Force distributions and force chains in random stiff fiber networks

We study the elasticity of random stiff fiber networks. The elastic response of the fibers is characterized by a central force stretching stiffness as well as a bending stiffness that acts transverse to the fiber contour. Previous studies have shown that this model displays an anomalous elastic regime where the stretching mode is fully frozen out and the elastic energy is completely dominated by the bending mode. We demonstrate by simulations and scaling arguments that, in contrast to the bending dominated \emph{elastic energy}, the equally important \emph{elastic forces} are to a large extent stretching dominated. By characterizing these forces on microscopic, mesoscopic and macroscopic scales we find two mechanisms of how forces are transmitted in the network. While forces smaller than a threshold $F_c$ are effectively balanced by a homogeneous background medium, forces larger than $F_c$ are found to be heterogeneously distributed throughout the sample, giving rise to highly localized force-chains known from granular media.Comment: 7 pages, 7 figures, final version as publishe

Kramers-Kronig, Bode, and the meaning of zero

The implications of causality, as captured by the Kramers-Kronig relations between the real and imaginary parts of a linear response function, are familiar parts of the physics curriculum. In 1937, Bode derived a similar relation between the magnitude (response gain) and phase. Although the Kramers-Kronig relations are an equality, Bode's relation is effectively an inequality. This perhaps-surprising difference is explained using elementary examples and ultimately traces back to delays in the flow of information within the system formed by the physical object and measurement apparatus.Comment: 8 pages; American Journal of Physics, to appea

Non-universality of elastic exponents in random bond-bending networks

We numerically investigate the rigidity percolation transition in two-dimensional flexible, random rod networks with freely rotating cross-links. Near the transition, networks are dominated by bending modes and the elastic modulii vanish with an exponent f=3.0\pm0.2, in contrast with central force percolation which shares the same geometric exponents. This indicates that universality for geometric quantities does not imply universality for elastic ones. The implications of this result for actin-fiber networks is discussed.Comment: 4 pages, 3 figures, minor clarifications and amendments. To appear in PRE Rap. Com

Scaling of impact fragmentation near the critical point

We investigated two-dimensional brittle fragmentation with a flat impact experimentally, focusing on the low impact energy region near the fragmentation-critical point. We found that the universality class of fragmentation transition disagreed with that of percolation. However, the weighted mean mass of the fragments could be scaled using the pseudo-control parameter multiplicity. The data for highly fragmented samples included a cumulative fragment mass distribution that clearly obeyed a power-law. The exponent of this power-law was 0.5 and it was independent of sample size. The fragment mass distributions in this regime seemed to collapse into a unified scaling function using weighted mean fragment mass scaling. We also examined the behavior of higher order moments of the fragment mass distributions, and obtained multi-scaling exponents that agreed with those of the simple biased cascade model.Comment: 6 pages, 6 figure

Steady-State Cracks in Viscoelastic Lattice Models II

We present the analytic solution of the Mode III steady-state crack in a square lattice with piecewise linear springs and Kelvin viscosity. We show how the results simplify in the limit of large width. We relate our results to a model where the continuum limit is taken only along the crack direction. We present results for small velocity, and for large viscosity, and discuss the structure of the critical bifurcation for small velocity. We compute the size of the process zone wherein standard continuum elasticity theory breaks down.Comment: 17 pages, 3 figure

Yield-biodiversity trade-off in patchy fields of Miscanthus × giganteus

Increasing crop productivity to meet rising demands for food and energy, but doing so in an environmentally sustainable manner, is one of the greatest challenges for agriculture to date. In Ireland, Miscanthus 9 giganteus has the potential to become a major feedstock for bioenergy production, but the economic feasibility of its cultivation depends on high yields. Miscanthus fields can have a large number of gaps in crop cover, adversely impacting yield and hence economic viability. Predominantly positive effects of Miscanthus on biodiversity reported from previous research might be attributable to high crop patchiness, particularly during the establishment phase. The aim of this research was to assess crop patchiness on a field scale and to analyse the relationship between Miscanthus yield and species richness and abundance of selected taxa of farmland wildlife. For 14 Miscanthus fields at the end of their establishment phase (4–5 years after planting), which had been planted either on improved grassland (MG) or tilled arable land (MT), we determined patchiness of the crop cover, percentage light penetration (LP) to the lower canopy, Miscanthus shoot density and height, vascular plants and epigeic arthropods. Plant species richness and noncrop vegetation cover in Miscanthus fields increased with increasing patchiness, due to higher levels of LP to the lower canopy. The species richness of ground beetles and the activity density of spiders followed the increase in vegetation cover. Plant species richness and activity density of spiders on both MT and MG fields, as well as vegetation cover and activity density of ground beetles on MG fields, were negatively associated with Miscanthus yield. In conclusion, positive effects of Miscanthus on biodiversity can diminish with increasing productivity. This matter needs to be considered when assessing the relative ecological impacts of developing biomass crops in comparison with other land use. Keywords: Araneae, Carabidae, crop cover, light penetration, Miscanthus establishment, patchiness, vascular plants, vegetation coverYield-biodiversity trade-off in patchy fields of Miscanthus × giganteuspublishedVersio

Transition from damage to fragmentation in collision of solids

We investigate fracture and fragmentation of solids due to impact at low energies using a two-dimensional dynamical model of granular solids. Simulating collisions of two solid discs we show that, depending on the initial energy, the outcome of a collision process can be classified into two states: a damaged and a fragmented state with a sharp transition in between. We give numerical evidence that the transition point between the two states behaves as a critical point, and we discuss the possible mechanism of the transition.Comment: Revtex, 12 figures included. accepted by Phys. Rev.