Consistent operator semigroups and their interpolation

Under a mild regularity condition we prove that the generator of the interpolation of two C0-semigroups is the interpolation of the two generators

H\"older estimates for parabolic operators on domains with rough boundary

We investigate linear parabolic, second-order boundary value problems with mixed boundary conditions on rough domains. Assuming only boundedness and ellipticity on the coefficient function and very mild conditions on the geometry of the domain, including a very weak compatibility condition between the Dirichlet boundary part and its complement, we prove H\"older continuity of the solution in space and time.Comment: 1 figur

Parabolic equations with dynamical boundary conditions and source terms on interfaces

We consider parabolic equations with mixed boundary conditions and domain inhomogeneities supported on a lower dimensional hypersurface, enforcing a jump in the conormal derivative. Only minimal regularity assumptions on the domain and the coefficients are imposed. It is shown that the corresponding linear operator enjoys maximal parabolic regularity in a suitable $L^p$-setting. The linear results suffice to treat also the corresponding nondegenerate quasilinear problems.Comment: 30 pages. Revised version. To appear in Annali di Matematica Pura ed Applicat

Reversing a granular flow on a vibratory conveyor

Experimental results are presented on the transport properties of granular materials on a vibratory conveyor. For circular oscillations of the shaking trough a non-monotonous dependence of the transport velocity on the normalized acceleration is observed. Two maxima are separated by a regime, where the granular flow is much slower and, in a certain driving range, even reverses its direction. A similar behavior is found for a single solid body with a low coefficient of restitution, whereas an individual glass bead of 1 mm diameter is propagated in the same direction for all accelerations.Comment: 4 pages, 5 figures, submitted to Applied Physics Letter

Hölder estimates for second-order operators with mixed boundary conditions

In this paper we investigate linear elliptic, second-order boundary value problems with mixed boundary conditions. Assuming only boundedness/ellipticity on the coefficient function and very mild conditions on the geometry of the domain -- including a very weak compatibility condition between the Dirichlet boundary part and its complement -- we prove first Hölder continuity of the solution. Secondly, Gaussian Hölder estimates for the corresponding heat kernel are derived. The essential instruments are De Giorgi and Morrey-Campanato estimates

Strangeness Production Incorporating Chiral Symmetry

Chiral symmetry is known to be decisive for an understanding of the low energy sector of strong interactions. It is thus important for a model of relativistic heavy ion collisions to incorporate the dynamical breaking and restoration of chiral symmetry. Thus we study an expansion scenario for a quark-meson plasma using the Nambu--Jona-Lasinio (NJL) model in its three flavor version. The equations of motion for light and strange quarks as well as for pions, kaons and etas are solved using a QMD type algorithm, which is based on a parametrization of the Wigner function. The scattering processes incorporated into this calculation are of the types qq qq, q\bar q q\bar q, q\bar q MM and M q\bar q.Comment: Talk presented at the 4th International Symposium on Strangeness in Quark Matter, Padova, Italy, July 20--2

Period tripling causes rotating spirals in agitated wet granular layers

Pattern formation of a thin layer of vertically agitated wet granular matter is investigated experimentally. Rotating spirals with three arms, which correspond to the kinks between regions with different colliding phases, are the dominating pattern. This preferred number of arms corresponds to period tripling of the agitated granular layer, unlike predominantly subharmonic Faraday crispations in dry granular matter. The chirality of the spatiotemporal pattern corresponds to the rotation direction of the spirals.Comment: 4 pages, 6 figures, to appear in Physical Review Letter

On the numerical range of sectorial forms

We provide a sharp and optimal generic bound for the angle of the sectorial form associated to a non-symmetric second-order elliptic differential operator with various boundary conditions. Consequently this gives an, in general, sharper H∞-angle for the H∞-calculus on Lp for all p ∈ (1, ∞) if the coefficients are real valued

Essential boundedness for solutions of the Neumann problem on general domains

Let the domain under consideration be bounded. Under the suppositions of very weak Sobolev embeddings we prove that the solutions of the Neumann problem for an elliptic, second order divergence operator are essentially bounded, if the right hand sides are taken from the dual of a Sobolev space which is adapted to the above embedding