{2,2′‐[(R,R)‐Cyclo­hexane‐1,2‐diyl­bis(nitrilo­methyl­idyne)]­bis[6‐tert‐butyl‐4‐(tri­phenyl­phosphonio­methyl)­phenol­ato]‐O,N,N′,O′}copper(II) dichloride hexakis­(deutero­chloro­form) solvate

The title compound, [Cu(C₆₆H₆₈N₂O₂P₂)]Cl₂·6CDCl₃, consists of complex cations, chloride ions and deutero­chloro­form solvate mol­ecules. The complex cation crystallizes in two different conformations. In both cases, Cu^II ions lie on twofold axes and the geometry around them is slightly distorted square planar. The dihedral angles between the N/Cu/N and O/Cu/O planes are 5.6 (9) and 3.9 (10)° for mol­ecules A and B, respectively.     

Influence of mesh deformation on the quality of large eddy simulations

The influence of mesh motion on the quality of large eddy simulation (LES) was studied in the present article. A three‐dimensional, turbulent pipe flow (Re_τ=360) was considered as a test case. Simulations with both stretching and static meshes were carried out in order to understand how mesh motion affects the turbulence statistics. The spatial filtering of static and moving mesh direct numerical simulation (DNS) data showed how an ideal LES would perform, while the comparison of DNS cases with static and moving meshes revealed that no significant numerical errors arise from the mesh motion when the simulation is fully resolved. The comparison of the filtered fields of the DNS with a moving mesh with the corresponding LES fields revealed different responses to mesh motion from different numerical approaches. A straightforward test was applied in order to verify that the moving mesh works consistently in LES: when the mesh is stretched in the streamwise direction, the moving mesh results should be in between the two extremal resolutions between which the mesh is stretched. Numerical investigations using four different LES approaches were carried out. In addition to the Smagorinsky model, three implicit LES approaches were used: linear interpolation (non‐dissipative), the Gamma limiter (dissipative), and the scale‐selective discretisation (slightly dissipative). The results indicate that while the Smagorinsky and the scale‐selective discretisation approaches produce results consistent with the resolution of the non‐static mesh, the implicit LES with linear interpolation or the Gamma scheme do not. Copyright © 2016 John Wiley & Sons, Ltd.     

Homeomorphisms of Bounded Variation

We show that the inverse of a planar homeomorphism of bounded variation is also of bounded variation. In higher dimensions we show that f ⁻¹ is of bounded variation provided that f ϵ W ^1,1(Ω; R ⁿ ) is a homeomorphism with |Df| in the Lorentz space L ^n-1,1(Ω). Dedicated to Tadeusz Iwaniec on his 60th birthday     

Axial super-resolution by mirror-reflected stimulated emission depletion microscopy

In stimulated emission depletion (STED) microscopy, the lateral resolution is in the range of tens of nanometers depending on the sample and the instrument. The axial resolution, however, is in standard systems limited by diffraction to about 500 nm. We present an approach to three-dimensional diffraction-unlimited resolution by observing the sample at two optical angles. The system is realized by using an atomic force microscope (AFM) chip as a microreflector to deflect the STED beams near the region-of-interest (ROI), thus allowing observations at an angle ∠. Consequently, the superior lateral resolution can be utilized to resolve details in the axial direction of the main optical axis of the microscope. Here, fluorescent nanoparticles 90 nm apart and biological structures 80 nm apart along axial direction were distinguished by utilizing an off-the-shelf, commercial STED microscope, coupled with an AFM and an AFM chip micro-reflector.     

Quasiconformal extension fields

We consider extensions of differential fields of mappings and obtain a lower bound for energy of quasiconformal extension fields in terms of the topological degree. We also consider the related minimization problem for the q-harmonic energy, and show that the energy minimizers admit higher integrability.     

Membraneless energy conversion and storage using immiscible electrolyte solutions

Breakthrough alternative technologies are urgently required to alleviate the critical need to decarbonise our energy supply. We showcase non-conventional approaches to battery and solar energy conversion and storage (ECS) system designs that harness key attributes of immiscible electrolyte solutions, especially the membraneless separation of redox active species and ability to electrify certain liquid–liquid interfaces. We critically evaluate the recent development of membraneless redox flow batteries based on biphasic systems, where one redox couple is confined to an immiscible ionic liquid or organic solvent phase, and the other couple to an aqueous phase. Common to all solar ECS devices are the abilities to harvest light, leading to photo-induced charge carrier separation, and separate the products of the photo-reaction, minimising recombination. We summarise recent progress towards achieving this accepted solar ECS design using immiscible electrolyte solutions in photo-ionic cells, to generate redox fuels, and biphasic “batch” water splitting, to generate solar fuels.     

A homogeneous quenching resonance energy transfer assay for the kinetic analysis of the GTPase nucleotide exchange reaction

A quenching resonance energy transfer (QRET) assay for small GTPase nucleotide exchange kinetic monitoring is demonstrated using nanomolar protein concentrations. Small GTPases are central signaling proteins in all eukaryotic cells acting as a “molecular switches” that are active in the GTP-state and inactive in the GDP-state. GTP-loading is highly regulated by guanine nucleotide exchange factors (GEFs). In several diseases, most prominently cancer, this process in misregulated. The kinetics of the nucleotide exchange reaction reports on the enzymatic activity of the GEF reaction system and is, therefore, of special interest. We determined the nucleotide exchange kinetics using europium-labeled GTP (Eu-GTP) in the QRET assay for small GTPases. After GEF catalyzed GTP-loading of a GTPase, a high time-resolved luminescence signal was found to be associated with GTPase bound Eu-GTP, whereas the non-bound Eu-GTP fraction was quenched by soluble quencher. The association kinetics of the Eu-GTP was measured after GEF addition, whereas the dissociation kinetics could be determined after addition of unlabeled GTP. The resulting association and dissociation rates were in agreement with previously published values for H-Ras^Wt, H-Ras^Q61G, and K-Ras^Wt, respectively. The broader applicability of the QRET assay for small GTPases was demonstrated by determining the kinetics of the Ect2 catalyzed RhoA^Wt GTP-loading. The QRET assay allows the use of nanomolar protein concentrations, as more than 3-fold signal-to-background ratio was achieved with 50 nM GTPase and GEF proteins. Thus, small GTPase exchange kinetics can be efficiently determined in a HTS compatible 384-well plate format.