Preconditioning of two-by-two block matrix systems with square matrix blocks,with applications

Two-by-two block matrices of special form with square matrix blocks arise in important applications, such as in optimal control of partial differential equations and in high order time integration methods.Two solution methods involving very efficient preconditioned matrices, one based on a Schur complement reduction of the given system and one based on a transformation matrix with a perturbation of one of the given matrix blocks are presented. The first method involves an additional inner solution with the pivot matrix block but gives a very tight condition number bound when applied for a time integration method. The second method does not involve this matrix block but only inner solutions with a linear combination of the pivot block and the off-diagonal matrix blocks.Both the methods give small condition number bounds that hold uniformly in all parameters involved in the problem, i.e. are fully robust. The paper presents shorter proofs, extended and new results compared to earlier publications.     

Laser-induced fluorescence of formaldehyde in combustion using third harmonic Nd:YAG laser excitation

Formaldehyde (CH2O) is an important intermediate species in combustion processes and it can through laser-induced fluorescence measurements be used for instantaneous flame front detection. The present study has focussed on the use of the third harmonic of a Nd:YAG laser at 355 nm as excitation wavelength for formaldehyde, and different dimethyl ether (C2H6O) flames were used as sources of formaldehyde in the experiments. The investigations included studies of the overlap between the laser profile and the absorption lines of formaldehyde, saturation effects and the potential occurrence of laser-induced photochemistry. The technique was applied for detection of formaldehyde in an internal combustion engine operated both as a spark ignition engine and as a homogenous charge compression ignition engine.     

Constraining the QCD phase diagram by tricritical lines at imaginary chemical potential

We present unambiguous evidence, from lattice simulations of QCD with three degenerate quark species, for two tricritical points in the (T, m) phase diagram at fixed imaginary chemical potential μ/T = iπ/3 mod2π/3, one in the light and one in the heavy mass regime. These represent the boundaries of the chiral and deconfinement critical lines continued to imaginary μ, respectively. It is demonstrated that the shape of the deconfinement critical line for real chemical potentials is dictated by tricritical scaling and implies the weakening of the deconfinement transition with real chemical potential. The generalization to nondegenerate and light quark masses is discussed.     

Comparison of Novel Sampling Methods for the Analysis of Capillary Electrophoresis Fractions by Matrix-assisted Laser Desorption/Ionization Time-of-flight Mass Spectrometry

Two methods for the collection of capillary electrophoresis fractions for analysis by matrix-assisted laser desorption/ionization have been investigated; the first using a novel ion-porous joint design for dropwise fraction collection and the second, a process of electrospray deposition. Sensitivity, shot-to-shot reproducibility, effect of matrix preparation and influence of buffer additives encountered in micellar electrokinetic capillary chromatography (MECC) have been examined using a standard peptide, methionine enkephalin. The direct collection of droplets from the capillary outlet was found to give a superior signal intensity, whereas the electrospray method, in its first stage of development, suffered through dilution effects and excessively wide sample distribution. The target compound was successfully collected by electrospray deposition and results indicated that signal intensity and sample homogeneity would be enhanced if the sprayed output could be collected into the sample wells in its entirety. The advantage of using electrospray deposition for the preparation of matrix layers followed by direct droplet collection onto the electrosprayed matrix was clearly demonstrated by improvements in both sensitivity and shot-to-shot variance in signal intensity across the sample well compared with collection onto spotted matrix. In addition, compatibility of the droplet collection method with MECC was illustrated by the recovery of the compound of interest from a buffer containing 30 mm sodium dodecyl sulphate. © 1997 John Wiley & Sons, Ltd.     

Conjugate gradient type methods for unsymmetric and inconsistent systems of linear equations

Conjugate gradient type methods are discussed for unsymmetric and inconsistent system of equations. For unsymmetric problems, besides conjugate gradient methods based on the normal equations, we also present a (modified) minimal residual (least square) method, which converges for systems with matrices that have a positive definite symmetric part. For inconsistent problems, for completeness we discuss briefly various (well-known) versions of the conjugate gradient method. Preconditioning and rate of convergence are also discussed.     

Effect of E1 decay in the population of superdeformed structures

Spectra of the yrast and excited superdeformed bands, forming the E2 quasi-continuum, are measured with the EUROBALL array for the nucleus ¹⁴³Eu, in coincidence with high-energy γ-rays (E_γ>3 MeV). It is found that the intensity population of the superdeformed states is enhanced by a factor of ≈1.6 when a coincidence with a γ-ray with energy >6 MeV is required, in reasonable agreement with the increase of the line shape of the Giant Dipole Resonance built on a superdeformed configuration. This result shows that when an high energy E1 γ-ray is involved in the decay it is more likely connected with a SD rather than a ND nucleus. In addition, the analysis of the rotational quasi-continuum suggests the presence of a superdeformed component. The data are also compared and found consistent with simulation calculations of the relative intensities of the SD states, including the E1 decay of superdeformed nature.     

A nanofluidic switching device

We present a nanofluidic switching function which allows directed transport in lipid bilayer nanotubes ( approximately 100 nm in diameter) between any two or several nanotube-connected vesicle containers (5-10 mum radius) in a large network. Liquid is transported in the form of small vesicular structures (10-15-10-18 L), and the transport direction is controlled by a two-point perturbation technique, where the surface membrane tension is decreased in one container while it is increased in another container. When reaching a target container, the transported vesicular structures could also inject their material into it.     

Experimental techniques,data treatment for studying the dynamics of ethanol production/consumption in baker's yeast

The dynamics of ethanol production/consumption in baker's yeast were studied under feed- rate controlled conditions. The yeast was grown on molasses in an 8-l fed-batch reactor and experiments were done at cell concentrations between 5 and 65 g l^?1. Small changes in the feed rate were made around a feed rate corresponding to the critical growth rate, at which the yeast cell metabolism switches between ethanol consumption and production. A membrane gas sensor was used for on-line measurement of the ethanol concentration in the broth. The measured ethanol signal was used for control and the system was excited through changes in the regulator set-point. The closed-loop experiments ensured that feed variations were within the critical range, and thus facilitated reproducible experiments. Data were fitted to a second-order difference equation by statistical methods. Results were compared with a theoretically derived model. The process gain could be understood in terms of the underlying stoichiometry by using the “bottleneck” view of yeast glucose metabolism. The process time constant was found to be longer than is implied by a simple Monod relation between glucose uptake rate and concentration.     

Organic Polymer Dots Photocatalyze CO2 Reduction in Aqueous Solution

Developing low-cost and efficient photocatalysts to convert CO₂ into valuable fuels is desirable to realize a carbon-neutral society. In this work, we report that polymer dots (Pdots) of poly[(9,9′-dioctylfluorenyl-2,7-diyl)-co-(1,4-benzo-thiadiazole)] (PFBT), without adding any extra co-catalyst, can photocatalyze reduction of CO₂ into CO in aqueous solution, rendering a CO production rate of 57 μmol g⁻¹ h⁻¹ with a detectable selectivity of up to 100 %. After 5 cycles of CO₂ re-purging experiments, no distinct decline in CO amount and reaction rate was observed, indicating the promising photocatalytic stability of PFBT Pdots in the photocatalytic CO₂ reduction reaction. A mechanistic study reveals that photoexcited PFBT Pdots are reduced by sacrificial donor first, then the reduced PFBT Pdots can bind CO₂ and reduce it into CO via their intrinsic active sites. This work highlights the application of organic Pdots for CO₂ reduction in aqueous solution, which therefore provides a strategy to develop highly efficient and environmentally friendly nanoparticulate photocatalysts for CO₂ reduction.