Arnold Kirsch and mathematics education

This article pays tribute to the German mathematics educator Arnold Kirsch (1922–2013), especially for his contributions to calculus education. The main aim of his work was to make mathematics accessible to learners so that they are able to genuinely understand the subject.     

Development of an optical trap for microparticle clouds in dilute gases

Long-duration experiments with clouds of microparticles are planned for the ICAPS facility on board the International Space Station ISS. The scientific objectives of such experiments are widespread and are ranging from the simulation of aerosol behaviour in Earths atmosphere to the formation of planets in the early solar system. It is, however, even under microgravity conditions, impossible to sustain a cloud of free-floating, microscopic particles for an extended period of time, due to thermal diffusion and due to unavoidable external accelerations. Therefore, a trap for dust clouds is required which prevents the diffusion of the particles, which provides a source of relative velocities between the dust grains and which can also concentrate the dust to higher number densities that are otherwise not achievable. We are planning to use the photophoretic effect for such a particle trap. First short-duration microgravity experiments on the photophoretic motion of microscopic particles show that such an optical particle-cloud trap is feasible. First tests of a two-dimensional trap were performed in the Bremen drop tower.     

H-transfer catalysis with Ru3(CO)12

Ru₃(CO)₁₂ , in the presence of tolane, catalyzes the formation of esters from the following three systems: alcohol + aldehyde, alcohol and aldehyde.     

Tuning the electronic structure of octahedral iron complexes [FeL(X)] (L = 1-alkyl-4,7-bis(4-tert-butyl-2-mercaptobenzyl)-1,4,7-triazacyclononane,X = Cl,CH(3)O,CN, NO). The S = 1/2 <==>3/2 Spin equilibrium of [FeL(Pr)(NO)

Two new pentadentate, pendent arm macrocyclic ligands of the type 1-alkyl-4,7-bis(4-tert-butyl-2-mercaptobenzyl)-1,4,7-triazacyclononane where alkyl represents an isopropyl, (L(Pr))(2-), or an ethyl group, (L(Et))(2-), have been synthesized. It is shown that they bind strongly to ferric ions generating six-coordinate species of the type [Fe(L(alk))X]. The ground state of these complexes is governed by the nature of the sixth ligand, X: [Fe(III)(L(Et))Cl] (2) possesses an S = 5/2 ground state as do [Fe(III)(L(Et))(OCH(3))] (3) and [Fe(III)(L(Pr))(OCH(3))] (4). In contrast, the cyano complexes [Fe(III)(L(Et))(CN)] (5) and [Fe(III)(L(Pr))(CN)] (6) are low spin ferric species (S = 1/2). The octahedral [FeNO](7) nitrosyl complex [Fe(L(Pr))(NO)] (7) displays spin equilibrium behavior S = 1/2<==>S = (3)/(2) in the solid state. Complexes [Zn(L(Pr))] (1), 4.CH(3)OH, 5.0.5toluene.CH(2)Cl(2), and 7.2.5CH(2)Cl(2) have been structurally characterized by low-temperature (100 K) X-ray crystallography. All iron complexes have been carefully studied by zero- and applied-field M?ssbauer spectroscopy. In addition, Sellmann's complexes [Fe(pyS(4))(NO)](0/1+) and [Fe(pyS(4))X] (X = PR(3), CO, SR(2)) have been studied by EPR and M?ssbauer spectroscopies and DFT calculations (pyS(4) = 2,6-bis(2-mercaptophenylthiomethyl)pyridine(2-)). It is concluded that the electronic structure of 7 with an S = 1/2 ground state is low spin ferrous (S(Fe) = 0) with a coordinated neutral NO radical (Fe(II)-NO) whereas the S = 3/2 state corresponds to a high spin ferric (S(Fe) = 5/2) antiferromagnetically coupled to an NO(-) anion (S = 1). The S = 1/2<==>S = 3/2 equilibrium is then that of valence tautomers rather than that of a simple high spin<==>low spin crossover.     

Extension of the Quantum Mechanical Principle of Superposition to Non-Identical States with Short Life Times

We apply the principle of superposition to two quantum mechanical states of which one has a short life time 1/Γ. They must be identical, but may have a small difference in energy-momentum comparable to Γ. This produces new effects resulting from the linear relationship that appears between the S-matrix element and the production cross section of the decay products of the short lived state. An optical theorem for diffraction dissociation processes is proposed. This mechanism also provides a measure of the non-orthogonality between unstable particles that are eigenstates of a non-Hermitian Hamiltonian. Talk presented on the Workshop on Resonances and Time Asymmetric Quantum Theory, Jaca (Spain), 30 May to 4 June 2001     

Sticky model of charged colloids

Summary We use the Sticky Electrolyte Model, which we solved before in PY/MSA, to obtain the equation of state of a charge colloid taking into account both sticky and charge contribution. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

A technique for generating shear waves in cylindrical shells under radial impact

Experimental techniques are developed to study and measure the shear-wave velocity in an aluminum cylindrical shell subjected to a radial impact. The radial impact is obtained by exploding an electrical detonator inserted in plastic plugs mounted on the end of the shell. Strain gages, mounted on the outside surface of the shell at various axial locations, are used to obtain oscilloscope traces from which the shear-wave velocity can be calculated.     

A tetrathiafulvalene-functionalized schiff base macrocycle: synthesis, electrochemical, and photophysical properties

Highly selective formation of 2+2 macrocycle 1 from 2,5-bis(3-formyl-2-hydroxyphenyl)-1,3,4-oxadiazole and a diamine-functionalized tetrathiafulvalene derivative is reported. Its electronic properties have been studied experimentally by the combination of electrochemistry and UV-vis-NIR spectroscopy. Particularly, its largely extended π-conjugation renders this novel macrocycle simultaneously a good multielectron donor and a strong chromophore, which is rationalized on the basis of density functional theory.     

Electron-hole correlation effects in core-level spectroscopy probed by the resonant inelastic soft x-ray scattering map of C60

We have employed a unique spectroscopic approach, a resonant inelastic soft x-ray scattering (RIXS) map, to identify and separate electron-hole correlation effects in core-level spectroscopy. With this approach, we are able to derive a comprehensive picture of the electronic structure, separating ground state properties (such as the HOMO-LUMO separation) from excited state properties (such as the C 1s core-exciton binding energy of C(60)). In particular, our approach allows us to determine the difference between core- and valence exciton binding energies in C(60) [0.5 (±0.2) eV]. Furthermore, the RIXS map gives detailed insight into the symmetries of the intermediate and final states of the RIXS process.