Mathematics Seminar 5 April 2013
Hancock Center Room 2005, 3:30 PM
Nicole Bender - Marist College (Class of 2014)
Quadratic Forms and their Application to Whale Localization
This presentation will cover the topic of Quadratic forms, which can be represented as a square matrix or a multivariate polynomial where each term has total degree two. There are two-dimensional and three-dimensional forms, both of which can be applicable to many real world situations. This talk will introduce the Principal Axes Theorem and investigate how it relates to ellipses in the Cartesian plane. We will then discuss the application of three-dimensional quadratic forms to the localization of blue whales based on vocalizations recorded on ocean bottom seismometers.
Laura Tobak - Marist College (Class of 2013)
Modeling Underwater Acoustic Interface Waves
Sound waves can travel much farther than any other type of wave in the ocean, making them useful for studying marine life, submarine communication and seafloor topography. Interface waves, also called Rayleigh waves, can occur on a boundary between any water---sediment or sediment---sediment interface and contribute to the underwater acoustic field. Rayleigh waves require simultaneous incidence of both compressional waves, in which the particles travel parallel to the wave, and shear waves, in which particles travel perpendicular to the wave. This talk will focus on interface waves at the water-sediment interface in an environment with one elastic layer underneath a water layer. We will use the rotated variable elastic parabolic method to create models and then compare the interface wave amplitudes to theoretical results.