arXiv subjects

Srdjan Ostojic

Publications and source records attributed to Srdjan Ostojic.

25 records · Page 2Linked to original sources

arXiv2007

Universal Anisotropy in Force Networks under Shear

Scaling properties of patterns formed by large contact forces are studied as a function of the applied shear stress, in two-dimensional static packings generated from the force network ensemble. An anisotropic finite-size-scaling analysis shows that the applied shear does not affect the universal scaling properties of these patterns, but simply induces different length scales in the principal directions of the macroscopic stress tensor. The ratio of these length scales quantifies the anisotropy of the force networks, and is found not to depend on the details of the underlying contact network, in contrast with other properties such as the yield stress.

cond-mat.soft↗

arXiv2006

Elasticity from the Force Network Ensemble in Granular Media

Transmission of forces in static granular materials are studied within the framework of the force network ensemble, by numerically evaluating the mechanical response of hexagonal packings of frictionless grains and rectangular packings of frictional grains. In both cases, close to the point of application of the overload, the response is non-linear and displays two peaks, while at larger length-scales it is linear and elastic-like. The cross-over between these two behaviors occurs at a depth that increases with the magnitude of the overload, and decreases with increasing friction.

cond-mat.soft↗

arXiv2006

Scale invariance and universality of force networks in static granular matter

Force networks form the skeleton of static granular matter. They are the key ingredient to mechanical properties, such as stability, elasticity and sound transmission, which are of utmost importance for civil engineering and industrial processing. Previous studies have focused on the global structure of external forces (the boundary condition), and on the probability distribution of individual contact forces. The disordered spatial structure of the force network, however, has remained elusive so far. Here we report evidence for scale invariance of clusters of particles that interact via relatively strong forces. We analyzed granular packings generated by molecular dynamics simulations mimicking real granular matter; despite the visual variation, force networks for various values of the confining pressure and other parameters have identical scaling exponents and scaling function, and thus determine a universality class. Remarkably, the flat ensemble of force configurations--a simple generalization of equilibrium statistical mechanics--belongs to the same universality class, while some widely studied simplified models do not.

cond-mat.soft↗

arXiv2005

Universality Classes for Force Networks in Jammed Matter

We study the geometry of forces in some simple models for granular stackings. The information contained in geometry is complementary to that in the distribution of forces in a single inter-particle contact, which is more widely studied. We present a method which focuses on the fractal nature of the force network and find good evidence of scale invariance. The method enables us to distinguish universality classes characterized by critical exponents. Our approach can be applied to force networks in other athermal jammed systems.

cond-mat.stat-mech↗

arXiv2005

Response of a Hexagonal Granular Packing under a Localized External Force

We study the response of a two-dimensional hexagonal packing of rigid, frictionless spherical grains due to a vertically downward point force on a single grain at the top layer. We use a statistical approach, where each configuration of the contact forces is equally likely. We show that this problem is equivalent to a correlated $q$-model. We find that the response displays two peaks which lie precisely on the downward lattice directions emanating from the point of application of the force. With increasing depth, the magnitude of the peaks decreases, and a central peak develops. On the bottom of the pile, only the middle peak persists. The response of different system sizes exhibits self-similarity.

cond-mat.stat-mech↗

arXiv2005

Response of a Hexagonal Granular Packing under a Localized External Force: Exact Results

We study the response of a two-dimensional hexagonal packing of massless, rigid, frictionless spherical grains due to a vertically downward point force on a single grain at the top layer. We use a statistical approach, where each mechanically stable configuration of contact forces is equally likely. We show that this problem is equivalent to a correlated $q$-model. We find that the response is double-peaked, where the two peaks, sharp and single-grain diameter wide, lie on the two downward lattice directions emanating from the point of the application of the external force. For systems of finite size, the magnitude of these peaks decreases towards the bottom of the packing, while progressively a broader, central maximum appears between the peaks. The response behaviour displays a remarkable scaling behaviour with system size $N$: while the response in the bulk of the packing scales as $\frac{1}{N}$, on the boundary it is independent of $N$, so that in the thermodynamic limit only the peaks on the lattice directions persist. This qualitative behaviour is extremely robust, as demonstrated by our simulation results with different boundary conditions. We have obtained expressions of the response and higher correlations for any system size in terms of integers corresponding to an underlying discrete structure.

cond-mat.stat-mech↗

arXiv2004

Clustering in a One-dimensional Inelastic Lattice Gas

We analyze a lattice model closely related to the one-dimensional inelastic gas with periodic boundary condition. The one-dimensional inelastic gas tends to form high density clusters of particles with almost the same velocity, separated by regions of low density; plotted as a function of particle indices, the velocities of the gas particles exhibit sharp gradients, which we call shocks. Shocks and clusters are seen to form in the lattice model too, although no true positions of the particles are taken into account. The locations of the shocks in terms of the particle index show remarkable independence on the coefficient of restitution and the sequence of collisions used to update the system, but they do depend on the initial configuration of the particle velocities. We explain the microscopic origin of the shocks. We show that dynamics of the velocity profile inside a cluster satisfies a simple continuum equation, thereby allowing us to study cluster-cluster interactions at late times.

cond-mat.soft↗