Null orbital frustration at the pseudogap boundary in a layered cuprate superconductor

We assess the relative importance of orbital frustration at the pseudogap closing field H(pg). Using interlayer tunneling transport in pulsed magnetic fields nearly up to 60 T, we track the field-temperature (H-T) phase diagram for fields parallel ( parallel ab) and normal ( parallel c) to the layered structure of Bi(2)Sr(2)CaCu(2)O(8+y). In contrast to large orientational anisotropy of the superconducting state related to the orbital motion of Cooper pairs, we find anisotropy of H(pg) temperature independent and small, due solely to the g factor. The obtained Zeeman relation with the pseudogap temperature T small star, filled, g( parallel c)micro(B)H( parallel c)(pg)=g( parallel ab)micro(B)H( parallel ab)(pg) approximately k(B)T small star, filled, is fully consistent with the correlations only in the spin channel.     

Über maximaleL p-Regularität für Differentialgleichungen in Banach- und Hilbert-Räumen

Ohne ZusammenfassungDie Forschung wurde teilweise unterstützt durch die Deutsche Forschungsgemeinschaft (DFG), Bonn, Nr. Ki 131/3-1     

Dispersive and long-time behavior of oscillations in lattices

We study the long-time dynamics of oscillations in lattices of infinitely many particles interacting via harmonic springs and adumbrate how decay rates for the displacements are proved analytically applying methods for oscillatory integrals. After recapitulating the results of an infinite chain with nearest-neighbour interaction, we highlight the differences to the case of next-nearest-neighbour interaction. Finally we give an outlook on the two dimensional lattice with nearest-neighbour interaction where more complicated singularities occur. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On nonlinear problems of mixed type: A qualitative theory using infinite-dimensional center manifolds

We consider the equation a(y)u_xx+div_y(b(y)_yu)+c(y)u=g(y, u) in the cylinder (–l,l)×, being elliptic where b(y)>0 and hyperbolic where b(y)<0. We construct self-adjoint realizations in L₂() of the operatorAu= (1/a) div_y(b_yu)+(c/a) in the case ofb changing sign. This leads to the abstract problem u_xx+Au=g(u), whereA has a spectrum extending to + as well as to –. For l= it is shown that all sufficiently small solutions lie on an infinite-dimensional center manifold and behave like those of a hyperbolic problem. Anx-independent cross-sectional integral E=E(u, u_x) is derived showing that all solutions on the center manifold remain bounded forx ±. For finitel, all small solutionsu are close to a solution on the center manifold such that u(x)-(x) Ce ^-(1-|x|) for allx, whereC and are independent ofu. Hence, the solutions are dominated by hyperbolic properties, except close to the terminal ends {±1}×, where boundary layers of elliptic type appear.     

Saint-Venant's problem and semi-inverse solutions in nonlinear elasticity

Saint-Venant's problem consists in finding elastic deformations of an infinite prismatic body taking given values for the cross-sectional resultants of force and moment. Using the center manifold approach we show that all deformations having sufficiently small bounded strains lie on a finite-dimensional manifold. In particular, the flow on this manifold is described by a set of equations having exactly the form of the classical rod equations. Moreover, the set of semi-inverse solutions can be analyzed locally.