401 research outputs found

    Scaling of interfaces in brittle fracture and perfect plasticity

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    The roughness properties of two-dimensional fracture surfaces as created by the slow failure of random fuse networks are considered and compared to yield surfaces of perfect plasticity with similar disorder. By studying systems up to a linear size L=350 it is found that in the cases studied the fracture surfaces exhibit self-affine scaling with a roughness exponent close to 2/3, which is asymptotically exactly true for plasticity though finite-size effects are evident for both. The overlap of yield or minimum energy and fracture surfaces with exactly the same disorder configuration is shown to be a decreasing function of the system size and to be of a rather large magnitude for all cases studied. The typical ``overlap cluster'' length between pairs of such interfaces converges to a constant with LL increasing.Comment: Accepted for publication in Phys. Rev.

    Elasticity of Stiff Polymer Networks

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    We study the elasticity of a two-dimensional random network of rigid rods (``Mikado model''). The essential features incorporated into the model are the anisotropic elasticity of the rods and the random geometry of the network. We show that there are three distinct scaling regimes, characterized by two distinct length scales on the elastic backbone. In addition to a critical rigidiy percolation region and a homogeneously elastic regime we find a novel intermediate scaling regime, where elasticity is dominated by bending deformations.Comment: 4 pages, 4 figure

    Using impact response surfaces to analyse the likelihood of impacts on crop yield under probabilistic climate change

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    Conventional methods of modelling impacts of future climate change on crop yields often rely on a limited selection of projections for representing uncertainties in future climate. However, large ensembles of climate projections offer an opportunity to estimate yield responses probabilistically. This study demonstrates an approach to probabilistic yield estimation using impact response surfaces (IRSs). These are constructed from a set of sensitivity simulations that explore yield responses to a wide range of changes in temperature and precipitation. Options for adaptation and different levels of future atmospheric carbon dioxide concentration [CO2] defined by representative concentration pathways (RCP4.5 and RCP8.5) were also considered. Model-based IRSs were combined with probabilistic climate projections to estimate impact likelihoods for yields of spring barley (Hordeum vulgare L.) in Finland during the 21st century. Probabilistic projections of climate for the same RCPs were overlaid on IRSs for corresponding [CO2] levels throughout the century and likelihoods of yield shortfall calculated with respect to a threshold mean yield for the baseline (1981–2010). Results suggest that cultivars combining short pre- and long post-anthesis phases together with earlier sowing dates produce the highest yields and smallest likelihoods of yield shortfall under future scenarios. Higher [CO2] levels generally compensate for yield losses due to warming under the RCPs. Yet, this does not happen fully under the more moderate warming of RCP4.5 with a weaker rise in [CO2], where there is a chance of yield shortfall throughout the century. Under the stronger warming but more rapid [CO2] increase of RCP8.5, the likelihood of yield shortfall drops to zero from mid-century onwards. Whilst the incremental IRS-based approach simplifies the temporal and cross-variable complexities of projected climate, it was found to offer a close approximation of evolving future likelihoods of yield impacts in comparison to a more conventional scenario-based approach. The IRS approach is scenario-neutral and existing plots can be used in combination with any new scenario that falls within the sensitivity range without the need to perform new runs with the impact model. A single crop model is used for demonstration, but an ensemble IRS approach could additionally capture impact model uncertainties.peerReviewe

    Failure of planar fiber networks

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    We study the failure of planar random fiber networks with computer simulations. The networks are grown by adding flexible fibers one by one on a growing deposit [K. J. Niskanen and M. J. Alava, Phys. Rev. Lett. 73, 3475 (1994)], a process yielding realistic three dimensional network structures. The network thus obtained is mapped to an electrical analogue of the elastic problem, namely to a random fuse network with separate bond elements for the fiber-to-fiber contacts. The conductivity of the contacts (corresponding to the efficiency of stress transfer between fibers) is adjustable. We construct a simple effective medium theory for the current distribution and conductivity of the networks as a function of intra-fiber current transfer efficiency. This analysis compares favorably with the computed conductivity and with the fracture properties of fiber networks with varying fiber flexibility and network thickness. The failure characteristics are shown to obey scaling behavior, as expected of a disordered brittlematerial, which is explained by the high current end of the current distribution saturating in thick enough networks. For bond breaking, fracture load and strain can be estimated with the effective medium theory. For fiber breaking, we find the counter-intuitive result that failure is more likely to nucleate far from surfaces, as the stress is transmitted more effectively to the fibers in the interior.Peer reviewe
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