Optimality conditions for state constrained nonlinear control problems

The problem of optimal control of nonlinear control and state constrained control problems, where the state constraint may involve differential operators and the cost functionals may be nonsmooth, is studied. For this class of problems, necessary optimality conditions using techniques from infinite dimensional optimization theory adapted to the framework of control problems are derived. It is shown that the underlying structure admits a considerable relaxation of the classical constraint qualifications. The theory then is applied to examples of various nonlinear elliptic equations and state constraints.     

High-resolution non-invasive 3D imaging of paint microstructure by synchrotron-based X-ray laminography

The characterisation of the microstructure and micromechanical behaviour of paint is key to a range of problems related to the conservation or technical art history of paintings. Synchrotron-based X-ray laminography is demonstrated in this paper to image the local sub-surface microstructure in paintings in a non-invasive and non-destructive way. Based on absorption and phase contrast, the method can provide high-resolution 3D maps of the paint stratigraphy, including the substrate, and visualise small features, such as pigment particles, voids, cracks, wood cells, canvas fibres etc. Reconstructions may be indicative of local density or chemical composition due to increased attenuation of X-rays by elements of higher atomic number. The paint layers and their interfaces can be distinguished via variations in morphology or composition. Results of feasibility tests on a painting mockup (oak panel, chalk ground, vermilion and lead white paint) are shown, where lateral and depth resolution of up to a few micrometres is demonstrated. The method is well adapted to study the temporal evolution of the stratigraphy in test specimens and offers an alternative to destructive sampling of original works of art.     

Nitroxide‐mediated homo‐ and block copolymerization of styrene and multifunctional acryl‐ and methacryl derivatives

The ability of different alkoxyamines ( I1 , I2 , I3 , I4 , and I5 ) to initiate controlled radical polymerization of styrene was evaluated. Among them, 2‐hydroxymethyl‐2‐[(2‐methyl‐1‐phenyl‐propyl)‐(1‐phenyl‐ethoxy)‐amino]‐propane‐1,3‐diol ( I5 ) gave the highest polymerization rate of styrene, and the best control over the molecular weight and the molecular weight distribution of polystyrene. Kinetic studies confirmed that with initiator I5 the polymerization of styrene proceeded in a controlled way. The controlled radical homopolymerization of multifunctional acryl‐ and methacryl derivatives using initiator I5 could not be realized as demonstrated by the high polydispersities (PD) obtained. However, it was possible to polymerize multifunctional acryl‐ and methacryl derivatives using a polystyrene macroinitiator ( Pst ) and, thus, novel amphiphilic block copolymers with a narrow molecular weight distribution were obtained. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 1873–1882, 2005     

The dynamic differential forms of the Klein-Gordon field and the conformal group

Dynamic differential forms are the natural generalization of conserved currents. We discover the entire class for the real Klein-Gordon field, and find that each dynamic form is equivalent to a Noetherian form, that is, a form based on a canonical symmetry. Going to the complex case, we classify also its dynamic currents. It appears that some of them are definitely not equivalent to Noetherian forms.     

Winkelkorrelations- und Lebensdauer-Messungen am59Co

γγ angular correlations and delayed β-γ coincidences have been measured in the decay of⁵⁹Fe to⁵⁹Co.M1 andE2 transition probabilities were determined for the 143, 192, and 335 keV transition by measuring the 192–1099 keV, 335–1099 keV and 143–1292 keV correlations, and the half lives of the 1292 and 1434 keV levels. Theg-factor of the 1292 keV state was derived to beg=+1.09 ± 0.08 from the perturbation of the 143–1292 keV γγ angular correlation in ferromagnetic⁵⁹CoFe and⁵⁹CoNi samples. The results are discussed in terms of the weak coupling model.     

Momentum in relativistic four-particle interactions

A new proof of the recent theorem of Jordan and Shukre is given showing that if momentum is an integral of the motion then the interaction is zero. The new proof is based on a theorem about three curves in space time, which also implies the desired result for some four-particle interactions.     

Interatomic electronic decay driven by nuclear motion

The interatomic electronic decay after inner-valence ionization of a neon atom by a single photon in a neon-helium dimer is investigated. The excited neon atom relaxes via interatomic Coulombic decay and the excess energy is transferred to the helium atom and ionizes it. We show that the decay process is only possible if the dimer's bond stretches up to 6.2 ?, i.e., to more than twice the equilibrium interatomic distance of the neutral dimer. Thus, it is demonstrated that the electronic decay, taking place at such long distances, is driven by the nuclear motion.     

Mechanical properties of silk: interplay of deformation on macroscopic and molecular length scales

Using an in situ combination of tensile tests and x-ray diffraction, we have determined the mechanical properties of both the crystalline and the disordered phase of the biological nanocomposite silk by adapting a model from linear viscoelastic theory to the semicrystalline morphology of silk. We observe a strong interplay between morphology and mechanical properties. Silk's high extensibility results principally from the disordered phase; however, the crystals are also elastically deformed.     

Cell transmembrane receptors determine tissue pattern stability

The analysis of biological systems requires mathematical tools that represent their complexity from the molecular scale up to the tissue level. The formation of cell aggregates by chemotaxis is investigated using Delaunay object dynamics. It is found that when cells migrate fast such that the chemokine distribution is far from equilibrium, the details of the chemokine receptor dynamics can induce an internalization driven instability of cell aggregates. The instability occurs in a parameter regime relevant for lymphoid tissue and is similar to ectopic lymphoid structures.