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Dispersion relations for supersonic multiple virtual jets

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  • In this paper, a special type of circulant matrices, circulant trinity matrices, are first introduced and some properties of these matrices are investigated. Then, in studying a supersonic circular N-jet vortex sheet model, circulant trinity matrices are used to classify the general solutions of the $N$-jet model into 2$N$ families. Finally, the dispersion relations of $N$-jets for each family are derived by using Graf’s Addition Theorem.
    Mathematics Subject Classification: 76J20, 76E99.


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