554 research outputs found
Cauchy problem and quasi-stationary limit for the Maxwell-Landau-Lifschitz and Maxwell-Bloch equations
In this paper we continue the investigation of the Maxwell-Landau-Lifschitz
and Maxwell-Bloch equations. In particular we extend some previous results
about the Cauchy problem and the quasi-stationary limit to the case where the
magnetic permeability and the electric permittivity are variable
Justification of the log-KdV equation in granular chains: the case of precompression
For travelling waves with nonzero boundary conditions, we justify the
logarithmic Korteweg-de Vries equation as the leading approximation of the
Fermi-Pasta-Ulam lattice with Hertzian nonlinear potential in the limit of
small anharmonicity. We prove control of the approximation error for the
travelling solutions satisfying differential advance-delay equations, as well
as control of the approximation error for time-dependent solutions to the
lattice equations on long but finite time intervals. We also show nonlinear
stability of the travelling waves on long but finite time intervals.Comment: 29 page
On the weak solutions to the Maxwell-Landau-Lifshitz equations and to the Hall-Magneto-Hydrodynamic equations
In this paper we deal with weak solutions to the Maxwell-Landau-Lifshitz
equations and to the Hall-Magneto-Hydrodynamic equations. First we prove that
these solutions satisfy some weak-strong uniqueness property. Then we
investigate the validity of energy identities. In particular we give a
sufficient condition on the regularity of weak solutions to rule out anomalous
dissipation. In the case of the Hall-Magneto-Hydrodynamic equations we also
give a sufficient condition to guarantee the magneto-helicity identity. Our
conditions correspond to the same heuristic scaling as the one introduced by
Onsager in hydrodynamic theory. Finally we examine the sign, locally, of the
anomalous dissipations of weak solutions obtained by some natural approximation
processes.Comment: 45 page
Geometric optics and instability for NLS and Davey-Stewartson models
We study the interaction of (slowly modulated) high frequency waves for
multi-dimensional nonlinear Schrodinger equations with gauge invariant
power-law nonlinearities and non-local perturbations. The model includes the
Davey--Stewartson system in its elliptic-elliptic and hyperbolic-elliptic
variant. Our analysis reveals a new localization phenomenon for non-local
perturbations in the high frequency regime and allows us to infer strong
instability results on the Cauchy problem in negative order Sobolev spaces,
where we prove norm inflation with infinite loss of regularity by a
constructive approach.Comment: 33 page
From Newton's cradle to the discrete p-Schr\"odinger equation
We investigate the dynamics of a chain of oscillators coupled by
fully-nonlinear interaction potentials. This class of models includes Newton's
cradle with Hertzian contact interactions between neighbors. By means of
multiple-scale analysis, we give a rigorous asymptotic description of small
amplitude solutions over large times. The envelope equation leading to
approximate solutions is a discrete p-Schr\"odinger equation. Our results
include the existence of long-lived breather solutions to the original model.
For a large class of localized initial conditions, we also estimate the maximal
decay of small amplitude solutions over long times
The Central Kiloparsec of Seyfert and Inactive Host Galaxies: a Comparison of Two-Dimensional Stellar and Gaseous Kinematics
We investigate the properties of the two-dimensional distribution and
kinematics of ionised gas and stars in the central kiloparsecs of a matched
sample of nearby active (Seyfert) and inactive galaxies, using the SAURON
Integral Field Unit on the William Herschel Telescope. The ionised gas
distributions show a range of low excitation regions such as star formation
rings in Seyferts and inactive galaxies, and high excitation regions related to
photoionisation by the AGN. The stellar kinematics of all galaxies in the
sample show regular rotation patterns typical of disc-like systems, with
kinematic axes which are well aligned with those derived from the outer
photometry and which provide a reliable representation of the galactic line of
nodes. After removal of the non-gravitational components due to e.g. AGN-driven
outflows, the ionised gas kinematics in both the Seyfert and inactive galaxies
are also dominated by rotation with global alignment between stars and gas in
most galaxies. This result is consistent with previous findings from
photometric studies that the large-scale light distribution of Seyfert hosts
are similar to inactive hosts. However, fully exploiting the two-dimensional
nature of our spectroscopic data, deviations from axisymmetric rotation in the
gaseous velocity fields are identified that suggest the gaseous kinematics are
more disturbed at small radii in the Seyfert galaxies compared with the
inactive galaxies, providing a tentative link between nuclear gaseous streaming
and nuclear activity.Comment: Accepted for publication in MNRAS, 34 pages, 20 figure
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