Essential self-adjointness for combinatorial Schr\"odinger operators II- Metrically non complete graphs

We consider weighted graphs, we equip them with a metric structure given by a weighted distance, and we discuss essential self-adjointness for weighted graph Laplacians and Schr\"odinger operators in the metrically non complete case.Comment: Revisited version: Ognjen Milatovic wrote to us that he had discovered a gap in the proof of theorem 4.2 of our paper. As a consequence we propose to make an additional assumption (regularity property of the graph) to this theorem. A new subsection (4.1) is devoted to the study of this property and some details have been changed in the proof of theorem 4.

Effect of pressure-driven MHD instabilities on confinement in reactor-relevant high-beta helical plasmas

Through the experiment data analysis in the large helical device (LHD), the influence of the global MHD instability and the relatively short wave length MHD instabilities driven turbulence on the confinement performance in reactor-relevant high-beta helical plasmas is studied. The comparison of the energy confinement time between just before global MHD instability disappears and after that, and the estimation of the saturated mode structure by the multi-channel soft x-ray measurement enable us to quantitatively estimate the influence of the global interchange type MHD instability with different saturated mode structures on the confinement performance. According to the comparison between thermal conductivities in experiments and those predicted by theoretical transport models, the transport properties in the peripheral region of high beta LHD plasmas are quite similar with anomalous transport model based on an interchange type MHD instability driven turbulence, and that result is supported by the dependence of the density fluctuation with relatively short wave length on beta value