10,238 research outputs found
Linear response of the two-dimensional pure electron plasma: Quasimodes for some model profiles
After examining the initial value problem for the linear, diocotron response of a long cylinder of pure-electron plasma, the "quasimodes" associated with convex, power-law density profiles are studied. For these profiles, exact, analytic results are available. The "quasimodes," which are damped by phase mixing, may be characterized by their angular variation, flatness, and the magnitude of the gap separating the plasma from the containing wall
Symplectic Structures for the Cubic Schrodinger equation in the periodic and scattering case
We develop a unified approach for construction of symplectic forms for 1D
integrable equations with the periodic and rapidly decaying initial data. As an
example we consider the cubic nonlinear Schr\"{o}dinger equation.Comment: This is expanded and corrected versio
Whittaker-Hill equation and semifinite-gap Schroedinger operators
A periodic one-dimensional Schroedinger operator is called semifinite-gap if
every second gap in its spectrum is eventually closed. We construct explicit
examples of semifinite-gap Schroedinger operators in trigonometric functions by
applying Darboux transformations to the Whittaker-Hill equation. We give a
criterion of the regularity of the corresponding potentials and investigate the
spectral properties of the new operators.Comment: Revised versio
Relative Oscillation Theory, Weighted Zeros of the Wronskian, and the Spectral Shift Function
We develop an analog of classical oscillation theory for Sturm-Liouville
operators which, rather than measuring the spectrum of one single operator,
measures the difference between the spectra of two different operators.
This is done by replacing zeros of solutions of one operator by weighted
zeros of Wronskians of solutions of two different operators. In particular, we
show that a Sturm-type comparison theorem still holds in this situation and
demonstrate how this can be used to investigate the finiteness of eigenvalues
in essential spectral gaps. Furthermore, the connection with Krein's spectral
shift function is established.Comment: 26 page
Stability Analysis in Magnetic Resonance Elastography II
We consider the inverse problem of finding unknown elastic parameters from
internal measurements of displacement fields for tissues. In the sequel to
Ammari, Waters, Zhang (2015), we use pseudodifferential methods for the problem
of recovering the shear modulus for Stokes systems from internal data. We prove
stability estimates in with reduced regularity on the estimates and
show that the presence of a finite dimensional kernel can be removed. This
implies the convergence of the Landweber numerical iteration scheme. We also
show that these hypotheses are natural for experimental use in constructing
shear modulus distributions.Comment: 14 page
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