FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W3033008719> ?p ?o ?g. }

• W3033008719 abstract "Classical Maxwell's equations have been fundamental to our understanding of physics since their inception in the 19th century. Any research which contributes to our understanding of them is of importance. In 1989, Ranada introduced a topological formalism of Maxwell's equations in vacuum - investigating a set of solutions involving a mapping between spherical spaces projected into the electric and magnetic field lines - named the Hopf fibration. This research has been furthered by Ranada and other prominent scientists to include: the family of torus knots within the field lines; a theory of the fundamental charge; and a description of the number of right and left handed photons. The Hopf fibration, embedded into charge-free electric and magnetic field lines as exact solutions to Maxwell's equations, is a central component to this body of work. Topological, classical electromagnetism is, therefore, an area that has the potential to further our understanding of Maxwell's equations. This thesis describes a project that advances the knowledge of knotted electromagnetic fi elds and electromagnetism in two, distinct areas: zilches of unusual electromagnetic fi elds; and a multipole expansion on the vector spherical harmonics of the knotted electromagnetic fi elds. Zilches are a set of little-known conserved quantities within the charge-free Maxwell's equations. They were originally posited by Lipkin as new and potentially exciting - if their physical nature could be determined. This research examines the zilches in three unusual topologically non-trivial sets of electromagnetic fi elds - starting with the knotted solutions to Maxwell's equations. The results show a profound connection between the zilches and the fi elds' topology. It conjectures that this is the case for all integrable solutions. Alongside this, it is shown that the zilches can be written in terms of other, known conserved quantities of the fi elds. The latter half of this thesis focuses on delivering a generalised multipole expansion of the vector spherical harmonics for the knotted electromagnetic fi elds, after outlining various flaws in the assumptions made by previous literature. Finally, the results from generating the generalised multipolar expansion coefficients are analysed and presented. A summary of the fi rst 3680 coefficients are given in 18 equations - after noticing patterns occurring between them. Firstly, this research further develops the area of knotted electromagnetic fields, providing a platform from which to generate them experimentally and to develop the theory further. Secondly, it sheds considerable light on the interpretation of the zilches and suggests a more central role in electromagnetism." @default.
• W3033008719 created "2020-06-12" @default.
• W3033008719 creator A5012253685 @default.
• W3033008719 date "2019-06-01" @default.
• W3033008719 modified "2023-09-24" @default.
• W3033008719 title "Properties of knotted solutions to Maxwell's equations : an exploration of Lipkin's zilches in vacuum electromagnetic fields, and a multipole expansion of the vector spherical harmonics of knotted electromagnetic fields" @default.
• W3033008719 hasPublicationYear "2019" @default.
• W3033008719 type Work @default.
• W3033008719 sameAs 3033008719 @default.
• W3033008719 citedByCount "0" @default.
• W3033008719 crossrefType "dissertation" @default.
• W3033008719 hasAuthorship W3033008719A5012253685 @default.
• W3033008719 hasConcept C115260700 @default.
• W3033008719 hasConcept C121332964 @default.
• W3033008719 hasConcept C154452299 @default.
• W3033008719 hasConcept C193614536 @default.
• W3033008719 hasConcept C28843909 @default.
• W3033008719 hasConcept C33332235 @default.
• W3033008719 hasConcept C3768446 @default.
• W3033008719 hasConcept C43498160 @default.
• W3033008719 hasConcept C52765159 @default.
• W3033008719 hasConcept C59282198 @default.
• W3033008719 hasConcept C62520636 @default.
• W3033008719 hasConcept C74650414 @default.
• W3033008719 hasConcept C76969448 @default.
• W3033008719 hasConcept C77237485 @default.
• W3033008719 hasConcept C91748784 @default.
• W3033008719 hasConceptScore W3033008719C115260700 @default.
• W3033008719 hasConceptScore W3033008719C121332964 @default.
• W3033008719 hasConceptScore W3033008719C154452299 @default.
• W3033008719 hasConceptScore W3033008719C193614536 @default.
• W3033008719 hasConceptScore W3033008719C28843909 @default.
• W3033008719 hasConceptScore W3033008719C33332235 @default.
• W3033008719 hasConceptScore W3033008719C3768446 @default.
• W3033008719 hasConceptScore W3033008719C43498160 @default.
• W3033008719 hasConceptScore W3033008719C52765159 @default.
• W3033008719 hasConceptScore W3033008719C59282198 @default.
• W3033008719 hasConceptScore W3033008719C62520636 @default.
• W3033008719 hasConceptScore W3033008719C74650414 @default.
• W3033008719 hasConceptScore W3033008719C76969448 @default.
• W3033008719 hasConceptScore W3033008719C77237485 @default.
• W3033008719 hasConceptScore W3033008719C91748784 @default.
• W3033008719 hasLocation W30330087191 @default.
• W3033008719 hasOpenAccess W3033008719 @default.
• W3033008719 hasPrimaryLocation W30330087191 @default.
• W3033008719 hasRelatedWork W1608717137 @default.
• W3033008719 hasRelatedWork W1613669795 @default.
• W3033008719 hasRelatedWork W1650234485 @default.
• W3033008719 hasRelatedWork W1845146090 @default.
• W3033008719 hasRelatedWork W1979148811 @default.
• W3033008719 hasRelatedWork W1981157747 @default.
• W3033008719 hasRelatedWork W1992283368 @default.
• W3033008719 hasRelatedWork W2015580504 @default.
• W3033008719 hasRelatedWork W2033531660 @default.
• W3033008719 hasRelatedWork W2045398854 @default.
• W3033008719 hasRelatedWork W2153138229 @default.
• W3033008719 hasRelatedWork W2275987408 @default.
• W3033008719 hasRelatedWork W2343500380 @default.
• W3033008719 hasRelatedWork W2963479030 @default.
• W3033008719 hasRelatedWork W2964177331 @default.
• W3033008719 hasRelatedWork W3041223808 @default.
• W3033008719 hasRelatedWork W3045528991 @default.
• W3033008719 hasRelatedWork W3099373842 @default.
• W3033008719 hasRelatedWork W3201899915 @default.
• W3033008719 hasRelatedWork W16787455 @default.
• W3033008719 isParatext "false" @default.
• W3033008719 isRetracted "false" @default.
• W3033008719 magId "3033008719" @default.
• W3033008719 workType "dissertation" @default.