Twisted factorization of a banded matrix

The twisted factorization of a tridiagonal matrix T plays an important role in inverse iteration as featured in the MRRR algorithm. The twisted structure simplifies the computation of the eigenvector approximation and can also improve the accuracy. A tridiagonal twisted factorization is given by T=M _k Δ _k N _k where Δ _k is diagonal, M _k ,N _k have unit diagonals, and the k-th column of M _k and the k-th row of N _k correspond to the k-th column and row of the identity, that is . This paper gives a constructive proof for the existence of the twisted factorizations of a general banded matrix A. We show that for a given twist index k, there actually are two such factorizations. We also investigate the implications on inverse iteration and discuss the role of pivoting.      

Emission measurement and safety assessment for the production process of silicon nanoparticles in a pilot-scale facility

Emission into the workplace was measured for the production process of silicon nanoparticles in a pilot-scale facility at the Institute of Energy and Environmental Technology e.V. (IUTA). The silicon nanoparticles were produced in a hot-wall reactor and consisted of primary particles around 60 nm in diameter. We employed real-time aerosol instruments to measure particle number and lung-deposited surface area concentrations and size distribution; airborne particles were also collected for off-line electron microscopic analysis. Emission of silicon nanoparticles was not detected during the processes of synthesis, collection, and bagging. This was attributed to the completely closed production system and other safety measures against particle release which will be discussed briefly. Emission of silicon nanoparticles significantly above the detection limit was only observed during the cleaning process when the production system was open and manually cleaned. The majority of the detected particles was in the size range of 100–400 nm and were silicon nanoparticle agglomerates first deposited in the tubing then re-suspended during the cleaning process. Appropriate personal protection equipment is recommended for safety protection of the workers during cleaning.     

Catalyst Control over Threefold Stereogenicity: Selective Synthesis of Atropisomeric Sulfones with Stereogenic C−S Axes

Catalyst control over higher-order stereogenicity addresses significantly extended stereochemical space, but selective methods to govern threefold stereogenic units remained elusive. Herein, we report the stereoselective synthesis of threefold stereogenic triptycyl sulfones with atropisomerism arising from a C(sp³)−S bond. An oxidation of a stereodynamic thioether controlled by a chiral phosphoric acid catalyst allowed selective access to enantioenriched triptycyl sulfoxides. The ensuing enantiospecific and diastereoselective catalytic oxidation to a threefold stereogenic sulfone provided overall control over the stereogenic C−S axis. All three stereoisomers were addressable with enantio- and diastereodivergence and a stereoselectivity of up to (−sc): (+sc) : (ap)=94 : 6 :<1.     

Substrate-Bound Diarylethene-Based Anisotropic Metal–Organic Framework Films as Photoactuators with a Directed Response

Molecular machines and responsive materials open a plethora of new opportunities in nanotechnology. We present an oriented crystalline array of diarylethene (DAE)-based photoactuators, arranged in a way to yield an anisotropic response. The DAE units are assembled, together with a secondary linker, into a monolithic surface-mounted metal–organic framework (SURMOF) film. By Infrared (IR) and UV/Vis spectroscopy as well as by synchrotron X-ray diffraction, we show that the light-induced extension changes of the molecular DAE linkers multiply to yield mesoscopic and anisotropic length changes. Due to the special architecture and substrate-bonding of the SURMOF, these length changes are transferred to the macroscopic scale, leading to the bending of a cantilever and performing work. This research shows the potential of assembling light-powered molecules into SURMOFs to yield photoactuators with a directed response, presenting a path to advanced actuators.     

Variational integrators for open-loop and closed-loop optimal control of mechanical systems

Mechanical systems have structural properties, e.g. symplecticity, symmetry, and a specific energy behavior, which get lost in standard integration methods. Therefore, symplectic integration methods are used in simulation and control of mechanical systems. This paper combines two methods of the class of structure-preserving control methods, namely a recently developed feedback control method and open loop optimal control based on variational integrator discretization. The combination is applied to the benchmark example of a cart pendulum system. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Coupling of deterministic and stochastic simulation methods for gas‐solid‐flows

A new simulation method is proposed coupling deterministic and stochastic methods by an adaptive domain decomposition based on local granular equilibrium rating. This method reduces the computational effort compared to the fully stochastic method by roughly an order of magnitude, without significant loss of accuracy. Furthermore with this method appropriate boundary conditions for the solid phase can easily be derived.     

Automated Parallel Temperature Optimization and Determination of Activation Energy for the Living Cationic Polymerization of 2‐Ethyl‐2‐oxazoline

Sixteen parallel polymerization reactions of 2‐ethyl‐2‐oxazoline have been performed at different temperatures in an automated synthesizer that allowed individual heating of each reactor. During the reactions samples were taken automatically, which were characterized by means of both online GPC and offline GC, in order to optimize the reaction temperature and to determine the activation energy of the polymerization.