On the Triality Theory for a Quartic Polynomial Optimization Problem

This paper presents a detailed proof of the triality theorem for a class of fourth-order polynomial optimization problems. The method is based on linear algebra but it solves an open problem on the double-min duality left in 2003. Results show that the triality theory holds strongly in a tri-duality form if the primal problem and its canonical dual have the same dimension; otherwise, both the canonical min-max duality and the double-max duality still hold strongly, but the double-min duality holds weakly in a symmetrical form. Four numerical examples are presented to illustrate that this theory can be used to identify not only the global minimum, but also the largest local minimum and local maximum.Comment: 16 pages, 1 figure; J. Industrial and Management Optimization, 2011. arXiv admin note: substantial text overlap with arXiv:1104.297

Diblock copolymer ordering induced by patterned surfaces

We use a Ginzburg-Landau free energy functional to investigate diblock copolymer morphologies when the copolymer melt interacts with one surface or is confined between two chemically patterned surfaces. For temperatures above the order-disorder transition a complete linear response description of the copolymer melt is given, in terms of an arbitrary two-dimensional surface pattern. The appearance of order in the direction parallel to the surface is found as a result of the order in the perpendicular direction. Below the order-disorder point and in a thin-film geometry, our procedure enables the analytic calculation of distorted perpendicular and tilted lamellar phases in the presence of uniform or modulated surface fields.Comment: 8 pages, 3 figures, to be published in Europhys. Let

Noise suppressor for turbo fan jet engines

A noise suppressor is disclosed for installation on the discharge or aft end of a turbo fan engine. Within the suppressor are fixed annular airfoils which are positioned to reduce the relative velocity between the high temperature fast moving jet exhaust and the low temperature slow moving air surrounding it. Within the suppressor nacelle is an exhaust jet nozzle which constrains the shape of the jet exhaust to a substantially uniform elongate shape irrespective of the power setting of the engine. Fixed ring airfoils within the suppressor nacelle therefore have the same salutary effects irrespective of the power setting at which the engine is operated

Human environmental heat transfer simulation with CFD – the advances and challenges

The modelling and prediction of human thermoregulatory responses and comfort have gone a long way during the past decades. Sophisticated and detailed human models, i.e. the active multi-nodal thermal models with physiological regulatory responses, have been developed and widely adopted in both research and industrial practice. The recent trend is to integrate human models with environmental models in order to provide more insight into the thermal comfort issues, especially in the non-homogeneous and transient conditions. This paper reviews the logics and expectations of coupling human models with computational fluid dynamics (CFD) models. One of main objectives of such approaches is to take the advantage of the high resolution achievable with the CFD, to replace the empirical methods used in the human models. We aim to initiate debates on the validity of this objective, and to identify the technical requirements for achieving this goal. A simple experiment with 3D human models of different sizes and shapes is also reported. Initial results shows the presence of arms may be important. Further experiments are required to establish the impact of size and shape on simulation result

Improved plasma accelerator

Converging, coaxial accelerator electrode configuration operates in vacuum as plasma gun. Plasma forms by periodic injections of high pressure gas that is ionized by electrical discharges. Deflagration mode of discharge provides acceleration, and converging contours of plasma gun provide focusing

Berry's phase and the anomalous velocity of Bloch wavepackets

The semiclassical equations of motion for a Bloch electron include an anomalous velocity term analogous to a $k$-space "Lorentz force", with the Berry connection playing the role of a vector potential. By examining the adiabatic evolution of Bloch states in a monotonically-increasing vector potential, I show that the anomalous velocity can be explained as the difference in the Berry's phase acquired by adjacent Bloch states within a wavepacket.Comment: 2 pages, 1 figur