29,292 research outputs found
Space-modulated Stability and Averaged Dynamics
In this brief note we give a brief overview of the comprehensive theory,
recently obtained by the author jointly with Johnson, Noble and Zumbrun, that
describes the nonlinear dynamics about spectrally stable periodic waves of
parabolic systems and announce parallel results for the linearized dynamics
near cnoidal waves of the Korteweg-de Vries equation. The latter are expected
to contribute to the development of a dispersive theory, still to come.Comment: Proceedings of the "Journ\'ees \'Equations aux d\'eriv\'ees
partielles", Roscoff 201
Linear Asymptotic Stability and Modulation Behavior near Periodic Waves of the Korteweg-de Vries Equation
We provide a detailed study of the dynamics obtained by linearizing the
Korteweg-de Vries equation about one of its periodic traveling waves, a cnoidal
wave. In a suitable sense, linearly analogous to space-modulated stability, we
prove global-in-time bounded stability in any Sobolev space, and asymptotic
stability of dispersive type. Furthermore, we provide both a leading-order
description of the dynamics in terms of slow modulation of local parameters and
asymptotic modulation systems and effective initial data for the evolution of
those parameters. This requires a global-in-time study of the dynamics
generated by a non normal operator with non constant coefficients. On the road
we also prove estimates on oscillatory integrals particularly suitable to
derive large-time asymptotic systems that could be of some general interest
Microscopic Model for Sequential Tunneling in Semiconductor Multiple Quantum Wells
We propose a selfconsistent microscopic model of vertical sequential
tunneling through a multi-quantum well.The model includes a detailed
description of the contacts,uses the Transfer Hamiltonian for expressions of
the current and it treats the Coulomb interaction within a mean field
approximation. We analyze the current density through a double well and a
superlattice and study the formation of electric field domains and
multistability coming from the Coulomb interaction. Phase diagrams of parameter
regions (bias, doping in the heterostructure and in the contacts,etc) where the
different solutions exist are given.Comment: 4 pages, 8 Postscript Figure
The planar-to-tubular structural transition in boron clusters from optical absorption
The optical response of the lowest energy isomers of the B_20 family is
calculated using time-dependent density functional theory within a real-space,
real-time scheme. Significant differences are found among the absorption
spectra of the clusters studied. We show that these differences can be easily
related to changes in the overall geometry. Optical spectroscopy is thus an
efficient tool to characterize the planar to tubular structural transition,
known to be present in these boron based systems
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