Optimal control with stochastic PDE constraints and uncertain controls

The optimal control of problems that are constrained by partial differential equations with uncertainties and with uncertain controls is addressed. The Lagrangian that defines the problem is postulated in terms of stochastic functions, with the control function possibly decomposed into an unknown deterministic component and a known zero-mean stochastic component. The extra freedom provided by the stochastic dimension in defining cost functionals is explored, demonstrating the scope for controlling statistical aspects of the system response. One-shot stochastic finite element methods are used to find approximate solutions to control problems. It is shown that applying the stochastic collocation finite element method to the formulated problem leads to a coupling between stochastic collocation points when a deterministic optimal control is considered or when moments are included in the cost functional, thereby forgoing the primary advantage of the collocation method over the stochastic Galerkin method for the considered problem. The application of the presented methods is demonstrated through a number of numerical examples. The presented framework is sufficiently general to also consider a class of inverse problems, and numerical examples of this type are also presented. © 2011 Elsevier B.V.

A model for diffusive and displacive phase transitions: Thermo-chemo-mechanical coupling effects

A diffuse interface phase field model is proposed for the unified analysis of diffusive and displacive phase transitions under nonisothermal conditions. Two order parameters are used for the description of the phenomena: one is related to the solute mass fraction and the other to the strain. The model governing equations come from the balance of linear momentum, the solute mass balance (which will lead to the Cahn-Hilliard equation) and the balance of internal energy. Thermodynamic restrictions allow to define constitutive relations for the thermodynamic forces and for the mechanical and chemical dissipations. Numerical tests carried out at different values of the initial temperature show that the model is able to describe the main features of both the displacive and the diffusive phase transitions, as well as their effect on the temperature. © 2010, Advanced Engineering Solutions.

A microfluidic device for high density hydrodynamic cell trapping, growth and super-resolution imaging

Super-Resolution imaging techniques such as Fluorescent Photo-Activation Localisation Microscopy (FPALM) have created a powerful new toolkit for investigating living cells, however a simple platform for growing, trapping, holding and controlling the cells is needed before the approach can become truly widespread. We present a microfluidic device formed in polydimethylsiloxane (PDMS) with a fluidic design which traps cells in a high-density array of wells and holds them very still throughout the life cycle, using hydrodynamic forces only. The device meets or exceeds all the necessary criteria for FPALM imaging of Schizosaccharomyces pombe and is designed to remain flexible, robust and easy to use. © 2011 IEEE.

Energy stable and momentum conserving hybrid finite element method for the incompressible Navier-Stokes equations

A hybrid method for the incompressible Navier-Stokes equations is presented. The method inherits the attractive stabilizing mechanism of upwinded discontinuous Galerkin methods when momentum advection becomes significant, equal-order interpolations can be used for the velocity and pressure fields, and mass can be conserved locally. Using continuous Lagrange multiplier spaces to enforce flux continuity across cell facets, the number of global degrees of freedom is the same as for a continuous Galerkin method on the same mesh. Different from our earlier investigations on the approach for the Navier-Stokes equations, the pressure field in this work is discontinuous across cell boundaries. It is shown that this leads to very good local mass conservation and, for an appropriate choice of finite element spaces, momentum conservation. Also, a new form of the momentum transport terms for the method is constructed such that global energy stability is guaranteed, even in the absence of a pointwise solenoidal velocity field. Mass conservation, momentum conservation, and global energy stability are proved for the time-continuous case and for a fully discrete scheme. The presented analysis results are supported by a range of numerical simulations. © 2012 Society for Industrial and Applied Mathematics.

Analysis of defect-related localized emission processes in InGaN/GaN-based LEDs

This paper reports an extensive analysis of the defect-related localized emission processes occurring in InGaN/GaN-based light-emitting diodes (LEDs) at low reverse- and forward-bias conditions. The analysis is based on combined electrical characterization and spectrally and spatially resolved electroluminescence (EL) measurements. Results of this analysis show that: (i) under reverse bias, LEDs can emit a weak luminescence signal, which is directly proportional to the injected reverse current. Reverse-bias emission is localized in submicrometer-size spots; the intensity of the signal is strongly correlated to the threading dislocation (TD) density, since TDs are preferential paths for leakage current conduction. (ii) Under low forward-bias conditions, the intensity of the EL signal is not uniform over the device area. Spectrally resolved EL analysis of green LEDs identifies the presence of localized spots emitting at 600 nm (i.e., in the yellow spectral region), whose origin is ascribed to localized tunneling occurring between the quantum wells and the barrier layers of the diodes, with subsequent defect-assisted radiative recombination. The role of defects in determining yellow luminescence is confirmed by the high activation energy of the thermal quenching of yellow emission (Ea =0.64&eV). © 2012 IEEE.

Short-term in vitro responses of human peripheral blood monocytes to ferritic stainless steel fiber networks.

Beneficial effects on bone-implant bonding may accrue from ferromagnetic fiber networks on implants which can deform in vivo inducing controlled levels of mechanical strain directly in growing bone. This approach requires ferromagnetic fibers that can be implanted in vivo without stimulating undue inflammatory cell responses or cytotoxicity. This study examines the short-term in vitro responses, including attachment, viability, and inflammatory stimulation, of human peripheral blood monocytes to 444 ferritic stainless steel fiber networks. Two types of 444 networks, differing in fiber cross section and thus surface area, were considered alongside austenitic stainless steel fiber networks, made of 316L, a widely established implant material. Similar high percent seeding efficiencies were measured by CyQuant® on all fiber networks after 48 h of cell culture. Extensive cell attachment was confirmed by fluorescence and scanning electron microscopy, which showed round monocytes attached at various depths into the fiber networks. Medium concentrations of lactate dehydrogenase (LDH) and tumor necrosis factor alpha (TNF-α) were determined as indicators of viability and inflammatory responses, respectively. Percent LDH concentrations were similar for both 444 fiber networks at all time points, whereas significantly lower than those of 316L control networks at 24 h. All networks elicited low-level secretions of TNF-α, which were significantly lower than that of the positive control wells containing zymosan. Collectively, the results indicate that 444 networks produce comparable responses to medical implant grade 316L networks and are able to support human peripheral blood monocytes in short-term in vitro cultures without inducing significant inflammatory or cytotoxic effects.

Properties of trench defects in InGaN/GaN quantum well structures

The structural and optical properties of trench defects, which are poorly understood yet commonly occurring defects observed on the surfaces of InGaN multiple quantum wells (MQW), are reported. These defects comprise near-circular trenches which enclose areas of MQW which give rise to a red shift in peak photoluminescence emission and a change in cathodoluminescence intensity with respect to the surrounding material. Atomic force microscopy shows that the height of trench-enclosed areas differs from that of the surrounding quantum well structure, and that trenches are unrelated to the commonly observed V-defects in InGaN films, despite being occasionally intersected by them. Cross-sectional electron microscopy analysis of trenches with raised centres suggests that the red shift in the observed cathodoluminescence peak emission may be due to the quantum wells being thicker in the trench-enclosed regions than in the surrounding quantum well area. The mechanism of trench formation and its implication for the control of the emission properties of light-emitting diodes is discussed. Copyright © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Short-term cytotoxic and inflammatory responses of human monocytes to stainless steel fibre networks

The aim of the current work was to examine the human monocyte response to 444 ferritic stainless steel fibre networks. 316L austenitic fibre networks, of the same fibre volume fraction, were used as control surfaces. Fluorescence and scanning electron microscopies suggest that the cells exhibited a good degree of attachment and penetration throughout both networks. Lactate Dehydrogenase (LDH) and TNF-α releases were used as indicators of cytotoxicity and inflammatory responses respectively. LDH release indicated similar levels of monocyte viability when in contact with the 444 and 316L fibre networks. Both networks elicited a low level secretion of TNF-α, which was significantly lower than that of the positive control wells containing zymosan. Collectively, the results suggest that 444 ferritic and 316L austenitic networks induced similar cytotoxic and inflammatory responses from human monocytes. © 2012 Materials Research Society.

Automated computational modelling for solid mechanics

We present some recent developments in automated computational modelling with an emphasis on solid mechanics applications. The automation process permits an abstract mathematical model of a physical problem to be translated into computer code rapidly and trivially, and can lead to computer code which is faster than hand-written and optimised code. Crucial to the approach is ensuring that mathematical abstractions inherent in the mathematical model are inherited by the software library. © Springer Science+Business Media B.V. 2008.

Structural tunability and switchable exciton emission in inorganic-organic hybrids with mixed halides

Room-temperature tunable excitonic photoluminescence is demonstrated in alloy-tuned layered Inorganic-Organic (IO) hybrids, (C12H 25NH3)2PbI4(1-y)Br4y (y = 0 to 1). These perovskite IO hybrids adopt structures with alternating stacks of low-dimensional inorganic and organic layers, considered to be naturally self-assembled multiple quantum wells. These systems resemble stacked monolayer 2D semiconductors since no interlayer coupling exists. Thin films of IO hybrids exhibit sharp and strong photoluminescence (PL) at room-temperature due to stable excitons formed within the low-dimensional inorganic layers. Systematic variation in the observed exciton PL from 510 nm to 350 nm as the alloy composition is changed, is attributed to the structural readjustment of crystal packing upon increase of the Br content in the Pb-I inorganic network. The energy separation between exciton absorption and PL is attributed to the modified exciton density of states and diffusion of excitons from relatively higher energy states corresponding to bromine rich sites towards the lower energy iodine sites. Apart from compositional fluctuations, these excitons show remarkable reversible flips at temperature-induced phase transitions. All the results are successfully correlated with thermal and structural studies. Such structural engineering flexibility in these hybrids allows selective tuning of desirable exciton properties within suitable operating temperature ranges. Such wide-range PL tunability and reversible exciton switching in these novel IO hybrids paves the way to potential applications in new generation of optoelectronic devices. © 2013 AIP Publishing LLC.

Unified form language: A domain-specific language for weak formulations of partial differential equations

We present the Unified Form Language (UFL), which is a domain-specific language for representing weak formulations of partial differential equations with a view to numerical approximation. Features of UFL include support for variational forms and functionals, automatic differentiation of forms and expressions, arbitrary function space hierarchies formultifield problems, general differential operators and flexible tensor algebra. With these features, UFL has been used to effortlessly express finite element methods for complex systems of partial differential equations in near-mathematical notation, resulting in compact, intuitive and readable programs. We present in this work the language and its construction. An implementation of UFL is freely available as an open-source software library. The library generates abstract syntax tree representations of variational problems, which are used by other software libraries to generate concrete low-level implementations. Some application examples are presented and libraries that support UFL are highlighted. © 2014 ACM.

Identification and characterization of Bacillus anthracis by multiplex PCR on DNA chip

Bacillus anthracis can be identified by detecting virulence factor genes located on two plasmids, pXO1 and pXO2. Combining multiplex PCR with arrayed anchored primer PCR and biotin-avidin alkaline phosphatase indicator system, we developed a qualitative DNA chip method for characterization of B. anthracis, and simultaneous confirmation of the species identity independent of plasmid contents. The assay amplifies pag gene (in pXO1), cap gene (in pXO2) and Ba813 gene (a B. anthracis specific chromosomal marker), and the results were indicated by an easy-to-read profile based on the color reaction of alkaline phosphatase. About 1 pg of specific DNA fragments on the chip wells could be detected after PCR. With the proposed method, the avirulent (pXO1(+)/2(-), pXO1(-)/2(+) and pXO1(-)/2(-)) strains of B. anthracis and distinguished 'anthrax-like' strains from other B. cereus group bacteria were unambiguously identified, while the genera other than Bacillus gave no positive signal. (C) 2004 Elsevier B.V. All rights reserved.