Harmonic maps with torsion

In this article we introduce a natural extension of the well-studied equation for harmonic maps between Riemannian manifolds by assuming that the target manifold is equipped with a connection that is metric but has non-vanishing torsion. Such connections have already been classified in the work of Cartan(1924).The maps under consideration do not arise as critical points of an energy functional leading to interesting mathematical challenges. We will perform a first mathematical analysis of these maps which we will call harmonic maps with torsion.     

An experimental and modeling study of the oxidation of n-heptane,ethylbenzene, and n-butylbenzene in a jet-stirred reactor at pressures up to 10 bar

In the context of better understanding pollutant formation from internal combustion engines, new experimental speciation data were obtained in a high-pressure jet-stirred reactor for the oxidation of three molecules, which are considered in surrogates of diesel fuel, n-heptane, ethylbenzene, and n-butylbenzene. These experiments were performed at pressures up to 10 bar, at temperatures ranging from 500 to 1 100 K, and for a residence time of 2 s. Based on results previously obtained close to the atmospheric pressure for the same molecules, the pressure effect on fuel conversion and product selectivity was discussed. In addition, for the three fuels, the experimental temperature dependence of species mole fractions was compared with simulations using recent literature models with generally a good agreement. For n-heptane, the obtained experimental data, at 10 bar for stoichiometric mixtures, included the temperature dependence of the mole fractions of the reactants and those of 21 products. Interestingly, the formation of species previously identified as C₇ diones was found significantly enhanced at 10 bar compared with lower pressures. The oxidation of ethyl- and n-butylbenzenes was investigated at 10 bar for equivalence ratios of 0.5, 1, and 2. The obtained experimental data included the temperature dependence of the mole fractions of the reactants and those of 13 products for the C₈ fuels and of 19 products for the C₁₀ one. For ethylbenzene under stoichiometric conditions, the pressure dependence (from 1 to 10 bar) of species mole fraction was also recorded and compared with simulations with more deviations obtained than for temperature dependence. For both aromatic reactants, a flow rate analysis was used to discuss the main pressure influence on product selectivities.     

Spatiotemporal Studies of the One-Dimensional Coordination Polymer [Fe(ebtz)2(C2H5CN)2](BF4)2: Tug of War between the Nitrile Reorientation Versus Crystal Lattice as a Tool for Tuning the Spin Crossover Properties**

Reaction of 1,2-di(tetrazol-2-yl)ethane (ebtz) with Fe(BF₄)₂⋅6 H₂O in different nitriles yields one-dimensional coordination polymers [Fe(ebtz)₂(RCN)₂](BF₄)₂⋅nRCN (n=2 for R=CH₃ ( 1 ) and n=0 for R=C₂H₅ ( 2 ) C₃H₇ ( 3 ), C₃H₅ ( 4 ), CH₂Cl ( 5 )) exhibiting spin crossover (SCO). SCO in 1 and 3 – 5 is complete and occurs above 160 K. In 2 , it is shifted to lower temperatures and is accompanied by wide hysteresis (T_1/2^↓=78 K, T_1/2^↑=123 K) and proceeds extremely slowly. Isothermal (80 K) time-resolved single-crystal X-ray diffraction studies revealed a complex nature for the HS→LS transition in 2 . An initial, slow stage is associated with shrinkage of polymeric chains and with reduction of volume at 77 % (in relation to the difference between cell volumes V_HS−V_LS) whereas only 16 % of iron(II) ions change spin state. In the second stage, an abrupt SCO occurs, associated with breathing of the crystal lattice along the direction of the Fe–nitrile bonds, while the nitriles reorient. HS→LS switching triggered by light (808 nm) reveals the coupling of spin state and nitrile orientation. The importance of this coupling was confirmed by studies of [Fe(ebtz)₂(C₂H₅CN/C₃H₇CN)₂](BF₄)₂ mixed crystals ( 2 a , 2 b ), showing a shift of T_1/2 to higher values and narrowing of the hysteresis loop concomitant with an increase of the fraction of butyronitrile. This increase reduces the capability of nitrile molecules to reorient. Density functional theory (DFT) studies of models of 1 – 5 suggest a particular possibility of 2 to adopt a low (140–145°) value of its Fe-N-C(propionitrile) angle.     

Half-a-century of gamma-ray astrophysics at the Max-Planck Institute for Extraterrestrial Physics

The European Physical Journal H - This is a tutorial for the many-worlds theory by Everett, which includes some of my personal views. It has two main parts. The first main part shows the emergence...