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Lamb's problem on random mass density fields with fractal and Hurst effects.

ABSTRACT: This paper reports on a generalization of Lamb's problem to a linear elastic, infinite half-space with random fields (RFs) of mass density, subject to a normal line load. Both, uncorrelated and correlated (with fractal and Hurst characteristics) RFs without any weak noise restrictions, are proposed. Cellular automata (CA) is used to simulate the wave propagation. CA is a local computational method which, for rectangular discretization of spatial domain, is equivalent to applying the finite difference method to the governing equations of classical elasticity. We first evaluate the response of CA to an uncorrelated mass density field, more commonly known as white-noise, of varying coarseness as compared to CA's node density. We then evaluate the response of CA to multiscale mass density RFs of Cauchy and Dagum type; these fields are unique in that they are able to model and decouple the field's fractal dimension and Hurst parameter. We focus on stochastic imperfection sensitivity; we determine to what extent the fractal or the Hurst parameter is a significant factor in altering the solution to the planar stochastic Lamb's problem by evaluating the coefficient of variation of the response when compared with the coefficient of variation of the RF.

SUBMITTER: Nishawala VV

PROVIDER: S-EPMC5247527 | biostudies-literature | 2016 Dec

REPOSITORIES: biostudies-literature

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Lamb's problem on random mass density fields with fractal and Hurst effects.

Nishawala V V VV Ostoja-Starzewski M M Leamy M J MJ Porcu E E

Proceedings. Mathematical, physical, and engineering sciences 20161201 2196

This paper reports on a generalization of Lamb's problem to a linear elastic, infinite half-space with random fields (RFs) of mass density, subject to a normal line load. Both, uncorrelated and correlated (with fractal and Hurst characteristics) RFs without any weak noise restrictions, are proposed. Cellular automata (CA) is used to simulate the wave propagation. CA is a local computational method which, for rectangular discretization of spatial domain, is equivalent to applying the finite diffe ...[more]

PMID: 28119551

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Project description:In arable fields, plant species richness consistently increases at field edges. This potentially makes the field edge an important habitat for the conservation of the ruderal arable flora (or 'weeds') and the invertebrates and birds it supports. Increased diversity and abundance of weeds in crop edges could be owing to either a reduction in agricultural inputs towards the field edge and/or spatial mass effects associated with dispersal from the surrounding landscape.We contend that the diversity of weed species in an arable field is a combination of resident species, that can persist under the intense selection pressure of regular cultivation and agrochemical inputs (typically more ruderal species), and transient species that rely on regular dispersal from neighbouring habitats (characterised by a more 'competitive' ecological strategy).We analysed a large dataset of conventionally managed arable fields in the UK to study the effect of the immediate landscape on in-field plant diversity and abundance and to quantify the contribution of spatial mass effects to plant diversity in arable fields in the context of the ecological strategy of the resulting community.We demonstrated that the decline in diversity with distance into an arable field is highly dependent on the immediate landscape, indicating the important role of spatial mass effects in explaining the increased species richness at field edges in conventionally managed fields.We observed an increase in the proportion of typical arable weeds away from the field edge towards the centre. This increase was dependent on the immediate landscape and was associated with a higher proportion of more competitive species, with a lower fidelity to arable habitats, at the field edge. Synthesis and applications. Conserving the ruderal arable plant community, and the invertebrates and birds that use it as a resource, in conventionally managed arable fields typically relies on the targeted reduction of fertilisers and herbicides in so-called 'conservation headlands'. The success of these options will depend on the neighbouring habitat and boundary. They should be placed along margins where the potential for ingress of competitive species, that may become dominant in the absence of herbicides, is limited. This will enhance ecosystem services delivered by the ruderal flora and reduce the risk of competitive species occurring in the crop.

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Lamb's problem on random mass density fields with fractal and Hurst effects.

Publications

Lamb's problem on random mass density fields with fractal and Hurst effects.

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