In the framework of schematic hard spheres lattice models we discuss Edwards' Statistical Mechani... more In the framework of schematic hard spheres lattice models we discuss Edwards' Statistical Mechanics approach to granular media. As this approach appears to hold here to a very good approximation, by analytical calculations of Edwards' partition function at a mean field level we derive the system phase diagram and show that ``jamming'' corresponds to a phase transition from a ``fluid'' to a ``glassy'' phase, observed when crystallization is avoided. The nature of such a ``glassy'' phase turns out to be the same found in mean field models for glass formers. In the same context, we also briefly discuss mixing/segregation phenomena of binary mixtures: the presence of fluid-crystal phase transitions drives segregation as a form of phase separation and, within a given phase, gravity can also induce a kind of ``vertical'' segregation, usually not associated to phase transitions.
We discuss some recent results on Statistical Mechanics approach to dense granular media. In part... more We discuss some recent results on Statistical Mechanics approach to dense granular media. In particular, by analytical mean field investigation we derive the phase diagram of monodisperse and bydisperse granular assemblies. We show that "jamming" corresponds to a phase ...
Complexity, Metastability and Nonextensivity - 31st Workshop of the International School of Solid State Physics, 2005
We discuss some recent results on Statistical Mechanics approach to dense granular media. In part... more We discuss some recent results on Statistical Mechanics approach to dense granular media. In particular, by analytical mean field investigation we derive the phase diagram of monodisperse and bydisperse granular assemblies. We show that "jamming" corresponds to a phase transition from a "fluid" to a "glassy" phase, observed when crystallization is avoided. The nature of such a "glassy" phase turns
The European Physical Journal Special Topics, 2014
ABSTRACT A long standing problem in glassy dynamics is the geometrical interpretation of clusters... more ABSTRACT A long standing problem in glassy dynamics is the geometrical interpretation of clusters and the role they play in the observed scaling laws. In this context, the mode-coupling theory (MCT) of type-A transition and the sol-gel transition are both characterized by a structural arrest to a disordered state in which the long-time limit of the correlator continuously approaches zero at the transition point. In this paper, we describe a cluster approach to the sol-gel transition and explore its predictions, including universal scaling laws and a new stretched relaxation regime close to criticality. We show that while MCT consistently describes gelation at mean-field level, the percolation approach elucidates the geometrical character underlying MCT scaling laws.
We study the dynamical behavior in chemical gelation, as the gelation threshold is approached fro... more We study the dynamical behavior in chemical gelation, as the gelation threshold is approached from the sol phase. On the basis of the heterogeneous diffusion due to the cluster size distribution, as expected by the percolation theory, we predict the long time decay of the self-overlap as a power law in time t(-3/2). Moreover, under the hypothesis that the cluster diffusion coefficient decreases in size as a power law, s(-x), the fluctuation of the self-overlap, χ(4)(t), exhibits growth at short time as t((3-τ)/x), where τ is the cluster size distribution critical exponent. At longer times, χ(4)(t) decays as t(-3/2) while, at intermediate times, it reaches a maximum at time t*, which scales as s*(x), where s* is the size of the critical cluster. Finally, the value of the maximum χ(4)(t*) scales as the mean cluster size. The theoretical predictions are in agreement with molecular dynamic calculations in a model system, where spherical monomers are bonded by a finite extendable nonlinear elastic (FENE) potential.
... Author(s): MASSIMO PICA CIAMARRA CNISM, Second University of Naples, 81031 Aversa (CE), Italy... more ... Author(s): MASSIMO PICA CIAMARRA CNISM, Second University of Naples, 81031 Aversa (CE), Italy ANTONIO DE CANDIA Dip. ... di Scienze Fisiche and Coherentia, Universitá di Napoli Federico II, via Cintia, 80129, Napoli, Italy MARIO NICODEMI Complexity Science Centre ...
We study the dynamical properties of a model for charged colloidal particles, performing molecula... more We study the dynamical properties of a model for charged colloidal particles, performing molecular dynamics simulations and observing the behavior of bond persistence functions, self-intermediate scattering functions at different wave vectors, and mean-square displacements of the particles, in three different regimes of the volume fraction. At the lowest volume fraction the system displays properties very similar to those of a gelling system, which can be interpreted in terms of the distribution of cluster sizes, with a peak in the dynamical susceptibility at the lowest wave vector. At the highest volume fraction, a percolating network of bonds is always present, and the system is strongly reminiscent of strong glasses, with the maximum in the dynamical susceptibility increasing when the temperature is lowered, and an Arrhenius dependence of the relaxation times. At intermediate volume fractions, a complex behavior is found, where both the distribution of cluster sizes and the intercluster correlations due to crowding are important.
In the framework of schematic hard spheres lattice models we discuss Edwards' Statistical Mechani... more In the framework of schematic hard spheres lattice models we discuss Edwards' Statistical Mechanics approach to granular media. As this approach appears to hold here to a very good approximation, by analytical calculations of Edwards' partition function at a mean field level we derive the system phase diagram and show that ``jamming'' corresponds to a phase transition from a ``fluid'' to a ``glassy'' phase, observed when crystallization is avoided. The nature of such a ``glassy'' phase turns out to be the same found in mean field models for glass formers. In the same context, we also briefly discuss mixing/segregation phenomena of binary mixtures: the presence of fluid-crystal phase transitions drives segregation as a form of phase separation and, within a given phase, gravity can also induce a kind of ``vertical'' segregation, usually not associated to phase transitions.
We discuss some recent results on Statistical Mechanics approach to dense granular media. In part... more We discuss some recent results on Statistical Mechanics approach to dense granular media. In particular, by analytical mean field investigation we derive the phase diagram of monodisperse and bydisperse granular assemblies. We show that "jamming" corresponds to a phase ...
Complexity, Metastability and Nonextensivity - 31st Workshop of the International School of Solid State Physics, 2005
We discuss some recent results on Statistical Mechanics approach to dense granular media. In part... more We discuss some recent results on Statistical Mechanics approach to dense granular media. In particular, by analytical mean field investigation we derive the phase diagram of monodisperse and bydisperse granular assemblies. We show that "jamming" corresponds to a phase transition from a "fluid" to a "glassy" phase, observed when crystallization is avoided. The nature of such a "glassy" phase turns
The European Physical Journal Special Topics, 2014
ABSTRACT A long standing problem in glassy dynamics is the geometrical interpretation of clusters... more ABSTRACT A long standing problem in glassy dynamics is the geometrical interpretation of clusters and the role they play in the observed scaling laws. In this context, the mode-coupling theory (MCT) of type-A transition and the sol-gel transition are both characterized by a structural arrest to a disordered state in which the long-time limit of the correlator continuously approaches zero at the transition point. In this paper, we describe a cluster approach to the sol-gel transition and explore its predictions, including universal scaling laws and a new stretched relaxation regime close to criticality. We show that while MCT consistently describes gelation at mean-field level, the percolation approach elucidates the geometrical character underlying MCT scaling laws.
We study the dynamical behavior in chemical gelation, as the gelation threshold is approached fro... more We study the dynamical behavior in chemical gelation, as the gelation threshold is approached from the sol phase. On the basis of the heterogeneous diffusion due to the cluster size distribution, as expected by the percolation theory, we predict the long time decay of the self-overlap as a power law in time t(-3/2). Moreover, under the hypothesis that the cluster diffusion coefficient decreases in size as a power law, s(-x), the fluctuation of the self-overlap, χ(4)(t), exhibits growth at short time as t((3-τ)/x), where τ is the cluster size distribution critical exponent. At longer times, χ(4)(t) decays as t(-3/2) while, at intermediate times, it reaches a maximum at time t*, which scales as s*(x), where s* is the size of the critical cluster. Finally, the value of the maximum χ(4)(t*) scales as the mean cluster size. The theoretical predictions are in agreement with molecular dynamic calculations in a model system, where spherical monomers are bonded by a finite extendable nonlinear elastic (FENE) potential.
... Author(s): MASSIMO PICA CIAMARRA CNISM, Second University of Naples, 81031 Aversa (CE), Italy... more ... Author(s): MASSIMO PICA CIAMARRA CNISM, Second University of Naples, 81031 Aversa (CE), Italy ANTONIO DE CANDIA Dip. ... di Scienze Fisiche and Coherentia, Universitá di Napoli Federico II, via Cintia, 80129, Napoli, Italy MARIO NICODEMI Complexity Science Centre ...
We study the dynamical properties of a model for charged colloidal particles, performing molecula... more We study the dynamical properties of a model for charged colloidal particles, performing molecular dynamics simulations and observing the behavior of bond persistence functions, self-intermediate scattering functions at different wave vectors, and mean-square displacements of the particles, in three different regimes of the volume fraction. At the lowest volume fraction the system displays properties very similar to those of a gelling system, which can be interpreted in terms of the distribution of cluster sizes, with a peak in the dynamical susceptibility at the lowest wave vector. At the highest volume fraction, a percolating network of bonds is always present, and the system is strongly reminiscent of strong glasses, with the maximum in the dynamical susceptibility increasing when the temperature is lowered, and an Arrhenius dependence of the relaxation times. At intermediate volume fractions, a complex behavior is found, where both the distribution of cluster sizes and the intercluster correlations due to crowding are important.
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