Global asymptotic stability in a rational recursive sequence

In this paper, we study the global stability of the difference equation x(n) = a + bx(n-1) + cx(n-1)(2)/d - x(n-2), n = 1,2,....., where a, b greater than or equal to 0 and c, d > 0. We show that one nonnegative equilibrium point of the equation is a global attractor with a basin that is determined by the parameters, and every positive Solution of the equation in the basin exponentially converges to the attractor. (C) 2003 Elsevier Inc. All rights reserved.

A finite difference scheme for inviscid flows with non-eequilibrium chemistry and internal energy

A finite difference scheme is presented for the inviscid terms of the equations of compressible fluid dynamics with general non-equilibrium chemistry and internal energy.

On a class of non-self-adjoint periodic eigenproblems with boundary and interior singularities

We prove that all the eigenvalues of a certain highly non-self-adjoint Sturm–Liouville differential operator are real. The results presented are motivated by and extend those recently found by various authors (Benilov et al. (2003) [3], Davies (2007) [7] and Weir (2008) [18]) on the stability of a model describing small oscillations of a thin layer of fluid inside a rotating cylinder.

A statistical mechanical approach for the computation of the climatic response to general forcings

The climate belongs to the class of non-equilibrium forced and dissipative systems, for which most results of quasi-equilibrium statistical mechanics, including the fluctuation-dissipation theorem, do not apply. In this paper we show for the first time how the Ruelle linear response theory, developed for studying rigorously the impact of perturbations on general observables of non-equilibrium statistical mechanical systems, can be applied with great success to analyze the climatic response to general forcings. The crucial value of the Ruelle theory lies in the fact that it allows to compute the response of the system in terms of expectation values of explicit and computable functions of the phase space averaged over the invariant measure of the unperturbed state. We choose as test bed a classical version of the Lorenz 96 model, which, in spite of its simplicity, has a well-recognized prototypical value as it is a spatially extended one-dimensional model and presents the basic ingredients, such as dissipation, advection and the presence of an external forcing, of the actual atmosphere. We recapitulate the main aspects of the general response theory and propose some new general results. We then analyze the frequency dependence of the response of both local and global observables to perturbations having localized as well as global spatial patterns. We derive analytically several properties of the corresponding susceptibilities, such as asymptotic behavior, validity of Kramers-Kronig relations, and sum rules, whose main ingredient is the causality principle. We show that all the coefficients of the leading asymptotic expansions as well as the integral constraints can be written as linear function of parameters that describe the unperturbed properties of the system, such as its average energy. Some newly obtained empirical closure equations for such parameters allow to define such properties as an explicit function of the unperturbed forcing parameter alone for a general class of chaotic Lorenz 96 models. We then verify the theoretical predictions from the outputs of the simulations up to a high degree of precision. The theory is used to explain differences in the response of local and global observables, to define the intensive properties of the system, which do not depend on the spatial resolution of the Lorenz 96 model, and to generalize the concept of climate sensitivity to all time scales. We also show how to reconstruct the linear Green function, which maps perturbations of general time patterns into changes in the expectation value of the considered observable for finite as well as infinite time. Finally, we propose a simple yet general methodology to study general Climate Change problems on virtually any time scale by resorting to only well selected simulations, and by taking full advantage of ensemble methods. The specific case of globally averaged surface temperature response to a general pattern of change of the CO2 concentration is discussed. We believe that the proposed approach may constitute a mathematically rigorous and practically very effective way to approach the problem of climate sensitivity, climate prediction, and climate change from a radically new perspective.

A stable one-step-ahead predictive control of non-linear systems

In this paper stability of one-step ahead predictive controllers based on non-linear models is established. It is shown that, under conditions which can be fulfilled by most industrial plants, the closed-loop system is robustly stable in the presence of plant uncertainties and input–output constraints. There is no requirement that the plant should be open-loop stable and the analysis is valid for general forms of non-linear system representation including the case out when the problem is constraint-free. The effectiveness of controllers designed according to the algorithm analyzed in this paper is demonstrated on a recognized benchmark problem and on a simulation of a continuous-stirred tank reactor (CSTR). In both examples a radial basis function neural network is employed as the non-linear system model.

Neurofuzzy control using Kalman filtering state feedback with coloured noise for unknown non-linear processes

This paper presents a controller design scheme for a priori unknown non-linear dynamical processes that are identified via an operating point neurofuzzy system from process data. Based on a neurofuzzy design and model construction algorithm (NeuDec) for a non-linear dynamical process, a neurofuzzy state-space model of controllable form is initially constructed. The control scheme based on closed-loop pole assignment is then utilized to ensure the time invariance and linearization of the state equations so that the system stability can be guaranteed under some mild assumptions, even in the presence of modelling error. The proposed approach requires a known state vector for the application of pole assignment state feedback. For this purpose, a generalized Kalman filtering algorithm with coloured noise is developed on the basis of the neurofuzzy state-space model to obtain an optimal state vector estimation. The derived controller is applied in typical output tracking problems by minimizing the tracking error. Simulation examples are included to demonstrate the operation and effectiveness of the new approach.

A robust non-orthogonal space-time block code for four transmit antennas

Several non-orthogonal space-time block coding (NO-STBC) schemes have recently been proposed to achieve full rate transmission. Some of these schemes, however, suffer from weak robustness: their channel matrices will become ill conditioned in the case of highly correlated channels (HCC). To address this issue, this paper derives a family of robust NO-STBC schemes for four Tx antennas based on the worst case of HCC. These codes turned out to be a superset of Jafarkhani's quasi-orthogonal STBC codes. A computationally affordable linear decoder is also proposed. Although these codes achieve a similar performance to the non-robust schemes under normal channel conditions, they offer a strong robustness against HCC (although possibly yielding a poorer performance). Finally, computer simulations are presented to verify the algorithm design.

Space-time block coding for four transmit antennas over time-selective fading channels: orthogonal or non-orthogonal design?

The paper deals with an issue in space time block coding (STBC) design. It considers whether, over a time-selective channel, orthogonal STBC (O-STBC) or non-orthogonal STBC (NO-STBC) performs better. It is shown that, under time-selectiveness, once vehicle speed has risen above a certain value, NO-STBC always outperforms O-STBC across the whole SNR range. Also, considering that all existing NO-STBC schemes have been investigated under quasi-static channels only, a new simple receiver is derived for the NO-STBC system under time-selective channels.

Composite control of non-linear singularly perturbed systems: meeting a design objective

Using the integral manifold approach, a composite control—the sum of a fast control and a slow control—is derived for a particular class of non-linear singularly perturbed systems. The fast control is designed completely at the outset, thus ensuring the stability of the fast transients of the system and, furthermore, the existence of the integral manifold. A new method is then presented which simplifies the derivation of a slow control such that the singularly perturbed system meets a preselected design objective to within some specified order of accuracy. Though this approach is, by its very nature, ad hoc, the underlying procedure is easily extended to more general classes of singularly perturbed systems by way of three examples.

Technologies for biological containment of GM and Non-GM crops

International Perspective The development of GM technology continues to expand into increasing numbers of crops and conferred traits. Inevitably, the focus remains on the major field crops of soybean, maize, cotton, oilseed rape and potato with introduced genes conferring herbicide tolerance and/or pest resistance. Although there are comparatively few GM crops that have been commercialised to date, GM versions of 172 plant species have been grown in field trials in 31 countries. European Crops with Containment Issues Of the 20 main crops in the EU there are four for which GM varieties are commercially available (cotton, maize for animal feed and forage, and oilseed rape). Fourteen have GM varieties in field trials (bread wheat, barley, durum wheat, sunflower, oats, potatoes, sugar beet, grapes, alfalfa, olives, field peas, clover, apples, rice) and two have GM varieties still in development (rye, triticale). Many of these crops have hybridisation potential with wild and weedy relatives in the European flora (bread wheat, barley, oilseed rape, durum wheat, oats, sugar beet and grapes), with escapes (sunflower); and all have potential to cross-pollinate fields non-GM crops. Several fodder crops, forestry trees, grasses and ornamentals have varieties in field trials and these too may hybridise with wild relatives in the European flora (alfalfa, clover, lupin, silver birch, sweet chestnut, Norway spruce, Scots pine, poplar, elm, Agrostis canina, A. stolonifera, Festuca arundinacea, Lolium perenne, L. multiflorum, statice and rose). All these crops will require containment strategies to be in place if it is deemed necessary to prevent transgene movement to wild relatives and non-GM crops. Current Containment Strategies A wide variety of GM containment strategies are currently under development, with a particular focus on crops expressing pharmaceutical products. Physical containment in greenhouses and growth rooms is suitable for some crops (tomatoes, lettuce) and for research purposes. Aquatic bioreactors of some non-crop species (algae, moss, and duckweed) expressing pharmaceutical products have been adopted by some biotechnology companies. There are obvious limitations of the scale of physical containment strategies, addressed in part by the development of large underground facilities in the US and Canada. The additional resources required to grow plants underground incurs high costs that in the long term may negate any advantage of GM for commercial productioNatural genetic containment has been adopted by some companies through the selection of either non-food/feed crops (algae, moss, duckweed) as bio-pharming platforms or organisms with no wild relatives present in the local flora (safflower in the Americas). The expression of pharmaceutical products in leafy crops (tobacco, alfalfa, lettuce, spinach) enables growth and harvesting prior to and in the absence of flowering. Transgenically controlled containment strategies range in their approach and degree of development. Plastid transformation is relatively well developed but is not suited to all traits or crops and does not offer complete containment. Male sterility is well developed across a range of plants but has limitations in its application for fruit/seed bearing crops. It has been adopted in some commercial lines of oilseed rape despite not preventing escape via seed. Conditional lethality can be used to prevent flowering or seed development following the application of a chemical inducer, but requires 100% induction of the trait and sufficient application of the inducer to all plants. Equally, inducible expression of the GM trait requires equally stringent application conditions. Such a method will contain the trait but will allow the escape of a non-functioning transgene. Seed lethality (‘terminator’ technology) is the only strategy at present that prevents transgene movement via seed, but due to public opinion against the concept it has never been trialled in the field and is no longer under commercial development. Methods to control flowering and fruit development such as apomixis and cleistogamy will prevent crop-to-wild and wild-to-crop pollination, but in nature both of these strategies are complex and leaky. None of the genes controlling these traits have as yet been identified or characterised and therefore have not been transgenically introduced into crop species. Neither of these strategies will prevent transgene escape via seed and any feral apomicts that form are arguably more likely to become invasives. Transgene mitigation reduces the fitness of initial hybrids and so prevents stable introgression of transgenes into wild populations. However, it does not prevent initial formation of hybrids or spread to non-GM crops. Such strategies could be detrimental to wild populations and have not yet been demonstrated in the field. Similarly, auxotrophy prevents persistence of escapes and hybrids containing the transgene in an uncontrolled environment, but does not prevent transgene movement from the crop. Recoverable block of function, intein trans-splicing and transgene excision all use recombinases to modify the transgene in planta either to induce expression or to prevent it. All require optimal conditions and 100% accuracy to function and none have been tested under field conditions as yet. All will contain the GM trait but all will allow some non-native DNA to escape to wild populations or to non-GM crops. There are particular issues with GM trees and grasses as both are largely undomesticated, wind pollinated and perennial, thus providing many opportunities for hybridisation. Some species of both trees and grass are also capable of vegetative propagation without sexual reproduction. There are additional concerns regarding the weedy nature of many grass species and the long-term stability of GM traits across the life span of trees. Transgene stability and conferred sterility are difficult to trial in trees as most field trials are only conducted during the juvenile phase of tree growth. Bio-pharming of pharmaceutical and industrial compounds in plants Bio-pharming of pharmaceutical and industrial compounds in plants offers an attractive alternative to mammalian-based pharmaceutical and vaccine production. Several plantbased products are already on the market (Prodigene’s avidin, β-glucuronidase, trypsin generated in GM maize; Ventria’s lactoferrin generated in GM rice). Numerous products are in clinical trials (collagen, antibodies against tooth decay and non-Hodgkin’s lymphoma from tobacco; human gastric lipase, therapeutic enzymes, dietary supplements from maize; Hepatitis B and Norwalk virus vaccines from potato; rabies vaccines from spinach; dietary supplements from Arabidopsis). The initial production platforms for plant-based pharmaceuticals were selected from conventional crops, largely because an established knowledge base already existed. Tobacco and other leafy crops such as alfalfa, lettuce and spinach are widely used as leaves can be harvested and no flowering is required. Many of these crops can be grown in contained greenhouses. Potato is also widely used and can also be grown in contained conditions. The introduction of morphological markers may aid in the recognition and traceability of crops expressing pharmaceutical products. Plant cells or plant parts may be transformed and maintained in culture to produce recombinant products in a contained environment. Plant cells in suspension or in vitro, roots, root cells and guttation fluid from leaves may be engineered to secrete proteins that may be harvested in a continuous, non-destructive manner. Most strategies in this category remain developmental and have not been commercially adopted at present. Transient expression produces GM compounds from non-GM plants via the utilisation of bacterial or viral vectors. These vectors introduce the trait into specific tissues of whole plants or plant parts, but do not insert them into the heritable genome. There are some limitations of scale and the field release of such crops will require the regulation of the vector. However, several companies have several transiently expressed products in clinical and pre-clinical trials from crops raised in physical containment.

Enhanced second order non-linear optical properties of silica sol-gel thin films through photo-induced poling

Sol-gel derived inorganic materials are of interest as hosts for non-linear optically active guest molecules and they offer particular advantages in the field of non-linear optics. Orientationally ordered glasses have been prepared using a sol-gel system based on tetramethoxysilane, methyltrimethoxysilane and a non-linear optical chromophore Disperse Red 1. The novel technique of photo-induced poling was used to generate enhanced levels of polar order. The level of enhancement is strongly dependent on the extent of gelation and an optimum preparation time of ∼100 h led to an enhancement factor of ∼5. Films prepared in this manner exhibited a high stability of the polar order.

Communities of practice in UK large contracting firms: contrasting application and non-utilized merits

The idea of a community of practice (CoP) has been offered as the engine to unlock the potential of organizational resources, mainly knowledge and people, to achieve the strategic goal of sustained competitiveness. The relevance and application of CoPs in large UK contracting companies was investigated using two case studies. Contrasting variations in the understanding of the concept between the two contracting companies were observed. While a CoP was applied in one company with strategic intent, the concept was not fully understood in the other. In one company, only a third of CoP members surveyed agreed that CoPs were a vehicle for driving best practice and innovation throughout the business; this compared with more than 60% in agreement in the other contracting firm. The higher agreement and satisfaction of CoP members in the latter case study was the result of the management's understanding and commitment. CoPs require time and organizational support to mature. The strategic inception and management support of CoP application is vital for their maturation and progress. Although the construction industry change discourses portray CoPs as fostering an environment of trust, and hence serving as innovation and competiveness enablers, their potential contribution to contracting firms does not provide a compelling case and hence merits further research studies.

Influence of a non-ionic amphiphilic copolymer on the self-assembly of a peptide amphiphile that forms nanotapes

The influence of a non-ionic polymeric surfactant on the self-assembly of a peptide amphiphile (PA) that forms nanotapes is investigated using a combination of microscopic, scattering and spectroscopic techniques. Mixtures of Pluronic copolymer P123 with the PA C16-KTTKS in aqueous solution were studied at a fixed concentration of the PA at which it is known to self-assemble into extended nanotapes, but varying P123 concentration. We find that P123 can disrupt the formation of C16- KTTKS nanotapes, leading instead to cylindrical nanofibril structures. The spherical micelles formed by P123 at room temperature are disrupted in the presence of the PA. There is a loss of cloudiness in the solutions as the large nanotape aggregates formed by C16-KTTKS are broken up, by P123 solubilization. At least locally, b-sheet structure is retained, as confirmed by XRD and FTIR spectroscopy, even for solutions containing 20 wt% P123. This indicates, unexpectedly, that peptide secondary structure can be retained in solutions with high concentration of non-ionic surfactant. Selfassembly in this system exhibits slow kinetics towards equilibrium, the initial self-assembly being dependent on the order of mixing. Heating above the lipid chain melting temperature assists in disrupting trapped non-equilibrium states.

Turbulence dynamics near a turbulent/non-turbulent interface

The characteristics of the boundary layer separating a turbulence region from an irrotational (or non-turbulent) flow region are investigated using rapid distortion theory (RDT). The turbulence region is approximated as homogeneous and isotropic far away from the bounding turbulent/non-turbulent (T/NT) interface, which is assumed to remain approximately flat. Inviscid effects resulting from the continuity of the normal velocity and pressure at the interface, in addition to viscous effects resulting from the continuity of the tangential velocity and shear stress, are taken into account by considering a sudden insertion of the T/NT interface, in the absence of mean shear. Profiles of the velocity variances, turbulent kinetic energy (TKE), viscous dissipation rate (epsilon), turbulence length scales, and pressure statistics are derived, showing an excellent agreement with results from direct numerical simulations (DNS). Interestingly, the normalized inviscid flow statistics at the T/NT interface do not depend on the form of the assumed TKE spectrum. Outside the turbulent region, where the flow is irrotational (except inside a thin viscous boundary layer), epsilon decays as z^{-6}, where z is the distance from the T/NT interface. The mean pressure distribution is calculated using RDT, and exhibits a decrease towards the turbulence region due to the associated velocity fluctuations, consistent with the generation of a mean entrainment velocity. The vorticity variance and epsilon display large maxima at the T/NT interface due to the inviscid discontinuities of the tangential velocity variances existing there, and these maxima are quantitatively related to the thickness delta of the viscous boundary layer (VBL). For an equilibrium VBL, the RDT analysis suggests that delta ~ eta (where eta is the Kolmogorov microscale), which is consistent with the scaling law identified in a very recent DNS study for shear-free T/NT interfaces.

Asymptotic gravity wave drag expressions for non-hydrostatic rotating flow over a ridge

Asymptotic expressions are derived for the mountain wave drag in flow with constant wind and static stability over a ridge when both rotation and non-hydrostatic effects are important. These expressions, which are much more manageable than the corresponding exact drag expressions (when these do exist) are found to provide accurate approximations to the drag, even when non-hydrostatic and rotation effects are strong, despite having been developed for cases where these effects are weak. The derived expressions are compared with approximations to the drag found previously, and their asymptotic behaviour in various limits is studied.