results for au:Carmona_H in:cond-mat

- May 16 2018 cond-mat.stat-mech arXiv:1805.05892v1We investigate the dynamics of overdamped $D$-dimensional systems of particles repulsively interacting through short-ranged power-law potentials, $V(r)\sim r^{-\lambda}\;(\lambda/D>1)$. We show that such systems obey a non-linear diffusion equation, and that their stationary state extremizes a $q$-generalized nonadditive entropy. Here we focus on the dynamical evolution of these systems. Our first-principle $D=1,2$ many-body numerical simulations (based on Newton's law) confirm the predictions obtained from the time-dependent solution of the non-linear diffusion equation, and show that the one-particle space-distribution $P(x,t)$ appears to follow a compact-support $q$-Gaussian form, with $q=1-\lambda/D$. We also calculate the velocity distributions $P(v_x,t)$ and, interestingly enough, they follow the same $q$-Gaussian form (apparently precisely for $D=1$, and nearly so for $D=2$). The satisfactory match between the continuum description and the molecular dynamics simulations in a more general, time-dependent, framework neatly confirms the idea that the present dissipative systems indeed represent suitable applications of the $q$-generalized thermostatistical theory.
- Jun 14 2017 cond-mat.stat-mech arXiv:1706.03853v1We investigate the properties of a two-state sandpile model subjected to a confining potential in two dimensions. From the microdynamical description, we derive a diffusion equation, and find a stationary solution for the case of a parabolic confining potential. By studying the systems at different confining conditions, we observe two scale-invariant regimes. At a given confining potential strength, the cluster size distribution takes the form of a power law. This regime corresponds to the situation in which the density at the center of the system approaches the critical percolation threshold. The analysis of the fractal dimension of the largest cluster frontier provides evidence that this regime is reminiscent of gradient percolation. By increasing further the confining potential, most of the particles coalesce in a giant cluster, and we observe a regime where the jump size distribution takes the form of a power law. The onset of this second regime is signaled by a maximum in the fluctuation of energy.
- Mar 01 2016 cond-mat.stat-mech arXiv:1602.09086v1We propose a general coarse-graining method to derive a continuity equation that describes any dissipative system of repulsive particles interacting through short-ranged potentials. In our approach, the effect of particle-particle correlations is incorporated to the overall balance of energy, and a non-linear diffusion equation is obtained to represent the overdamped dynamics. In particular, when the repulsive interaction potential is a short-ranged power-law, our approach reveals a distinctive correspondence between particle-particle energy and the generalized thermostatistics of Tsallis for any non-positive value of the entropic index q. Our methodology can also be applied to microscopic models of superconducting vortices and complex plasma, where particle-particle correlations are pronounced at low concentrations. The resulting continuum descriptions provide elucidating and useful insights on the microdynamical behavior of these physical systems. The consistency of our approach is demonstrated by comparison with molecular dynamics simulations.
- Sep 04 2015 cond-mat.mtrl-sci cond-mat.soft arXiv:1509.00979v1The brittle fragmentation of spheres is studied numerically by a 3D Discrete Element Model. Large scale computer simulations are performed with models that consist of agglomerates of many spherical particles, interconnected by beam-truss elements. We focus on a detailed description of the fragmentation process and study several fragmentation mechanisms involved. The evolution of meridional cracks is studied in detail. These cracks are found to initiate in the inside of the specimen with quasi-periodic angular distribution and give a broad peak in the fragment mass distribution for large fragments that can be fitted by a two-parameter Weibull distribution. The results prove to be independent of the degree of disorder in the model, but mean fragment sizes scale with velocity. Our results reproduce many experimental observations of fragment shapes, impact energy dependence or mass distribution, and significantly improve the understanding of the fragmentation process for impact fracture since we have full access to the failure conditions and evolution.
- Sep 04 2015 cond-mat.mtrl-sci cond-mat.stat-mech arXiv:1509.01003v1Discrete element modelling (DEM) is one of the most efficient computational approaches to the fracture processes of heterogeneous materials on mesoscopic scales. From the dynamics of single crack propagation through the statistics of crack ensembles to the rapid fragmentation of materials DEM had a substantial contribution to our understanding over the past decades. Recently, the combination of DEM with other simulation techniques like Finite Element Modelling further extended the field of applicability. In this paper we briefly review the motivations and basic idea behind the DEM approach to cohesive particulate matter and then we give an overview of on-going developments and applications of the method focusing on two fields where recent success has been achieved. We discuss current challenges of this rapidly evolving field and outline possible future perspectives and debates.
- Dec 22 2014 cond-mat.mtrl-sci arXiv:1412.6300v1We investigate the fragmentation process of solid materials with crystalline and amorphous phases using the discrete element method. Damage initiates inside spherical samples above the contact zone in a region where the circumferential stress field is tensile. Cracks initiated in this region grow to form meridional planes. If the collision energy exceeds a critical value which depends on the material's internal structure, cracks reach the sample surface resulting in fragmentation. We show that this primary fragmentation mechanism is very robust with respect to the internal structure of the material. For all configurations, a sharp transition from the damage to the fragmentation regime is observed, with smaller critical collision energies for crystalline samples. The mass distribution of the fragments follows a power law for small fragments with an exponent that is characteristic for the branching merging process of unstable cracks. Moreover this exponent depends only on the dimensionally of the system and not on the micro structure.
- Apr 03 2014 cond-mat.stat-mech arXiv:1404.0632v1We investigate the behavior of a two-state sandpile model subjected to a confining potential in one and two dimensions. From the microdynamical description of this simple model with its intrinsic exclusion mechanism, it is possible to derive a continuum nonlinear diffusion equation that displays singularities in both the diffusion and drift terms. The stationary-state solutions of this equation, which maximizes the Fermi-Dirac entropy, are in perfect agreement with the spatial profiles of time-averaged occupancy obtained from model numerical simulations in one as well as in two dimensions. Surprisingly, our results also show that, regardless of dimensionality, the presence of a confining potential can lead to the emergence of typical attributes of critical behavior in the two-state sandpile model, namely, a power-law tail in the distribution of avalanche sizes.
- Jan 24 2008 cond-mat.mtrl-sci cond-mat.dis-nn arXiv:0801.3664v1One of the most important scaling laws of time dependent fracture is Basquin's law of fatigue, namely, that the lifetime of the system increases as a power law with decreasing external load amplitude, $t_f\sim \sigma_0^{-\alpha}$, where the exponent $\alpha$ has a strong material dependence. We show that in spite of the broad scatter of the Basquin exponent $\alpha$, the fatigue fracture of heterogeneous materials exhibits intriguing universal features. Based on stochastic fracture models we propose a generic scaling form for the macroscopic deformation and show that at the fatigue limit the system undergoes a continuous phase transition when changing the external load. On the microlevel, the fatigue fracture proceeds in bursts characterized by universal power law distributions. We demonstrate that in a range of systems, including deformation of asphalt, a realistic model of deformation, and a fiber bundle model, the system dependent details are contained in Basquin's exponent for time to failure, and once this is taken into account, remaining features of failure are universal.
- Nov 20 2007 cond-mat.stat-mech arXiv:0711.2993v1We study the brittle fragmentation of spheres by using a three-dimensional Discrete Element Model. Large scale computer simulations are performed with a model that consists of agglomerates of many particles, interconnected by beam-truss elements. We focus on the detailed development of the fragmentation process and study several fragmentation mechanisms. The evolution of meridional cracks is studied in detail. These cracks are found to initiate in the inside of the specimen with quasi-periodic angular distribution. The fragments that are formed when these cracks penetrate the specimen surface give a broad peak in the fragment mass distribution for large fragments that can be fitted by a two-parameter Weibull distribution. This mechanism can only be observed in 3D models or experiments. The results prove to be independent of the degree of disorder in the model. Our results significantly improve the understanding of the fragmentation process for impact fracture since besides reproducing the experimental observations of fragment shapes, impact energy dependence and mass distribution, we also have full access to the failure conditions and evolution.
- Oct 04 2006 cond-mat.dis-nn arXiv:cond-mat/0610080v2We study the fatigue fracture of disordered materials by means of computer simulations of a discrete element model. We extend a two-dimensional fracture model to capture the microscopic mechanisms relevant for fatigue, and we simulate the diametric compression of a disc shape specimen under a constant external force. The model allows to follow the development of the fracture process on the macro- and micro-level varying the relative influence of the mechanisms of damage accumulation over the load history and healing of microcracks. As a specific example we consider recent experimental results on the fatigue fracture of asphalt. Our numerical simulations show that for intermediate applied loads the lifetime of the specimen presents a power law behavior. Under the effect of healing, more prominent for small loads compared to the tensile strength of the material, the lifetime of the sample increases and a fatigue limit emerges below which no macroscopic failure occurs. The numerical results are in a good qualitative agreement with the experimental findings.
- Mar 07 2002 cond-mat.str-el arXiv:cond-mat/0203137v1The ground state of a classical two-dimensional (2D) system with finite number of charged particles, trapped by two positive impurities charges localized at a distance (zo) from the 2D plane and separated from each other by a distance xp are obtained. The impurities are allowed to carry more than one positive charge. This classical system can form a 2D-like classical molecule that exhibits structural transitions and spontaneous symmetry breaking as a function of the separation between the positive charges before it transforms into two independent 2D-like classical atoms. We also observe structural transitions as a function of the dielectric constant of the substrate which supports the charged particles, in addition to broken symmetry states and unbinding of particles.
- Nov 20 2000 cond-mat.soft cond-mat.stat-mech arXiv:cond-mat/0011308v1A simple model is presented for the appearance of attraction between two like charged polyions inside a polyelectrolyte solution. The polyions are modeled as rigid cylinders in a continuum dielectric solvent. The strong electrostatic interactions between the polyions and the counterions results in counterion condensation. If the two polyions are sufficiently close to each other their layers of condensed counterions can become correlated resulting in attraction between the macromolecules. To explore the counterion induced attraction we calculate the correlation functions for the condensed counterions. It is found that the correlations are of very short range. For the parameters specific to the double stranded DNA, the correlations and the attraction appear only when the surface-to-surface separation is less than 7 /AA.