College of Engineering and Science
http://hdl.handle.net/11141/2675
Aerospace, Physics & Space Sciences, Biomedical & Chemical Engineering & Sciences, Computer Engineering & Sciences, Mathematical Sciences, Mechanical & Civil Engineering, and Ocean Engineering & Marine Sciences2022-05-21T02:49:56ZRelaxation of Variational Principles for Z-problems in Effective Media Theory
http://hdl.handle.net/11141/3497
Relaxation of Variational Principles for Z-problems in Effective Media Theory
Beard, Kenneth
In this thesis, we consider a class of Z-problems and their associated effective operators on Hilbert spaces which arise in effective media theory, especially within the theory of composites. We provide a unified approach to obtaining solutions of the Z-problem, formulas for the effective operator in terms of generalized Schur complements, and their associated variational principles (e.g., the Dirichlet minimization principle), while allowing for relaxation of the standard hypotheses on positivity and invertibility for the classes of operators usually considered in such problems. The Hilbert space framework developed here is inspired by the methods of orthogonal projections and Hodge decompositions. However, we focus on finite-dimensional Hilbert spaces. Our theoretical development utilizes the theory of block operator matrices, the Moore-Penrose pseudoinverse (as a replacement for the inverse), the generalized Schur complement, and the generalized principal pivot transform. With this unified framework, we are able to recover the classical minimization principle for the Schur complement and derive its extension, as well as provide a new maximization principle for the generalized principal pivot transform. We also present several applications. First, we give an operator-theoretic reformulation of the discrete Dirichlet-to-Neumann (DtN) map for an electrical network on a finite linear graph and relate the DtN map to the effective operator of an associated Z-problem. Second, we show how the classical electrical conductivity of an electrical network (on a finite linear graph) is essentially the effective operator of an associated Z-problem. Next, we consider periodic linear graphs and develop a discrete analog to the periodic conductivity equation and effective conductivity in the continuum. Finally, we conclude with a discussion of future work and open problems based on this thesis.
Thesis (M.S.) - Florida Institute of Technology, 2022.
2022-05-01T00:00:00ZThe Development of a New All-in-one Allsky Camera and Radiometer System
http://hdl.handle.net/11141/3495
The Development of a New All-in-one Allsky Camera and Radiometer System
Hughes, Ashley Suzanne
We developed a new all-in-one camera and radiometer system for meteor surveillance.
It proved successful during its first bolide event on 13 April 2021, as reported in the
journal Meteoritics and Planetary Science, volume 57, number 3, pages 575-587. The
event capture produced both video and radiometric data, and with the video data we
were able to calculate a trajectory and orbit, and determine the fragmentation characteristics of the meteor as it traveled through the atmosphere.
Thesis (M.S.) - Florida Institute of Technology, 2022.
2022-05-01T00:00:00ZThe Second Indian River Research Symposium Foreword
http://hdl.handle.net/11141/3490
The Second Indian River Research Symposium Foreword
Turner, Richard L.
1990-01-01T00:00:00ZBiodiversity of the Indian River Lagoon System: a cautionary tale from the birds
http://hdl.handle.net/11141/3489
Biodiversity of the Indian River Lagoon System: a cautionary tale from the birds
Turner, Richard L.
Prevailing dogma on comparative biodiversity of the Indian River Lagoon (IRL) stems
mainly from one claim about ichthyofauna and two about avifauna. The extensive network of birdwatchers,
clarity of bird taxonomy, long history of the Christmas Bird Count (CBC), and burgeoning
database on ebird.org make birds excellent for geographic comparison. The 1985 claim that Merritt
Island CBCs are often the ‘‘most speciose count’’ in the U.S. is unfounded. CBCs there in 1970–1985
never had the highest count, even compared to the nearby Cocoa site. For the 114th CBC (2013), it
ranked 11th in Florida and 44th nationally. The 1989 claim that IRL has ‘‘the most diverse avifauna in
the United States’’ also is unfounded. Of 543 hotspots (.250 species) in coastal continental states on
ebird.org in December 2019, Merritt Island National Wildlife Refuge had 300 species; but 110 other
sites listed more species of bird. Because government agencies, legislators, media, and the public rely
on scientists for information, scientific statements must rely on evidence. Scientists should abandon
the current dogma about the high relative biodiversity of the IRL. Studies should focus on increasing
our knowledge of diversity of all taxa; and geographic comparisons should be attempted with great
caution.
2021-01-01T00:00:00Z