DeepAI AI Chat
Log In Sign Up

Minimal Object Characterisations using Harmonic Generalised Polarizability Tensors and Symmetry Groups

by   P. D. Ledger, et al.
Keele University

We introduce a new type of object characterisation, which is capable of accurately describing small isolated inclusions for potential field inverse problems such as in electrostatics, magnetostatics and related low frequency Maxwell problems. Relevant applications include characterising ferrous unexploded ordnance (UXO) from magnetostatic field measurements in magnetometry, describing small conducting inclusions for medical imaging using electrical impedance tomography (EIT), performing geological ground surveys using electrical resistivity imaging (ERT), characterising objects by electrosensing fish to navigate and identify food as well as describing the effective properties of dilute composites. Our object characterisation builds on the generalised polarizability tensor (GPT) object characterisation concept and provides an alternative to the compacted GPT (CGPT). We call the new characterisations harmonic GPTs (HGPTs) as their coefficients correspond to products of harmonic polynomials. Then, we show that the number of independent coefficients of HGPTs needed to characterise objects can be significantly reduced by considering the symmetry group of the object and propose a systematic approach for determining the subspace of symmetric harmonic polynomials that is fixed by the group and its dimension. This enable us to determine the independent HGPT coefficients for different symmetry groups.


Accurate Benchmark Computations of the Polarizability Tensor for Characterising Small Conducting Inclusions

The characterisation of small conducting inclusions with low conductivit...

Harmonic Tutte polynomials of matroids II

In this work, we introduce the harmonic generalization of the m-tuple we...

Implementing geometric complexity theory: On the separation of orbit closures via symmetries

Understanding the difference between group orbits and their closures is ...

The Group Theoretic Roots of Information I: permutations, symmetry, and entropy

We propose a new interpretation of measures of information and disorder ...

Tensors with maximal symmetries

We classify tensors with maximal and next to maximal dimensional symmetr...

Two Algorithms to Compute Symmetry Groups for Landau-Ginzburg Models

Landau-Ginzburg mirror symmetry studies isomorphisms between graded Frob...

Efficient Computation of the Magnetic Polarizability Tensor Spectral Signature using POD

Our interest lies in the identification of hidden conducting permeable o...