37,598 research outputs found
On the Born-Oppenheimer approximation of diatomic molecular resonances
We give a new reduction of a general diatomic molecular Hamiltonian, without
modifying it near the collision set of nuclei. The resulting effective
Hamiltonian is the sum of a smooth semiclassical pseudodifferential operator
(the semiclassical parameter being the inverse of the square-root of the
nuclear mass), and a semibounded operator localised in the elliptic region
corresponding to the nuclear collision set. We also study its behaviour on
exponential weights, and give several applications where molecular resonances
appear and can be well located.Comment: 22 page
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Optimized Multimode Interference Fiber Based Refractometer in A Reflective Interrogation Scheme
A fiber based refractometer in a reflective interrogation scheme is investigated and optimized. A thin gold film was deposited on the tip of a coreless fiber section, which is spliced with a single mode fiber. The coreless fiber is a multimode waveguide, and the observed effects are due to multimode interference. To investigate and optimize the structure, the multimode part of the sensor is built with 3 different lengths: 58 mm, 29 mm and 17 mm. We use a broadband light source ranging from 1475 nm to 1650 nm and we test the sensors with liquids of varying refractive indices, from 1.333 to 1.438. Our results show that for a fixed wavelength, the sensor sensitivity is independent of the multimode fiber length, but we observed a sensitivity increase of approximately 0.7 nm/RIU for a one-nanometer increase in wavelength
Towards a theory of differential constraints of a hydrodynamic hierarchy
We present a theory of compatible differential constraints of a hydrodynamic
hierarchy of infinite-dimensional systems. It provides a convenient point of
view for studying and formulating integrability properties and it reveals some
hidden structures of the theory of integrable systems. Illustrative examples
and new integrable models are exhibited.Comment: Published by JNMP at http://www.sm.luth.se/math/JNMP
Analyses of shocked quartz at the global K-P boundary indicate an origin from a single, high-angle, oblique impact at Chicxulub
Accepted versio
On the Whitham hierarchy: dressing scheme, string equations and additional symmetrie
A new description of the universal Whitham hierarchy in terms of a
factorization problem in the Lie group of canonical transformations is
provided. This scheme allows us to give a natural description of dressing
transformations, string equations and additional symmetries for the Whitham
hierarchy. We show how to dress any given solution and prove that any solution
of the hierarchy may be undressed, and therefore comes from a factorization of
a canonical transformation. A particulary important function, related to the
-function, appears as a potential of the hierarchy. We introduce a class
of string equations which extends and contains previous classes of string
equations considered by Krichever and by Takasaki and Takebe. The scheme is
also applied for an convenient derivation of additional symmetries. Moreover,
new functional symmetries of the Zakharov extension of the Benney gas equations
are given and the action of additional symmetries over the potential in terms
of linear PDEs is characterized
Dispersionless scalar integrable hierarchies, Whitham hierarchy and the quasi-classical dbar-dressing method
The quasi-classical limit of the scalar nonlocal dbar-problem is derived and
a quasi-classical version of the dbar-dressing method is presented.
Dispersionless KP, mKP and 2DTL hierarchies are discussed as illustrative
examples. It is shown that the universal Whitham hierarchy it is nothing but
the ring of symmetries for the quasi-classical dbar-problem. The reduction
problem is discussed and, in particular, the d2DTL equation of B type is
derived.Comment: LaTex file,19 page
On the Whitham hierarchy: dressing scheme, string equations and additional symmetrie
A new description of the universal Whitham hierarchy in terms of a
factorization problem in the Lie group of canonical transformations is
provided. This scheme allows us to give a natural description of dressing
transformations, string equations and additional symmetries for the Whitham
hierarchy. We show how to dress any given solution and prove that any solution
of the hierarchy may be undressed, and therefore comes from a factorization of
a canonical transformation. A particulary important function, related to the
-function, appears as a potential of the hierarchy. We introduce a class
of string equations which extends and contains previous classes of string
equations considered by Krichever and by Takasaki and Takebe. The scheme is
also applied for an convenient derivation of additional symmetries. Moreover,
new functional symmetries of the Zakharov extension of the Benney gas equations
are given and the action of additional symmetries over the potential in terms
of linear PDEs is characterized
Vortex distribution in the Lowest Landau Level
We study the vortex distribution of the wave functions minimizing the Gross
Pitaevskii energy for a fast rotating condensate in the Lowest Landau Level
(LLL): we prove that the minimizer cannot have a finite number of zeroes thus
the lattice is infinite, but not uniform. This uses the explicit expression of
the projector onto the LLL. We also show that any slow varying envelope
function can be approximated in the LLL by distorting the lattice. This is used
in particular to approximate the inverted parabola and understand the role of
``invisible'' vortices: the distortion of the lattice is very small in the
Thomas Fermi region but quite large outside, where the "invisible" vortices
lie.Comment: 4 pages, 1 figur
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Enhancing the Sensitivity of SMS Fiber Sensors by the Use of High Refractive Index Coatings
This paper presents a study on the behavior of single-mode/multimode/single-mode sensors with diamond-like carbon coating of high refractive index. Spectra and response for different values of the external medium refractive index are recorded and analyzed
Skyrmion morphology in ultrathin magnetic films
Nitrogen-vacancy magnetic microscopy is employed in quenching mode as a
non-invasive, high resolution tool to investigate the morphology of isolated
skyrmions in ultrathin magnetic films. The skyrmion size and shape are found to
be strongly affected by local pinning effects and magnetic field history.
Micromagnetic simulations including static disorder, based on a physical model
of grain-to-grain thickness variations, reproduce all experimental observations
and reveal the key role of disorder and magnetic history in the stabilization
of skyrmions in ultrathin magnetic films. This work opens the way to an
in-depth understanding of skyrmion dynamics in real, disordered media.Comment: 9 pages, 8 figures, including supplementary information
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