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.

Active control of high-frequency vibration: Optimisation using the hybrid modelling method

This work presents active control of high-frequency vibration using skyhook dampers. The choice of the damper gain and its optimal location is crucial for the effective implementation of active vibration control. In vibration control, certain sensor/actuator locations are preferable for reducing structural vibration while using minimum control effort. In order to perform optimisation on a general built-up structure to control vibration, it is necessary to have a good modelling technique to predict the performance of the controller. The present work exploits the hybrid modelling approach, which combines the finite element method (FEM) and statistical energy analysis (SEA) to provide efficient response predictions at medium to high frequencies. The hybrid method is implemented here for a general network of plates, coupled via springs, to allow study of a variety of generic control design problems. By combining the hybrid method with numerical optimisation using a genetic algorithm, optimal skyhook damper gains and locations are obtained. The optimal controller gain and location found from the hybrid method are compared with results from a deterministic modelling method. Good agreement between the results is observed, whereas results from the hybrid method are found in a significantly reduced amount of time. © 2012 Elsevier Ltd. All rights reserved.

Implementation of a PI phase angle controller for finite element analysis of the BDFM

Time-stepping finite element analysis of the BDFM for a specific load condition is shown to be a challenging problem because the excitation required cannot be predetermined and the BDFM is not open loops stable for all operating conditions. A simulation approach using feedback control to set the torque and stabilise the BDFM is presented together with implementation details. The performance of the simulation approach is demonstrated with an example and computed results are compared with measurements.

Stability control of a railway vehicle using absolute stiffness and inerters

Work presented in this paper studies the potential of employing inerters -a novel mechanical device used successfully in racing cars- in active suspension configurations with the aim to enhance railway vehicle system performance. The particular element of research in this paper concerns railway wheelset lateral stability control. Controlled torques are applied to the wheelsets using the concept of absolute stiffness. The effects of a reduced set of arbitrary passive structures using springs, dampers and inerters integrated to the active solution are discussed. A multi-objective optimisation problem is defined for tuning the parameters of the proposed configurations. Finally, time domain simulations are assessed for the railway vehicle while negotiating a curved track. A simplification of the design problem for stability is attained with the integration of inerters to the active solutions. © 2012 IEEE.

Genesis of Th-230 excess in basalts from mid-ocean ridges and ocean islands: Constraints from the global U-series isotope database and major and rare earth element geochemistry

Based on Th-230-U-238 disequilibrium and major element data from mid-ocean ridge basalts (MORBs) and ocean island basalts (OIBs), this study calculates mantle melting parameters, and thereby investigates the origin of Th-230 excess. (Th-230/U-238) in global MORBs shows a positive correlation with Fe-8, P (o), Na-8, and F-melt (Fe-8 and Na-8 are FeO and Na2O contents respectively after correction for crustal fractionation relative to MgO = 8 wt%, P (o)=pressure of initial melting and F (melt)=degree of melt), while Th-230 excess in OIBs has no obvious correlation with either initial mantle melting depth or the average degree of mantle melting. Furthermore, compared with the MORBs, higher (Th-230/U-238) in OIBs actually corresponds to a lower melting degree. This suggests that the Th-230 excess in MORBs is controlled by mantle melting conditions, while the Th-230 excess in OIBs is more likely related to the deep garnet control. The vast majority of calculated initial melting pressures of MORBs with excess Th-230 are between 1.0 and 2.5 GPa, which is consistent with the conclusion from experiments in recent years that D (U)> D (Th) for Al-clinopyroxene at pressures of > 1.0 GPa. The initial melting pressure of OIBs is 2.2-3.5 GPa (around the spinel-garnet transition zone), with their low excess Ra-226 compared to MORBs also suggesting a deeper mantle source. Accordingly, excess Th-230 in MORBs and OIBs may be formed respectively in the spinel and garnet stability field. In addition, there is no obvious correlation of K2O/TiO2 with (Th-230/U-238) and initial melting pressure (P (o)) of MORBs, so it is proposed that the melting depth producing excess Th-230 does not tap the spinel-garnet transition zone. OIBs and MORBs in both (Th-230/U-238) vs. K2O/TiO2 and (Th-230/U-238) vs. P (o) plots fall in two distinct areas, indicating that the mineral phases which dominate their excess Th-230 are different. Ce/Yb-Ce curves of fast and slow ridge MORBs are similar, while, in comparison, the Ce/Yb-Ce curve for OIBs shows more influence from garnet. The mechanisms generating excess Th-230 in MORBs and OIBs are significantly different, with formation of excess Th-230 in the garnet zone only being suitable for OIBs.

Towards Intelligent Structures: Active Control of Buckling

The buckling of compressively-loaded members is one of the most important factors limiting the overall strength and stability of a structure. I have developed novel techniques for using active control to wiggle a structural element in such a way that buckling is prevented. I present the results of analysis, simulation, and experimentation to show that buckling can be prevented through computer-controlled adjustment of dynamical behavior.sI have constructed a small-scale railroad-style truss bridge that contains compressive members that actively resist buckling through the use of piezo-electric actuators. I have also constructed a prototype actively controlled column in which the control forces are applied by tendons, as well as a composite steel column that incorporates piezo-ceramic actuators that are used to counteract buckling. Active control of buckling allows this composite column to support 5.6 times more load than would otherwise be possible.sThese techniques promise to lead to intelligent physical structures that are both stronger and lighter than would otherwise be possible.

Control of radiative processes using tunable plasmonic nanopatch antennas.

The radiative processes associated with fluorophores and other radiating systems can be profoundly modified by their interaction with nanoplasmonic structures. Extreme electromagnetic environments can be created in plasmonic nanostructures or nanocavities, such as within the nanoscale gap region between two plasmonic nanoparticles, where the illuminating optical fields and the density of radiating modes are dramatically enhanced relative to vacuum. Unraveling the various mechanisms present in such coupled systems, and their impact on spontaneous emission and other radiative phenomena, however, requires a suitably reliable and precise means of tuning the plasmon resonance of the nanostructure while simultaneously preserving the electromagnetic characteristics of the enhancement region. Here, we achieve this control using a plasmonic platform consisting of colloidally synthesized nanocubes electromagnetically coupled to a metallic film. Each nanocube resembles a nanoscale patch antenna (or nanopatch) whose plasmon resonance can be changed independent of its local field enhancement. By varying the size of the nanopatch, we tune the plasmonic resonance by ∼ 200 nm, encompassing the excitation, absorption, and emission spectra corresponding to Cy5 fluorophores embedded within the gap region between nanopatch and film. By sweeping the plasmon resonance but keeping the field enhancements roughly fixed, we demonstrate fluorescence enhancements exceeding a factor of 30,000 with detector-limited enhancements of the spontaneous emission rate by a factor of 74. The experiments are supported by finite-element simulations that reveal design rules for optimized fluorescence enhancement or large Purcell factors.

Process Modelling for Control of Product Wall Thickness in Thermoforming

The present paper describes the results of an investigation into the modelling of plug assisted thermoforming. The objective of this work was to improve the finite element modelling of thermoforming through an enhanced understanding of the physical elements underlying the process. Experiments were carried out to measure the effects on output of changes in major parameters and simultaneously simple finite element models were constructed. The experimental results show that the process creates conflicting and interrelated contact friction and heat transfer effects that largely dictate the final wall thickness distribution. From the simulation work it was demonstrated that a high coefficient of friction and no heat transfer can give a good approximation of the actual wall thickness distribution. However, when conduction was added to the model the results for lower friction values were greatly improved. It was concluded that further work is necessary to provide realistic measurements and models for contact effects in thermoforming.

Cox-2 Promotes Chromogranin A Expression and Bioactivity: Evidence for a PGE2-Dependent Mechanism and the Involvement of a Proximal cAMP-Responsive Element.

Abstract The prostanoid biosynthetic enzyme cyclooxygenase-2 (Cox-2) is upregulated in several neuroendocrine tumors. The aim of the current study was to employ a neuroendocrine cell (PC12) model of Cox-2 over-expression to identify gene products that might be implicated in the oncogenic and/or inflammatory actions of this enzyme in the setting of neuroendocrine neoplasia. Expression array and real-time PCR analysis demonstrated that levels of the neuroendocrine marker chromogranin A (CGA) were 2-fold and 3.2-fold higher, respectively, in Cox-2 over-expressing cells (PCXII) vs their control (PCMT) counterparts. Immunocytochemical and immunoblotting analyses confirmed that both intracellular and secreted levels of CGA were elevated in response to Cox-2 induction. Moreover, exogenous addition of prostaglandin E2 (1u�­M), mimicked this effect in PCMT cells, while treatment of PCXII cells with the Cox-2 selective inhibitor NS-398 (100 nM) reduced CGA expression levels, thereby confirming the biospecificity of this finding. Levels of neurone specific enolase (NSE) were similar in the two cell lines, suggesting that the effect of Cox-2 on CGA expression was specific and not due to a global enhancement of neuroendocrine marker expression/differentiation. Cox-2-dependent CGA upregulation was associated with significantly increased chromaffin granule number and intracellular and secreted levels of dopamine. CGA promoter-driven reporter gene expression studies provided evidence that prostaglandin E2-dependent upregulation required a proximal cAMP-responsive element (CRE; -71 - -64 bp). This study is the first to demonstrate that Cox-2 upregulates both CGA expression and bioactivity in a neuroendocrine cell line and has major implications for the role of this polypeptide in the pathogenesis of neuroendocrine cancers in which Cox-2 is upregulated.

Simple control of the polarisation in uniform hybrid waveguide-planar leaky-wave antennas

A simple and original mechanism to control the polarisation of uniform hybrid waveguide-planar leaky-wave antennas is proposed. The operation is based on introducing simple modifications of the planar dimensions of the structure cross-section, which is shown to control the horizontal and vertical components of the radiated fields. The proposed antenna dispenses with the need for periodic elements, commonly used in flexible polarised leaky-wave antennas, and therefore significantly reduces the design complexity. Parametric curves have been obtained to assist in the simple and efficient design of the proposed antenna. The novel mechanism is illustrated by means of several antenna prototypes operating at 5.7 GHz, producing linear, elliptical and circular polarisations. Commercial three-dimensional Finite Element Method has been used for the simulations, and the results are validated with experimental testing.[br].

Amplitude and Phase Controlled Reflectarray Element Based on an Impedance Transformation Unit

An architecture to simultaneously affect both amplitude and phase control from a reflectarray element using an impedance transformation unit is demonstrated. It is shown that a wide range of control is possible from a single element, removing the conventional necessity for variable sized elements across an array in order to form a desired reflectarray far-field pattern. Parallel plate waveguide measurements for a 2.2 GHz prototype element validate the phase and amplitude variation available from the element. It is demonstrated that there is sufficient control of the element's reflection response to allow Dolph-Tschebyscheff weighting coefficients for major-lobe to side-lobe ratios of up to 36 dB to be implemented.

A finite element solution scheme for an elastic–viscoplastic soil model

A Newton–Raphson solution scheme with a stress point algorithm is presented for the implementation of an elastic–viscoplastic soilmodel in a finite element program. Viscoplastic strain rates are calculated using the stress and volumetric states of the soil. Sub-incrementsof time are defined for each iterative calculation of elastic–viscoplastic stress changes so that their sum adds up to the time incrementfor the load step. This carefully defined ‘iterative time’ ensures that the correct amount of viscoplastic straining is accumulated overthe applied load step. The algorithms and assumptions required to implement the solution scheme are provided. Verification of the solutionscheme is achieved by using it to analyze typical boundary value problems.

Toenail trace element status and risk of Barrett's oesophagus and oesophageal adenocarcinoma. Results from the FINBAR study

Trace elements have been cited as both inhibitory and causative agents of cancer but importantly exposure to them is potentially modifiable. Our study aimed to examine toenail trace element status and risk of Barrett's oesophagus (BO) and oesophageal adenocarcinoma (OAC). Toenail clippings from each hallux were obtained from 638 participants of the FINBAR (Factors Influencing the Barrett's Adenocarcinoma Relationship) study comprising 221 healthy controls, 98 reflux oesophagitis, 182 BO and 137 OAC cases. The concentrations of eight toenail trace elements were determined using instrumental neutron activation analysis. Using multivariable adjusted logistic regression analysis, odds ratios (OR) and 95% confidence intervals (CIs) were calculated within tertiles of trace element concentrations. A twofold increased risk of BO was observed, but not OAC, among individuals in the highest tertile of toenail zinc status OR 2.21 (95% CI, 1.11-4.40). A higher toenail selenium status was not associated with risk of OAC OR 0.94 (95% CI, 0.44-2.04) or BO OR 0.89 (95% CI, 0.37-2.12). A borderline significant increased risk of BO was detected with a higher toenail cobalt concentration, OR 1.97 (95% CI, 1.01-3.85). No association was found between toenail levels of chromium, cerium, mercury and OAC or BO risk. This is the first case-control study to investigate a variety of trace elements in relation to OAC and BO risk. Despite antioxidant and proapoptotic properties, no associations were found with selenium. Higher concentrations of toenail zinc and cobalt were associated with an increased BO risk, but not OAC. These findings need confirmation in prospective analysis.

Design of latch-based C-element

The C-element logic gate is a key component for constructing asynchronous control in silicon integrated circuits. The purpose of this reported work is to introduce a new speed-independent C-element design, which is synthesised by the asynchronous Petrify design tool to ensure it is composed of sequential digital latches rather than complex gates. The benefits are that it guarantees correct speed-independent operation, together with easy integration in modern design flows and processes. It is compared to an equivalent speed-independent complex gate C-element design generated by Petrify in a 130 nm semiconductor process.

Hypoxia response element-driven cytosine deaminase/5-fluorocytosine gene therapy system:a highly effective approach to overcome the dynamics of tumour hypoxia and enhance the radiosensitivity of prostate cancer cells in vitro

BACKGROUND: We proposed to exploit hypoxia-inducible factor (HIF)-1alpha overexpression in prostate tumours and use this transcriptional machinery to control the expression of the suicide gene cytosine deaminase (CD) through binding of HIF-1alpha to arrangements of hypoxia response elements. CD is a prodrug activation enzyme, which converts inactive 5-fluorocytosine to active 5-fluorouracil (5-FU), allowing selective killing of vector containing cells.

METHODS: We developed a pair of vectors, containing either five or eight copies of the hypoxia response element (HRE) isolated from the vascular endothelial growth factor (pH5VCD) or glycolytic enzyme glyceraldehyde-3-phosphate dehydrogenase (pH8GCD) gene, respectively. The kinetics of the hypoxic induction of the vectors and sensitization effects were evaluated in 22Rv1 and DU145 cells in vitro.

RESULTS: The CD protein as selectively detected in lysates of transiently transfected 22Rv1 and DU145 cells following hypoxic exposure. This is the first evidence of GAPDH HREs being used to control a suicide gene therapy strategy. Detectable CD levels were sustained upon reoxygenation and prolonged hypoxic exposures. Hypoxia-induced chemoresistance to 5-FU was overcome in both cell lines treated with this suicide gene therapy approach. Hypoxic transfectants were sensitized to prodrug concentrations that were ten-fold lower than those that are clinically relevant. Moreover, the surviving fraction of reoxygenated transfectants could be further reduced with the concomitant delivery of clinically relevant single radiation doses.

CONCLUSIONS: This strategy thus has the potential to sensitize the hypoxic compartment of prostate tumours and improve the outcome of current therapies.