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Simulations of the growth of cities

Abstract : In this thesis we propose and test models that describe the growth and morphology of cities. The first of these models is used from previously developed correlated gradient percolation model. The second model is related to a stochastic differential equation and has never been proposed before. Both models are parameterizable. The parameters we chose in applications are well justified by physical observations: proximily to axes and accessibility of sites. The result is consistent with actual data. We also study the gradient percolation as a mathematical object. We prove, following Nolin's ideas, that the front of gradient percolation cluster is localised in a neighborhood of the critical curve with width and length depending on density gradient. Finally, we also study SLE growth processes. We calculate (computer assisted demonstration) the expected value of square of moduli for SLE_2 and SLE_6 related to the Bieberbach conjecture.
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Submitted on : Wednesday, January 15, 2014 - 11:38:00 PM
Last modification on : Tuesday, October 12, 2021 - 5:20:09 PM
Long-term archiving on: : Wednesday, April 16, 2014 - 4:40:15 AM


  • HAL Id : tel-00931857, version 1


Nga Nguyen. Simulations of the growth of cities. Modeling and Simulation. Université d'Orléans, 2014. English. ⟨NNT : ⟩. ⟨tel-00931857⟩



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