國立虎尾科技大學 |

Mixing with Piecewise Isometries.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Mixing with Piecewise Isometries./
Author:	Park, Paul P.
Description:	1 online resource (167 pages)
Notes:	Source: Dissertation Abstracts International, Volume: 78-05(E), Section: B.
Contained By:	Dissertation Abstracts International78-05B(E).
Subject:	Applied mathematics. -
Online resource:	click for full text (PQDT)
ISBN:	9781369448511

Mixing with Piecewise Isometries.
Park, Paul P.

Mixing with Piecewise Isometries. - 1 online resource (167 pages)

Source: Dissertation Abstracts International, Volume: 78-05(E), Section: B.

Thesis (Ph.D.)

Includes bibliographical references

This item is not available from ProQuest Dissertations & Theses.

Mixing of granular materials is an important engineering process, and a very complex problem. In this thesis, I use granular mixing in a half-full biaxial spherical tumbler (BST), a spherical container that rotates sequentially about two orthogonal axes, to motivate the study of mixing with piecewise isometries (PWIs), a rich discrete dynamical system with potential applications in mixing design. The set of rotations for the BST constitutes an iteration, which corresponds to a PWI transformation under simplifying assumptions. Trajectories for singularities of a PWI in the limit of infinite iterations reveal an inherent structure defined as the exceptional set, and we show that its complement comprises non-mixing regions. The measures of different exceptional sets are compared to established measures of mixing, and conditions limiting the dynamics of the BST to that of a PWI are relaxed to understand the impact of a theoretical exceptional set in physical applications for future studies.

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

Mode of access: World Wide Web

ISBN: 9781369448511Subjects--Topical Terms:

1069907
Applied mathematics.
Index Terms--Genre/Form:

554714
Electronic books.

Mixing with Piecewise Isometries.
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245 1 0 $a Mixing with Piecewise Isometries.
264 0 $c 2016
300 $a 1 online resource (167 pages)
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500 $a Source: Dissertation Abstracts International, Volume: 78-05(E), Section: B.
500 $a Advisers: Richard M. Lueptow; Julio M. Ottino.
502 $a Thesis (Ph.D.) $c Northwestern University $d 2016.
504 $a Includes bibliographical references
506 $a This item is not available from ProQuest Dissertations & Theses.
520 $a Mixing of granular materials is an important engineering process, and a very complex problem. In this thesis, I use granular mixing in a half-full biaxial spherical tumbler (BST), a spherical container that rotates sequentially about two orthogonal axes, to motivate the study of mixing with piecewise isometries (PWIs), a rich discrete dynamical system with potential applications in mixing design. The set of rotations for the BST constitutes an iteration, which corresponds to a PWI transformation under simplifying assumptions. Trajectories for singularities of a PWI in the limit of infinite iterations reveal an inherent structure defined as the exceptional set, and we show that its complement comprises non-mixing regions. The measures of different exceptional sets are compared to established measures of mixing, and conditions limiting the dynamics of the BST to that of a PWI are relaxed to understand the impact of a theoretical exceptional set in physical applications for future studies.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2018
538 $a Mode of access: World Wide Web
650 4 $a Applied mathematics. $3 1069907
655 7 $a Electronic books. $2 local $3 554714
690 $a 0364
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a Northwestern University. $b Engineering Sciences and Applied Mathematics. $3 1180565
773 0 $t Dissertation Abstracts International $g 78-05B(E).
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