On Ludvig Lorenz and his 1890 treatise on light scattering by spheres

The European Physical Journal H - This paper offers background and perspective on a little-known memoir by Ludvig Lorenz on light scattering by spheres, which was published in Danish in 1890. It is...     

Modulation of Mn3+ Spin State by Guest Molecule Inclusion

Spin state preferences for a cationic Mn³⁺ chelate complex in four different crystal lattices are investigated by crystallography and SQUID magnetometry. The [MnL₁]⁺ complex cation was prepared by complexation of Mn³⁺ to the Schiff base chelate formed from condensation of 4-methoxysalicylaldehyde and 1,2-bis(3-aminopropylamino)ethane. The cation was crystallized separately with three polyatomic counterions and in one case was found to cocrystallize with a percentage of unreacted 4-methoxysalicylaldehyde starting material. The spin state preferences of the four resultant complexes [MnL₁]CF₃SO₃·xH₂O, (1), [MnL₁]PF₆·xH₂O, (2), [MnL₁]PF₆·xsal·xH₂O, (2b), and [MnL₁]BPh₄, (3), were dependent on their ability to form strong intermolecular interactions. Complexes (1) and (2), which formed hydrogen bonds between [MnL₁]⁺, lattice water and in one case also with counterion, showed an incomplete thermal spin crossover over the temperature range 5–300 K. In contrast, complex (3) with the BPh₄⁻, counterion and no lattice water, was locked into the high spin state over the same temperature range, as was complex (2b), where inclusion of the 4-methoxysalicylaldehyde guest blocked the H-bonding interaction.     

Five New Coordination Polymers with a Bifunctional Phosphonate‐Sulfonate Linker Molecule

The bifunctional linker molecule [5‐(phosphonomethyl)‐2,4‐bis(sulfonomethyl)phenyl]methanesulfonic acid (HO₃S‐CH₂)₃‐C₆H₂‐CH₂PO₃H₂ (abbreviated as H₅L4) was employed in systematic high‐throughput investigations in order to discover new coordination polymers (CPs). Employing 27 metal salts of 17 different metals in this investigation, five new compounds [Mg₂(HL4)(H₂O)₆] ( 1 ), [Pb₄(L4)(OH)₃] ( 2 ), [Ba₂(H₂L4)(OH)(H₂O)] ( 3 ), [Ba₂(HL4)(H₂O)₄] ( 4 ), and [Cd_2,5(L4)(H₂O)₇] ( 5 ) were discovered and their crystal structures were determined. In all compounds, the sulfonate and phosphonate groups could not be resolved since the P and S atoms are statistically occupying the atom site with a ratio of 0.25 to 0.75. This is reflected in the P–O and S–O bond lengths. Four of the structures were determined from single‐crystal X‐ray diffraction data, whereas the structure of 4 was solved ab initio from powder data using real‐space methods and refined using Rietveld methods.     

A novel approach to rigid spheroid models in viscous flows using operator splitting methods

Numerical Algorithms - Calculating cost-effective solutions to particle dynamics in viscous flows is an important problem in many areas of industry and nature. We implement a second-order symmetric...     

Isolation,total synthesis and quantification of caffeoylisocitric acid,a characteristic ingredient of the superfood amaranth

Amaranth is regarded as a new “super-vegetable” in western countries, albeit it is consumed for centuries in Africa and Asia. In addition to common carotenoids, flavonoids and polyphenols, caffeoylisocitric acid has been described as amaranth type-specific secondary metabolite. Remarkably, nothing is known on biological effects of this specific polyphenol. Here we detail a concise, diastereoselective synthesis of caffeoylisocitric acid, deuterium-labelling studies and a quantitative determination of the caffeoylisocitric acid content of three different amaranth types.     

Coherence and Reynolds stresses in the turbulent wake behind a curved circular cylinder

The turbulent wake behind a curved circular cylinder is investigated based on data obtained from a direct numerical simulation. Here, emphasis is placed in the assessment of two approaches for simplified modelling: reduced-order modelling (ROM) and Reynolds-averaged Navier–Stokes equations. To this end, the instantaneous vortical structures, the proper orthogonal decomposition (POD) of the flow, and relevant Reynolds stress components have been analysed. The results show that despite the complexity of the instantaneous vortical structures, the wake dynamics are governed by the quasi-periodic shedding of primary vortices. Between 24% and 50% of the kinetic energy in the POD is captured by the two most energetic modes, and about 200 modes are needed to capture 90% of the kinetic energy. These findings suggest that, as long as the large-scale structures of the von Kármán vortex shedding are concerned, the present case can be approached by ROM; but a detailed representation of the flow dynamics without an eddy viscosity model that accounts for the unresolved turbulent fluctuations would require a large amount of degrees of freedom. Concerning the Reynolds stresses, their magnitude varies considerably depending on the depth at which they have been sampled. This dependence is related to the strength of the vortex shedding, and the intensity of the secondary flows induced by the curvature of the cylinder. As a consequence of the combination of these two effects, the correlation between streamwise and vertical velocity fluctuations is highest in the wake behind the midspan of the curved cylinder, and the correlation between cross-flow and vertical velocity fluctuations reaches large values in the lower wake.     

The Kernel of the Adjoint Representation of a p-Adic Lie Group Need Not Have an Abelian Open Normal Subgroup

Let G be a p-adic Lie group with Lie algebra 𝔤 and Ad: G → Aut(𝔤) be the adjoint representation. It was claimed in the literature that the kernel K?ker(Ad) always has an abelian open normal subgroup. We show by means of a counterexample that this assertion is false. It can even happen that K = G, but G has no abelian subnormal subgroup except for the trivial group. The arguments are based on auxiliary results on subgroups of free products with central amalgamation.