61 citations · 202 across the 47 of their papers we have counts for
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nlin.PS2005★ 8 cited
Use the information dimension, not the Hausdorff
A. J. Roberts
Multi-fractal patterns occur widely in nature. In developing new algorithms to determine multi-fractal spectra of experimental data I am lead to the conclusion that generalised dim…
math.DS2005
Accurately model the Kuramoto--Sivashinsky dynamics with holistic discretisation
T. MacKenzie, A. J. Roberts
We analyse the nonlinear Kuramoto--Sivashinsky equation to develop accurate discretisations modeling its dynamics on coarse grids. The analysis is based upon centre manifold theory…
math.DS2005★ 2 cited
Resolve the multitude of microscale interactions to model stochastic partial differential equations
A. J. Roberts
Constructing numerical models of noisy partial differential equations is very delicate. Our long term aim is to use modern dynamical systems theory to derive discretisations of dis…