Reduced basis approximation and a posteriori error estimation for Stokes flows in parametrized geometries: roles of the inf-sup stability constants

In this paper we review and we extend the reduced basis approximation and a posteriori error estimation for steady Stokes flows in affinely parametrized geometries, focusing on the role played by the Brezzi’s and Babu?ka’s stability constants. The crucial ingredients of the methodology are a Galerkin projection onto a low-dimensional space of basis functions properly selected, an affine parametric dependence enabling to perform competitive Offline-Online splitting in the computational procedure and a rigorous a posteriori error estimation on field variables. The combinatiofn of these three factors yields substantial computational savings which are at the basis of an efficient model order reduction, ideally suited for real-time simulation and many-query contexts (e.g. optimization, control or parameter identification). In particular, in this work we focus on (i) the stability of the reduced basis approximation based on the Brezzi’s saddle point theory and the introduction of a supremizer operator on the pressure terms, (ii) a rigorous a posteriori error estimation procedure for velocity and pressure fields based on the Babu?ka’s inf-sup constant (including residuals calculations), (iii) the computation of a lower bound of the stability constant, and (iv) different options for the reduced basis spaces construction. We present some illustrative results for both interior and external steady Stokes flows in parametrized geometries representing two parametrized classical Poiseuille and Couette flows, a channel contraction and a simple flow control problem around a curved obstacle.     

Bistability and spatiotemporal irregularity in neuronal networks with nonlinear synaptic transmission

We present a mean-field theory for spiking networks operating in the balanced excitation-inhibition regime, with synapses displaying short-term plasticity. The theory reveals a novel mechanism for bistability which relies on the nonlinearity of the synaptic interactions. As synaptic nonlinearity is mainly controlled by the spiking rates, the different states are stabilized by dynamically generated changes in the noise level. Thus, in both states, the network operates in the fluctuation-driven regime, producing activity patterns characterized by strong spatiotemporal irregularity.     

Enantioselective HPLC combined with spectroscopic methods: A valid strategy to determine the absolute configuration of potential β-secretase inhibitors

A direct HPLC enantioseparation of three representative compounds of a new family of potential non-peptide β-secretase inhibitors was performed on the immobilized Chiralpak IA chiral stationary phase. Semipreparative amounts of enantiopure forms were collected and submitted to stereochemical characterization. The absolute configuration was assigned by a multi-step methodology based on the combination of Mosher's method with circular dichroism (CD) spectroscopy. The results from the NMR/CD study fully correlated the configurational assignment obtained by a second approach involving single crystal X-ray diffraction.     

Model reduction of semiaffinely parameterized partial differential equations by two-level affine approximation

We propose an improvement to the reduced basis method for parametric partial differential equations. An assumption of affine parameterization leads to an efficient offline–online decomposition when the problem is solved for many different parametric configurations. We consider an advection–diffusion problem, where the diffusive term is non-affinely parameterized and treated with a two-level affine approximation given by the empirical interpolation method. The offline stage and a posteriori error estimation is performed using the coarse-level approximation, while the fine-level approximation is used to perform a correction iteration that reduces the actual error of the reduced basis approximation while keeping the same certified error bounds.     

Atom Economic and Highly Syn‐selective Prolinamide‐Catalyzed Cross‐aldol Addition of Hydroxyacetone to Aromatic Aldehydes

The highly selective cross‐aldol addition of hydroxyacetone (HA) to p‐nitro and m‐nitrobenzaldehyde is reported; the reaction is catalyzed by three different di‐ or tripeptides all containing D‐Pro in the N‐terminal position and one or two residues of β³‐homophenylglycine (β³‐hPhg): H‐D‐Pro‐(R)‐β³‐hPhg‐OBn, H‐D‐Pro‐(R)‐β³‐hPhg‐(S)‐β³‐hPhg‐OBn and H‐D‐Pro‐[(S)‐β³‐hPhg]₂‐OBn. Several reaction conditions have been tested, always in the absence of a protecting group on the HA hydroxyl. This reaction affords the desired compounds with complete regioselectivities being the other regioisomer completely avoided. Furthermore high enantioselectivities and satisfactory diastereoselectivities, always favouring the syn diastereoisomers, were obtained. The stereochemistry of the diols was further confirmed by the analysis of the ¹H NMR spectrum of the corresponding carbonates, obtained by reaction of the syn/anti mixtures with triphosgene in presence of dimethylamino‐pyridine (DMAP).     

ED‐XRF set‐up for size‐segregated aerosol samples analysis

The knowledge of size‐segregated elemental concentrations in atmospheric particulate matter (PM) gives a useful contribution to the complete chemical characterisation; this information can be obtained by sampling with multi‐stage cascade impactors. In this work, samples were collected using a low‐pressure 12‐stage Small Deposit Impactor and a 13‐stage rotating Micro Orifice Uniform Deposit Impactor^?. Both impactors collect the aerosol in an inhomogeneous geometry, which needs a special set‐up for X‐ray analysis. This work aims at setting up an energy dispersive X‐ray fluorescence (ED‐XRF) spectrometer to analyse quantitatively size‐segregated samples obtained by these impactors. The analysis of cascade impactor samples by ED‐XRF is not customary; therefore, as additional consistency test some samples were analysed also by particle‐induced X‐ray emission (PIXE), which is more frequently applied to size‐segregated samples characterised by small PM quantities. A very good agreement between ED‐XRF and PIXE results was obtained for all the detected elements in samples collected with both impactors. The good inter‐comparability proves that our methodology is reliable for analysing size‐segregated samples by ED‐XRF technique. The advantage of this approach is that ED‐XRF is cheaper, easier to use, and more widespread than PIXE, thus promoting an intensive use of multi‐stage impactors. Copyright © 2011 John Wiley & Sons, Ltd.     

Au nanoparticle monolayers covered with sol-gel oxide thin films: optical and morphological study

In this work, we provide a detailed study of the influence of thermal annealing on submonolayer Au nanoparticle deposited on functionalized surfaces as standalone films and those that are coated with sol-gel NiO and TiO(2) thin films. The systems are characterized through the use of UV-vis absorption, X-ray diffraction (XRD), atomic force microscopy (AFM), scanning electron microscopy (SEM), and spectroscopic ellipsometry. The surface plasmon resonance peak of the Au nanoparticles was found to red-shift and increase in intensity with increasing surface coverage, an observation that is directly correlated to the complex refractive index properties of Au nanoparticle layers. The standalone Au nanoparticles sinter at 200 °C, and a relationship between the optical properties and the annealing temperature is presented. When overcoated with sol-gel metal oxide films (NiO, TiO(2)), the optical properties of the Au nanoparticles are strongly affected by the metal oxide, resulting in an intense red shift and broadening of the plasmon band; moreover, the temperature-driven sintering is strongly limited by the metal oxide layer. Optical sensing tests for ethanol vapor are presented as one possible application, showing reversible sensing dynamics and confirming the effect of Au nanoparticles in increasing the sensitivity and in providing a wavelength dependent response, thus confirming the potential use of such materials as optical probes.     

Proton evolved local field solid-state nuclear magnetic resonance using Hadamard encoding: theory and application to membrane proteins

NMR anisotropic parameters such as dipolar couplings and chemical shifts are central to structure and orientation determination of aligned membrane proteins and liquid crystals. Among the separated local field experiments, the proton evolved local field (PELF) scheme is particularly suitable to measure dynamically averaged dipolar couplings and give information on local molecular motions. However, the PELF experiment requires the acquisition of several 2D datasets at different mixing times to optimize the sensitivity for the complete range of dipolar couplings of the resonances in the spectrum. Here, we propose a new PELF experiment that takes the advantage of the Hadamard encoding (HE) to obtain higher sensitivity for a broad range of dipolar couplings using a single 2D experiment. The HE scheme is obtained by selecting the spin operators with phase switching of hard pulses. This approach enables one to detect four spin operators, simultaneously, which can be processed into two 2D spectra covering a broader range of dipolar couplings. The advantages of the new approach are illustrated for a U-(15)N NAL single crystal and the U-(15)N labeled single-pass membrane protein sarcolipin reconstituted in oriented lipid bicelles. The HE-PELF scheme can be implemented in other multidimensional experiments to speed up the characterization of the structure and dynamics of oriented membrane proteins and liquid crystalline samples.