Knowledge Does Not Fall Far from the Tree - A Case Study on the Diffusion of Solar Cells in Germany

The purpose of this paper is to illuminate the geographical diffusion of photovoltaic installations in Germany quantitatively and to test if preexisting photovoltaic systems stimulate further installations nearby; thus we investigate to which extent knowledge flows depend on geographic proximity. We develop an econometric model, which is discrete in time and space, but the level of geographical agglomeration is adjustable in arbitrarily small steps. We find that the probability to install a photovoltaic system dependents on the geographic proximity to agents, who have previously installed a photovoltaic system. In conclusion, our results confirm that knowledge exchange attenuates with distance.

Interaction of modulated pulses in the nonlinear Schroedinger equation with periodic potential

We consider a cubic nonlinear Schroedinger equation with periodic potential. In a semiclassical scaling the nonlinear interaction of modulated pulses concentrated in one or several Bloch bands is studied. The notion of closed mode systems is introduced which allows for the rigorous derivation of a finite system of amplitude equations describing the macroscopic dynamics of these pulses

Leptoquark Pair Production at epep Colliders

The pair production cross section for scalar and vector leptoquarks at $ep$ colliders is calculated for the case of photon--gluon fusion. In a model independent analysis we consider the most general $C$ and $P$ conserving couplings of gluons and photons to both scalar and vector leptoquarks described by an effective low--energy Lagangian which obeys $U(1)_{em} \times SU(3)_c$ invariance. Numerical predictions are given for the kinematical regime at HERA and LEP~$\otimes$~LHC.Comment: 15 p., postscript encoded with uufiles; DESY 94--07

High-frequency averaging in semi-classical Hartree-type equations

We investigate the asymptotic behavior of solutions to semi-classical Schroedinger equations with nonlinearities of Hartree type. For a weakly nonlinear scaling, we show the validity of an asymptotic superposition principle for slowly modulated highly oscillatory pulses. The result is based on a high-frequency averaging effect due to the nonlocal nature of the Hartree potential, which inhibits the creation of new resonant waves. In the proof we make use of the framework of Wiener algebras.Comment: 13 pages; Version 2: Added Remark 2.