Colloidal Hybrid Nanostructures: A New Type of Functional Materials

One key goal of nanocrystal research is the development of experimental methods to selectively control the composition and shape of nanocrystals over a wide range of material combinations. The ability to selectively arrange nanosized domains of metallic, semiconducting, and magnetic materials into a single hybrid nanoparticle offers an intriguing route to engineer nanomaterials with multiple functionalities or the enhanced properties of one domain. In this Review, we focus on recent strategies used to create semiconductor–metal hybrid nanoparticles, present the emergent properties of these multicomponent materials, and discuss their potential applicability in different technologies.     

Elemental mercury vapour in air: the origins and validation of the ‘Dumarey equation’ describing the mass concentration at saturation

The Dumarey equation has been the dominant relationship used to calculate the mass concentration of saturated elemental mercury vapour in air for the calibration of mercury vapour measurement equipment for over 25 years. However, the origin of the equation, and the validation data supporting its accuracy have never been published. This paper addresses that deficiency, compares the Dumarey equation with other data sets to which it has been wrongly attributed in the past, and describes why it remains superior to the use of mercury vapour pressure data in combination with the ideal gas law, for the purposes of calibrating mercury vapour measurement equipment.     

Reduction of chemical reaction networks using quasi-integrals

We present a numerical method to identify possible candidates for quasi-stationary manifolds in complex reaction networks governed by systems of ordinary differential equations. Inspired by singular perturbation theory, we examine the ratios of certain components of the reaction rate vector. Those ratios that rapidly approach a nearly constant value define a slow manifold for the original flow in terms of quasi-integrals, that is, functions that are nearly constant along the trajectories. The dimensionality of the original system is thus effectively reduced without reliance on a priori knowledge of the different time scales in the system. We also demonstrate the relation of our approach to singular perturbation theory which, in its simplest form, is just the well-known quasi-steady-state approximation. In two case studies, we apply our method to oscillatory chemical systems: the 6-dimensional hemin-hydrogen peroxide-sulfite pH oscillator and a 10-dimensional mechanistic model for the peroxidase-oxidase (PO) reaction system. We conjecture that the presented method is especially suited for a straightforward reduction of higher dimensional dynamical systems where analytical methods fail to identify the different time scales associated with the slow invariant manifolds present in the system.     

The application of joint sparsity and total variation minimization algorithms to a real-life art restoration problem

On March 11, 1944, the famous Eremitani Church in Padua (Italy) was destroyed in an Allied bombing along with the inestimable frescoes by Andrea Mantegna et al. contained in the Ovetari Chapel. In the last 60 years, several attempts have been made to restore the fresco fragments by traditional methods, but without much success. One of the authors contributed to the development of an efficient pattern recognition algorithm to map the original position and orientation of the fragments, based on comparisons with an old gray level image of the fresco prior to the damage. This innovative technique allowed for the partial reconstruction of the frescoes. Unfortunately, the surface covered by the colored fragments is only 77 m², while the original area was of several hundreds. This means that we can reconstruct only a fraction (less than 8%) of this inestimable artwork. In particular the original color of the blanks is not known. This begs the question of whether it is possible to estimate mathematically the original colors of the frescoes by making use of the potential information given by the available fragments and the gray level of the pictures taken before the damage. Moreover, is it possible to estimate how faithful such a restoration is? In this paper we retrace the development of the recovery of the frescoes as an inspiring and challenging real-life problem for the development of new mathematical methods. Then we shortly review two models recently studied independently by the authors for the recovery of vector valued functions from incomplete data, with applications to the recolorization problem. The models are based on the minimization of a functional which is formed by the discrepancy with respect to the data and additional regularization constraints. The latter refer to joint sparsity measures with respect to frame expansions, in particular wavelet or curvelet expansions, for the first functional and functional total variation for the second. We establish relations between these two models. As a major contribution of this work we perform specific numerical test on the real-life problem of the A. Mantegna’s frescoes and we compare the results due to the two methods.     

Reaction Rate of Small Diffusing Molecules on a Cylindrical Membrane

Biomembranes consist of a lipid bi-layer into which proteins are embedded to fulfill numerous tasks in localized regions of the membrane. Often, the proteins have to reach these regions by simple diffusion. Motivated by the observation that IP₃ receptor channels (IP₃R) form clusters on the surface of the endoplasmic reticulum (ER) during ATP-induced calcium release, the reaction rate of small diffusing molecules on a cylindrical membrane is calculated based on the Smoluchowski approach. In this way, the cylindrical topology of the tubular ER is explicitly taken into account. The problem can be reduced to the solution of the diffusion equation on a finite cylindrical surface containing a small absorbing hole. The solution is constructed by matching appropriate ‘inner’ and ‘outer’ asymptotic expansions. The asymptotic results are compared with those from numerical simulations and excellent agreement is obtained. For realistic parameter sets, we find reaction rates in the range of experimentally measured clustering rates of IP₃R. This supports the idea that clusters are formed by a purely diffusion limited process.     

A new technique of analysis for the investigation of kinetic data using the differential scanning calorimeter

This method of analysis for kinetic data of solid state chemical reactions takes advantage of the binomial series expansion to normalize various mathematical expressions related to various solid state models into a power series. This facilitates analysis by computer methods, in that deviations of the various models will be perceptible at the outset.     

Fe(III)-Catalyzed direct C3 chalcogenylation of indole: The effect of iodide ions

A mild and efficient iron (III)-catalyzed C3 chalcogenylation of indoles has been developed and the role of the iodide ions in this transformation was investigated. EPR experiments revealed the reduction of Fe(III) to Fe(II) under the reaction conditions, supporting the formation of molecular iodine in the system, which in effect catalyze the reaction. The scope of the chalcogenylation was broad and the synthesis of more functionalized 3-selenylindoles was explored.     

Reducing thermal noise in future gravitational wave detectors by employing Khalili etalons

Reduction of thermal noise in dielectric mirror coatings is a key issue for the sensitivity improvement in the second and third generation interferometric gravitational wave detectors. Replacing an end mirror of the interferometer by an anti-resonant cavity (a so-called Khalili cavity) has been proposed to realize the reduction of the overall thermal noise level. In this article we show that the use of a Khalili etalon, which requires less hardware than a Khalili cavity, yields still a significant reduction of thermal noise. We identify the optimum distribution of coating layers on the front and rear surfaces of the etalon and compare the total noise budget with a conventional mirror. In addition we briefly discuss advantages and disadvantages of the Khalili etalon compared with the Khalili cavity in terms of technical aspects, such as interferometric length control and thermal lensing.     

Synthesis of Glycoborine,Glybomine A and B,the Phytoalexin Carbalexin A and the β‐Adrenoreceptor Antagonists Carazolol and Carvedilol

We describe a regioselective synthesis of 4‐ or 5‐substituted carbazoles by oxidative cyclisation of meta‐oxygen‐substituted N‐phenylanilines. Using the regiodirecting effect of a pivaloyloxy group, we prepared 4‐hydroxycarbazole, a precursor for the enantiospecific synthesis of the β‐adrenoreceptor antagonists (?)‐(S)‐carazolol ( 5 ) and (?)‐(S)‐carvedilol ( 6 ). Regioselective palladium(II)‐catalysed cyclisation of different diarylamines led to total synthesis of glycoborine ( 7 ) and the first total syntheses of the phytoalexin carbalexin A ( 8 ), glybomine A ( 9 ) and glybomine B ( 10 ). For glybomine B ( 10 ), a 5‐hydroxycarbazole was converted into the corresponding triflate and utilized for introduction of a prenyl substituent.