Rotational superposition and least squares: the SVD and quaternions approaches yield identical results. Reply to the preceding comment by G. Kneller

We clarify once again that Kabsch's method and the Quaternion method are mathematically equivalent methods, that is, that they contain identical information and, when properly understood and applied, lead to identical answers to any questions regarding least-squares rotational superposition, either by proper rotations or by rotation-reflections. We also provide the correct bounds for the eigenvalue spectrum.     

Cationic surfactant-based polyfluorate salts: phase separation and analytical applications in the extraction and preconcentration of ionic species prior to liquid chromatography

The liquid-solid phase separation originating from the formation of cationic surfactant-based polyfluorate salts (CSBPS) has been explored for extracting and preconcentrating ionic species. Two cationic surfactants were tested; one with aliphatic hydrocarbon tail [Cetyltrimethylammonium bromide (CTAB)]and the other containing a heterocyclic ring [Hexadecylpyridinium bromide (HPyBr)]. Phase separation possibility was investigated with the use of hexafluorophosphates (PF6-) and tetrafluoroborates (BF4-). The effect of added acid, base and salt on the phase separation and analyte extraction was also investigated. In all cases the obtained phase diagrams consisted of two regions: a homogeneous liquid region and a solid-liquid region. Analytes of hydrophilic and hydrophobic nature such as amines, amino acids and organic chromophores were used as test compounds in both their anionic and cationic forms. The respective recoveries ranged from over 90% for anionic species and in the proximity of 50% for cationic species, remaining below 20% for neutral species. Extracts from alkaline aqueous and plasma samples spiked with tyrosine and phenylalanine were also subjected to HPLC separation with UV detection with satisfactory results. On line application was also enabled using a flow through-solid phase extraction-HPLC hyphenated apparatus, thus adding the element of automatization and increased reproducibility.     

Computational studies of (HIO3) isomers and the HO2 + IO reaction pathways

The geometries, harmonic vibrational frequencies, relative energetics, and enthalpies of formation of (HIO3) isomers have been examined using quantum mechanical methods. At all levels of theory employed, MP2, B3LYP, and CCSD(T), the lowest energy structure is found to be the HOIO2 form, which shows particular stability. The two isomers HOOOI and HOOIO are closely located at the CCSD(T) level of theory. The higher energy structure is HIO3. The interisomerization transition states have been determined, along with the transition states involved in the various pathways of the reaction HO2 + IO.     

Preparation of annulated nitrogen-containing heterocycles via a one-pot palladium-catalyzed alkylation/direct arylation sequence

[reaction: see text] A palladium-catalyzed/norbornene-mediated sequential coupling reaction involving an aromatic sp(2) C-H functionalization as the key step is described, in which an alkyl-aryl bond and an aryl-heteroaryl bond are formed in one pot. A variety of highly substituted six- and seven-membered annulated pyrroles and pyrazoles were synthesized in a one-step process in good yields from readily accessible N-bromoalkyl pyrroles or pyrazoles and aryl iodides.     

Hybrid pricing in a coupled European power market with more wind power

In the European electricity market, the promotion of wind power leads to more network congestion. Zonal pricing (market coupling), which does not take the physical characteristics of transmission into account, is the most commonly used method to relieve network congestion in Europe. However, zonal pricing fails to provide adequate locational price signals regarding scarcity of energy and thus creates a large amount of unscheduled cross-border flows originating from wind-generated power. In this paper, we investigate the effects of applying a hybrid congestion management model, i.e., a nodal pricing model for one country embedded in a zonal pricing system for the rest of the market. We find that, compared to full nodal pricing, hybrid pricing fails to fully utilize all the resources in the network and some wrong price signals might be given. However, hybrid pricing still outperforms zonal pricing. The results from the study cases show that, within the area applying nodal pricing, better price signals are given; the need for re-dispatching is reduced; more congestion rent is collected domestically and the unit cost of power is reduced.     

The use of pseudo-faults for damage location in SHM: An experimental investigation on a Piper Tomahawk aircraft wing

The application of pattern recognition-based approaches in damage localisation and quantification will eventually require the use of some kind of supervised learning algorithm. The use, and most importantly, the success of such algorithms will depend critically on the availability of data from all possible damage states for training. It is perhaps well known that the availability of damage data through destructive means cannot generally be afforded in the case of high value engineering structures outside laboratory conditions. This paper presents the attempt to use added masses in order to identify features suitable for training supervised learning algorithms and then to test the trained classifiers with damage data, with the ultimate purpose of damage localisation. In order to test the approach of adding masses, two separate cases of a dual-class classification problem, representing two distinct locations, and a three-class problem representing three distinct locations, are examined with the help of a full-scale aircraft wing. It was found that an excellent rate of correct classification could be achieved in both the dual-class and three-class cases. However, it was also found that the rate of correct classification was sensitive to the choices made in training the supervised learning algorithm. The results for the dual-class problem demonstrated a comparatively high level of robustness to these choices with a substantially lower robustness found in the three-class case.     

Global dynamics of a reaction–diffusion system with mass conservation

We study global dynamics of a mass conserved reaction–diffusion system. First, we show the global-in-time existence of the solution with compact orbit. Then the dynamical stability of local minima associated with a variational function is proven.     

Machine learning-based rock characterisation models for rotary-percussive drilling

Nonlinear Dynamics - Vibro-impact drilling has shown huge potential of delivering better rate of penetration, improved tools lifespan and better borehole stability. However, being resonantly...