Goal‐oriented error estimation for Cahn–Hilliard models of binary phase transition

A posteriori estimates of errors in quantities of interest are developed for the nonlinear system of evolution equations embodied in the Cahn–Hilliard model of binary phase transition. These involve the analysis of wellposedness of dual backward‐in‐time problems and the calculation of residuals. Mixed finite element approximations are developed and used to deliver numerical solutions of representative problems in one‐ and two‐dimensional domains. Estimated errors are shown to be quite accurate in these numerical examples. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010     

What’s so Good about a Wise and Knowledgeable Public?

Philosophers have been concerned for some time with the epistemic caliber of the general public, qua the body that is, ultimately, tasked with political decision-making in democratic societies. Unfortunately, the empirical data paint a pretty dismal picture here, indicating that the public tends to be largely ignorant on the issues relevant to governance. To make matters worse, empirical research on how ignorance tends to breed overconfidence suggests that the public will not only lack knowledge on the relevant issues, but also wisdom, in the Socratic sense of an awareness of your ignorance. While increasing the knowledge and wisdom of the public might be thought an obvious remedy, there is, as far as sound political decision-making and action are concerned, nothing particularly valuable about knowledge or wisdom per se. In fact, it might just be that what the public needs is nothing but the most basic epistemic good: true belief.     

Erratum: Fluorescent gel particles in the nanometer range for detection of metabolites in living cells

In the article above published in Volume 17 of Polymers for Advanced Technologies, pages 790–793 (2006) and online in Wiley InterScience , ( www.wileyinterscience.wiley.com ) DOI 10.1002/pat.786 the following changes should be recognised: On the second page of the paper, page 791, the sentence above figure 2 should have read ‘Since the headgroup areas of surfactants are a weak function of the condition under which they are used the function …’     

Anisotropy enhanced X‐ray scattering from solvated transition metal complexes

Time‐resolved X‐ray scattering patterns from photoexcited molecules in solution are in many cases anisotropic at the ultrafast time scales accessible at X‐ray free‐electron lasers (XFELs). This anisotropy arises from the interaction of a linearly polarized UV–Vis pump laser pulse with the sample, which induces anisotropic structural changes that can be captured by femtosecond X‐ray pulses. In this work, a method for quantitative analysis of the anisotropic scattering signal arising from an ensemble of molecules is described, and it is demonstrated how its use can enhance the structural sensitivity of the time‐resolved X‐ray scattering experiment. This method is applied on time‐resolved X‐ray scattering patterns measured upon photoexcitation of a solvated di‐platinum complex at an XFEL, and the key parameters involved are explored. It is shown that a combined analysis of the anisotropic and isotropic difference scattering signals in this experiment allows a more precise determination of the main photoinduced structural change in the solute, i.e. the change in Pt—Pt bond length, and yields more information on the excitation channels than the analysis of the isotropic scattering only. Finally, it is discussed how the anisotropic transient response of the solvent can enable the determination of key experimental parameters such as the instrument response function.     

Shear-induced nano-macro structural transition in a polymeric bicontinuous microemulsion

Bicontinuous microemulsions arise in a narrow concentration range for ternary blends containing two immiscible homopolymers and the corresponding diblock copolymer. Steady shear reveals four distinct regimes of response as a function of shear rate, corresponding to flow-induced transitions in fluid structure. In situ neutron scattering shows flow-induced anisotropy in the nanometer-scale microemulsion structure at moderate shear rates, while higher rates induce bulk phase separation, with micron-size morphology, which is characterized with in situ light scattering and optical microscopy.     

Combining aryltriazenes and electrogenerated acids to create well-defined aryl-tethered films and patterns on surfaces

Immobilization of submonolayers to 4-5 multilayers of organic molecules on carbon surfaces can be performed by in situ generation of aryl radicals from aryltriazenes. The central idea consists of oxidatively forming an electrogenerated acid of N,N'-diphenylhydrazine to convert the aryltriazene to the corresponding diazonium salt in the diffusion layer of the electrode. In a second step, the diazonium salt is reduced at the same electrode to give a surface of covalently attached aryl groups. In this manner, various moieties tethered to the aryl groups can be immobilized on the surface. Here a ferrocenyl group was introduced as redox marker, the electrochemical signal of which is extraordinarily well-defined. This behavior is independent of film thickness, the latter being easily controlled by the number of repetitive cycles performed. It is also demonstrated that the new approach is suitable for patterning of surfaces using scanning electrochemical microscopy.     

A new chiral, poly-imidazole N8-ligand and the related di- and tri-copper(II) complexes: synthesis, theoretical modelling, spectroscopic properties, and biomimetic stereoselective oxidations

The new poly-imidazole N(8) ligand (S)-2-piperazinemethanamine-1,4-bis[2-((N-(1-acetoxy-3-(1-methyl-1H-imidazol-4-yl))-2-(S)-propyl)-(N-(1-methyl-1H-imidazol-2-ylmethyl)))ethyl]-N-(phenylmethyl)-N-(acetoxy), also named (S)-Pz-(C2-(HisIm))(2) (L), containing three chiral (S) centers, was obtained by a multi-step synthesis and used to prepare dinuclear [Cu(2)(L)](4+) and trinuclear [Cu(3)(L)](6+) copper(II) complexes. Low-temperature EPR experiments performed on [Cu(2)(L)](4+) demonstrated that the two S = ? centers behaved as independent paramagnetic units, while the EPR spectra used to study the trinuclear copper complex, [Cu(3)(L)](6+), were consistent with a weakly coupled three-spin ? system. Theoretical models for the two complexes were obtained by DFT/RI-BP86/TZVP geometry optimization, where the structural and electronic characteristics nicely supported the EPR experimental findings. In addition, the theoretical analysis unveiled that the conformational flexibility encoded in both [Cu(2)(L)](4+) and [Cu(3)(L)](6+) arises not only from the presence of several σ-bonds and the bulky residues attached to the (S)-Pz-(C2-(HisIm))(2) ligand scaffold, but also from the poor coordination ability of the tertiary amino groups located in the ligand side-chains containing the imidazole units towards the copper(II) ions. Both the dinuclear and trinuclear complexes are efficient catalysts in the stereoselective oxidation of several catechols and flavonoid compounds, yielding the corresponding quinones. The structural features of the substrate-catalyst adduct intermediates were assessed by searching the conformational space of the molecule through MMFF94/Monte Carlo (MMFF94/MC) methods. The conformational flexibility of the bound ligand in the complexes proves to be beneficial for substrate binding and recognition. For the dinuclear complex, chiral recognition of the optically active substrates derives from weak electrostatic interactions between bound substrates and folded regions of the ligand scaffold. For the trinuclear complex, in the case of L/D-Dopa, the chiral recognition has a remarkable stereoselectivity index of 75%, the highest so far reported for this type of reaction. Here the dominant contribution to stereoselectivity arises from the direct interaction between a donor group (the Dopa carboxylate) far from the substrate reaction site (the catechol ring) with the additional (third) copper center not involved in the oxidative catalysis. On the other hand, in the case of bulky substrates, such as L/D-catechin, the observed poor substrate recognition is associated with much weaker interactions between the chiral regions of the complex and the chiral part of the substrate.