A gradient estimate to a degenerate parabolic equation with a singular absorption term: The global quenching phenomena

We prove global existence of nonnegative solutions to the one dimensional degenerate parabolic problems containing a singular term. We also show the global quenching phenomena for L1 initial datums. Moreover, the free boundary problem is considered in this paper.

Long-range effects on optical absorption in quasiperiodic lattices

We consider exciton optical absorption in quasiperiodic lattices, focusing our attention on the Fibonacci case as a typical example. The absorption spectrum is evaluated by solving numerically the equation of motion of the Frenkel-exciton problem on the lattice, in which on-site energies take on two values according to the Fibonacci sequence. We find that the quasiperiodic order causes the occurrence of well-defined characteristic features in the absorption spectra. We also develop an analytical method that relates satellite lines with the Fourier pattern of the lattice. Our predictions can be used to determine experimentally the long-range quasiperiodic order from optical measurements.

X-ray absorption study of the ferromagnetic Cu moment at the YBa_(2)Cu_(3)O_(7)/La_(2/3)Ca_(1/3)MnO_(3) interface and variation of its exchange interaction with the Mn moment

With x-ray absorption spectroscopy and polarized neutron reflectometry we studied how the magnetic proximity effect at the interface between the cuprate high-TC superconductor YBa_(2)Cu_(3)O_(7) (YBCO) and the ferromagnet La_(2/3)Ca_(1/3)MnO_(3) (LCMO) is related to the electronic and magnetic properties of the LCMO layers. In particular, we explored how the magnitude of the ferromagnetic Cu moment on the YBCO side depends on the strength of the antiferromagnetic (AF) exchange coupling with the Mn moment on the LCMO side. We found that the Cu moment remains sizable if the AF coupling with the Mn moments is strongly reduced or even entirely suppressed. The ferromagnetic order of the Cu moments thus seems to be intrinsic to the interfacial CuO_(2) planes and related to a weakly ferromagnetic intraplanar exchange interaction. The latter is discussed in terms of the partial occupation of the Cu 3d_(3z^(2)−r^(2)) orbitals, which occurs in the context of the so-called orbital reconstruction of the interfacial Cu ions.