Nonlinear normal modes and band zones in granular chains with no pre-compression

We study standing waves (nonlinear normal modes—NNMs) and band zones in finite granular chains composed of spherical granular beads in Hertzian contact, with fixed boundary conditions. Although these are homogeneous dynamical systems in the notation of Rosenberg (Adv. Appl. Mech. 9:155–242, 1966), we show that the discontinuous nature of the dynamics leads to interesting effects such as separation between beads, NNMs that appear as traveling waves (these are characterized as pseudo-waves), and localization phenomena. In the limit of infinite extent, we study band zones, i.e., pass and stop bands in the frequency–energy plane of these dynamical systems, and classify the essentially nonlinear responses that occur in these bands. Moreover, we show how the topologies of these bands significantly affect the forced dynamics of these granular media subject to narrowband excitations. This work provides a classification of the coherent (regular) intrinsic dynamics of one-dimensional homogeneous granular chains with no pre-compression, and provides a rigorous theoretical foundation for further systematic study of the dynamics of granular systems, e.g., the effects of disorders or clearances, discrete breathers, nonlinear localized modes, and high-frequency scattering by local disorders. Moreover, it contributes toward the design of granular media as shock protectors, and in the passive mitigation of transmission of unwanted disturbances.     

Diastereoselective Coupling of Chiral Acetonide Trisubstituted Radicals with Alkenes

The stereochemical outcome of reactions of chiral nucleophilic trisubstituted acetonide radicals with electron‐deficient alkenes is dictated by a delicate balance between destabilizing non‐bonding interactions and stabilizing hydrogen‐bonding between substituents on the α and β carbons.     

Global solution of nonlinear mixed-integer bilevel programs

An algorithm for the global optimization of nonlinear bilevel mixed-integer programs is presented, based on a recent proposal for continuous bilevel programs by Mitsos et al. (J Glob Optim 42(4):475–513, 2008). The algorithm relies on a convergent lower bound and an optional upper bound. No branching is required or performed. The lower bound is obtained by solving a mixed-integer nonlinear program, containing the constraints of the lower-level and upper-level programs; its convergence is achieved by also including a parametric upper bound to the optimal solution function of the lower-level program. This lower-level parametric upper bound is based on Slater-points of the lower-level program and subsets of the upper-level host sets for which this point remains lower-level feasible. Under suitable assumptions the KKT necessary conditions of the lower-level program can be used to tighten the lower bounding problem. The optional upper bound to the optimal solution of the bilevel program is obtained by solving an augmented upper-level problem for fixed upper-level variables. A convergence proof is given along with illustrative examples. An implementation is described and applied to a test set comprising original and literature problems. The main complication relative to the continuous case is the construction of the parametric upper bound to the lower-level optimal objective value, in particular due to the presence of upper-level integer variables. This challenge is resolved by performing interval analysis over the convex hull of the upper-level integer variables.     

Development of a time-resolved white-light interference microscope for optical phase measurements during fs-laser material processing

A modified Mach–Zehnder interferometer set-up combined with microscope objectives has been developed for the measurement of phase changes in the processed material sample, like modification and melting of glass. The white light is generated by focusing ultrafast laser radiation (t _p=80 fs) in a sapphire crystal using a micro-lens array to minimize temporal and spatial fluctuations in the white-light continuum. Lateral and coaxial pump-probe measurements of the phase changes during material processing are performed using two coupled ultrafast laser sources at different repetition rates (f _rep=1 Hz–1 MHz). The optical phase shift and therefore the refractive index of the material are calculated from the interference images using two approaches. The knowledge of the refractive index during the laser processing with a temporal resolution in the ps-range and a spatial resolution of several microns leads to a better understanding of the initial processes for the permanent material modifications.     

Minimalistic Ditopic Ligands: An α‐S,N‐Donor‐Substituted Alkyne as Effective Intermetallic Conjugation Linker

The capability of donor‐substituted alkynes to link different metal ions in a side‐on carbon donor‐chelate coordination mode is extended from the donor centers S and P to the second period element N. The complex [Tp′W(CO)₂{η²‐C₂(S)(NHBn)}] (Tp′=hydrido‐tris(3,5‐dimethylpyrazolyl)borate, Bn=benzyl) bearing a terminal sulfur atom and a secondary amine substituent is accessible by a metal‐template synthesis. Subsequent deprotonation allowed the formation of remarkably stable heterobimetallic complexes with the [(η⁵‐C₅H₅)Ru(PPh₃)] and the [Ir(ppy)₂] moiety. Electrochemical and spectroscopic investigations (cyclic voltammetry, IR, UV/Vis, luminescence, EPR), as well as DFT calculations, and X‐ray structure determinations of the W–Ru complex in two oxidation states reveal a strong metal–metal coupling but also a limited delocalization of excited states.