東華大學圖書館 |

Language: English

Help

回圖書館首頁

手機版館藏查詢

Back

Switch To: Labeled | MARC Mode | ISBD

The Biot-Savart operator and electro...

Parsley, Robert Jason.

Linked to FindBook

Google Book

Amazon

博客來

The Biot-Savart operator and electrodynamics on bounded subdomains of the three-sphere.

Record Type:	Electronic resources : Monograph/item
Title/Author:	The Biot-Savart operator and electrodynamics on bounded subdomains of the three-sphere./
Author:	Parsley, Robert Jason.
Description:	123 p.
Notes:	Source: Dissertation Abstracts International, Volume: 65-03, Section: B, page: 1357.
Contained By:	Dissertation Abstracts International65-03B.
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3125886
ISBN:	0496731750

The Biot-Savart operator and electrodynamics on bounded subdomains of the three-sphere.
Parsley, Robert Jason.

The Biot-Savart operator and electrodynamics on bounded subdomains of the three-sphere. - 123 p.

Source: Dissertation Abstracts International, Volume: 65-03, Section: B, page: 1357.

Thesis (Ph.D.)--University of Pennsylvania, 2004.

We study the generalization of the Biot-Savart law from electrodynamics in the presence of curvature. We define the integral operator BS acting on all vector fields on subdomains of the three-dimensional sphere, the set of points in R4 that are one unit away from the origin. By doing so, we establish a geometric setting for electrodynamics in positive curvature. When applied to a vector field, the Biot-Savart operator behaves like a magnetic field; we display suitable electric fields so that Maxwell's equations hold. Specifically, the Biot-Savart operator applied to a "current" V is a right inverse to curl; thus BS is important in the study of curl eigenvalue energy-minimization problems in geometry and physics. We show that the Biot-Savart operator is self-adjoint and bounded. The helicity of a vector field, a measure of the coiling of its flow, is expressed as an inner product of BS(V) with V. We find upper bounds for helicity on the three-sphere; our bounds are not sharp but we produce explicit examples within an order of magnitude. In all instances, the formulas we give are geometrically meaningful: they are preserved by orientation-preserving isometries of the three-sphere. Applications of the Biot-Savart operator include plasma physics, geometric knot theory, solar physics, and DNA replication.

ISBN: 0496731750Subjects--Topical Terms:

515831
Mathematics.

The Biot-Savart operator and electrodynamics on bounded subdomains of the three-sphere.
LDR:02275nmm 2200289 4500 001 1844330
005 20051017073458.5
008 130614s2004 eng d
020 $a 0496731750
035 $a (UnM)AAI3125886
035 $a AAI3125886
040 $a UnM $c UnM
100 1 $a Parsley, Robert Jason. $3 1932526
245 1 4 $a The Biot-Savart operator and electrodynamics on bounded subdomains of the three-sphere.
300 $a 123 p.
500 $a Source: Dissertation Abstracts International, Volume: 65-03, Section: B, page: 1357.
500 $a Advisers: Dennis DeTurck; Herman Gluck.
502 $a Thesis (Ph.D.)--University of Pennsylvania, 2004.
520 $a We study the generalization of the Biot-Savart law from electrodynamics in the presence of curvature. We define the integral operator BS acting on all vector fields on subdomains of the three-dimensional sphere, the set of points in R4 that are one unit away from the origin. By doing so, we establish a geometric setting for electrodynamics in positive curvature. When applied to a vector field, the Biot-Savart operator behaves like a magnetic field; we display suitable electric fields so that Maxwell's equations hold. Specifically, the Biot-Savart operator applied to a "current" V is a right inverse to curl; thus BS is important in the study of curl eigenvalue energy-minimization problems in geometry and physics. We show that the Biot-Savart operator is self-adjoint and bounded. The helicity of a vector field, a measure of the coiling of its flow, is expressed as an inner product of BS(V) with V. We find upper bounds for helicity on the three-sphere; our bounds are not sharp but we produce explicit examples within an order of magnitude. In all instances, the formulas we give are geometrically meaningful: they are preserved by orientation-preserving isometries of the three-sphere. Applications of the Biot-Savart operator include plasma physics, geometric knot theory, solar physics, and DNA replication.
590 $a School code: 0175.
650 4 $a Mathematics. $3 515831
650 4 $a Physics, Fluid and Plasma. $3 1018402
690 $a 0405
690 $a 0759
710 2 0 $a University of Pennsylvania. $3 1017401
773 0 $t Dissertation Abstracts International $g 65-03B.
790 1 0 $a DeTurck, Dennis, $e advisor
790 1 0 $a Gluck, Herman, $e advisor
790 $a 0175
791 $a Ph.D.
792 $a 2004
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3125886