Mean curvature flows and isotopy of maps between spheres

Let f be a smooth map between unit spheres of possibly different dimensions. We prove the global existence and convergence of the mean curvature flow of the graph of f under various conditions. A corollary is that any area‐decreasing map between unit spheres (of possibly different dimensions) is isotopic to a constant map. © 2004 Wiley Periodicals, Inc.     

High‐mobility solution‐processed zinc oxide thin films on silicon nitride

A high effective electron mobility of 33 cm² V^–1 s^–1 was achieved in solution‐processed undoped zinc oxide (ZnO) thin films. The introduction of silicon nitride (Si₃N₄) as growth substrate resulted in a mobility improvement by a factor of 2.5 with respect to the commonly used silicon oxide (SiO₂). The solution‐processed ZnO thin films grown on Si₃N₄, prepared by low‐pressure chemical vapor deposition, revealed bigger grain sizes, lower strain and better crystalline quality in comparison to the films grown on thermal SiO₂. These results show that the nucleation and growth mechanisms of solution‐processed films are substrate dependent and affect the final film structure accordingly. The substantial difference in electron mobilities suggests that, in addition to the grain morphology and crystalline structure effects, defect chemistry is a contributing factor that also depends on the particular substrate. In this respect, interface trap densities measured in high‐κ HfO₂/ZnO MOSCAPs were about ten times lower in those fabricated on Si₃N₄ substrates. (© 2014 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)

     

Astability and negative differential resistance of the Wigner solid

We report spontaneous narrow band oscillations in the high field Wigner solid. These oscillations are similar to the recently seen and yet unexplained oscillations in the reentrant integer quantum Hall states. The current-voltage characteristic has a region of negative differential resistance in the current biased setup and it is hysteretic in the voltage biased setup. As a consequence of the unusual breakdown, the oscillations in the Wigner solid are of the relaxation type.     

Stereoselective Palladium‐Catalyzed C−F Bond Alkynylation of Tetrasubstituted gem‐Difluoroalkenes

A stereoselective Pd(PPh₃)₄‐catalyzed C?F bond alkynylation of tetrasubstituted gem‐difluoroalkenes with terminal alkynes has been developed. This method gives access to a great variety of conjugated monofluoroenynes bearing a tetrasubstituted alkene moiety with well‐defined stereochemistry. Chelation‐assisted oxidative addition of Pd to the C?F bond is proposed to account for the high level of stereocontrol. An X‐ray crystal structure of a key monofluorovinyl Pd^II intermediate has been obtained for the first time as evidence for the proposed mechanism.