arXiv subjects

J. E. S. Socolar

Publications and source records attributed to J. E. S. Socolar.

5 recordsLinked to original sources

arXiv2007

Nonlinear elastic stress response in granular packings

We study the nonlinear elastic response of a two-dimensional material to a localized boundary force, with the particular goal of understanding the differences observed between isotropic granular materials and those with hexagonal anisotropy. Corrections to the classical Boussinesq result for the stresses in an infinite half-space of a linear, isotropic material are developed in a power series in inverse distance from the point of application of the force. The breakdown of continuum theory on scales of order of the grain size is modeled with phenomenological parameters characterizing the strengths of induced multipoles near the point of application of the external force. We find that the data of Geng et al. on isotropic and hexagonal packings of photoelastic grains can be fit within this framework. Fitting the hexagonal packings requires a choice of elastic coefficients with hexagonal anisotropy stronger than that of a simple ball and spring model. For both the isotropic and hexagonal cases, induced dipole and quadrupole terms produce propagation of stresses away from the vertical direction over short distances. The scale over which such propagation occurs is significantly enhanced by the nonlinearities that generate hexagonal anisotropy.

cond-mat.soft↗

arXiv2006

Network growth models and genetic regulatory networks

We study a class of growth algorithms for directed graphs that are candidate models for the evolution of genetic regulatory networks. The algorithms involve partial duplication of nodes and their links, together with innovation of new links, allowing for the possibility that input and output links from a newly created node may have different probabilities of survival. We find some counterintuitive trends as parameters are varied, including the broadening of indegree distribution when the probability for retaining input links is decreased. We also find that both the scaling of transcription factors with genome size and the measured degree distributions for genes in yeast can be reproduced by the growth algorithm if and only if a special seed is used to initiate the process.

q-bio.MN↗

arXiv2003

Anisotropy in granular media: classical elasticity and directed force chain network

A general approach is presented for understanding the stress response function in anisotropic granular layers in two dimensions. The formalism accommodates both classical anisotropic elasticity theory and linear theories of anisotropic directed force chain networks. Perhaps surprisingly, two-peak response functions can occur even for classical, anisotropic elastic materials, such as triangular networks of springs with different stiffnesses. In such cases, the peak widths grow linearly with the height of the layer, contrary to the diffusive spreading found in `stress-only' hyperbolic models. In principle, directed force chain networks can exhibit the two-peak, diffusively spreading response function of hyperbolic models, but all models in a particular class studied here are found to be in the elliptic regime.

cond-mat.stat-mech↗

arXiv2002

Directed force chain networks and stress response in static granular materials

A theory of stress fields in two-dimensional granular materials based on directed force chain networks is presented. A general equation for the densities of force chains in different directions is proposed and a complete solution is obtained for a special case in which chains lie along a discrete set of directions. The analysis and results demonstrate the necessity of including nonlinear terms in the equation. A line of nontrivial fixed point solutions is shown to govern the properties of large systems. In the vicinity of a generic fixed point, the response to a localized load shows a crossover from a single, centered peak at intermediate depths to two propagating peaks at large depths that broaden diffusively.

cond-mat↗

arXiv1993

Relaxation Oscillations in Model Sandpiles

We introduce a simple one-dimensional sandpile model that undergoes relaxation oscillations. A single model can account for self-organized critical behavior and relaxation oscillations, depending on the manner in which it is driven, mirroring the experimental situation for real sandpiles. The relaxation oscillations are robust with respect to minor modifications of the avalanche rules, including the application of probabilistic rules.

cond-mat↗