Flexible fiber scopes are widely used in industry and medicine. Typical scopes are made using conventional optical components and order-packed flexible image bundles. The optical performance of a flexible scope is largely determined by that of the...
Spectral theory is the subfield of differential geometry which provided the solution to Kac''s famous question, "Can you hear the shape of a drum?" That is, can we use the Laplace spectrum of a manifold to draw conclusions about its geometry or...
Lowest order charged particle motion in the Earth''s magnetosphere can be explained using simple adiabatic theory. However, nonadiabatic theory is required to explain particle behavior in cases such as when the particle's gyroradius is large...
Ionospheric radio wave propagation -- Observations. Hiss (Radio meteorology). Auroras -- Antarctica -- Observations.
A VersatIle Electromagnetic Waveform (VIEW) receiver was deployed at South Pole station in December 2002 in order to measure the fine structure of auroral radio emissions with high resolution and an unprecedented 500-1000 kHz bandwidth. Using this...
Most theoretical and computational studies of turbulence in Navier-Stokes fluids and/or guiding-center plasmas have been carried out in the presence of spatially periodic boundary conditions. In view of the frequently-reproduced result that...
Experimental and theoretical aspects of macroscopic and mesoscopic elastic instability are investigated in this thesis. For the theoretical investigations we utilize a Lagrangian formulation of nonlinear continuum elasticity theory, the novel...
We prove the existence of nontrivial multiparameter isospectral deformations of metrics on the classical compact simple Lie groups SO (n) (n = 9, n ≥11), Spin(n) (n = 9, n ≥11), SU (n) (n ≥7), and Sp (n) (n ≥5). The proof breaks into three...
Boundary integral methods have long been used to solve boundary value problems for elliptic partial differential equations with piecewise constant coefficients, since they have several numerical advantages over conventional volume discretization....
We provide a theoretical model for a design involving a dc voltage biased Josephson junction (JJ) that strongly drives a high quality factor microwave cavity via the ac Josephson effect. We explore the rich classical dynamics of the resultant...
Motivated by quantum mechanics and geometric optics, it is a long-standing problem whether the length spectrum of a compact Riemannian manifold can be recovered from its Laplace spectrum. One route to proving that the length spectrum depends on the...
The main driving force behind the development of computers was the attempt to solve problems that would otherwise require a large amount of time to be solved. Despite the technological development that has made computers ubiquitous in daily lives,...
Plant genetic engineering. ; Plants -- Effect of cadmium on. ; Cadmium -- Physiological transport.
Iron plays a central role in key biological processes in both plants and animals. Lack of available iron commonly limits plant growth and nutritional value. Worldwide, dietary iron is primarily obtained from plant sources and, despite our best...
In the late 1960s, Ihara began work that led to the Ihara zeta function, a zeta function which is defined on a finite graph. This function is an interesting graph invariant which gives information on expansion properties of the graph. It also...
Riemannian manifolds. Singularities (Mathematics). Laplacian operator. Spectral theory (Mathematics). Riemann surfaces. Curves on surfaces. Geometry
Historically, inverse spectral theory has been concerned with the relationship between the geometry and the spectrum of compact Riemannian manifolds, where spectrum means the eigenvalue spectrum of the Laplace operator as it acts on smooth...