Geometric origin of mechanical properties of granular materials

Some remarkable generic properties, related to isostaticity and potential energy minimization, of equilibrium configurations of assemblies of rigid, frictionless grains are studied. Isostaticity -the uniqueness of the forces, once the list of contacts is known- is established in a quite general context, and the important distinction between isostatic problems under given external loads and isostatic (rigid) structures is presented. Complete rigidity is only guaranteed, on stability grounds, in the case of spherical cohesionless grains. Otherwise, the network of contacts might deform elastically in response to load increments, even though grains are rigid. This sets an uuper bound on the contact coordination number. The approximation of small displacements (ASD) allows to draw analogies with other model systems studied in statistical mechanics, such as minimum paths on a lattice. It also entails the uniqueness of the equilibrium state (the list of contacts itself is geometrically determined) for cohesionless grains, and thus the absence of plastic dissipation. Plasticity and hysteresis are due to the lack of such uniqueness and may stem, apart from intergranular friction, from small, but finite, rearrangements, in which the system jumps between two distinct potential energy minima, or from bounded tensile contact forces. The response to load increments is discussed. On the basis of past numerical studies, we argue that, if the ASD is valid, the macroscopic displacement field is the solution to an elliptic boundary value problem (akin to the Stokes problem).Comment: RevTex, 40 pages, 26 figures. Close to published paper. Misprints and minor errors correcte

Rotational dynamics of colloidal spheresprobed with fluorescence recovery after photobleaching

We report a polarized fluorescence recovery after photobleaching (pFRAP) method to measure the rotational dynamics of fluorescent colloids over a wide dynamic range. The method is based on the polarization anisotropy in the fluorescence intensity, generated by bleaching of fluorescently labeled particles with an intense pulse of linearly polarized laser light. The rotational mobilities of the fluorescent particles can be extracted from the relaxation kinetics of the postbleach fluorescence polarization anisotropy. Our pFRAP setup has access to correlation times over a range of time scales from tens of microseconds to tens of seconds, and is highly sensitive, so very low concentrations of labeled particles can be probed. We present a detailed description of the theoretical background of pFRAP. The performance of the equipment is demonstrated for fluorescent colloidal silica spheres, dispersed in pure solvents as well as in fd-virus suspensions

Static and dynamic patient characteristics as predictors of criminal recidivism: A prospective study in a Dutch forensic psychiatric sample

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