Picture water droplets

Developing mathematical theories of the physical world: Open Access research on fluid dynamics from Strathclyde

Strathprints makes available Open Access scholarly outputs by Strathclyde's Department of Mathematics & Statistics, where continuum mechanics and industrial mathematics is a specialism. Such research seeks to understand fluid dynamics, among many other related areas such as liquid crystals and droplet evaporation.

The Department of Mathematics & Statistics also demonstrates expertise in population modelling & epidemiology, stochastic analysis, applied analysis and scientific computing. Access world leading mathematical and statistical Open Access research!

Explore all Strathclyde Open Access research...

Enabling and exploiting self-similar central symmetry formations

Punzo, Giuliano and Karagiannakis, Philippos and Bennet, Derek James and Macdonald, Malcolm and Weiss, Stephan (2014) Enabling and exploiting self-similar central symmetry formations. IEEE Transactions on Aerospace and Electronic Systems, 50 (1). pp. 689-703. ISSN 0018-9251

[img] PDF

Download (878kB)


In this work a formation flying based architecture is presented within the context of a distributed antenna array. An artificial potential function method is used to control the formation whereby deviation from an all-to-all interaction scheme and swarm shaping are enabled through a self-similar connection network. Introduction of an asymmetric term in the potential function formulation results in the emergence of structures with a central symmetry. The connection network then groups these identical structures through a hierarchical scheme. This produces a fractal shape which is considered for the first time as a distributed antenna array exploiting the recursive arrangement of its elements to augment performance. A 5-element Purina fractal is used as the base formation which is then replicated a number of times increasing the antenna-array aperture and resulting in a highly directional beam from a relatively low number of elements. Justifications are provided in support of the claimed benefits for distributed antenna arrays exploiting fractal geometries. The formation deployment is simulated in Earth orbit together with analytical proofs completing the arguments aimed to demonstrate feasibility of the concept and the advantages provided by grouping antenna elements into coherent structures.