Applications of Rosenbrock-type methods to the p-version of finite elements

In quasistatic solid mechanics the spatial as well as the temporal domain need to be discetized. For the spatial discretization usually elements with linear shape functions are used even though it has been shown that generally the p-version of the finite elemente method yields more effective discretizations, see e.g. [1], [2]. For the temporal discretization diagonal-implicit, see e.g. [4], and especially linear-implicit Runge-Kutta schemes, see e.g. [5], [6], have for smooth problems proven to be superior to the frequently applied Backward-Euler scheme (BE). Thus an approach combining the p-version of the finite element method with linear-implicit Runge-Kutta schemes, so-called Rosenbrock-type methods, is presented. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Bonding modes of stanna-closo-dodecaborate: eta1(Sn) to eta3(BH) rearrangement reactions in zwitterionic stanna-closo-dodecaborate ruthenium complexes

Reaction of the stanna-closo-dodecaborate salt [Bu3MeN]2[SnB11H11] with the dimeric ruthenium complex [Ru2(mu-Cl)3(triphos)2]Cl (triphos = {MeC(CH2PPh2)3}) in refluxing acetonitrile yields the zwitterionic compound [Ru(SnB11H11)(MeCN)2(triphos)] (4) which has been characterized by single-crystal X-ray diffraction analysis and solid-state NMR spectroscopy. Refluxing the zwitterion in acetone leads to an eta1(Sn) to eta3(BH) rearrangement with formation of [Ru(SnB1)H11)(triphos)] (5) whose structure has been confirmed by X-ray diffraction and multinuclear NMR spectroscopy in solution and in the solid state. Furthermore, two isomeric zwitterions fac- and mer-[Ru(SnB11H11)(dppb)(MeCN)3] (6a, 6b) and their rearrangement reactions as well as their NMR properties are described.     

Anisotropic finite strain hyperelasticity based on the multiplicative decomposition of the deformation gradient

In this contribution a new constitutive model for transversely isotropic materials is presented. The proposed model is based on the multiplicative decomposition of the deformation gradient into one part containing the deformation only in the direction of anisotropy and another part describing the remaining deformation. This clear assignment leads to a decoupling of the stress-state. The model is investigated analytically in view of simple tension. Moreover, an inhomogenous deformation is solved using a finite elements simulation. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Magnetic-field probing of an SU(4) Kondo resonance in a single-atom transistor

Semiconductor devices have been scaled to the point that transport can be dominated by only a single dopant atom. As a result, in a Si fin-type field effect transistor Kondo physics can govern transport when one electron is bound to the single dopant. Orbital (valley) degrees of freedom, apart from the standard spin, strongly modify the Kondo effect in such systems. Owing to the small size and the s-like orbital symmetry of the ground state of the dopant, these orbital degrees of freedom do not couple to external magnetic fields which allows us to tune the symmetry of the Kondo effect. Here we study this tunable Kondo effect and demonstrate experimentally a symmetry crossover from an SU(4) ground state to a pure orbital SU(2) ground state as a function of magnetic field. Our claim is supported by theoretical calculations that unambiguously show that the SU(2) symmetric case corresponds to a pure valley Kondo effect of fully polarized electrons.     

Matrix infrared measurement of TiN

Gas-phase reaction of active nitrogen with TiCl₄ produces TiN, which has been stabilized in a Kr matrix at 10 K and measured by FTIR. The vibrational frequency of 1037 cm^?1 in the matrix confirms the newest gas-phase analysis giving 1039.6 cm^?1.     

First synthesis of chiral 3-vinylindoles as 4π-components for diels-alder reactions

The first syntheses of chiral 3- and 2-vinylindoles bearing sulfoxide or (-)-menthyloxy functional groups at the β-vinyl positions by way of procedures based on the Horner-Wadsworth-Emmons and Wittig reactions, respectively, are described. Some Diels-Alder reactions demonstrating the 4π-reactivity of these compounds are reported.     

Asymptotic expansions in the conditional central limit theorem

Let X_n, n , be i.i.d. with mean 0, variance 1, and E(¦X_n¦^r) < ∞ for some r 3. Assume that Cramér's condition is fulfilled. We prove that the conditional probabilities P(1/√n Σ_{i = 1}ⁿ X_i t¦B) can be approximated by a modified Edgeworth expansion up to order o(1/n^{(r − 2)/2)}), if the distances of the set B from the σ-fields σ(X₁, …, X_n) are of order O(1/n^{(r − 2)/2)}(lg n)^β), where β < −(r − 2)/2 for r and β < −r/2 for r . An example shows that if we replace β < −(r − 2)/2 by β = −(r − 2)/2 for r (β < −r/2 by β = −r/2 for r ) we can only obtain the approximation order O(1/n^{(r − 2)/2)}) for r (O(lg lgn/n^{(r − 2)/2)}) for r ).     

Assembly of triple-stranded beta-sheet peptides at interfaces

A 30-residue peptide, BS30, which incorporates two proline residues to induce reverse turns, was designed to form a triple-stranded beta-sheet monolayer at the air-water interface. To discern the structural role of proline, a second peptide, BS30G, identical to BS30 but with glycine residues replacing proline, was prepared and examined in parallel fashion. Surface pressure-molecular area isotherms indicated a limiting area per molecule (ca. 460 A(2)) for BS30 that corresponds well to that estimated from the known dimensions of crystalline beta-sheet monolayers (492 A(2)). Comparable measurements on BS30G yielded a smaller molecular area (380 A(2)). Grazing incidence X-ray diffraction measurements performed on the BS30 monolayer at nominal area per molecule of 500 A(2), exhibited two Bragg peaks corresponding to 4.79 and 34.9 A spacings, consistent with formation of triple-stranded beta-sheet structures that assemble into two-dimensional crystallites at the air-water interface. Visualized by Brewster angle microscopy, BS30 monolayers displayed uniform, solidlike domains, whereas BS30G appeared to be disordered.