Approximate symmetry group classification for a nonlinear fractional filtration equation of diffusion-wave type

A one-dimensional nonlinear fractional filtration equation with the Riemann–Liouville time-fractional derivative is proposed for modeling fluid flow through a porous medium. This equation is derived under an assumption that the fluid has a fractional equation of state in which the fluid density depends on the time-fractional derivative of pressure. The obtained equation belongs to the diffusion-wave type of equations. A case when the order of fractional differentiation is close to an integer number is considered, and a small parameter is introduced into the fractional filtration equation under consideration. An expansion of the Riemann–Liouville time-fractional derivative into the series with respect to this small parameter is obtained. Using this expansion, a first-order approximation of the derived fractional filtration equation is performed. Next, the problem of approximate Lie point symmetry group classification for this approximate nonlinear filtration equation with a small parameter is studied. It is shown that approximate symmetry groups admitted by different realizations of the approximate filtration equation have much more dimensions than the corresponding exact Lie point symmetry groups admitted by unperturbed fractional diffusion-wave equations. Obtained classification results permit to construct approximate invariant solutions for the considered nonlinear time-fractional filtration equations.     

Modal analysis of wingtip vortices by means of Proper Orthogonal Decomposition

This paper discusses the influence of different wingtip geometries on the first eigenmodes of wingtip vortices. With the use of Proper Orthogonal Decomposition (POD) of a turbulent velocity field, a modal decomposition of coherent structures, high energetic eigenmodes are determined. Based on the results found by Fabre et al. [1], these eigenmodes may be a key factor for the stability analysis. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Single‐wall carbon nanotube interactions with copper‐oxamato building block of molecule‐based magnets probed by resonance Raman spectroscopy

The electronic interactions between the [Cu(opba)]²⁻ anions (where opba is orthophenylenebis (oxamato)) and single‐wall carbon nanotubes (SWCNTs) were investigated by resonance Raman spectroscopy. The opba can form molecular magnets, and the interactions of opba with SWCNTs can produce materials with very different magnetic/electronic properties. It is observed that the electronic interaction shows a dependence on the SWCNT diameter independent of whether they are metallic or semiconducting, although the interaction is stronger for metallic tubes. The interaction also is dependent on the amount of complex that is probably adsorbed on the carbon surface of the SWCNTs. Some charge transfer can be also occurring between the metallic complex and the SWCNTs. Copyright © 2012 John Wiley & Sons, Ltd.     

Single-Atom Catalysts on Covalent Triazine Frameworks: at the Crossroad between Homogeneous and Heterogeneous Catalysis

Heterogeneous single-site and single-atom catalysts potentially enable combining the high catalytic activity and selectivity of molecular catalysts with the easy continuous operation and recycling of solid catalysts. In recent years, covalent triazine frameworks (CTFs) found increasing attention as support materials for particulate and isolated metal species. Bearing a high fraction of nitrogen sites, they allow coordinating molecular metal species and stabilizing particulate metal species, respectively. Dependent on synthesis method and pretreatment of CTFs, materials resembling well-defined highly crosslinked polymers or materials comparable to structurally ill-defined nitrogen-containing carbons result. Accordingly, CTFs serve as model systems elucidating the interaction of single-site, single-atom and particulate metal species with such supports. Factors influencing the transition between molecular and particulate systems are discussed to allow deriving tailored catalyst systems.     

Solid-Adsorbed Polymer-Electrolyte Interphases for Stabilizing Metal Anodes in Aqueous Zn and Non-Aqueous Li Batteries

Polymers are known to adsorb spontaneously from liquid solutions in contact with high-energy substrates to form configurationally complex, but robust phases that often exhibit higher durability than might be expected from the individual physical bonds formed with the substrate. Rational control of the physical, chemical, and transport properties of such interphases has emerged as a fundamental opportunity for scientific and technological advances in energy storage technology but requires in-depth understanding of the conformation states and electrochemical effect of the adsorbed polymers. Here, we analyze the interfacial adsorption of oligomeric polyethylene glycol (PEG) chains of moderate sizes dissolved in protic and aprotic liquid electrolytes and find that there is an optimum polymer molecular weight of approximately 400 Da at which the highest columbic efficiency is achieved for both Zn and Li deposition. These findings point to a simple, versatile approach for extending the lifetime of batteries.