Examinando por Autor "Tiemblo, Alfredo"

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Null Electromagnetic Fields from Dilatation and Rotation Transformations of the Hopfion
(MDPI, 2019-09-02) Arrayás, Manuel; Fernández-Rañada, Antonio; Tiemblo, Alfredo; Trueba, José Luis
The application of topology concepts to Maxwell equations has led to the developing of the whole area of electromagnetic knots. In this paper, we apply some symmetry transformations to a particular electromagnetic knot, the hopfion field, to get a new set of knotted solutions with the properties of being null. The new fields are obtained by a homothetic transformation (dilatation) and a rotation of the hopfion, and we study the constraints that the transformations must fulfill in order to generate valid electromagnetic fields propagating in a vacuum. We make use of the Bateman construction and calculate the four-potentials and the electromagnetic helicities. It is observed that the topology of the field lines does not seem to be conserved as it is for the hopfion.
The quest of null electromagnetics knots from Seifert fibration
(Elsevier, 2022) Arrayás, Manuel; Tiemblo, Alfredo; Trueba, José L.
In this work we find new null electromagnetic fields that are exact solutions of Maxwell equations in vacuum and generalize the hopfion. The hopfion is an exact solution of Maxwell equations in vacuum in which all the field lines (both electric and magnetic) are topologically equivalent to closed and linked circles, forming a mathematical structure called Hopf fibration. Here we present a generalization to include other field lines topology, such as the Seifert fibration in which the field lines form linked torus knots. Included in this generalization are fields that ergodically fill torus surfaces.