Space-time generation of high intensity patterns using growth-interaction processes |
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Authors: | Eric Renshaw Carlos Comas |
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Institution: | 1. Department of Statistics and Modelling Science, University of Strathclyde, Livingstone Tower, 26 Richmond Street, Glasgow, G1 1XH, UK 2. Departamento de Matemáticas, Universitat Jaume I, 12071, Castellón, Spain
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Abstract: | We describe a novel spatial-temporal algorithm for generating packing structures of disks and spheres, which not only incorporates
all the attractive features of existing algorithms but is also more flexible in defining spatial interactions and other control
parameters. The advantage of this approach lies in the ability of marks to exploit to best advantage the space available to
them by changing their size in response to the interaction pressure of their neighbours. Allowing particles to move in response
to such pressure results in high-intensity packing. Indeed, since particles may temporarily overlap, even under hard-packing
scenarios, they possess a greater potential for rearranging themselves, and thereby creating even higher packing intensities
than exist under other strategies. Non-overlapping pattern structures are achieved simply by allowing the process to ‘burn-out’
at the end of its development period. A variety of different growth-interaction regimes are explored, both symmetric and asymmetric,
and the convergence issues that they raise are examined. We conjecture that not only may this algorithm be easily generalised
to cover a large variety of situations across a wide range of disciplines, but that appropriately targeted generalisations
may well include established packing algorithms as special cases. |
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