Linear stability of WENO schemes coupled with explicit Runge–Kutta schemes

This paper focuses on the results of the linear stability analysis of the finite‐difference weighted essentially non‐oscillatory (WENO) schemes with optimal weights. The standard WENO schemes between the third and 11th order, the order‐optimised WENO schemes of the sixth and eighth order and the bandwidth‐optimised WENO schemes of the third and fourth order are considered. Several explicit Runge–Kutta schemes including the recently published strong stability‐preserving explicit Runge–Kutta schemes are considered for time discretisation. The stability limits as well as dissipation and dispersion properties dependent on the Courant–Friedrichs–Lewy number are presented for a hyperbolic model equation. The different combinations of space and time discretisation schemes are compared in terms of their accuracy and efficiency. For a parabolic model equation, the viscous term is discretised with high‐order central differences. The stability limits for the parabolic problem are presented as well. Numerical results of linear test cases are shown. Copyright © 2011 John Wiley & Sons, Ltd.     

The explicit synthesis of stabilizing (time optimal) feedback controls for the attitude control of a rotating satelite

The attitude stabilization problem for a spinning satellite controlled by two small jets may be modelled as a four-dimensional, nonlinear control system, linear in the controls. The recent feedback linearization theorem of Hunt and Su may be applied to transform this system, via state feedback and a local coordinate change, to a pair of uncoupled, two-dimensional, linear systems. Feedback controls for the problem of time optimal transfer to the origin for these linear systems are explicitly calculated and then transformed to give explicit feedback controls for time optimal stabilization in the original nonlinear problem. The theory is illustrated by sample calculations.     

Polyesters from Macrolactones Using Commercial Lipase NS 88011 and Novozym 435 as Biocatalysts

The demand for environmentally friendly products allied with the depletion of natural resources has increased the search for sustainable materials in chemical and pharmaceutical industries. Polyesters are among the most widely used biodegradable polymers in biomedical applications. In this work, aliphatic polyesters (from globalide and ω-pentadecalactone) were synthesized using a new commercial biocatalyst, the low-cost immobilized NS 88011 lipase (lipase B from Candida antarctica immobilized on a hydrophobic support). Results were compared with those obtained under the same conditions using a traditional, but more expensive, commercial biocatalyst, Novozym 435 (lipase B from C. antarctica immobilized on Lewatit VP OC). When NS 88011 was used in the polymerization of globalide, longer reaction times (240 min)—when compared to Novozym 435—were required to obtain high yields (80–90 wt%). However, higher molecular weights were achieved. When poly(ω-pentadecalactone) was synthesized, high yields and molecular weights (130,000 g mol^?1) were obtained and the enzyme concentration showed strong influence on the polyester properties. This is the first report describing NS 88011 in polymer synthesis. The use of this cheaper enzymatic preparation can provide an alternative for polyester synthesis via enzymatic ring-opening polymerization.     

Selective nucleation and growth of metal-organic open framework thin films on patterned COOH/CF3-terminated self-assembled monolayers on Au(111)

Metal-Organic open Framework coordination polymers (MOFs) are a fascinating class of materials. We demonstrate the selective growth of patterned thin films of MOF-5 and the subsequent loading with a palladium organic compound, which acts as a precursor for the deposition of palladium nanoclusters inside the cavities of the MOF-5 material.