JUST A MOMENT: TORSIONAL RIGIDITY AS A NON-SPECTRAL GEOMETRIC INVARIANT

Permanent Link:

http://ncf.sobek.ufl.edu/AA00024726/00001

Material Information

Title:

JUST A MOMENT: TORSIONAL RIGIDITY AS A NON-SPECTRAL GEOMETRIC INVARIANT

Physical Description:

Book

Language:

English

Creator:

Comer, Joseph F.

Publisher:

New College of Florida

Place of Publication:

Sarasota, Fla.

Publication Date:

2014

Thesis/Dissertation Information

Degree:

Bachelor's ( B.A.)

Degree Grantor:

New College of Florida

Degree Divisions:

Natural Sciences

Area of Concentration:

Mathematics

Faculty Sponsor:

McDonald, Patrick

Subjects

Genre:

bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, territorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract:

The research of Gordon, Wolpert and Webb showed that the Dirichlet eigenspectrum of a planar domain is not sufficient to identify the domain uniquely, sparking a search for a new, stronger, natural geometric invariant. Colladay, Kaganovskiy and McDonald performed calculations indicating that the torsional rigidity--the first moment of heat content may be such an invariant. We investigate this possibility by calculating the torsional rigidities of two isospectral domain pairs. In the first--a pair of disconnected planar domains constructed by S.J. Chapman--we find that the torsional rigidities are given sums of functions in two variables and, by constructing upper and lower bounds for such sums, show that the torsional rigidities do indeed differ. Our second investigation is of a quantum graph analog of the original isospectral pair example of Gordon, Wolpert and Webb. The quantum graph construction follows that of Colladay, et al. We find, unlike Colladay, et al. that the pair is not distinguished by torsional rigidity for all sets of edge-lengths.

Statement of Responsibility:

by Joseph F. Comer

Thesis:

Thesis (B.A.) -- New College of Florida, 2014

General Note:

RESTRICTED TO NCF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE

Bibliography:

Includes bibliographical references.

General Note:

This bibliographic record is available under the Creative Commons CC0 public domain dedication. The New College of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.

General Note:

Faculty Sponsor: McDonald, Patrick

Record Information

Source Institution:

New College of Florida

Holding Location:

New College of Florida

Rights Management:

Applicable rights reserved.

Resource Identifier:

Classification:

S.T. 2014 C6

System ID:

AA00024726:00001