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3D computer simulations and experiments are employed to study random packings of compressible spherical grains under external confining stress. In the rigid ball limit, we find a continuous transition in which the stress vanishes as (straight phi-straight phi(c))(beta), where straight phi is the (solid phase) volume density. The value of straight phi(c) depends on whether the grains interact via only normal forces (giving rise to random close packings) or by a combination of normal and friction generated transverse forces (producing random loose packings). In both cases, near the transition, the system's response is controlled by localized force chains.

Experiments on isotropic compression of a granular assembly of spheres show that the shear and bulk moduli vary with the confining pressure faster than the 1/3 power law predicted by HertzMindlin effective medium theories (EMT) of contact elasticity. Moreover, the ratio between the moduli is found to be larger than the prediction of the elastic theory by a constant value. The understanding of these discrepancies has been a longstanding question in the field of granular matter.Here we perform a test of the applicability of elasticity theory to granular materials. We perform sound propagation experiments, numerical simulations and theoretical studies to understand the elastic response of a deforming granular assembly of soft spheres under isotropic loading. Our results for the behavior of the elastic moduli of the system agree very well with experiments. We show that the elasticity partially describes the experimental and numerical results for a system under compressional loads. However, it drastically fails for systems under shear perturbations, particularly for packings without tangential forces and friction. Our work indicates that a correct treatment should include not only the purely elastic response but also collective relaxation mechanisms related to structural disorder and nonaffine motion of grains.

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Experimentally it is known that the bulk modulus, K, and shear modulus, µ, of a granular assembly of elastic spheres increase with pressure, p, faster than the p 1/3 law predicted by effective medium theory (EMT) based on Hertz-Mindlin contact forces. Further, the ratio K/µ is found to be roughly pressure independent but the measured values are considerably larger than the EMT predictions. To understand the origin of these discrepancies, we have undertaken numerical simulations of a granular assembly of spherical elastic grains. Our results for K(p) and µ(p) are in good agreement with the existing experimental data. We show, also, that EMT can describe their pressure dependence if one takes into account the fact that the number of grain-grain contacts increases with p. Most important, the affine assumption (which underlies EMT), is found to be valid for K(p) but to breakdown seriously for µ(p). This explains why the experimental and numerical values of µ(p) are much smaller than the EMT predictions.

During development, large numbers of cells die by a nonpathological process referred to as programmed cell death. In many tissues, dying cells display similar changes in morphology and chromosomal DNA organization, which has been termed apoptosis. Apoptosis is such a widely documented phenomenon that many authors have assumed all programmed cell deaths occur by this process. Two well-characterized model systems for programmed cell death are (i) the death of T cells during negative selection in the mouse thymus and (ii) the loss of intersegmental muscles of the moth Manduca sexta at the end of metamorphosis. In this report we compare the patterns of cell death displayed by T cells and the intersegmental muscles and find that they differ in terms of cell-surface morphology, nuclear ultrastructure, DNA fragmentation, and polyubiquitin gene expression. Unlike the T cells, which are known to die via apoptosis, we find that the intersegmental muscles display few of the features that characterize apoptosis. These data suggest that more than one cell death mechanism is used during development.