NMR spectral analysis of strongly second-order 6-, 8-, 9- and 10- spin-systems (1H─19F, 19F─19F,and 13C─19F) in perfluorotoluyl- and tetrafluoro-pyridyl-aromatics using the lineshape method ANATOLIA

A simple to use nuclear magnetic resonance analysis method has been tested on complex ¹H, ¹⁹F, and ¹³C multiplets. This open-source line-shape analysis method analysis of total lineshape (ANATOLIA)¹ provides some significant advantages over traditional assign-iterate methods of NMR spectral analysis by avoiding false minima and progressing optimisation to the global minimum. The target molecules are 1-perfluorotol-4-yl-2-perfluorotol-4-yl-oxymethyl-1H-benzimidazole (molecule-I) and 1-tetrafluoropyrid-4-yl-2-tetrafluoropyrid-4-yl-thio-1H-benzimidazole (molecule-II) which were produced as part of a family of fluorinated drug scaffolds prepared for anticancer and antiparasitic screening. Spectra display significant second-order effects with ¹H Δδ = 3.68 and 4.67 Hz for the aromatic hydrogen “triplets”, with ¹⁹F ⁴J_AA', ⁴J_BB', ⁴J_XX', and ⁴J_YY' coupling constants range from +4.8 to −14.0 Hz and for ¹³C-isotopomers ¹⁹F Δδ of up to 111.56 Hz. A spin-system of six coupling nuclei (H_aH_bH_cH_d F_YF_Y') was analysed in 12 s, a spin-system of nine coupling fluorine nuclei (AA'BB'CCC-YY') was analysed within 2 min, and 10 coupling nuclei (XX'YY'ZZZ-BB'-H_d) was optimised in 6 min using a laptop computer. ANATOLIA was also robust enough to be able to yield accurate spectral values from inaccurate input values. In both compounds, a fluorine–fluorine coupling constant was identified between the two fluoro-aromatic rings (F_BB' and F_YY') of +4.05 and +4.67 Hz and attributed to a through-space interaction. Ab initio structure optimisations and coupling constant calculations provided useful input data for spectral analysis. A modern ¹⁹F nuclear magnetic resonance spectrum of perfluorotoluene (octafluorotoluene) and analysis from 1975 was used as a test data set to assess ANATOLIA.     

A new study of associating inhomogeneous fluids with classical density functional theory

ABSTRACT

A new density functional for the study of associating inhomogeneous fluids based on Wertheim's first-order thermodynamic perturbation theory is presented and compared to the most currently used associating density functionals. This functional is developed using the weighted density approximation in the range of association of hard spheres. We implement this functional within the framework of classical density functional theory together with modified fundamental measure theory to account for volume exclusion of hard spheres. This approach is tested against molecular simulations from literature of pure associating hard spheres and mixtures of non-associationg and associating hard spheres with different number of bonding sites close to a hard uniform wall. Furthermore, we compare and review our results with the performance of associating functionals from literature, one based on fundamental measure theory and the inhomogeneous version of Wertheim's perturbation theory. Results obtained with classical DFT and the three functionals show excellent agreement with molecular simulations in systems with one hard wall. For the cases of small pores where only one or two layers of fluid are allowed discrepancies between results with classical DFT and molecular simulations were found.     

Continuation of travelling‐wave solutions of the Navier–Stokes equations

An efficient way of obtaining travelling waves in a periodic fluid system is described and tested. We search for steady states in a reference frame travelling at the wave phase velocity using a first‐order pseudospectral semi‐implicit time scheme adapted to carry out the Newton's iterations. The method is compared to a standard Newton–Raphson solver and is shown to be highly efficient in performing this task, even when high‐resolution grids are used. This method is well suited to three‐dimensional calculations in cylindrical or spherical geometries. Copyright © 2006 John Wiley & Sons, Ltd.     

Neutral Community Theory: How Stochasticity and Dispersal-Limitation Can Explain Species Coexistence

Neutral community theory explains biodiversity, i.e. the coexistence of several species, as the result of a stochastic balance between immigration and extinction on a local level, and between speciation and extinction on a regional level. The most popular model, presented by Hubbell in 2001, has seen many analytical developments in recent years, which can be used in model analysis, model testing and model comparison. We review these developments here, and present alternative derivations and shine previously unnoticed lights on them.     

Sets of reflections defining twisted Bruhat orders

Twisted Bruhat orders are certain partial orders on a Coxeter system (W,S) associated to initial sections of reflection orders, which are certain subsets of the set of reflections T of a Coxeter system. We determine which subsets of T give rise to a partial order on W in the same way.     

Integrable semiclassical deformations of general algebraic curves and associated conservation laws

Based on the Lenard relations, we completely classify integrable deformations of general algebraic curves. We construct the general solution of the Lenard relation from the invariance condition with respect to an element of the Galois group of the curve. We give some examples and also some associated conservation laws. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 151, No. 3, pp. 458–469, June, 2007.