312 research outputs found
Orbital stability: analysis meets geometry
We present an introduction to the orbital stability of relative equilibria of
Hamiltonian dynamical systems on (finite and infinite dimensional) Banach
spaces. A convenient formulation of the theory of Hamiltonian dynamics with
symmetry and the corresponding momentum maps is proposed that allows us to
highlight the interplay between (symplectic) geometry and (functional) analysis
in the proofs of orbital stability of relative equilibria via the so-called
energy-momentum method. The theory is illustrated with examples from finite
dimensional systems, as well as from Hamiltonian PDE's, such as solitons,
standing and plane waves for the nonlinear Schr{\"o}dinger equation, for the
wave equation, and for the Manakov system
Global bifurcation for asymptotically linear Schr\"odinger equations
We prove global asymptotic bifurcation for a very general class of
asymptotically linear Schr\"odinger equations \begin{equation}\label{1}
\{{array}{lr} \D u + f(x,u)u = \lam u \quad \text{in} \ {\mathbb R}^N, u \in
H^1({\mathbb R}^N)\setmimus\{0\}, \quad N \ge 1. {array}. \end{equation} The
method is topological, based on recent developments of degree theory. We use
the inversion in an appropriate Sobolev space
, and we first obtain bifurcation from the line of
trivial solutions for an auxiliary problem in the variables (\lambda,v) \in
{\mathbb R} \x X. This problem has a lack of compactness and of regularity,
requiring a truncation procedure. Going back to the original problem, we obtain
global branches of positive/negative solutions 'bifurcating from infinity'. We
believe that, for the values of covered by our bifurcation approach,
the existence result we obtain for positive solutions of \eqref{1} is the most
general so fa
Imaging Transient Blood Vessel Fusion Events by Correlative Volume Electron Microscopy
Extended abstract of a paper presented at Microscopy and Microanalysis 2010 in Portland, Oregon, USA, August 1 - August 5, 201
A series of algebras generalizing the octonions and Hurwitz-Radon identity
International audienceWe study non-associative twisted group algebras over (ℤ2)n with cubic twisting functions. We construct a series of algebras that extend the classical algebra of octonions in the same way as the Clifford algebras extend the algebra of quaternions. We study their properties, give several equivalent definitions and prove their uniqueness within some natural assumptions. We then prove a simplicity criterion. We present two applications of the constructed algebras and the developed technique. The first application is a simple explicit formula for the following famous square identity: (a21+⋯+a2N)(b21+⋯+b2ρ(N))=c21+⋯+c2N , where c k are bilinear functions of the a i and b j and where ρ(N) is the Hurwitz-Radon function. The second application is the relation to Moufang loops and, in particular, to the code loops. To illustrate this relation, we provide an explicit coordinate formula for the factor set of the Parker loop
Cancellation of probe effects in measurements of spin polarized momentum density by electron positron annihilation
Measurements of the two dimensional angular correlation of the
electron-positron annihilation radiation have been done in the past to detect
the momentum spin density and the Fermi surface. We point out that the momentum
spin density and the Fermi Surface of ferromagnetic metals can be revealed
within great detail owing to the large cancellation of the electron-positron
matrix elements which in paramagnetic multiatomic systems plague the
interpretation of the experiments. We prove our conjecture by calculating the
momentum spin density and the Fermi surface of the half metal CrO2, who has
received large attention due to its possible applications as spintronics
material
Effect of a noisy driving field on a bistable polariton system
International audienceWe report on the effect of noise on the characteristics of the bistable polariton emission system. The present experiment provides a time-resolved access to the polariton emission intensity. We evidence the noise-induced transitions between the two stable states of the bistable polaritons. It is shown that the external noise specifications, intensity and correlation time, can efficiently modify the polariton Kramers time and residence time. We find that there is a threshold noise strength that provokes the collapse of the hysteresis loop. The experimental results are reproduced by numerical simulations using Gross-Pitaevskii equation driven by a stochastic excitation
Spin-to-Orbital Angular Momentum Conversion in Semiconductor Microcavities
We experimentally demonstrate a technique for the generation of optical beams
carrying orbital angular momentum using a planar semiconductor microcavity.
Despite being isotropic systems, the transverse electric - transverse magnetic
(TE-TM) polarization splitting featured by semiconductor microcavities allows
for the conversion of the circular polarization of an incoming laser beam into
the orbital angular momentum of the transmitted light field. The process
implies the formation of topological entities, a pair of optical half-vortices,
in the intracavity field
Scanning Tunneling Microscope-Induced Luminescence Spectroscopy on Semiconductor Heterostructures
Scanning tunneling microscope (STM)-induced luminescence is explored as a technique for the characterization of semiconductor quantum wells and quantum wire heterostructures. By injecting minority carriers into the cleaved cross section of these structures, luminescence excitation on a nanometer scale is demonstrated. Using spectrally resolved STM-induced luminescence for the tip placed at various positions across the cleaved heterostructure, it is possible to obtain local spectroscopic information on closely spaced quantum structures
Frieze Patterns of Integers
The famous theorem of Conway and Coxeter on frieze patterns gave a geometric
interpretation to integral friezes via triangulations of polygons. In this
article, we review this result and show some of the development it has led to.
The last decade has seen a lot of activities on friezes. One reason behind this
is the connection to cluster combinatorics.Comment: 9 pages, 6 figure
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