Decay of confined,two-dimensional,spatially periodic arrays of vortices: A numerical investigation

The disarrangement of a perturbed lattice of vortices was studied numerically. The basic state is an exponentially decaying, exact solution of the Navier-Stokes equations. Square arrays of vortices with even numbers of vortex cells along each side were perturbed and their evolution was investigated. Whether the energy in the perturbation grows somewhat before it decays or decays monotonically depends on the initial strength of the vortices of the basic state, the extent of lateral confinement and the structure of the perturbation. The critical condition for temporally local instability, i.e. the critical amplitude of the basic state that must be exceeded to allow energy transfer from the basic state to the perturbation, is discussed. In the strongly confined case of a square lattice of four vortices the appearance of enchancement of global rotation is the result of energy transfer from the basic state to a temporally local unstable mode. Energy is transferred from the basic state to larger-scaled structures (inverse cascade) only if the scales of the larger structures are inherently contained in the initial structure of the perturbation. The initial structure of the double array of vortices is not maintained except for a very special form of perturbation. The facts that large scales decay more slowly than small scales and that, when non-linearities are sufficiently strong, energy is transferred from one scale to another explain the differences in the disarrangement process for different initial strengths of the vortices of the basic state. The stronger vortices, i.e. the vortices perturbed in a manner that increases their strength, tend to dominate the weaker vortices. The pairing and subsequent merging (or capture) of vortices of like sense into larger-scale vortices are described in terms of peaks in the evolution of the square root of the palinstrophy divided by the enstrophy.     

Alternativ-Liganden. XXIII. Rhodium(I)-Komplexe mit Donor/Akzeptor-Liganden des Typs (Me2PCH2CH2SiX2 und (2-Me2PC6H4)SiXMe2 (X = F,Cl)

Alternative Ligands. XXIII Rhodium(I) Complexes with Donor/Acceptor Ligands of the Type (Me₂PCH₂CH₂)₂SiX₂ and (2-Me₂PC₆H₄)SiXMe₂ (X = F, Cl) Donor/acceptor ligands of the type (Me₂PCH₂CH₂)₂SiX₂ and (2-Me₂PC₆H₄)SiXMe₂ (X = F, Cl) react with [Rh(CO)₂Cl]₂ (₁) to give the mononuclear complexes RhCl(CO)(Me₂PCH₂CH₂)₂SiX₂ [X = F( 4 ), Cl ( 5 )] and RhCl(CO)[2-Me₂PC₆H₄)SixMe₂]₂ [X = F ( 8 ), Cl ( 9 )], respectively. In case of the ligands (Me₂PCH₂CH₂)₂SiCl₂ ( 3 ) and (2-Me₂PC₆H₆)SiClMe₂ ( 7 ) the Rh(I) complexes formed in the first step partly undergo oxidative addition reactions of SiCl bonds yielding rhodium(III) compounds of low solubility. Only for 8 the coordination shifts Δδ = δ(complex)?δ(ligand) and coupling constants give some indication to possible Rh→Si interactions. However, the molecular structure of 8 determined by X-ray diffraction does not show RhSi or RhF bonding contacts. The new compounds were characterized by analytical (C, H) and spectroscopic investigations (MS, IR,-NMR).     

Deep neural network analysis of nanoparticle ordering to identify defects in layered carbon materials

Smoothness/defectiveness of the carbon material surface is a key issue for many applications, spanning from electronics to reinforced materials, adsorbents and catalysis. Several surface defects cannot be observed with conventional analytic techniques, thus requiring the development of a new imaging approach. Here, we evaluate a convenient method for mapping such “hidden” defects on the surface of carbon materials using 1–5 nm metal nanoparticles as markers. A direct relationship between the presence of defects and the ordering of nanoparticles was studied experimentally and modeled using quantum chemistry calculations and Monte Carlo simulations. An automated pipeline for analyzing microscopic images is described: the degree of smoothness of experimental images was determined by a classification neural network, and then the images were searched for specific types of defects using a segmentation neural network. An informative set of features was generated from both networks: high-dimensional embeddings of image patches and statics of defect distribution.

Defectiveness of carbon material surface is a key issue for many applications. Pd-nanoparticle SEM imaging was used to highlight “hidden” defects and analyzed by neural networks to solve order/disorder classification and defect segmentation tasks.