The cluster problem in constrained global optimization

Deterministic branch-and-bound algorithms for continuous global optimization often visit a large number of boxes in the neighborhood of a global minimizer, resulting in the so-called cluster problem (Du and Kearfott in J Glob Optim 5(3):253–265, 1994). This article extends previous analyses of the cluster problem in unconstrained global optimization (Du and Kearfott 1994; Wechsung et al. in J Glob Optim 58(3):429–438, 2014) to the constrained setting based on a recently-developed notion of convergence order for convex relaxation-based lower bounding schemes. It is shown that clustering can occur both on nearly-optimal and nearly-feasible regions in the vicinity of a global minimizer. In contrast to the case of unconstrained optimization, where at least second-order convergent schemes of relaxations are required to mitigate the cluster problem when the minimizer sits at a point of differentiability of the objective function, it is shown that first-order convergent lower bounding schemes for constrained problems may mitigate the cluster problem under certain conditions. Additionally, conditions under which second-order convergent lower bounding schemes are sufficient to mitigate the cluster problem around a global minimizer are developed. Conditions on the convergence order prefactor that are sufficient to altogether eliminate the cluster problem are also provided. This analysis reduces to previous analyses of the cluster problem for unconstrained optimization under suitable assumptions.     

Long-Range Electron Transfer through DNA Films

Regardless of its position within the DNA film , cross-linked daunomycin (DM) is efficiently reduced electrochemically, indicating that the electron transfer exhibits a shallow distance dependence. Upon the introduction of an intervening cytosine–adenine (CA) mismatch, the electrochemical response is dramatically attenuated (shown schematically). Therefore, the DNA double helix can facilitate long-range electron transfer, but only in the presence of a well-stacked pathway.     

Improved laminar predictions using a stabilised time-dependent simple scheme

A new scheme which can solve unsteady incompressible flows is described in this paper. The scheme is a variant of the SIMPLE methodology. Typically, a scheme of this type tends to suffer from stability problems, which this new scheme overcomes by taking small intermediate steps within a time step. The calculations made in the intermediate steps are damped to enhance the stability of the scheme. The new stabilised scheme is evaluated for laminar flow around a square cylinder, impulsively started laminar flow over a backward-facing step and fluctuating laminar flow over a backward-facing step. Comparisons are made with other numerical predictions and experimental data. In general, good agreement is found, except for the fluctuating laminar flow over a backward-facing step problem. The new scheme is found to have the same level of accuracy, stability and efficiency in comparison with the PISO scheme, but it is easier to code. © 1998 John Wiley & Sons, Ltd.     

Aspects of epoxy resin curing reactions

The progress that has been made in establishing the mechanism of the curing reaction between epoxides and amines, particularly through the use of calorimetric methods (DSC), is discussed. A novel application of tritium-labelled compounds to the study of the reaction of epoxides with imidazoles is also presented. The radiochemical method has produced an enhanced understanding of the reaction mechanism and has given kinetic data in good agreement with DSC measurements.     

Observations on the dynamics of nonsolvent-induced phase inversion

The diffusion and gelation dynamics of nonsolvent-induced phase inversion in several polyethersulfone (PES)/solvent/nonsolvent systems are observed using a dark-ground optical technique. The observed dynamics are correlated with the resultant morphologies of the solidified gels obtained via scanning electron microscopy. In situ dynamic measurements show that rapid precipitations result in finger formation and delayed precipitations result in sponge formation. Rapid precipitations for some systems also exhibit an initial region of high, anomalous diffusion front motion which correlates well with the appearance of finger-like macrovoids in the film sublayer. Micrographs of both thin (200–300 μm) and thick (3 mm) films formed by liquid-liquid demixing clearly show that the overall morphologies scale with initial film thickness. However, as observed for the cellulose acetate (CA)/dimethylsulfoxide (DMSO)/H₂O system, the possibility of crystallization can complicate the scaling analysis. A ternary diffusion model is also employed to describe the isothermal diffusion encountered during the formation of PES membranes. Binary thermodynamic and kinetic parameters needed for computations are determined from experimental data. Model results agree well with experimental observations. The model accurately predicts the transition from finger-to-sponge formation, as well as other observed trends in dynamics and morphology. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys, 35: 569–585, 1997     

The application of high-speed TV-holography to time-resolved vibration measurements

We describe an electronic speckle pattern interferometer (ESPI) system that has enabled non-harmonic vibrations to be measured with μs temporal resolution. The short exposure period and high framing rate of a high-speed camera at up to 40,500 frames per second allow low-power CW laser illumination and fibre-optic beam delivery to be used, rather than the high peak power pulsed lasers normally used in ESPI for transient measurement. The technique has been demonstrated in the laboratory and tested in preliminary industrial trials. The ability to measure vibration with high spatial and temporal resolution, which is not provided by techniques such as scanning laser vibrometry, has many applications in manufacturing design, and in an illustrative application described here revealed previously unmeasured “rocking” vibrations of a car door. It has been possible to make the measurement on the door as part of a complete vehicle standing on its own tyres, wheels and suspension, and where the excitation was generated by the running of the vehicle's own engine.     

Superdeformation in Pb: Observation of three additional excited bands

The superdeformed nucleus ¹⁹³Pb has been studied following a heavy-ion fusion-evaporation reaction with the Gammasphere spectrometer array. Three new superdeformed bands, two of them probably signature partners, have been observed, bringing the total number of superdeformed bands known in this nucleus to nine. An estimate of the g-factor associated with one of the previously known pairs of strongly coupled excited bands has been made, confirming their configuration. The properties of the bands are compared with the results of cranked shell model calculations; good agreement is found and configurations are assigned to each band. The two new signature partner bands are suggested to be based on the two signatures of the [512]5/2 neutron orbital. The third new band is probably based on the 7₃ intruder orbital. In addition, the high-energy region of the spectrum in coincidence with the yrast superdeformed bands has been carefully studied. The current data provide no evidence for the previously reported transitions linking the superdeformed and normal-deformed states with energies around 2.2–2.4 MeV.