Comment on ``Granular Entropy: Explicit Calculations for Planar Assemblies''

A Comment on the Letter by Raphael Blumenfeld and Sam F. Edwards, [Phys. Rev. Lett. 90, 114303 (2003)]

Random walk, cluster growth, and the morphology of urban conglomerations

We propose a new model of cluster growth according to which the probability that a new unit is placed in a point at a distance $r$ from the city center is a Gaussian with mean equal to the cluster radius and variance proportional to the mean, modulated by the local density $\rho(r)$. The model is analytically solvable in $d=2$ dimensions, where the density profile varies as a complementary error function. The model reproduces experimental observations relative to the morphology of cities, determined via an original analysis of digital maps with a very high spatial resolution, and helps understanding the emergence of vehicular traffic.Comment: Physica A. To appea

High--order jamming crossovers and density anomalies

We demonstrate the existence of high--order jamming crossovers in systems of particles with repulsive contact interactions, which originate from the collapse of successive coordination shells. At zero temperature, these crossovers induce an anomalous behavior of the bulk modulus, which varies non--monotonically with the density, while at finite temperature they induce density anomalies consisting in an increased diffusivity upon isothermal compression and in a negative thermal expansion coefficient. We rationalize the dependence of these crossovers on the softness of the interaction potential, and relate the jamming crossovers and the anomalous diffusivity through the investigation of the vibrational spectrum

Density anomalies and high-order jamming crossovers

Jamming crossovers occur at zero temperature in assemblies of particles interacting via finite range repulsive potentials, when on increasing the density particles make contacts with those of subsequent coordination shells. Density anomalies, including an increased diffusivity upon isothermal compression and a negative thermal expansion coefficient, are the finite temperature signatures of the jamming crossovers. In this manuscript we show that the jamming crossovers are correlated to an increase of the non affine response of the system to density changes, and clarify that jammed systems evolve upon compression through subsequent Eshlby-like plastic instabilities

Dynamics and instantaneous normal modes in a liquid with density anomalies

We investigate the relation between the dynamical features of a supercooled liquid and those of its potential energy landscape, focusing on a model liquid with density anomalies. We consider, at fixed temperature, pairs of state points with different density but the same diffusion constant, and find that surprisingly they have identical dynamical features at all length and time scales. This is shown by the collapse of their mean square displacements and of their self--intermediate scattering functions at different wavevectors. We then investigate how the features of the energy landscape change with density, and establish that state points with equal diffusion constant have different landscapes. In particular, we find a correlation between the fraction of instantaneous normal modes connecting different energy minima and the diffusion constant, but unlike in other systems these two quantities are not in one--to--one correspondence with each other, showing that additional landscape features must be relevant in determining the diffusion constant

Attraction tames two-dimensional melting: from continuous to discontinuous transitions

Two-dimensional systems may admit a hexatic phase and hexatic-liquid transitions of different natures. The determination of their phase diagrams proved challenging, and indeed those of hard-disks, hard regular polygons, and inverse power-law potentials, have been only recently clarified. In this context, the role of attractive forces is currently speculative, despite their prevalence at both the molecular and colloidal scale. Here we demonstrate, via numerical simulations, that attraction promotes a discontinuous melting scenario with no hexatic phase. At high-temperature, Lennard-Jones particles and attractive polygons follow the shape-dominated melting scenario observed in hard-disks and hard polygons, respectively. Conversely, all systems melt via a first-order transition with no hexatic phase at low temperature, where attractive forces dominate. The intermediate temperature melting scenario is shape-dependent. Our results suggest that, in colloidal experiments, the tunability of the strength of the attractive forces allows for the observation of different melting scenario in the same system.Comment: SI include

Role of cell deformability in the two-dimensional melting of biological tissues

The size and shape of a large variety of polymeric particles, including biological cells, star polymers, dendrimes, and microgels, depend on the applied stresses as the particles are extremely soft. In high-density suspensions these particles deform as stressed by their neighbors, which implies that the interparticle interaction becomes of many-body type. Investigating a two-dimensional model of cell tissue, where the single particle shear modulus is related to the cell adhesion strength, here we show that the particle deformability affects the melting scenario. On increasing the temperature, stiff particles undergo a first-order solid/liquid transition, while soft ones undergo a continuous solid/hexatic transition followed by a discontinuous hexatic/liquid transition. At zero temperature the melting transition driven by the decrease of the adhesion strength occurs through two continuous transitions as in the Kosterlitz, Thouless, Halperin, Nelson, and Young scenario. Thus, there is a range of adhesion strength values where the hexatic phase is stable at zero temperature, which suggests that the intermediate phase of the epithelial-to-mesenchymal transition could be hexatic type

Pacman Percolation and the Glass Transition

We investigate via Monte Carlo simulations the kinetically constrained Kob-Andersen lattice glass model showing that, contrary to current expectations, the relaxation process and the dynamical heterogeneities seems to be characterized by different time scales. Indeed, we found that the relaxation time is related to a reverse percolation transition, whereas the time of maximum heterogeneity is related to the spatial correlation between particles. This investigation leads to a geometrical interpretation of the relaxation processes and of the different observed time scales.Comment: 12 pages, 8 figures. arXiv admin note: text overlap with arXiv:1109.428