29,429 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
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
Parametrizing growth in dark energy and modified gravity models
It is well-known that an extremely accurate parametrization of the growth
function of matter density perturbations in CDM cosmology, with errors
below , is given by with . In this work, we show that a simple modification of this
expression also provides a good description of growth in modified gravity
theories. We consider the model-independent approach to modified gravity in
terms of an effective Newton constant written as and show
that provides fits to the numerical
solutions with similar accuracy to that of CDM. In the
time-independent case with , simple analytic expressions for
and are presented. In the time-dependent (but
scale-independent) case , we show that has the same time
dependence as . As an example, explicit formalae are provided in the
DGP model. In the general case, for theories with , we obtain a
perturbative expansion for around the General Relativity case
which, for theories, reaches an accuracy below . Finally,
as an example we apply the obtained fitting functions in order to forecast the
precision with which future galaxy surveys will be able to measure the
parameter.Comment: 12 pages, 12 figures. New section on applications to forecasts for
galaxy surveys and new references included. Matches version published in PR
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