9 papers
Recovering elastic subdomains with strain-gradient elastic interfaces from force measurements: the antiplane shear setting
Govanni Granados, Jeremy L. Marzuola, Casey Rodriguez
We introduce and study a new inverse problem for antiplane shear in elastic bodies with strain-gradient interfaces. The setting is a homogeneous isotropic elastic body containing a…
Probing the influence of topological and geometric disorder on the spectrum of the differential Laplacian operator on networks
Charles Emmett Maher, Jeremy L. Marzuola, Katherine A. Newhall
Metric networks are network-shaped, one-dimensional structures on which one can solve differential equations to simulate a wide range of physical systems including conjugated molec…
Transmission and Reflection coefficients for Schrödinger Operators with Truncated Periodic Potentials that support defect states
Joseph C. Stellman, Jeremy L. Marzuola
We consider scattering waves through truncated periodic potentials with perturbations that support localized gap eigenstates. In a small complex neighborhood around an assumed posi…
Schr{ö}dinger maps to a K{ä}hler manifold in two dimensions
Benjamin Dodson, Jeremy L. Marzuola
We prove a global well--posedness and scattering result for Schr{ö}dinger maps to a general K{ä}hler manifold with small initial data in a Besov space.
Cauchy Data for 1D singular Schrödinger operators
Luc Hillairet, Jeremy L. Marzuola
We study semiclassical 1-D Schrödinger operators of the form on a finite interval for . We show…
Discrete Bound States in a Toy Model for Weak Turbulence and Implications for the Invariant Measure
Jeremy L. Marzuola, Jonathan C. Mattingly
A model Hamiltonian dynamical system has been derived to study frequency cascades in the cubic defocusing nonlinear Schrödinger equation on the torus. Here, we explore the framewo…