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
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
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