53,567 research outputs found
Creation of blenders in the conservative setting
In this work we prove that each C^r conservative diffeomorphism with a pair
of hyperbolic periodic points of co-index one can be C^1-approximated by C^r
conservative diffeomorphisms having a blender.Comment: 4 figures, 16 figure
Surface Waves and Forced Oscillations in QHE Planar Samples
Dispersion relations and polarizations for surface waves in infinite planar
samples in the QHE regime are explicitly determined in the small wavevector
limit in which the dielectric tensor can be considered as local. The wavelength
and frequency regions of applicability of the results extends to the infrared
region for typical experimental conditions. Then, standard samples with
millimetric sizes seem to be able to support such excitations. Forced
oscillations are also determined which should be generated in the 2DEG by
external electromagnetic sources. They show an almost frequency independent
wavevelength which decreases with the magnetic field. A qualitative model based
in these solutions is also presented to describe a recently found new class of
resonances appearing near the edge of a 2DEG in the QHE regime.Comment: latex file, 18 pages, 3 figures, spelling correcte
Identifying the lights position in photometric stereo under unknown lighting
Reconstructing the 3D shape of an object from a set of images is a classical
problem in Computer Vision. Photometric stereo is one of the possible
approaches. It stands on the assumption that the object is observed from a
fixed point of view under different lighting conditions. The traditional
approach requires that the position of the light sources is accurately known.
It has been proved that the lights position can be estimated directly from the
data, when at least 6 images of the observed object are available. In this
paper, we give a Matlab implementation of the algorithm for solving the
photometric stereo problem under unknown lighting, and propose a simple
shooting technique to solve the bas-relief ambiguity.Comment: new versio
Improving the applicability of radar rainfall estimates for urban pluvial flood modelling and forecasting
This work explores the possibility of improving the applicability of radar rainfall estimates (whose accuracy is generally insufficient) to the verification and operation of urban storm-water drainage models by employing a number of local gauge-based radar rainfall adjustment techniques. The adjustment techniques tested in this work include a simple mean-field bias (MFB) adjustment, as well as a more complex Bayesian radar-raingauge data merging method which aims at better preserving the spatial structure of rainfall fields. In addition, a novel technique (namely, local singularity analysis) is introduced and shown to improve the Bayesian method by better capturing and reproducing storm patterns and peaks. Two urban catchments were used as case studies in this work: the Cranbrook catchment (9 km2) in North-East London, and the Portobello catchment (53 km2) in the East of Edinburgh. In the former, the potential benefits of gauge-based adjusted radar rainfall estimates in an operational context were analysed, whereas in the latter the potential benefits of adjusted estimates for model verification purposes were explored. Different rainfall inputs, including raingauge, original radar and the aforementioned merged estimates were fed into the urban drainage models of the two catchments. The hydraulic outputs were compared against available flow and depth records. On the whole, the tested adjustment techniques proved to improve the applicability of radar rainfall estimates to urban hydrological applications, with the Bayesian-based methods, in particular the singularity sensitive one, providing more realistic and accurate rainfall fields which result in better reproduction of the urban drainage system’s dynamics. Further testing is still necessary in order to better assess the benefits of these adjustment methods, identify their shortcomings and improve them accordingly
Crossover between the Dense Electron-Hole Phase and the BCS Excitonic Phase in Quantum Dots
Second order perturbation theory and a Lipkin-Nogami scheme combined with an
exact Monte Carlo projection after variation are applied to compute the
ground-state energy of electron-hole pairs confined in a
parabolic two-dimensional quantum dot. The energy shows nice scaling properties
as N or the confinement strength is varied. A crossover from the high-density
electron-hole phase to the BCS excitonic phase is found at a density which is
roughly four times the close-packing density of excitons.Comment: Improved variational and projection calculations. 17 pages, 3 ps
figures. Accepted for publication in Int. J. Mod. Phys.
Generating Bounds for the Ground State Energy of the Infinite Quantum Lens Potential
Moment based methods have produced efficient multiscale quantization
algorithms for solving singular perturbation/strong coupling problems. One of
these, the Eigenvalue Moment Method (EMM), developed by Handy et al (Phys. Rev.
Lett.{\bf 55}, 931 (1985); ibid, {\bf 60}, 253 (1988b)), generates converging
lower and upper bounds to a specific discrete state energy, once the signature
property of the associated wavefunction is known. This method is particularly
effective for multidimensional, bosonic ground state problems, since the
corresponding wavefunction must be of uniform signature, and can be taken to be
positive. Despite this, the vast majority of problems studied have been on
unbounded domains. The important problem of an electron in an infinite quantum
lens potential defines a challenging extension of EMM to systems defined on a
compact domain. We investigate this here, and introduce novel modifications to
the conventional EMM formalism that facilitate its adaptability to the required
boundary conditions.Comment: Submitted to J. Phys.
Collective resonances in plasmonic crystals: Size matters
Periodic arrays of metallic nanoparticles may sustain Surface Lattice
Resonances (SLRs), which are collective resonances associated with the
diffractive coupling of Localized Surface Plasmon Resonances (LSPRs). By
investigating a series of arrays with varying number of particles, we traced
the evolution of SLRs to its origins. Polarization resolved extinction spectra
of arrays formed by a few nanoparticles were measured, and found to be in very
good agreement with calculations based on a coupled dipole model. Finite size
effects on the optical properties of the arrays are observed, and our results
provide insight into the characteristic length scales for collective plasmonic
effects: for arrays smaller than 5 x 5 particles, the Q-factors of SLRs are
lower than those of LSPRs; for arrays larger than 20 x 20 particles, the
Q-factors of SLRs saturate at a much larger value than those of LSPRs; in
between, the Q-factors of SLRs are an increasing function of the number of
particles in the array.Comment: 4 figure
Analytical results for a Bessel function times Legendre polynomials class integrals
When treating problems of vector diffraction in electromagnetic theory, the
evaluation of the integral involving Bessel and associated Legendre functions
is necessary. Here we present the analytical result for this integral that will
make unnecessary numerical quadrature techniques or localized approximations.
The solution is presented using the properties of the Bessel and associated
Legendre functions.Comment: 4 page
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