., Contucci; Giardina', Cristian; Giberti, Claudio; Vernia, Cecilia
abstract

Real-world phenomena are often described by complex systems with competitive and cooperative behaviour. Such systems, as much as the described phenomena, are hard to understand in a scientific perspective mainly due to the lack of general exact solutions. For cases like this, the computational sciences provide a very useful virtual laboratory. The case of disordered systems is an example of scientific computing techniques being used to test theoretical predictions and uncover new phenomena that remain unreachable by traditional analytical methods.


2009 - Structure of correlations in three dimensional spin glasses [Articolo su rivista]
P., Contucci; GIARDINA', Cristian; GIBERTI, Claudio; G., Parisi; VERNIA, Cecilia
abstract

We investigate the low temperature phase of the three dimensional Edward-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 have power law decay. Our findings are in agreement with the replica symmetry breaking theory and show that the overlap is a good order parameter. © 2009 The American Physical Society.


2008 - Answer to Comment on "Ultrametricity in the Edwards-Anderson Model" [Articolo su rivista]
P., Contucci; Giardina', Cristian; Giberti, Claudio; G., Parisi; Vernia, Cecilia
abstract

In this paper we reply to a critical comment by T. Jorg and F. Krzakala to the Letter "Ultrametricity in the Edwards-Anderson Model" PRL 99, 057206 (2007). We show that the procedure developed in the aforementioned paper to detect ultrametricity is able to discriminate the non-ultrametric behavior of the two-dimensional Edwards-Anderson model from the ultrametric three-dimensional one. Moreover, the interesting finding of Jorg and Krzakala that in the two-dimensional Edwards-Anderson model three random configurations have ordered overlaps fulfilling the ultrametric distribution is discussed and an explanation of this phenomenon is proposed.


2008 - Lack of monotonicity in spin glass correlation functions [Articolo su rivista]
P., Contucci; Unguendoli, Francesco; Vernia, Cecilia
abstract

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.


2008 - Numerical study of ground state energy fluctuations in spin glasses [Altro]
Giberti, Claudio; Vernia, Cecilia
abstract

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.


2008 - Sintering and crystallization of CaO-Al2O3-ZrO2-SiO2 glasses containing different amount of Al2O3 [Articolo su rivista]
Siligardi, Cristina; Montorsi, Monia; Lusvarghi, Luca; Vernia, Cecilia
abstract

In this work several complementary techniques have been employedto carefully characterize the sintering and crystallizationbehavior of CaO–Al2O3–ZrO2–SiO2 glass powder compactsafter different heat treatments. The research started from a newbase glass 33.69 CaO–1.00 Al2O3–7.68 ZrO2–55.43SiO2(mol%) to which 5 and 10 mol% Al2O3 were added. The glasseswith higher amounts of alumina sintered at higher temperatures(9531C [lower amount] vs. 9871C [higher amount]). Acombination of the linear shrinkage and viscosity data allowedto easily find the viscosity values corresponding to the beginningand the end of the sintering process. Anorthite and wollastonitecrystals formed in the sintered samples, especially at lowertemperatures. At higher temperatures, a new crystalline phasecontaining ZrO2 (2CaO. 4SiO2 . ZrO2) appeared in all studiedspecimens.


2007 - Temporal asymmetry of fluctuations in the nonequilibrium FPU model [Articolo su rivista]
Giberti, Claudio; L., Rondoni; Vernia, Cecilia
abstract

The large deviation theory recently developed by Bertini, De Sole, Gabrielli, Jona-Lasinio and Landim is meant to extend the Onsager–Machlup theory to nonequilibrium phenomena, and predicts that the fluctuations of densities and currents in certain stochastic processes are not symmetric with respect to the time reversal operation. In this paper, several notions of fluctuations are introduced for deterministic systems, and it is observed that temporally asymmetric (not necessarily large) fluctuations are ubiquitous, even in the context of time reversal invariant dynamics of particle systems, in nonequilibrium states. To illustrate these ideas, the nonequilibrium FPU chain devised by Lepri, Livi and Politi is studied in detail.


2007 - Ultrametricity in the Edwards-Anderson model. [Articolo su rivista]
P., Contucci; GIARDINA', Cristian; GIBERTI, Claudio; G., Parisi; VERNIA, Cecilia
abstract

We test the property of ultrametricity for the spin-glass three-dimensional Edwards-Anderson model in zero magnetic field with numerical simulations up to 203 spins. We find an excellent agreement with the prediction of the mean field theory. Since ultrametricity is not compatible with a trivial structure of the overlap distribution, our result contradicts the droplet theory. © 2007 The American Physical Society.


2006 - Asymmetric fluctuations-relaxations paths in FPU models [Articolo su rivista]
Giberti, Claudio; L., Rondoni; Vernia, Cecilia
abstract

A recent theory by Bertini, De Sole, Gabrielli, Jona-Lasinio and Landim predicts a temporal asymmetry in thefluctuation–relaxation paths of certain observables of nonequilibrium systems in local thermodynamic equilibrium. Wefind temporal asymmetries in the fluctuation–relaxation paths of a form of local heat flow, in the nonequilibrium FPU-bmodel of Lepri, Livi and Politi.


2006 - Overlap equivalence in the Edwards-Anderson model [Articolo su rivista]
P., Contucci; GIARDINA', Cristian; GIBERTI, Claudio; VERNIA, Cecilia
abstract

We study the relative fluctuations of the link overlap and the square standard overlap in the three-dimensional Gaussian Edwards-Anderson model with zero external field. We first analyze the correlation coefficient and find that the two quantities are uncorrelated above the critical temperature. Below the critical temperature we find that the link overlap has vanishing fluctuations for fixed values of the square standard overlap and large volumes. Our data show that the conditional variance scales to zero in the thermodynamic limit. This implies that, if one of the two random variables tends to a trivial one (i.e., deltalike distributed), then the other does also, and as a consequence, the "trivial-nontrivial" picture should be dismissed. Our results show that the two overlaps are completely equivalent in the description of the low temperature phase of the Edwards-Anderson model. © 2006 The American Physical Society.


2005 - Bifurcation of Homogeneous Solutions in a Chain of Logistic Maps [Articolo su rivista]
Giberti, Claudio; Vernia, Cecilia
abstract

In this paper we study the bifurcation of the homogeneous fixed point of a lattice of n diffusively coupled logistic maps. An analytical computation of the reduced map on the centermanifold is performed by taking into account the symmetries of the system. If n is even, a subcritical flip bifurcation causes a symmetry breaking of the homogeneous pattern whichproduces a traveling (rotating) wave with velocity 1 and time period 2. For odd n, since the bifurcation has a two dimensional normal form, we limit ourselves to consider only the simplest case (n = 3). In this case, a supercritical flip bifurcation is observed; three less symmetric periodic orbits of time period 2 are generated by the breaking of the homogeneous orbit. However, the bifurcation is rather degenerate and we have numerical hints that a second family of asymmetric periodic points is generated. Some details, pertaining to the dynamicsof the truncated map on the two dimensional center manifold for n = 3, are also presented.


2005 - Finding minima in complex landscapes: Annealed, greedy and reluctant algorithms. [Articolo su rivista]
P., Contucci; Giardina', Cristian; Giberti, Claudio; Vernia, Cecilia
abstract

We consider optimization problems for complex systems in which the cost function has a multivalleyed landscape. We introduce a new class of dynamical algorithms which, using a suitable annealing procedure coupled with a balanced greedy-reluctant strategy drive the systems towards the deepest minimum of the cost function. Results are presented for the Sherrington-Kirkpatrick model of spin-glasses. © World Scientific Publishing Company.


2005 - Interpolating greedy and reluctant algorithms [Articolo su rivista]
P., Contucci; Giardina', Cristian; Giberti, Claudio; Unguendoli, Francesco; Vernia, Cecilia
abstract

In a standard NP-complete optimization problem, we introduce an interpolating algorithm between the quick decrease along the steepest descent direction (greedy dynamics) and a slow decrease close to the level curves (reluctant dynamics). We find that, for a fixed elapsed computer time, the best performance of the optimization is reached at a special value of the interpolation parameter, considerably improving the results of the pure cases of greedy and reluctant. © 2005 Taylor & Francis Group Ltd.


2004 - Coexistence of chaotic and non-chaotic states in the two-dimensional Gauss-Navier-Stokes dynamics [Articolo su rivista]
Giberti, Claudio; L., Rondoni; Vernia, Cecilia
abstract

Recently, Gallavotti proposed an Equivalence Conjecture in hydrodynamics, which states that forced-damped fluids can be equally Well represented by means of the Navier-Stokes equations (NS) and by means of time reversible modifications of NS called Gauss-Navier-Stokes equations (GNS). This Equivalence Conjecture received numerical support in several recent papers concerning two-dimensional fluid mechanics. The corresponding results rely on the fact that the NS and GNS systems only, have one attracting set. Performing similar two-dimensional simulations, we find that there are conditions to be met by the GNS system for this to be the case. In particular, increasing the Reynolds number, while keeping fixed the number of Fourier modes, leads to the coexistence of different attractors. This makes difficult a test of the Equivalence Conjecture, but constitutes a spurious effect due to the insufficient spectral resolution. With sufficiently fine spectral resolution, the steady states are unique and the Equivalence Conjecture can be conveniently established.


2003 - Optimization Strategies in Complex Systems [Capitolo/Saggio]
L., Bussolari; P., Contucci; Giardina', Cristian; Giberti, Claudio; Unguendoli, Francesco; Vernia, Cecilia
abstract

We consider a class of combinatorial optimization problems that emerge in a variety of domains among which: condensed matter physics, theory of financial risks, error correcting codes in information transmissions, molecular and protein conformation, image restoration. We show the performances of two algorithms, the "greedy'' (quick decrease along the gradient) and the "reluctant'' (slow decrease close to the level curves) as well as those of a "stochastic convex interpolation'' of the two.Concepts like the average relaxation time and the wideness of theattraction basin are analyzed and their system size dependenceillustrated.


2002 - Numerical study of stability of non-chaotic patterns in coupled map lattices [Relazione in Atti di Convegno]
Giberti, Claudio; Vernia, Cecilia
abstract

The stability of non-chaotic structures in lattices ofcoupled logistic maps is analyzed in parameter space. We state theexistence of a few elementary structures the stability of whichdetermines that of almost all non-chaotic patterns of any size.This allows us to propose a technique for predicting whichattractors can exist in a given parameter region.


2002 - On quasiperiodic travelling waves in coupled map lattices [Articolo su rivista]
Franceschini, Valter; Giberti, Claudio; Vernia, Cecilia
abstract

We investigate quasiperiodic travelling waves (QTWs) in lattices of diffusively coupled logistic maps. Starting from the assumption that any spatial structure can be broken down into simpler elementary structures, a classification scheme for QTWs is introduced. Within this framework. the phenomenon of discrete velocities is reviewed and further investigated. In addition, a new technique is proposed for predicting whether QTWs can occur for given parameter values and which they might be.


2002 - Tori breakdown in coupled map lattices [Articolo su rivista]
Giberti, Claudio; Vernia, Cecilia
abstract

In this paper we present a numerical study of invariant tori in a lattice of coupled logistic maps. In particular, we are interested in bifurcations leading to chaos. Here we consider six different examples of tori breakdown: two of them completely confirm the theory of Afraimovich and Shilnikov, while the others appear peculiar to the model.


1998 - A few basic structures determine the behavior of a coupled map lattice [Articolo su rivista]
Franceschini, Valter; Vernia, Cecilia
abstract

The stability and formation of structures in lattices of diffusively coupled logistic maps are investigated for high nonlinearity and medium and large coupling. Two stability statements are given that relate the presence of the predominant attractors, i.e., cycles and quasiperiodic traveling waves, to the stability of a few simple periodic structures. They are supported by strong numerical evidence. Furthermore, they are justified through the description of some mechanisms that connect the formation of a stable structure to the cycles of the uncoupled lattice. As an important consequence, for given parameter values, an approximate prediction of the behavior of the lattice is allowed.


1998 - Formation, Stability and Predictability of Structures in Coupled Map Lattices [Articolo su rivista]
Franceschini, Valter; Giberti, Claudio; Vernia, Cecilia
abstract

Some significant non-chaotic behaviors of the lattices ofcoupled logistic maps are analyzed. In particular, the review concerns the organization of cycles for small coupling andthe fundamental role played by heteroclinic cycles and quasiperiodic traveling waves. Moreover, we point to the existence of a few elementary cycles the stability of which determines that of almost all non-chaotic structures of any size, in particular for high nonlinearity and medium and large coupling.This allows an approximate prediction of which attractors can occur for given parameter values.


1997 - On stability of structures and patterns in extended systems [Articolo su rivista]
L. A., Bunimovich; Franceschini, Valter; Giberti, Claudio; Vernia, Cecilia
abstract

We study the stability of spatial structures in extended systems. Each spatial structure consists of some simple (undecomposable) structures that we call. patterns. We show numerically for some classes of coupled map lattices that the stability of a spatial structure is determined by the stability of its pattern with the minimal (spatial) scale, i.e. by the most tiny detail of this structure.


1994 - Normally attracting manifolds and periodic behavior in one-dimensional and two-dimensional coupled map lattices [Articolo su rivista]
Giberti, Claudio; Vernia, Cecilia
abstract

We consider diffusively coupled logistic maps in one- and two-dimensional lattices. We investigate periodic behaviors as the coupling parameter varies, i.e., existence and bifurcations of some periodic orbits with the largest domain of attraction. Similarity and differences between the two lattices are shown. For small coupling the periodic behavior appears to be characterized by a number of periodic orbits structured in such a way to give rise to distinct, reverse period-doubling sequences. For intermediate values of the coupling a prominent role in the dynamics is played by the presence of normally attracting manifolds that contain periodic orbits. The dynamics on these manifolds is very weakly hyperbolic, which implies long transients. A detailed investigation allows the understanding of the mechanism of their formation. A complex bifurcation is found which causes an attracting manifold to become unstable.


1994 - Presence and stability regions of heteroclinic cycles in coupled map lattices [Articolo su rivista]
Vernia, Cecilia
abstract

We consider lattices of diffusively coupled logistic maps. We show that normally attracting heteroclinic cycles persist in large regions of the parameter space. A detailed study of the behavior of those with a short period is provided. Furthermore, various bifurcations which involve a heteroclinic cycle are discussed.


1993 - On the presence of Normally Atracting Manifolds Containing Periodic or Quasiperiodic Orbits in Coupled Map Lattices [Articolo su rivista]
Giberti, Claudio; Vernia, Cecilia
abstract

The significant presence of normally attracting invariant manifolds, formed by closed curves or two-tori, is investigated in two-dimensional lattices of coupled chaotic maps. In the case of a manifold formed by closed curves, it contains symmetrically placed periodic orbits, with the property of a very weak hyperbolicity along the manifold itself. The resulting dynamics is an extremely slow relaxation to periodic behavior. Analogously, a manifold consisting of two-tori includes very weakly hyperbolic periodic (or quasiperiodic) orbits, which in this case also implies quite a long time before any solution approaches periodicity or quasiperiodicity.The normally attracting manifolds and the contained weak attractors can undergo several global bifurcations. Some of them, including saddle-node bifurcation, period-doubling and Hopf bifurcation, are illustrated.Almost all the asymptotic solutions that we discuss have flat rows or flat columns, which means that they can occur also in one-dimensional lattices.