3,818 research outputs found
Stable self similar blow up dynamics for slightly L^2 supercritical NLS equations
We consider the focusing nonlinear Schr\"odinger equations in dimension and for slightly
supercritical nonlinearities p_c
with and 0<\e\ll 1. We prove the existence and stability in the energy space of a self similar finite time blow up dynamics and provide a qualitative description of the singularity formation near the blow up tim
Transparent photonic band in metallodielectric nanostructures
Under certain conditions, a transparent photonic band can be designed into a
one-dimensional metallodielectric nanofilm structure. Unlike conventional pass
bands in photonic crystals, where the finite thickness of the structure affects
the transmission of electromagnetic fields having frequency within the pass
band, the properties of the transparent band are almost unaffected by the
finite thickness of the structure. In other words, an incident field at a
frequency within the transparent band exhibits 100% transmission independent of
the number of periods of the structure. The transparent photonic band
corresponds to excitation of pure eigenstate modes across the entire Bloch band
in structures possessing mirror symmetry. The conditions to create these modes
and thereby to lead to a totally transparent band phenomenon are discussed.Comment: To be published in Phys. Rev.
Renormalization and blow up for charge one equivariant critical wave maps
We prove the existence of equivariant finite time blow up solutions for the
wave map problem from 2+1 dimensions into the 2-sphere. These solutions are the
sum of a dynamically rescaled ground-state harmonic map plus a radiation term.
The local energy of the latter tends to zero as time approaches blow up time.
This is accomplished by first "renormalizing" the rescaled ground state
harmonic map profile by solving an elliptic equation, followed by a
perturbative analysis
Characteristics of bound modes in coupled dielectric waveguides containing negative index media
We investigate the characteristics of guided wave modes in planar coupled
waveguides. In particular, we calculate the dispersion relations for TM modes
in which one or both of the guiding layers consists of negative index media
(NIM)-where the permittivity and permeability are both negative. We find that
the Poynting vector within the NIM waveguide axis can change sign and
magnitude, a feature that is reflected in the dispersion curves
RBF neural net based classifier for the AIRIX accelerator fault diagnosis
The AIRIX facility is a high current linear accelerator (2-3.5kA) used for
flash-radiography at the CEA of Moronvilliers France. The general background of
this study is the diagnosis and the predictive maintenance of AIRIX. We will
present a tool for fault diagnosis and monitoring based on pattern recognition
using artificial neural network. Parameters extracted from the signals recorded
on each shot are used to define a vector to be classified. The principal
component analysis permits us to select the most pertinent information and
reduce the redundancy. A three layer Radial Basis Function (RBF) neural network
is used to classify the states of the accelerator. We initialize the network by
applying an unsupervised fuzzy technique to the training base. This allows us
to determine the number of clusters and real classes, which define the number
of cells on the hidden and output layers of the network. The weights between
the hidden and the output layers, realising the non-convex union of the
clusters, are determined by a least square method. Membership and ambiguity
rejection enable the network to learn unknown failures, and to monitor
accelerator operations to predict future failures. We will present the first
results obtained on the injector.Comment: 3 pages, 4 figures, LINAC'2000 conferenc
Continuations of the nonlinear Schr\"odinger equation beyond the singularity
We present four continuations of the critical nonlinear \schro equation (NLS)
beyond the singularity: 1) a sub-threshold power continuation, 2) a
shrinking-hole continuation for ring-type solutions, 3) a vanishing
nonlinear-damping continuation, and 4) a complex Ginzburg-Landau (CGL)
continuation. Using asymptotic analysis, we explicitly calculate the limiting
solutions beyond the singularity. These calculations show that for generic
initial data that leads to a loglog collapse, the sub-threshold power limit is
a Bourgain-Wang solution, both before and after the singularity, and the
vanishing nonlinear-damping and CGL limits are a loglog solution before the
singularity, and have an infinite-velocity{\rev{expanding core}} after the
singularity. Our results suggest that all NLS continuations share the universal
feature that after the singularity time , the phase of the singular core
is only determined up to multiplication by . As a result,
interactions between post-collapse beams (filaments) become chaotic. We also
show that when the continuation model leads to a point singularity and
preserves the NLS invariance under the transformation and
, the singular core of the weak solution is symmetric
with respect to . Therefore, the sub-threshold power and
the{\rev{shrinking}}-hole continuations are symmetric with respect to ,
but continuations which are based on perturbations of the NLS equation are
generically asymmetric
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