國立虎尾科技大學 |

On the Construction and Dynamics of Knotted Fields.

紀錄類型:	書目-語言資料,手稿 : Monograph/item
正題名/作者:	On the Construction and Dynamics of Knotted Fields./
作者:	Kedia, Hridesh.
面頁冊數:	1 online resource (130 pages)
附註:	Source: Dissertation Abstracts International, Volume: 78-11(E), Section: B.
Contained By:	Dissertation Abstracts International78-11B(E).
標題:	Physics. -
電子資源:	click for full text (PQDT)
ISBN:	9780355075007

On the Construction and Dynamics of Knotted Fields.
Kedia, Hridesh.

On the Construction and Dynamics of Knotted Fields. - 1 online resource (130 pages)

Source: Dissertation Abstracts International, Volume: 78-11(E), Section: B.

Thesis (Ph.D.)

Includes bibliographical references

Representing a physical field in terms of its field lines has often enabled a deeper understanding of complex physical phenomena, from Faraday's law of magnetic induction, to the Helmholtz laws of vortex motion, to the free energy density of liquid crystals in terms of the distortions of the lines of the director field. At the same time, the application of ideas from topology---the study of properties that are invariant under continuous deformations---has led to robust insights into the nature of complex physical systems from defects in crystal structures, to the earth's magnetic field, to topological conservation laws.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2018

Mode of access: World Wide Web

ISBN: 9780355075007Subjects--Topical Terms:

564049
Physics.
Index Terms--Genre/Form:

554714
Electronic books.

On the Construction and Dynamics of Knotted Fields.
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100 1 $a Kedia, Hridesh. $3 1180583
245 1 0 $a On the Construction and Dynamics of Knotted Fields.
264 0 $c 2017
300 $a 1 online resource (130 pages)
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
500 $a Source: Dissertation Abstracts International, Volume: 78-11(E), Section: B.
500 $a Adviser: William T.M. Irvine.
502 $a Thesis (Ph.D.) $c The University of Chicago $d 2017.
504 $a Includes bibliographical references
520 $a Representing a physical field in terms of its field lines has often enabled a deeper understanding of complex physical phenomena, from Faraday's law of magnetic induction, to the Helmholtz laws of vortex motion, to the free energy density of liquid crystals in terms of the distortions of the lines of the director field. At the same time, the application of ideas from topology---the study of properties that are invariant under continuous deformations---has led to robust insights into the nature of complex physical systems from defects in crystal structures, to the earth's magnetic field, to topological conservation laws.
520 $a The study of knotted fields, physical fields in which the field lines encode knots, emerges naturally from the application of topological ideas to the investigation of the physical phenomena best understood in terms of the lines of a field. A knot---a closed loop tangled with itself which can not be untangled without cutting the loop---is the simplest topologically non-trivial object constructed from a line.
520 $a Remarkably, knots in the vortex (magnetic field) lines of a dissipationless fluid (plasma), persist forever as they are transported by the flow, stretching and rotating as they evolve. Moreover, deeply entwined with the topology-preserving dynamics of dissipationless fluids and plasmas, is an additional conserved quantity---helicity, a measure of the average linking of the vortex (magnetic field) lines in a fluid (plasma)---which has had far-reaching consequences for fluids and plasmas. Inspired by the persistence of knots in dissipationless flows, and their far-reaching physical consequences, we seek to understand the interplay between the dynamics of a field and the topology of its field lines in a variety of systems.
520 $a While it is easy to tie a knot in a shoelace, tying a knot in the the lines of a space-filling field requires contorting the lines everywhere to match the knotted region. The challenge of analytically constructing knotted field configurations has impeded a deeper understanding of the interplay between topology and dynamics in fluids and plasmas. We begin by analytically constructing knotted field configurations which encode a desired knot in the lines of the field, and show that their helicity can be tuned independently of the encoded knot.
520 $a The nonlinear nature of the physical systems in which these knotted field configurations arise, makes their analytical study challenging. We ask if a linear theory such as electromagnetism can allow knotted field configurations to persist with time. We find analytical expressions for an infinite family of knotted solutions to Maxwell's equations in vacuum and elucidate their connections to dissipationless flows. We present a design rule for constructing such persistently knotted electromagnetic fields, which could possibly be used to transfer knottedness to matter such as quantum fluids and plasmas.
520 $a An important consequence of the persistence of knots in classical dissipationless flows is the existence of an additional conserved quantity, helicity, which has had far-reaching implications. To understand the existence of analogous conserved quantities, we ask if superfluids, which flow without dissipation just like classical dissipationless flows, have an additional conserved quantity akin to helicity. We address this question using an analytical approach based on defining the particle relabeling symmetry---the symmetry underlying helicity conservation---in superfluids, and find that an analogous conserved quantity exists but vanishes identically owing to the intrinsic geometry of complex scalar fields. Furthermore, to address the question of a ``classical limit'' of superfluid vortices which recovers classical helicity conservation, we perform numerical simulations of \emph{bundles} of superfluid vortices, and find behavior akin to classical viscous flows.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2018
538 $a Mode of access: World Wide Web
650 4 $a Physics. $3 564049
650 4 $a Theoretical physics. $3 1180318
650 4 $a Applied mathematics. $3 1069907
655 7 $a Electronic books. $2 local $3 554714
690 $a 0605
690 $a 0753
690 $a 0364
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a The University of Chicago. $b Physics. $3 1180584
773 0 $t Dissertation Abstracts International $g 78-11B(E).
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10254574 $z click for full text (PQDT)