Convergence of path measures arising from a mean field or polaron type interaction

Summary We discuss the limiting path measures of Markov processes with either a mean field or a polaron type interaction of the paths. In the polaron type situation the strength is decaying at large distances on the time axis, and so the interaction is of short range in time. In contrast, in the mean field model, the interaction is weak, but of long range in time. Donsker and Varadhan proved that for the partition functions, there is a transition from the polaron type to the mean field interaction when passing to a limit by letting the strength tend to zero while increasing the range. The discussion of the path measures is more subtle. We treat the mean field case as an example of a differentiable interaction and discuss the transition from the polaron type to the mean field interaction for two instructive examples.Research supported by the Swiss National Foundation (21-29833.90)This article was processed by the authors using the Springer-Verlag T_EX ProbTh macro package 1991.     

Limit for pulse compression by pulse splitting

We have detected a fundamental pulse-compression limit for high-nonlinear fibers in the normal dispersion regime near the zero-dispersion wavelength. The desired generation of a broadband continuum by self-phase modulation is limited by already small amounts of third-order dispersion (TOD), which results in pulse splitting above a critical pulse power. We investigate the critical fiber length in dependence on pulse- and fiber parameters.     

TERAHERTZ QUALITY CONTROL OF POLYMERIC PRODUCTS

We report on experiments that evaluate the potential of terahertz (THz) time-domain spectroscopy (TDS) for quality control of polymeric compounds. We investigate specimens out of a polyethylene compound with silver-coated titanium dioxide nanospheres and a glass-fiber reinforced epoxy composite. We further examine an industrial polymer product produced by injection molding. Our data demonstrates that THz imaging is a powerful tool for contactless quality control in the polymer industry.     

Two modifications of a five‐coordinate silicon complex

TBPY‐5‐34‐(Butane‐1,4‐diyl)(2‐{[1‐(2‐oxidophenyl)ethylidene‐κO]amino‐κN}ethanolato‐κO)silicon, C₁₄H₁₉NO₂Si, crystallizes in two modifications. The monoclinic form, (IIm), was obtained by crystallization over a period of 2 d at room temperature; the orthorhombic form, (IIo), crystallized overnight at 248 K. The main difference between the two molecular structures involves the angles in the equatorial plane of the trigonal bipyramid around silicon. Form (IIm) has an O—Si—O angle of ca 121° and O—Si—C angles of ca 121 and 116°. In form (IIo), the corresponding angles are ∼123, 124 and 111°. There are also significant differences in the packing: (IIm) shows π stacking, whereas (IIo) does not.     

40 GHz Mode-Locked Semiconductor Lasers: Theory, Simulations and Experiment

We study both theoretically and experimentally typical operation regimes of 40 GHz monolithic mode-locked lasers. The underlying Traveling Wave Equation model reveals quantitative agreement for characteristics of the fundamental mode-locking as pulse width and repetition frequency tuning, as well as qualitative agreement with the experiments for other dynamic regimes. Especially the appearance of stable harmonic mode-locking at 80 GHz has been predicted theoretically and confirmed by measurements. Furthermore, we derive and apply a simplified Delay-Differential-Equation model which guides us to a qualitative analysis of bifurcations responsible for the appearance and the breakup of different mode-locking regimes. Higher harmonics of mode-locking are predicted by this model as well.