Stable blow up dynamics for the critical co-rotational Wave Maps and equivariant Yang-Mills problems

We exhibit stable finite time blow up regimes for the energy critical co-rotational Wave Map with the S^2 target in all homotopy classes and for the critical equivariant SO(4) Yang-Mills problem. We derive sharp asymptotics on the dynamics at the blow up time and prove quantization of the energy focused at the singularity

Dewetting on porous media with aspiration

We consider a porous solid covered with a water film (or with a drop) in situations where the liquid is pumped in, either spontaneously (if the porous medium is hydrophilic) or mechanically (by an external pump). The dynamics of dewetting is then strongly modified. We analyse a few major examples: a) horizontal films, which break at a certain critical thickness, b) the "modified Landau-Levich problem" where a porous plate moves up from a bath and carries a film: aspiration towards the plate limits the height H reached by the film, c) certain situation where the hysteresis of contact angles is important.Comment: Revised version: The analysis of the 'modified Landau-Levich problem' (section 3) has been significantly revised. It is now treated as a singular perturbation problem (using boundary-layer techniques), leading to a more accurate physical pictur

Characterizing the development of sectoral Gross Domestic Product composition

We consider the sectoral composition of a country's GDP, i.e. the partitioning into agrarian, industrial, and service sectors. Exploring a simple system of differential equations we characterize the transfer of GDP shares between the sectors in the course of economic development. The model fits for the majority of countries providing 4 country-specific parameters. Relating the agrarian with the industrial sector, a data collapse over all countries and all years supports the applicability of our approach. Depending on the parameter ranges, country development exhibits different transfer properties. Most countries follow 3 of 8 characteristic paths. The types are not random but show distinct geographic and development patterns.Comment: 7 pages, 4 figure

Dewetting of thin-film polymers

In this paper we present a theoretical model for the dewetting of ultra-thin polymer films. Assumming that the shear-thinning properties of these films can be described by a Cross-type constitutive equation, we analyze the front morphology of the dewetting film, and characterize the time evolution of the dry region radius, and of the rim height. Different regimes of growth are expected, depending on the initial film thickness, and on the power-law index involved in the constitutive equation. In the thin-films regime, the dry radius and the rim height obey power-law time dependences. We then compare our predictions with the experimental results obtained by Debr\'egeas {\it et al.} [Phys. Rev. Lett. {\bf 75}, 3886 (1995)] and by Reiter [Phys. Rev. Lett. {\bf 87}, 186101 (2001)].Comment: 12 pages, 14 figure

Financing Long-Term Care for Elderly People

Last year’s report of the Royal Commission on Long Term Care (1) and the expected Government response have prompted fresh interest in the debate on how to fund long-term care. To inform this debate the Personal Social Services Research Unit (PSSRU) has conducted a study, funded by the Department of Health, of long-term care demand and finance. This has involved the construction of a computer model to make projections of likely demand and expenditures to 2031. This article describes the model of long-term care demand and expenditure developed by the PSSRU. It then presents some of the results obtained and sensitivity analysis around them

Exoplanets imaging with a Phase-Induced Amplitude Apodization Coronagraph - I. Principle

Using 2 aspheric mirrors, it is possible to apodize a telescope beam without losing light or angular resolution: the output beam is produced by ``remapping'' the entrance beam to produce the desired light intensity distribution in a new pupil. We present the Phase-Induced Amplitude Apodization Coronagraph (PIAAC) concept, which uses this technique, and we show that it allows efficient direct imaging of extrasolar terrestrial planets with a small-size telescope in space. The suitability of the PIAAC for exoplanet imaging is due to a unique combination of achromaticity, small inner working angle (about 1.5 $\lambda/d$), high throughput, high angular resolution and large field of view. 3D geometrical raytracing is used to investigate the off-axis aberrations of PIAAC configurations, and show that a field of view of more than 100 $\lambda/d$ in radius is available thanks to the correcting optics of the PIAAC. Angular diameter of the star and tip-tilt errors can be compensated for by slightly increasing the size of the occulting mask in the focal plane, with minimal impact on the system performance. Earth-size planets at 10 pc can be detected in less than 30s with a 4m telescope. Wavefront quality requirements are similar to classical techniques.Comment: 35 pages, 16 figures, Accepted for publication in Ap

Synthesis, Crystal Structure and Photophysical Properties of Lanthanide Coordination Polymers of 4- 4-(9H-Carbazol-9-Yl)Butoxy Benzoate: The Effect of Bidentate Nitrogen Donors on Luminescence

A new aromatic carboxylate ligand, 4-[4-(9H-carbazol-9-yl)butoxy]benzoic acid (HL), has been synthesized by the replacement of the hydroxyl hydrogen of 4-hydroxy benzoic acid with a 9-butyl-9H-carbazole moiety. The anion derived from HL has been used for the support of a series of lanthanide coordination compounds [Ln = Eu (1), Gd (2) and Tb (3)]. The new lanthanide complexes have been characterized by a variety of spectroscopic techniques. Complex 3 was structurally authenticated by single-crystal X-ray diffraction and found to exist as a solvent-free 1D coordination polymer with the formula [Tb(L)(3)](n). The structural data reveal that the terbium atoms in compound 3 reside in an octahedral ligand environment that is somewhat unusual for a lanthanide. It is interesting to note that each carboxylate group exhibits only a bridging-bidentate mode, with a complete lack of more complex connectivities that are commonly observed for extended lanthanide-containing solid-state structures. Examination of the packing diagram for 3 revealed the existence of two-dimensional molecular arrays held together by means of CH-pi interactions. Aromatic carboxylates of the lanthanides are known to exhibit highly efficient luminescence, thus offering the promise of applicability as optical devices. However, due to difficulties that arise on account of their polymeric nature, their practical application is somewhat limited. Accordingly, synthetic routes to discrete molecular species are highly desirable. For this purpose, a series of ternary lanthanide complexes was designed, synthesized and characterized, namely [Eu(L)(3)(phen)] (4), [Eu(L)(3)(tmphen)] (5), [Tb(L)(3)(phen)] (6) and [Tb(L)(3)(tmphen)] (7) (phen = 1,10-phenanthroline and tmphen = 3,4,7,8-tetramethyl-1,10-phenanthroline). The photophysical properties of the foregoing complexes in the solid state at room temperature have been investigated. The quantum yields of the ternary complexes 4 (9.65%), 5 (21.00%), 6 (14.07%) and 7 (32.42%), were found to be significantly enhanced in the presence of bidentate nitrogen donors when compared with those of the corresponding binary compounds 1 (0.11%) and 3 (1.45%). Presumably this is due to effective energy transfer from the ancillary ligands.Council of Scientific and Industrial Research (CSIR-TAPSUN Project) SSL, NWP-55CSIR, New DelhiRobert A. Welch Foundation F-0003Chemistr

WKB Propagation of Gaussian Wavepackets

We analyze the semiclassical evolution of Gaussian wavepackets in chaotic systems. We prove that after some short time a Gaussian wavepacket becomes a primitive WKB state. From then on, the state can be propagated using the standard TDWKB scheme. Complex trajectories are not necessary to account for the long-time propagation. The Wigner function of the evolving state develops the structure of a classical filament plus quantum oscillations, with phase and amplitude being determined by geometric properties of a classical manifold.Comment: 4 pages, 4 figures; significant improvement