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Lattice model with power-law spatial dispersion for fractional elasticity

100%

Tarasov V.

Open Physics

2013

tom 11

nr 11

1580-1588

A lattice model with a spatial dispersion corresponding to a power-law type is suggested. This model serves as a microscopic model for elastic continuum with power-law non-locality. We prove that the continuous limit maps of the equations for the lattice with the power-law spatial dispersion into the continuum equations with fractional generalizations of the Laplacian operators. The suggested continuum equations, which are obtained from the lattice model, are fractional generalizations of the integral and gradient elasticity models. These equations of fractional elasticity are solved for two special static cases: fractional integral elasticity and fractional gradient elasticity.

Identification of Urban Sports Zones as a Potential Product of Sports Tourism Using Spatial Dispersion Indicators

86%

Ryśnik J. , Gibas P.

Studia Periegetica

2019

tom 27(3)

73-97

The purpose of this article is to identify urban sports zones (also known as sports cities) as a potential product of urban or sports tourism in Poland using the spatial dispersion indicator of residential buildings in relation to sports infrastructure buildings. In the study orthodromic distances (the shortest distances in Euclidean space) between over 7 million residential buildings and 5.4 thousands sports facilities were calculated using centroids of buildings data included in the Topographic Object Data Bank (BDOT10k). These orthodromic distances were then used to calculate the dispersion coefficient in order to identify concentration zones of sports infrastructure buildings. The outcome of the study was the distribution of sports infrastructure buildings in Poland along with concentration zones where communes were treated as functional units. The findings can be used to identify areas that could serve as sports cities, which are defined as varied, separate, large areas, whose development is associated with sport and recreation.