annalisa fierro - Academia.edu (original) (raw)

Papers by annalisa fierro

Nucleation and Atmospheric Aerosols, 2013

ABSTRACT Using molecular dynamics simulations, we study a DLVO-type model for attractive colloida... more ABSTRACT Using molecular dynamics simulations, we study a DLVO-type model for attractive colloidal systems. In particular we focus on the crossover from the gel-like regime, at low volume fraction, to the glassy-like regime, at higher volume fraction. In such crossover region, some features of chemical gels and some features of glassy systems are present. The former are due to long living clusters the latter to crowding effects, which both slow down the relaxation process. The contribution of the long living clusters is obtained from the fluctuations of the self-overlap, χ4(t), by summing only over pairs of particles, linked by persistent bonds (present at both times 0 and time t), the crowding contribution is instead obtained from the remaining pairs of particles. For small volume fractions and low enough temperature, where the lifetime of the bonds is dominant, essentially the cluster contribution is present. At higher volume fraction, where bond lifetime and relaxation time start to be of the same order of magnitude, both contributions are manifest. The dependence of these two contributions on the length scale a, which appears in the definition of χ4(t), is also interesting. The clustering contribution is highly suppressed as a decreases, like in chemical gels, while the contribution due to crowding has a non-monotonic behaviour, and it is maximum at intermediate values of a.

Journal of Statistical Mechanics: Theory and Experiment, Jul 11, 2016

The dynamical arrest of gels is the consequence of a well defined structural phase transition, le... more The dynamical arrest of gels is the consequence of a well defined structural phase transition, leading to the formation of a spanning cluster of bonded particles. The dynamical glass transition, instead, is not accompanied by any clear structural signature. Nevertheless, both transitions are characterized by the emergence of dynamical heterogeneities. Reviewing recent results from numerical simulations, we discuss the behavior of dynamical heterogeneities in different systems and show that a clear connection with the structure exists in the case of gels. The emerging picture may be also relevant for the more elusive case of glasses. We show, as an example, that the relaxation process of a simple glass-forming model can be related to a reverse percolation transition and discuss further perspective in this direction.

Combustion Theory and Modelling, Oct 20, 2016

Particle nucleation remains one of the most intriguing steps in the process of particle formation... more Particle nucleation remains one of the most intriguing steps in the process of particle formation in flames. Although stacking/clustering of polycyclic aromatic hydrocarbons (PAHs) has been identified as a key step in the nucleation process, uncertainties remain about the size of the PAHs undergoing clustering, the organisation of the PAHs in the forming clusters and the factors affecting the relative amounts of order and disorder present in the texture organisation. A molecular dynamics approach is presented to study the influence of the molecular weight and structure of PAHs on the nucleation and coagulation processes and on the morphology of the formed clusters. Two different types of macromolecules have been analysed: pericondensed aromatic hydrocarbons (PCAHs) and aromatic aliphatic linked hydrocarbons (AALHs), known to be present in flame environments depending on flame temperature, equivalence ratio and fuel chemical structure. Clustering of six organic molecules has been analysed at two extreme temperatures, namely 500 K and 1500 K. The six molecules have been chosen on the basis of their molecular weight (pyrene and coronene) and molecular structure (single molecules, covalent-bonded dimers and covalent-bonded trimers). Nucleation of single pyrene molecules is negligible at low temperature and practically absent at high temperature. Conversely, nucleation of single coronene molecules involves 33% of the initial molecules at low temperature. Molecules within the clusters are highly mobile at flame temperatures and just 5% of the initial molecules are in clusters. The presence of covalent bonds among the aromatic sub-units improves clustering and growth, both for pyrene and coronene sub-units. Looking at the structure and the fractal dimensionality of the formed clusters, an enhancement of the disorder of the clusters is observed in the case of the AALHs (dimers and trimers) with an increased number of molecules not arranged in parallel planes. The same behaviour is found for the higher temperature.

arXiv (Cornell University), Sep 2, 2014

The presence of phenomena analogous to phase transition in Statistical Mechanics, has been sugges... more The presence of phenomena analogous to phase transition in Statistical Mechanics, has been suggested in the evolution of a polygenic trait under stabilizing selection, mutation and genetic drift. By using numerical simulations of a model system, we analyze the evolution of a population of N diploid hermaphrodites in random mating regime. The population evolves under the effect of drift, selective pressure in form of viability on an additive polygenic trait, and mutation. The analysis allows to determine a phase diagram in the plane of mutation rate and strength of selection. The involved pattern of phase transitions is characterized by a line of critical points for weak selective pressure (smaller than a threshold), whereas discontinuous phase transitions, characterized by metastable hysteresis, are observed for strong selective pressure. A finite size scaling analysis suggests the analogy between our system and the mean field Ising model for selective pressure approaching the threshold from weaker values. In this framework, the mutation rate, which allows the system to explore the accessible microscopic states, is the parameter controlling the transition from large heterozygosity (disordered phase) to small heterozygosity (ordered one).

Springer eBooks, 2013

We construct a stochastic SIR model for influenza spreading on a D-dimensional lattice, which rep... more We construct a stochastic SIR model for influenza spreading on a D-dimensional lattice, which represents the underlying contact network of individuals. An age distributed population is placed on the lattice and can move on it. The displacement from a site to a nearest neighbor empty site allows individuals to change the number and identities of their contacts. The model is validated against the age-distributed Italian epidemiological data for the influenza A(H1N1) during the 2009/2010 season, with sensible predictions for the epidemiological parameters.

Physical review, Dec 10, 2002

We discuss a Statistical Mechanics approach in the manner of Edwards to the "inherent states" (de... more We discuss a Statistical Mechanics approach in the manner of Edwards to the "inherent states" (defined as the stable configurations in the potential energy landscape) of glassy systems and granular materials. We show that at stationarity the inherent states are distributed according a generalized Gibbs measure obtained assuming the validity of the principle of maximum entropy, under suitable constraints. In particular we consider three lattice models (a diluted Spin Glass, a monodisperse hard-sphere system under gravity and a hard-sphere binary mixture under gravity) undergoing a schematic "tap dynamics", showing via Monte Carlo calculations that the time average of macroscopic quantities over the tap dynamics and over such a generalized distribution coincide. We also discuss about the general validity of this approach to non thermal systems.

WORLD SCIENTIFIC eBooks, Oct 1, 2007

arXiv (Cornell University), Sep 2, 2014

The presence of phenomena analogous to phase transition in Statistical Mechanics, has been sugges... more The presence of phenomena analogous to phase transition in Statistical Mechanics, has been suggested in the evolution of a polygenic trait under stabilizing selection, mutation and genetic drift. By using numerical simulations of a model system, we analyze the evolution of a population of N diploid hermaphrodites in random mating regime. The population evolves under the effect of drift, selective pressure in form of viability on an additive polygenic trait, and mutation. The analysis allows to determine a phase diagram in the plane of mutation rate and strength of selection. The involved pattern of phase transitions is characterized by a line of critical points for weak selective pressure (smaller than a threshold), whereas discontinuous phase transitions, characterized by metastable hysteresis, are observed for strong selective pressure. A finite size scaling analysis suggests the analogy between our system and the mean field Ising model for selective pressure approaching the threshold from weaker values. In this framework, the mutation rate, which allows the system to explore the accessible microscopic states, is the parameter controlling the transition from large heterozygosity (disordered phase) to small heterozygosity (ordered one).

Physical Review E, Feb 22, 2006

The increase of the viscosity, which is observed in attractive colloidal systems by varying the t... more The increase of the viscosity, which is observed in attractive colloidal systems by varying the temperature or the volume fraction, can be related to the formation of structures due to particle aggregation. In particular we have studied the non trivial dependence of the viscosity from the temperature and the volume fraction in the copolymer-micellar system L64. The comparison of the experimental data with the results of numerical simulations in a simple model for gelation phenomena suggests that this intriguing behavior can be explained in terms of cluster formation and that this picture can be quite generally extended to other attractive colloidal systems.

Zenodo (CERN European Organization for Nuclear Research), Apr 27, 2023

info:eu-repo/semantics/nonPublishe

Unifying Concepts in Granular Media and Glasses, 2004

This chapter introduces a minimal model for gelling systems and examines the dynamic behavior by ... more This chapter introduces a minimal model for gelling systems and examines the dynamic behavior by means of numerical simulations. At the gelation transition, a viscous liquid transforms to an elastic disordered solid. This corresponds to the formation of a spanning structure that makes the system able to bear stress. In polymer systems, the structure formation is due to chemical bonding, producing a polymerization process. The gelling system typically displays critical power law behavior in the viscoelastic response and slow dynamics. The relaxation functions show, at long times, a stretched exponential decay, and at the gel point the relaxation process becomes critically slow. This suggests a unifying picture for gelation phenomena, connecting classical gelation and recent results on colloidal systems. By varying the model parameters, the slow dynamics present a crossover from the classical polymer gelation to dynamics more typical of colloidal systems, with a glassy regime that is interpreted in terms of effective clusters.

The Journal of Chemical Physics, 2009

A theoretical and numerically study of dynamical properties in the sol-gel transition is presente... more A theoretical and numerically study of dynamical properties in the sol-gel transition is presented. In particular, the complex phenomenology observed experimentally and numerically in gelling systems is reproduced in the framework of percolation theory, under simple assumptions on the relaxation of single clusters. By neglecting the correlation between particles belonging to different clusters, the quantities of interest (such as the self Intermediate Scattering Function, the dynamical susceptibility, the Van-Hove function, and the non-Gaussian parameter) are written as superposition of those due to single clusters. Connection between these behaviours and the critical exponents of percolation are given. The theoretical predictions are checked in a model for permanent gels, where bonds between monomers are described by a FENE potential. The data obtained in the numerical simulations are in good agreement with the analytical predictions.

Physica A: Statistical Mechanics and its Applications

We determine the dimensional dependence of the percolative exponents of the jamming transition vi... more We determine the dimensional dependence of the percolative exponents of the jamming transition via numerical simulations in four and five spatial dimensions. These novel results complement literature ones, and establish jamming as a mixed first-order percolation transition, with critical exponents β = 0, γ = 2, α = 0 and the finite size scaling exponent ν * = 2/d for values of the spatial dimension d ≥ 2. We argue that the upper critical dimension is d u = 2 and the connectedness length exponent is ν = 1.

Journal of Physics: Condensed Matter, 2009

We describe the sol-gel transition by introducing an order parameter, defined as the average of l... more We describe the sol-gel transition by introducing an order parameter, defined as the average of local variables, and its fluctuations. It can be shown that these quantities are related to percolation quantities, but in principle they can be measured without resorting to connectivity properties. In this framework it appears that the dynamical transition associated with gelation is a real thermodynamic transition, as happens in spin glasses. The strong analogies between the sol-gel transition and the spin glass transition are also discussed.

Nucleation and Atmospheric Aerosols, 2013

ABSTRACT Using molecular dynamics simulations, we study a DLVO-type model for attractive colloida... more ABSTRACT Using molecular dynamics simulations, we study a DLVO-type model for attractive colloidal systems. In particular we focus on the crossover from the gel-like regime, at low volume fraction, to the glassy-like regime, at higher volume fraction. In such crossover region, some features of chemical gels and some features of glassy systems are present. The former are due to long living clusters the latter to crowding effects, which both slow down the relaxation process. The contribution of the long living clusters is obtained from the fluctuations of the self-overlap, χ4(t), by summing only over pairs of particles, linked by persistent bonds (present at both times 0 and time t), the crowding contribution is instead obtained from the remaining pairs of particles. For small volume fractions and low enough temperature, where the lifetime of the bonds is dominant, essentially the cluster contribution is present. At higher volume fraction, where bond lifetime and relaxation time start to be of the same order of magnitude, both contributions are manifest. The dependence of these two contributions on the length scale a, which appears in the definition of χ4(t), is also interesting. The clustering contribution is highly suppressed as a decreases, like in chemical gels, while the contribution due to crowding has a non-monotonic behaviour, and it is maximum at intermediate values of a.

Journal of Statistical Mechanics: Theory and Experiment, Jul 11, 2016

The dynamical arrest of gels is the consequence of a well defined structural phase transition, le... more The dynamical arrest of gels is the consequence of a well defined structural phase transition, leading to the formation of a spanning cluster of bonded particles. The dynamical glass transition, instead, is not accompanied by any clear structural signature. Nevertheless, both transitions are characterized by the emergence of dynamical heterogeneities. Reviewing recent results from numerical simulations, we discuss the behavior of dynamical heterogeneities in different systems and show that a clear connection with the structure exists in the case of gels. The emerging picture may be also relevant for the more elusive case of glasses. We show, as an example, that the relaxation process of a simple glass-forming model can be related to a reverse percolation transition and discuss further perspective in this direction.

Combustion Theory and Modelling, Oct 20, 2016

Particle nucleation remains one of the most intriguing steps in the process of particle formation... more Particle nucleation remains one of the most intriguing steps in the process of particle formation in flames. Although stacking/clustering of polycyclic aromatic hydrocarbons (PAHs) has been identified as a key step in the nucleation process, uncertainties remain about the size of the PAHs undergoing clustering, the organisation of the PAHs in the forming clusters and the factors affecting the relative amounts of order and disorder present in the texture organisation. A molecular dynamics approach is presented to study the influence of the molecular weight and structure of PAHs on the nucleation and coagulation processes and on the morphology of the formed clusters. Two different types of macromolecules have been analysed: pericondensed aromatic hydrocarbons (PCAHs) and aromatic aliphatic linked hydrocarbons (AALHs), known to be present in flame environments depending on flame temperature, equivalence ratio and fuel chemical structure. Clustering of six organic molecules has been analysed at two extreme temperatures, namely 500 K and 1500 K. The six molecules have been chosen on the basis of their molecular weight (pyrene and coronene) and molecular structure (single molecules, covalent-bonded dimers and covalent-bonded trimers). Nucleation of single pyrene molecules is negligible at low temperature and practically absent at high temperature. Conversely, nucleation of single coronene molecules involves 33% of the initial molecules at low temperature. Molecules within the clusters are highly mobile at flame temperatures and just 5% of the initial molecules are in clusters. The presence of covalent bonds among the aromatic sub-units improves clustering and growth, both for pyrene and coronene sub-units. Looking at the structure and the fractal dimensionality of the formed clusters, an enhancement of the disorder of the clusters is observed in the case of the AALHs (dimers and trimers) with an increased number of molecules not arranged in parallel planes. The same behaviour is found for the higher temperature.

arXiv (Cornell University), Sep 2, 2014

The presence of phenomena analogous to phase transition in Statistical Mechanics, has been sugges... more The presence of phenomena analogous to phase transition in Statistical Mechanics, has been suggested in the evolution of a polygenic trait under stabilizing selection, mutation and genetic drift. By using numerical simulations of a model system, we analyze the evolution of a population of N diploid hermaphrodites in random mating regime. The population evolves under the effect of drift, selective pressure in form of viability on an additive polygenic trait, and mutation. The analysis allows to determine a phase diagram in the plane of mutation rate and strength of selection. The involved pattern of phase transitions is characterized by a line of critical points for weak selective pressure (smaller than a threshold), whereas discontinuous phase transitions, characterized by metastable hysteresis, are observed for strong selective pressure. A finite size scaling analysis suggests the analogy between our system and the mean field Ising model for selective pressure approaching the threshold from weaker values. In this framework, the mutation rate, which allows the system to explore the accessible microscopic states, is the parameter controlling the transition from large heterozygosity (disordered phase) to small heterozygosity (ordered one).

Springer eBooks, 2013

We construct a stochastic SIR model for influenza spreading on a D-dimensional lattice, which rep... more We construct a stochastic SIR model for influenza spreading on a D-dimensional lattice, which represents the underlying contact network of individuals. An age distributed population is placed on the lattice and can move on it. The displacement from a site to a nearest neighbor empty site allows individuals to change the number and identities of their contacts. The model is validated against the age-distributed Italian epidemiological data for the influenza A(H1N1) during the 2009/2010 season, with sensible predictions for the epidemiological parameters.

Physical review, Dec 10, 2002

We discuss a Statistical Mechanics approach in the manner of Edwards to the "inherent states" (de... more We discuss a Statistical Mechanics approach in the manner of Edwards to the "inherent states" (defined as the stable configurations in the potential energy landscape) of glassy systems and granular materials. We show that at stationarity the inherent states are distributed according a generalized Gibbs measure obtained assuming the validity of the principle of maximum entropy, under suitable constraints. In particular we consider three lattice models (a diluted Spin Glass, a monodisperse hard-sphere system under gravity and a hard-sphere binary mixture under gravity) undergoing a schematic "tap dynamics", showing via Monte Carlo calculations that the time average of macroscopic quantities over the tap dynamics and over such a generalized distribution coincide. We also discuss about the general validity of this approach to non thermal systems.

WORLD SCIENTIFIC eBooks, Oct 1, 2007

arXiv (Cornell University), Sep 2, 2014

The presence of phenomena analogous to phase transition in Statistical Mechanics, has been sugges... more The presence of phenomena analogous to phase transition in Statistical Mechanics, has been suggested in the evolution of a polygenic trait under stabilizing selection, mutation and genetic drift. By using numerical simulations of a model system, we analyze the evolution of a population of N diploid hermaphrodites in random mating regime. The population evolves under the effect of drift, selective pressure in form of viability on an additive polygenic trait, and mutation. The analysis allows to determine a phase diagram in the plane of mutation rate and strength of selection. The involved pattern of phase transitions is characterized by a line of critical points for weak selective pressure (smaller than a threshold), whereas discontinuous phase transitions, characterized by metastable hysteresis, are observed for strong selective pressure. A finite size scaling analysis suggests the analogy between our system and the mean field Ising model for selective pressure approaching the threshold from weaker values. In this framework, the mutation rate, which allows the system to explore the accessible microscopic states, is the parameter controlling the transition from large heterozygosity (disordered phase) to small heterozygosity (ordered one).

Physical Review E, Feb 22, 2006

The increase of the viscosity, which is observed in attractive colloidal systems by varying the t... more The increase of the viscosity, which is observed in attractive colloidal systems by varying the temperature or the volume fraction, can be related to the formation of structures due to particle aggregation. In particular we have studied the non trivial dependence of the viscosity from the temperature and the volume fraction in the copolymer-micellar system L64. The comparison of the experimental data with the results of numerical simulations in a simple model for gelation phenomena suggests that this intriguing behavior can be explained in terms of cluster formation and that this picture can be quite generally extended to other attractive colloidal systems.

Zenodo (CERN European Organization for Nuclear Research), Apr 27, 2023

info:eu-repo/semantics/nonPublishe

Unifying Concepts in Granular Media and Glasses, 2004

This chapter introduces a minimal model for gelling systems and examines the dynamic behavior by ... more This chapter introduces a minimal model for gelling systems and examines the dynamic behavior by means of numerical simulations. At the gelation transition, a viscous liquid transforms to an elastic disordered solid. This corresponds to the formation of a spanning structure that makes the system able to bear stress. In polymer systems, the structure formation is due to chemical bonding, producing a polymerization process. The gelling system typically displays critical power law behavior in the viscoelastic response and slow dynamics. The relaxation functions show, at long times, a stretched exponential decay, and at the gel point the relaxation process becomes critically slow. This suggests a unifying picture for gelation phenomena, connecting classical gelation and recent results on colloidal systems. By varying the model parameters, the slow dynamics present a crossover from the classical polymer gelation to dynamics more typical of colloidal systems, with a glassy regime that is interpreted in terms of effective clusters.

The Journal of Chemical Physics, 2009

A theoretical and numerically study of dynamical properties in the sol-gel transition is presente... more A theoretical and numerically study of dynamical properties in the sol-gel transition is presented. In particular, the complex phenomenology observed experimentally and numerically in gelling systems is reproduced in the framework of percolation theory, under simple assumptions on the relaxation of single clusters. By neglecting the correlation between particles belonging to different clusters, the quantities of interest (such as the self Intermediate Scattering Function, the dynamical susceptibility, the Van-Hove function, and the non-Gaussian parameter) are written as superposition of those due to single clusters. Connection between these behaviours and the critical exponents of percolation are given. The theoretical predictions are checked in a model for permanent gels, where bonds between monomers are described by a FENE potential. The data obtained in the numerical simulations are in good agreement with the analytical predictions.

Physica A: Statistical Mechanics and its Applications

We determine the dimensional dependence of the percolative exponents of the jamming transition vi... more We determine the dimensional dependence of the percolative exponents of the jamming transition via numerical simulations in four and five spatial dimensions. These novel results complement literature ones, and establish jamming as a mixed first-order percolation transition, with critical exponents β = 0, γ = 2, α = 0 and the finite size scaling exponent ν * = 2/d for values of the spatial dimension d ≥ 2. We argue that the upper critical dimension is d u = 2 and the connectedness length exponent is ν = 1.

Journal of Physics: Condensed Matter, 2009

We describe the sol-gel transition by introducing an order parameter, defined as the average of l... more We describe the sol-gel transition by introducing an order parameter, defined as the average of local variables, and its fluctuations. It can be shown that these quantities are related to percolation quantities, but in principle they can be measured without resorting to connectivity properties. In this framework it appears that the dynamical transition associated with gelation is a real thermodynamic transition, as happens in spin glasses. The strong analogies between the sol-gel transition and the spin glass transition are also discussed.