Dissipation anomaly and energy cascade in 3D incompressible flows

The purpose of this note is to present a mathematical evidence of dissipation anomaly in 3D turbulent flows within a general setting for the study of energy cascade in physical scales of 3D incompressible flows recently introduced by the authors.Comment: accepted to C. R. Math. Acad. Sci. Paris, final versio

Spin paramagnetism in d-wave superconductors

The Ginzburg-Landau equations are derived from the microscopic theory for clean layered superconductors with $d_{x^2-y^2}$ pairing symmetry, including the Pauli paramagnetism effect. The upper critical field $H_{c2}$ parallel to the $c$ axis is calculated. A comparison with the experimental data for YBCO suggests that, relative to the orbital effect, the Pauli paramagnetism contribution to $H_{c2}$ is significant. The reversible magnetization $M$ in high magnetic fields is also calculated, showing strong temperature dependence of the slope $dM/dH$, as a consequence of the spin paramagnetism. A simple expression for the high temperature spin susceptibility is derived, in a good agreement with the Knight shift measurements on YBCO.Comment: 8 pages, 3 figures; minor changes are included; reference 35 is added; shorter version will be published in Phys. Rev. B, scheduled issue 01 July 200