Flip Graphs of Bounded Degree Triangulations

We study flip graphs of triangulations whose maximum vertex degree is bounded by a constant k. In particular, we consider triangulations of sets of n points in convex position in the plane and prove that their flip graph is connected if and only if k > 6; the diameter of the flip graph is O(n ²). We also show that, for general point sets, flip graphs of pointed pseudo-triangulations can be disconnected for k ≤ 9, and flip graphs of triangulations can be disconnected for any k. Additionally, we consider a relaxed version of the original problem. We allow the violation of the degree bound k by a small constant. Any two triangulations with maximum degree at most k of a convex point set are connected in the flip graph by a path of length O(n log n), where every intermediate triangulation has maximum degree at most k + 4.     

Potential Screening at Electrode/Ionic Liquid Interfaces from In Situ X-ray Photoelectron Spectroscopy

A new approach to investigate potential screening at the interface of ionic liquids (ILs) and charged electrodes in a two-electrode electrochemical cell by in situ X-ray photoelectron spectroscopy has been introduced. Using identical electrodes, we deduce the potential screening at the working and the counter electrodes as a function of applied voltage from the potential change of the bulk IL, as derived from corresponding core level binding energy shifts for different IL/electrode combinations. For imidazolium-based ILs and Pt electrodes, we find a significantly larger potential screening at the anode than at the cathode, which we attribute to strong attractive interactions between the imidazolium cation and Pt. In the absence of specific ion/electrode interactions, asymmetric potential screening only occurs for ILs with different cation and anion sizes as demonstrated for an imidazolium chloride IL and Au electrodes, which we assign to the different thicknesses of the electrical double layers. Our results imply that potential screening in ILs is mainly established by a single layer of counterions at the electrode.     

Ionothermal Synthesis of Imide-Linked Covalent Organic Frameworks

Covalent organic frameworks (COFs) are an extensively studied class of porous materials, which distinguish themselves from other porous polymers in their crystallinity and high degree of modularity, enabling a wide range of applications. COFs are most commonly synthesized solvothermally, which is often a time-consuming process and restricted to well-soluble precursor molecules. Synthesis of polyimide-linked COFs (PI-COFs) is further complicated by the poor reversibility of the ring-closing reaction under solvothermal conditions. Herein, we report the ionothermal synthesis of crystalline and porous PI-COFs in zinc chloride and eutectic salt mixtures. This synthesis does not require soluble precursors and the reaction time is significantly reduced as compared to standard solvothermal synthesis methods. In addition to applying the synthesis to previously reported imide COFs, a new perylene-based COF was also synthesized, which could not be obtained by the classical solvothermal route. In situ high-temperature XRPD analysis hints to the formation of precursor–salt adducts as crystalline intermediates, which then react with each other to form the COF.     

Mechanistic Characterisation of Two Sesquiterpene Cyclases from the Plant Pathogenic Fungus Fusarium fujikuroi

Two sesquiterpene cyclases from Fusarium fujikuroi were expressed in Escherichia coli and purified. The first enzyme was inactive because of a critical mutation, but activity was restored by sequence correction through site‐directed mutagenesis. The mutated enzyme and two naturally functional homologues from other fusaria converted farnesyl diphosphate into guaia‐6,10(14)‐diene. The second enzyme produced eremophilene. The absolute configuration of guaia‐6,10(14)‐diene was elucidated by enantioselective synthesis, while that of eremophilene was evident from the sign of its optical rotation and is opposite to that in plants but the same as in Sorangium cellulosum. The mechanisms of both terpene cyclases were studied with various ¹³C‐ and ²H‐labelled FPP isotopomers.     

Unsaturated porous media flow with thermomechanical interaction

We propose a model for unsaturated poro‐plastic flow derived from the thermodynamic principles. For the isothermal case, the problem consists of a degenerate coupled system of two PDEs with two independent hysteresis operators describing hysteresis phenomena in both the solid and the pore fluids. Under natural hypotheses, we prove the existence of a global strong solution for this system. Copyright © 2015 John Wiley & Sons, Ltd.