3,595 research outputs found
Exponential decay for the damped wave equation in unbounded domains
We study the decay of the semigroup generated by the damped wave equation in
an unbounded domain. We first prove under the natural geometric control
condition the exponential decay of the semigroup. Then we prove under a weaker
condition the logarithmic decay of the solutions (assuming that the initial
data are smoother). As corollaries, we obtain several extensions of previous
results of stabilisation and control
Diffusion in pores and its dependence on boundary conditions
We study the influence of the boundary conditions at the solid liquid
interface on diffusion in a confined fluid. Using an hydrodynamic approach, we
compute numerical estimates for the diffusion of a particle confined between
two planes. Partial slip is shown to significantly influence the diffusion
coefficient near a wall. Analytical expressions are derived in the low and high
confinement limits, and are in good agreement with numerical results. These
calculations indicate that diffusion of tagged particles could be used as a
sensitive probe of the solid-liquid boundary conditions.Comment: soumis \`a J.Phys. Cond. Matt. special issue on "Diffusion in
Liquids, Polymers, Biophysics and Chemical Dynamics
Blow-Up of Test Fields Near Cauchy Horizons
The behaviour of test fields near a compact Cauchy horizon is investigated.
It is shown that solutions of nonlinear wave equations on Taub spacetime with
generic initial data cannot be continued smoothly to both extensions of the
spacetime through the Cauchy horizon. This is proved using an energy method.
Similar results are obtained for the spacetimes of Moncrief containing a
compact Cauchy horizon and for more general matter models.Comment: 10 pages, Plain TeX, MPA-AR-92-
Energy and position resolution of a CdZnTe gamma-ray detector with orthogonal coplanar anodes
We report on the simulation, construction and performance of prototype CZT imaging detectors employing orthogonal coplanar anodes. These detectors employ a novel electrode geometry with non-collecting anode strips in 1D and collecting anode pixels, interconnected in rows, in the orthogonal dimensions. These detectors retain the spectroscopic and detection efficiency advantages of single carried charge sensing devices as well as the principal advantage of conventional strip detectors with orthogonal anode and cathode strips, i.e. an N X N array of imagin pixels are realized with only 2N electronic channels. Charge signals induced on the various electrodes of a prototype detector with 8 X 8 unit cells are in good agreement with the simulations. The position resolution is about 1 mm in the direction perpendicular to the pixel lines while it is of the order of 100 micrometers in the other direction. Energy resolutions of 0.9 percent at 662 keV, 2.6 percent at 122 keV and 5.7 percent at 60 keV have been obtained at room temperature
Linear superposition in nonlinear wave dynamics
We study nonlinear dispersive wave systems described by hyperbolic PDE's in
R^{d} and difference equations on the lattice Z^{d}. The systems involve two
small parameters: one is the ratio of the slow and the fast time scales, and
another one is the ratio of the small and the large space scales. We show that
a wide class of such systems, including nonlinear Schrodinger and Maxwell
equations, Fermi-Pasta-Ulam model and many other not completely integrable
systems, satisfy a superposition principle. The principle essentially states
that if a nonlinear evolution of a wave starts initially as a sum of generic
wavepackets (defined as almost monochromatic waves), then this wave with a high
accuracy remains a sum of separate wavepacket waves undergoing independent
nonlinear evolution. The time intervals for which the evolution is considered
are long enough to observe fully developed nonlinear phenomena for involved
wavepackets. In particular, our approach provides a simple justification for
numerically observed effect of almost non-interaction of solitons passing
through each other without any recourse to the complete integrability. Our
analysis does not rely on any ansatz or common asymptotic expansions with
respect to the two small parameters but it uses rather explicit and
constructive representation for solutions as functions of the initial data in
the form of functional analytic series.Comment: New introduction written, style changed, references added and typos
correcte
Geometric optics and instability for semi-classical Schrodinger equations
We prove some instability phenomena for semi-classical (linear or) nonlinear
Schrodinger equations. For some perturbations of the data, we show that for
very small times, we can neglect the Laplacian, and the mechanism is the same
as for the corresponding ordinary differential equation. Our approach allows
smaller perturbations of the data, where the instability occurs for times such
that the problem cannot be reduced to the study of an o.d.e.Comment: 22 pages. Corollary 1.7 adde
Predicted FeII Emission-Line Strengths from Active Galactic Nuclei
We present theoretical FeII emission line strengths for physical conditions
typical of Active Galactic Nuclei with Broad-Line Regions. The FeII line
strengths were computed with a precise treatment of radiative transfer using
extensive and accurate atomic data from the Iron Project. Excitation mechanisms
for the FeII emission included continuum fluorescence, collisional excitation,
self-fluorescence amoung the FeII transitions, and fluorescent excitation by
Lyman-alpha and Lyman-beta. A large FeII atomic model consisting of 827 fine
structure levels (including states to E ~ 15 eV) was used to predict fluxes for
approximately 23,000 FeII transitions, covering most of the UV, optical, and IR
wavelengths of astrophysical interest. Spectral synthesis for wavelengths from
1600 Angstroms to 1.2 microns is presented. Applications of present theoretical
templates to the analysis of observations are described. In particular, we
discuss recent observations of near-IR FeII lines in the 8500 Angstrom -- 1
micron region which are predicted by the Lyman-alpha fluorescence mechanism. We
also compare our UV spectral synthesis with an empirical iron template for the
prototypical, narrow-line Seyfert galaxy I Zw 1. The theoretical FeII template
presented in this work should also applicable to a variety of objects with FeII
spectra formed under similar excitation conditions, such as supernovae and
symbiotic stars.Comment: 33 pages, 15 postscript figure
AI naturalists might hold the key to unlocking biodiversity data in social media imagery
The increasing availability of digital images, coupled with sophisticated artificial intelligence (AI) techniques for image classification, presents an exciting opportunity for biodiversity researchers to create new datasets of species observations. We investigated whether an AI plant species classifier could extract previously unexploited biodiversity data from social media photos (Flickr). We found over 60,000 geolocated images tagged with the keyword “flower” across an urban and rural location in the UK and classified these using AI, reviewing these identifications and assessing the representativeness of images. Images were predominantly biodiversity focused, showing single species. Non-native garden plants dominated, particularly in the urban setting. The AI classifier performed best when photos were focused on single native species in wild situations but also performed well at higher taxonomic levels (genus and family), even when images substantially deviated from this. We present a checklist of questions that should be considered when undertaking a similar analysis
- …