J P Wittmer

Jamming, Force Chains, and Fragile Matter

Consider a concentrated colloidal suspension of hard particles under shear [Fig. 1(a)]. Above a certain threshold of stress, this system may jam [1]. (To observe such an effect, stir a concentrated suspension of cornstarch with a spoon.) Jamming apparently occurs because the particles form “force chains” along the compressional direction [1]. Even for spherical particles the lubrication films cannot prevent contacts; once these arise, an array or network of force chains can support the shear stress indefinitely [2]. By this criterion, the material is a solid. In this Letter, we propose some simple models of jammed systems like this, whose solidity stems directly from the applied stress itself. We argue that such materials may show fundamentally new mechanical properties, very different from those of conventional (elastic or elastoplastic) bodies. We start from a simple model of a force chain: a linear string of rigid particles in point contact. Crucially, this chain can only support loads along its own axis[Fig. 2(a)]: successive contacts must be collinear, with the forces along the line of contacts, to prevent torques on particles within the chain [3]. (Neither friction at the contacts nor particle aspherity can obviate this.) Let us now model a jammed colloid by an assembly of such force chains, characterized by a director n ,i n a sea of “spectator” particles, and incompressible solvent. (We ignore for the moment any “collisions” between force chains or deflections caused by weak interaction with the spectators.) In static equilibrium, with no body forces acting, the pressure tensor pijs› 2sijd is then

Topological effects in ring polymers: A computer simulation study

Unconcatenated, unknotted polymer rings in the melt are subject to strong interactions with neighboring chains due to the presence of topological constraints. We study this by computer simulation using the bond-fluctuation algorithm for chains with up to N=512 statistical segments at a volume fraction ensuremath{Phi}=0.5 and show that rings in the melt are more compact than Gaussian chains. A careful finite-size analysis of the average ring size Rensuremath{propto}

Stress Propagation and Arching in Static Sandpiles

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Topological effects in ring polymers. II. Influence of persistence length

yields an exponent ensuremath{nu}ensuremath{approxeq}0.39ifmmodepmelsetextpmfi{}0.03 in agreement with a Flory-like argument for the topological interactions. We show (using the same algorithm) that the dynamics of molten rings is similar to that of linear chains of the same mass, confirming recent experimental findings. The diffusion constant varies effectively as

Models of stress fluctuations in granular media

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Stresses in silos: comparison between theoretical models and new experiments

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Dynamical Monte Carlo study of equilibrium polymers: Static properties

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DEVELOPMENT OF STRESSES IN COHESIONLESS POURED SAND

and is slightly higher than that of corresponding linear chains. For the ring sizes considered (up to 256 statistical segments) we find only one characteristic time scale

Diffusive growth of a polymer layer by in situ polymerization

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Jamming and stress propagation in particulate matter

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