A Global Optimization Algorithm using Lagrangian Underestimates and the Interval Newton Method

Convex relaxations can be used to obtain lower bounds on the optimal objective function value of nonconvex quadratically constrained quadratic programs. However, for some problems, significantly better bounds can be obtained by minimizing the restricted Lagrangian function for a given estimate of the Lagrange multipliers. The difficulty in utilizing Lagrangian duality within a global optimization context is that the restricted Lagrangian is often nonconvex. Minimizing a convex underestimate of the restricted Lagrangian overcomes this difficulty and facilitates the use of Lagrangian duality within a global optimization framework. A branch-and-bound algorithm is presented that relies on these Lagrangian underestimates to provide lower bounds and on the interval Newton method to facilitate convergence in the neighborhood of the global solution. Computational results show that the algorithm compares favorably to the Reformulation–Linearization Technique for problems with a favorable structure.     

A characterisation of thas maximal arcs in translation planes of square order

In 1974 J.A. Thas constructed a class of maximal arcs in certain translation planes of order q². We characterise these as being exactly those (non-trivial) maximal arcs that are stabilised by an homology of order q– 1.The first author gratefully acknowledges the support of an Australian Postgraduate Research Award.     

Propagation of X-rays in ultra-narrow slits

We study the propagation of X-rays in very narrow slits or waveguides. The onset of waveguiding effects is estimated analytically and quantified by finite-difference field calculations. A critical thickness is given below which waveguiding effects have to be taken into account. Finally, we consider the transmission of the smallest possible slits i.e. planar single-mode waveguides.     

Optimal finite-time processes in stochastic thermodynamics

For a small system like a colloidal particle or a single biomolecule embedded in a heat bath, the optimal protocol of an external control parameter minimizes the mean work required to drive the system from one given equilibrium state to another in a finite time. In general, this optimal protocol obeys an integro-differential equation. Explicit solutions both for a moving laser trap and a time-dependent strength of such a trap show finite jumps of the optimal protocol to be typical both at the beginning and at the end of the process.     

Material Discrimination in Nanoparticle Hetero-Aggregates by Analysis of Scanning Transmission Electron Microscopy Images

Hetero-contacts are interfaces between different materials at the nanoscale leading to novel functional properties. In hetero-aggregates, primary particles of at least two different materials are mixed at primary particle or cluster level. Double flame spray pyrolysis (DFSP) is a versatile technique for the controlled synthesis of such materials. Characterization of hetero-aggregates by scanning transmission electron microscopy (STEM) requires acquisition and evaluation of many aggregate images in order to derive statistically significant results. Usually, STEM energy dispersive X-ray spectroscopy (EDXS) is used to acquire elemental maps providing the material distribution of the primary particles within hetero-aggregates. However, the acquisition of a single EDXS map takes up to several minutes. For this reason, determination of material types of primary particles from the intensity in high-angle annular dark field STEM images alone is desirable. These images can be acquired within a couple of seconds. In the present work, a method is suggested which allows for achieving this objective. It can be applied to distinguish materials with a significant difference in their atomic number and hence sufficient material contrast in the STEM images.     

Caterpillar Track Complexes in Template‐Directed Synthesis and Correlated Molecular Motion

Small alterations to the structure of a star‐shaped template totally change its mode of operation. The hexapyridyl template directs the conversion of a porphyrin dimer to the cyclic hexamer, but deleting one pyridine site changes the product to the cyclic decamer, while deleting two binding sites changes the product to the cyclic octamer. This surprising switch in selectivity is explained by the formation of 2:1 caterpillar track complexes, in which two template wheels bind inside the nanoring. Caterpillar track complexes can also be prepared by binding the hexapyridyl template inside the 8‐ and 10‐porphyrin nanorings. NMR exchange spectroscopy (EXSY) experiments show that these complexes exhibit correlated motion, in which the conrotatory rotation of the two template wheels is coupled to rotation of the nanoring track. In the case of the 10‐porphyrin system, the correlated motion can be locked by binding palladium(II) dichloride between the two templates.