Projected SO(5) Hamiltonian for Cuprates and Its Applications

The projected SO(5) (pSO(5)) Hamiltonian incorporates the quantum spin and superconducting fluctuations of underdoped cuprates in terms of four bosons moving on a coarse grained lattice. A simple mean field approximation can explain some key feautures of the experimental phase diagram: (i) The Mott transition between antiferromagnet and superconductor, (ii) The increase of T_c and superfluid stiffness with hole concentration x and (iii) The increase of antiferromagnetic resonance energy as sqrt{x-x_c} in the superconducting phase. We apply this theory to explain the ``two gaps'' problem found in underdoped cuprate Superconductor-Normal- Superconductor junctions. In particular we explain the sharp subgap Andreev peaks of the differential resistance, as signatures of the antiferromagnetic resonance (the magnon mass gap). A critical test of this theory is proposed. The tunneling charge, as measured by shot noise, should change by increments of Delta Q= 2e at the Andreev peaks, rather than by Delta Q=e as in conventional superconductors.Comment: 3 EPS figure

A fair deal for care in older age? Public attitudes towards the funding of long-term care

The government has made nursing care in England and Wales free, while continuing to means-test personal care. This policy contrasts with the recommendation for free personal care made by the Royal Commission on Long-term Care in 1999. This article reports on a survey of attitudes towards financing care in old age from a representative sample of men and women in England aged 25 years and over. The majority of people feel that the state should finance care for older people. The article discusses the extent to which this is consistent with the government's position and the competing notions of equity that recent debate entails

Single Fiber Transport in a Fracture Slit: Influence of the Wall Roughness and of the Fiber Flexibility

International audienceThe transport of fibers by a fluid flow is investigated in transparent channels modelling rock fractures: the experiments use flexible polyester thread (mean diameter $280 \mu\mathrm{m}$) and water or a water-polymer solution. For a channel with smooth parallel walls and a mean aperture $\bar{a} = 0.65\,\mathrm{mm}$, both fiber segments of length $\ell = 20-150\, \mathrm{mm}$ and ``continuous'' fibers longer than the channel length have been used: in both cases, the velocity of the fibers and its variation with distance could be accounted for while neglecting friction with the walls. For rough self-affine walls and a continuous gradient of the local mean aperture transverse to the flow, transport of the fibers by a water flow is only possible in the region of larger aperture ($\bar{a} \gtrsim 1.1 \mathrm{mm}$) and is of ``stop and go'' type at low velocities. With the polymer solution, the fibers move faster and more continuously in high aperture regions and their interaction with the walls is reduced; fiber transport becomes also possible in narrower regions where irreversible pinning occurred for water. In a third rough model with parallel walls and a low mean aperture $\bar{a}=0.65 \mathrm{mm}$, fiber transport is only possible with the water-polymer solution. The dynamics of fiber deformations and entanglement during pinning-depinning events and permanent pinning is analyzed