Are polymer melts "ideal"?

It is commonly accepted that in concentrated solutions or melts high-molecular weight polymers display random-walk conformational properties without long-range correlations between subsequent bonds. This absence of memory means, for instance, that the bond-bond correlation function, $P(s)$, of two bonds separated by $s$ monomers along the chain should exponentially decay with $s$. Presenting numerical results and theoretical arguments for both monodisperse chains and self-assembled (essentially Flory size-distributed) equilibrium polymers we demonstrate that some long-range correlations remain due to self-interactions of the chains caused by the chain connectivity and the incompressibility of the melt. Suggesting a profound analogy with the well-known long-range velocity correlations in liquids we find, for instance, $P(s)$ to decay algebraically as $s^{-3/2}$. Our study suggests a precise method for obtaining the statistical segment length \bstar in a computer experiment.Comment: 4 pages, 3 figure

Jamming and Stress Propagation in Particulate Matter

We present simple models of particulate materials whose mechanical integrity arises from a jamming process. We argue that such media are generically "fragile", that is, they are unable to support certain types of incremental loading without plastic rearrangement. In such models, fragility is naturally linked to the marginal stability of force chain networks (granular skeletons) within the material. Fragile matter exhibits novel mechanical responses that may be relevant to both jammed colloids and cohesionless assemblies of poured, rigid grains.Comment: LATEX, 3 Figures, elsart.cls style file, 11 page

Scale-free static and dynamical correlations in melts of monodisperse and Flory-distributed homopolymers: A review of recent bond-fluctuation model studies

It has been assumed until very recently that all long-range correlations are screened in three-dimensional melts of linear homopolymers on distances beyond the correlation length $\xi$ characterizing the decay of the density fluctuations. Summarizing simulation results obtained by means of a variant of the bond-fluctuation model with finite monomer excluded volume interactions and topology violating local and global Monte Carlo moves, we show that due to an interplay of the chain connectivity and the incompressibility constraint, both static and dynamical correlations arise on distances $r \gg \xi$. These correlations are scale-free and, surprisingly, do not depend explicitly on the compressibility of the solution. Both monodisperse and (essentially) Flory-distributed equilibrium polymers are considered.Comment: 60 pages, 49 figure

Stress Transmission through Three-Dimensional Ordered Granular Arrays

We measure the local contact forces at both the top and bottom boundaries of three-dimensional face-centered-cubic and hexagonal-close-packed granular crystals in response to an external force applied to a small area at the top surface. Depending on the crystal structure, we find markedly different results which can be understood in terms of force balance considerations in the specific geometry of the crystal. Small amounts of disorder are found to create additional structure at both the top and bottom surfaces.Comment: 9 pages including 9 figures (many in color) submitted to PR

Properties of layer-by-layer vector stochastic models of force fluctuations in granular materials

We attempt to describe the stress distributions of granular packings using lattice-based layer-by-layer stochastic models that satisfy the constraints of force and torque balance and non-tensile forces at each site. The inherent asymmetry in the layer-by-layer approach appears to lead to an asymmetric force distribution, in disagreement with both experiments and general symmetry considerations. The vertical force component probability distribution is robust and in agreement with predictions of the scalar q model while the distribution of horizontal force components is qualitatively different and depends on the details of implementation.Comment: 18 pages, 12 figures (with subfigures), 1 table. Uses revtex, epsfig,subfigure, and cite. Submitted to PRE. Plots have been bitmapped. High-resolution version is available. Email [email protected] or download from http://rainbow.uchicago.edu/~mbnguyen/research/vm.htm

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.Comment: 34 pages, 17 figures (eps), submitted to PRE, figures amended, partially to compare better to recent exp. wor

Vector lattice model for stresses in granular materials

A vector lattice model for stresses in granular materials is proposed. A two dimensional pile built by pouring from a point is constructed numerically according to this model. Remarkably, the pile violates the Mohr Coulomb stability criterion for granular matter, probably because of the inherent anisotropy of such poured piles. The numerical results are also compared to the earlier continuum FPA model and the (scalar) lattice $q$-model

Continuum limit of amorphous elastic bodies: A finite-size study of low frequency harmonic vibrations

The approach of the elastic continuum limit in small amorphous bodies formed by weakly polydisperse Lennard-Jones beads is investigated in a systematic finite-size study. We show that classical continuum elasticity breaks down when the wavelength of the sollicitation is smaller than a characteristic length of approximately 30 molecular sizes. Due to this surprisingly large effect ensembles containing up to N=40,000 particles have been required in two dimensions to yield a convincing match with the classical continuum predictions for the eigenfrequency spectrum of disk-shaped aggregates and periodic bulk systems. The existence of an effective length scale \xi is confirmed by the analysis of the (non-gaussian) noisy part of the low frequency vibrational eigenmodes. Moreover, we relate it to the {\em non-affine} part of the displacement fields under imposed elongation and shear. Similar correlations (vortices) are indeed observed on distances up to \xi~30 particle sizes.Comment: 28 pages, 13 figures, 3 table

Stress response inside perturbed particle assemblies

The effect of structural disorder on the stress response inside three dimensional particle assemblies is studied using computer simulations of frictionless sphere packings. Upon applying a localised, perturbative force within the packings, the resulting {\it Green's} function response is mapped inside the different assemblies, thus providing an explicit view as to how the imposed perturbation is transmitted through the packing. In weakly disordered arrays, the resulting transmission of forces is of the double-peak variety, but with peak widths scaling linearly with distance from the source of the perturbation. This behaviour is consistent with an anisotropic elasticity response profile. Increasing the disorder distorts the response function until a single-peak response is obtained for fully disordered packings consistent with an isotropic description.Comment: 8 pages, 7 figure captions To appear in Granular Matte

Organization of atomic bond tensions in model glasses

In order to understand whether internal stresses in glasses are correlated or randomly distributed, we study the organization of atomic bond tensions (normal forces between pairs of atoms). Measurements of the invariants of the atomic bond tension tensor in simulated 2D and 3D binary Lennard-Jones glasses, reveal new and unexpected correlations and provide support for Alexander's conjecture about the non-random character of internal stresses in amorphous solids