Maximum principle for the optimal control of a hyperbolic equation in one space dimension,part 1: Theory

A maximum principle is developed for a class of problems involving the optimal control of a damped-parameter system governed by a linear hyperbolic equation in one space dimension that is not necessarily separable. A convex index of performance is formulated, which consists of functionals of the state variable, its first- and second-order space derivatives, its first-order time derivative, and a penalty functional involving the open-loop control force. The solution of the optimal control problem is shown to be unique. The adjoint operator is determined, and a maximum principle relating the control function to the adjoint variable is stated. The proof of the maximum principle is given with the help of convexity arguments. The maximum principle can be used to compute the optimal control function and is particularly suitable for problems involving the active control of structural elements for vibration suppression.     

Independent component analysis of 2-D electrophoresis gels

We present a novel application of independent component analysis (ICA), an exploratory data analysis technique, to two-dimensional electrophoresis (2-DE) gels, which have been used to analyze differentially expressed proteins across groups. Unlike currently used pixel-wise statistical tests, ICA is a data-driven approach that utilizes the information contained in the entire gel data. We also apply ICA on wavelet-transformed 2-DE gels to address the high dimensionality and noise problems typically found in 2-DE gels. Also, we use an analysis-of-variance (ANOVA) approach as a benchmark for comparison. Using simulated data, we show that ICA detects the group differences accurately in both the spatial and wavelet domains. We also apply these techniques to real 2-DE gels. ICA proves to be much faster than ANOVA, and unlike ANOVA it does not depend on the selection of a threshold. Application of principal component analysis reduces the dimensionality and tends to improve the performance by reducing the noise.     

In Situ Observation of Surface Species on Iridium Oxide Nanoparticles during the Oxygen Evolution Reaction

An iridium oxide nanoparticle electrocatalyst under oxygen evolution reaction conditions was probed in situ by ambient‐pressure X‐ray photoelectron spectroscopy. Under OER conditions, iridium undergoes a change in oxidation state from Ir^IV to Ir^V that takes place predominantly at the surface of the catalyst. The chemical change in iridium is coupled to a decrease in surface hydroxide, providing experimental evidence which strongly suggests that the oxygen evolution reaction on iridium oxide occurs through an OOH‐mediated deprotonation mechanism.     

Formation of hydroxyl and water layers on MgO films studied with ambient pressure XPS

To understand the interaction of water with MgO(100), a detailed quantitative assessment of the interfacial chemistry is necessary. We have used ambient pressure X-ray photoelectron spectroscopy (XPS) to measure molecular (H₂O) and dissociative (OH) water adsorption on a 4 monolayer (ML) thick MgO(100)/Ag(100) film under ambient conditions. Since the entire 4 ML metal oxide (Ox) film is probed by XPS, the reaction of the MgO film with water can be quantitatively studied. Using a multilayer model (Model 1) that measures changes in Ox thickness from O 1s (film) and Ag 3d (substrate) spectra, it is shown that the oxide portion of the MgO film becomes thinner upon hydroxylation. A reaction mechanism is postulated in which the top-most layer of MgO converts to Mg(OH)₂ upon dissociation of water. Based on this mechanism a second model (Model 2) is developed to calculate Ox and OH thickness changes based on OH/Ox intensity ratios from O 1s spectra measured in situ, with the known initial Ox thickness prior to hydroxylation. Models 1 and 2 are applied to a 0.15 Torr isobar experiment, yielding similar results for H₂O, OH and Ox thickness changes as a function of relative humidity.     

Optimization of a Thin-Walled,Anisotropic Curved Bar for Maximum Torsional Stiffness∗

ABSTRACT

ABSTRACT A curved bar in the form of a circular ring sector is under uniform torsion when acted upon by two equal and opposite forces directed alone the axis passing through the center of the ring and perpendicular to its plane, i.e., forces acting along the axis of rotation. The exact torsion theory can be extended to this case when the material of which the bar consists is cylindri-cally anisotropic, with the axis of anisotropy directed along the axis of rotation and having an elastic symmetry about any plane of the transverse cross section. In this paper, a thin-walled curved bar having the loading conditions and material properties described above is optimized so as to maximize its torsional stiffness. The optimization is carried out with respect to the cross-sectional shape of the bar subject to constraints on the transverse area (single-purpose design) and bending stiffness (multipurpose design). In the special case of an orthotropic material, the angle of inclination of the ortho-tropy axes with respect to the middle plane is optimally determined for a cross section with constant thickness. A perturbation method is used to obtain analytical solutions, and numerical results are presented indicating the efficiency of the designs and the optimal cross-sectional shapes.     

Optimal shape and non-homogeneity of a non-uniformly compressed column

The best possible distribution of Young's modulus and/or the cross-sectional area is found for a column which, for a given volume and length, carries the maximum possible axial loads which are non-uniformly distributed along its length and concentrated at the end-points. The column is elastically clamped at one end and free at the other, where the concentrated axial load is applied. The design variables are subject to upper and lower bounds. Sufficient optimality conditions are derived for a given function to be a solution of the optimization problem. The procedure to determine the optimal solutions is described. Numerical results are obtained by employing an iterative computational technique.     

Molecularly Imprinted Polymer Nanomaterials and Nanocomposites: Atom‐Transfer Radical Polymerization with Acidic Monomers

Molecularly imprinted polymers (MIPs) are artificial receptors which can be tailored to bind target molecules specifically. A new method, using photoinitiated atom‐transfer radical polymerization (ATRP) for their synthesis as monoliths, thin films and nanoparticles is described. The synthesis takes place at room temperature and is compatible with acidic monomers, two major limitations for the use of ATRP with MIPs. The method has been validated with MIPs specific for the drugs testosterone and S‐propranolol. This study considerably widens the range of functional monomers and thus molecular templates which can be used when MIPs are synthesized by ATRP, as well as the range of physical forms of these antibody mimics, in particular films and lithographic patterns, and their post‐functionalization from living chain‐ends.     

Comparison of level density models in (γ, n) reactions of some lanthanide nuclei

Level densities are required at excitation energies where discrete level information is not available or incomplete to get a reliable theoretical analysis of cross sections, spectra, and angular distributions. The total reaction cross sections of some lanthanides (¹⁴¹Pr, ¹⁴²Nd, ¹⁴⁴Sm, ¹⁵³Eu, ¹⁶⁰Gd, ¹⁵⁹Tb, ¹⁶⁵Ho, ¹⁷⁵Lu) were calculated using TALYS 1.2 code for gamma-induced reactions through the five level density models in the incident gamma energy range from 5 to 30 MeV. All calculations from the present study were compared with each other and with the experimental data obtained from EXFOR library. The total photo-neutron reaction cross-section values obtained from the model calculations and experimental measurements taken from EXFOR confirm the presence of systematical disagreements reported in the literature, except ¹⁶⁵Ho case where one can see a satisfactory agreement.