Periodic oscillations in feedback systems with combined pulse modulation

This paper presents a systematic method of investigating the existence of limit cycle oscillations in feedback systems with combined integral pulse frequency-pulse width (IPF-P/V) modulation. The method is based on the non-linear discrete equivalence of the continuous feedback system containing the IPF-PW modulator.

Factors influencing kinetic and equilibrium behaviour of sodium ion exchange with strong acid cation resin

This study reports an investigation of the ion exchange treatment of sodium chloride solutions in relation to use of resin technology for applications such as desalination of brackish water. In particular, a strong acid cation (SAC) resin (DOW Marathon C) was studied to determine its capacity for sodium uptake and to evaluate the fundamentals of the ion exchange process involved. Key questions to answer included: impact of resin identity; best models to simulate the kinetics and equilibrium exchange behaviour of sodium ions; difference between using linear least squares (LLS) and non-linear least squares (NLLS) methods for data interpretation; and, effect of changing the type of anion in solution which accompanied the sodium species. Kinetic studies suggested that the exchange process was best described by a pseudo first order rate expression based upon non-linear least squares analysis of the test data. Application of the Langmuir Vageler isotherm model was recommended as it allowed confirmation that experimental conditions were sufficient for maximum loading of sodium ions to occur. The Freundlich expression best fitted the equilibrium data when analysing the information by a NLLS approach. In contrast, LLS methods suggested that the Langmuir model was optimal for describing the equilibrium process. The Competitive Langmuir model which considered the stoichiometric nature of ion exchange process, estimated the maximum loading of sodium ions to be 64.7 g Na/kg resin. This latter value was comparable to sodium ion capacities for SAC resin published previously. Inherent discrepancies involved when using linearized versions of kinetic and isotherm equations were illustrated, and despite their widespread use, the value of this latter approach was questionable. The equilibrium behaviour of sodium ions form sodium fluoride solution revealed that the sodium ions were now more preferred by the resin compared to the situation with sodium chloride. The solution chemistry of hydrofluoric acid was suggested as promoting the affinity of the sodium ions to the resin.

Dynamics of a class of social interaction systems

A mathematical model of social interaction in the form of two coupler! first-order non-linear differential equations, forms the topic of this study. This non-conservative model io representative of such varied social interaction problems as coexisting sub-populations of two different species, arms race between two rival countries and the like. Differential transformation techniques developed elsewhere in the literature are seen to be effective tools of dynamic analysis of this non-linear non-conservative mode! of social interaction process.

Optimal adaptive sequential spatial sampling of soil using pair-copulas

A spatial sampling design that uses pair-copulas is presented that aims to reduce prediction uncertainty by selecting additional sampling locations based on both the spatial configuration of existing locations and the values of the observations at those locations. The novelty of the approach arises in the use of pair-copulas to estimate uncertainty at unsampled locations. Spatial pair-copulas are able to more accurately capture spatial dependence compared to other types of spatial copula models. Additionally, unlike traditional kriging variance, uncertainty estimates from the pair-copula account for influence from measurement values and not just the configuration of observations. This feature is beneficial, for example, for more accurate identification of soil contamination zones where high contamination measurements are located near measurements of varying contamination. The proposed design methodology is applied to a soil contamination example from the Swiss Jura region. A partial redesign of the original sampling configuration demonstrates the potential of the proposed methodology.

L_{2}- stability of a class of nonstationary feedback systems with dynamical nonlinear subsystems

A class of feedback systems, consisting of dynamical non-linear subsystems which arise in many diverse control applications, is analyzed for L2-stability. It is shown that, although a transformation of these systems to the familiar Lur'e configuration does not seem to be possible, a one-to-one correspondence may be effected between the stability properties of these and the Lur'e systems. Interesting stability criteria are developed by exploiting this characteristic.

An analytical approach to the study of a class of bi-state social interaction processes

Sufficient conditions for obtaining an equivalent linear model to classes of non-linear, bi-state, social interaction processes are derived. These parametric constraints, when satisfied, permit analytical determination of the dynamics of the non-linear process of social interaction.

Application of optimization methods to vibration control of stretched strings

In this paper, non-linear programming techniques are applied to the problem of controlling the vibration pattern of a stretched string. First, the problem of finding the magnitudes of two control forces applied at two points l1 and l2 on the string to reduce the energy of vibration over the interval (l1, l2) relative to the energy outside the interval (l1, l2) is considered. For this problem the relative merits of various methods of non-linear programming are compared. The more complicated problem of finding the positions and magnitudes of two control forces to obtain the desired energy pattern is then solved by using the slack unconstrained minimization technique with the Fletcher-Powell search. In the discussion of the results it is shown that the position of the control force is very important in controlling the energy pattern of the string.

Country-scale carbon accounting of the vegetation and mineral soils of Finland

The increase in global temperature has been attributed to increased atmospheric concentrations of greenhouse gases (GHG), mainly that of CO2. The threat of severe and complex socio-economic and ecological implications of climate change have initiated an international process that aims to reduce emissions, to increase C sinks, and to protect existing C reservoirs. The famous Kyoto protocol is an offspring of this process. The Kyoto protocol and its accords state that signatory countries need to monitor their forest C pools, and to follow the guidelines set by the IPCC in the preparation, reporting and quality assessment of the C pool change estimates. The aims of this thesis were i) to estimate the changes in carbon stocks vegetation and soil in the forests in Finnish forests from 1922 to 2004, ii) to evaluate the applied methodology by using empirical data, iii) to assess the reliability of the estimates by means of uncertainty analysis, iv) to assess the effect of forest C sinks on the reliability of the entire national GHG inventory, and finally, v) to present an application of model-based stratification to a large-scale sampling design of soil C stock changes. The applied methodology builds on the forest inventory measured data (or modelled stand data), and uses statistical modelling to predict biomasses and litter productions, as well as a dynamic soil C model to predict the decomposition of litter. The mean vegetation C sink of Finnish forests from 1922 to 2004 was 3.3 Tg C a-1, and in soil was 0.7 Tg C a-1. Soil is slowly accumulating C as a consequence of increased growing stock and unsaturated soil C stocks in relation to current detritus input to soil that is higher than in the beginning of the period. Annual estimates of vegetation and soil C stock changes fluctuated considerably during the period, were frequently opposite (e.g. vegetation was a sink but soil was a source). The inclusion of vegetation sinks into the national GHG inventory of 2003 increased its uncertainty from between -4% and 9% to ± 19% (95% CI), and further inclusion of upland mineral soils increased it to ± 24%. The uncertainties of annual sinks can be reduced most efficiently by concentrating on the quality of the model input data. Despite the decreased precision of the national GHG inventory, the inclusion of uncertain sinks improves its accuracy due to the larger sectoral coverage of the inventory. If the national soil sink estimates were prepared by repeated soil sampling of model-stratified sample plots, the uncertainties would be accounted for in the stratum formation and sample allocation. Otherwise, the increases of sampling efficiency by stratification remain smaller. The highly variable and frequently opposite annual changes in ecosystem C pools imply the importance of full ecosystem C accounting. If forest C sink estimates will be used in practice average sink estimates seem a more reasonable basis than the annual estimates. This is due to the fact that annual forest sinks vary considerably and annual estimates are uncertain, and they have severe consequences for the reliability of the total national GHG balance. The estimation of average sinks should still be based on annual or even more frequent data due to the non-linear decomposition process that is influenced by the annual climate. The methodology used in this study to predict forest C sinks can be transferred to other countries with some modifications. The ultimate verification of sink estimates should be based on comparison to empirical data, in which case the model-based stratification presented in this study can serve to improve the efficiency of the sampling design.

Steady mixed convection stagnation-point flow of upper convected Maxwell fluids with magnetic field

The steady MHD mixed convection flow of a viscoelastic fluid in the vicinity of two-dimensional stagnation point with magnetic field has been investigated under the assumption that the fluid obeys the upper-convected Maxwell (UCM) model. Boundary layer theory is used to simplify the equations of motion. induced magnetic field and energy which results in three coupled non-linear ordinary differential equations which are well-posed. These equations have been solved by using finite difference method. The results indicate the reduction in the surface velocity gradient, surface heat transfer and displacement thickness with the increase in the elasticity number. These trends are opposite to those reported in the literature for a second-grade fluid. The surface velocity gradient and heat transfer are enhanced by the magnetic and buoyancy parameters. The surface heat transfer increases with the Prandtl number, but the surface velocity gradient decreases.

Thermoelectric power in ultrathin films, quantum wires and carbon nanotubes under classically large magnetic field: Simplified theory and relative comparison

We study the thermoelectric power under classically large magnetic field (TPM) in ultrathin films (UFs), quantum wires (QWs) of non-linear optical materials on the basis of a newly formulated electron dispersion law considering the anisotropies of the effective electron masses, the spin-orbit splitting constants and the presence of the crystal field splitting within the framework of k.p formalism. The results of quantum confined III-V compounds form the special cases of our generalized analysis. The TPM has also been studied for quantum confined II-VI, stressed materials, bismuth and carbon nanotubes (CNs) on the basis of respective dispersion relations. It is found taking quantum confined CdGeAs2, InAs, InSb, CdS, stressed n-InSb and Bi that the TPM increases with increasing film thickness and decreasing electron statistics exhibiting quantized nature for all types of quantum confinement. The TPM in CNs exhibits oscillatory dependence with increasing carrier concentration and the signature of the entirely different types of quantum systems are evident from the plots. Besides, under certain special conditions, all the results for all the materials gets simplified to the well-known expression of the TPM for non-degenerate materials having parabolic energy bands, leading to the compatibility test. (C) 2009 Elsevier B.V. All rights reserved.

Predicting the temporal response of seagrass meadows to dredging using Dynamic Bayesian Networks

Predicting temporal responses of ecosystems to disturbances associated with industrial activities is critical for their management and conservation. However, prediction of ecosystem responses is challenging due to the complexity and potential non-linearities stemming from interactions between system components and multiple environmental drivers. Prediction is particularly difficult for marine ecosystems due to their often highly variable and complex natures and large uncertainties surrounding their dynamic responses. Consequently, current management of such systems often rely on expert judgement and/or complex quantitative models that consider only a subset of the relevant ecological processes. Hence there exists an urgent need for the development of whole-of-systems predictive models to support decision and policy makers in managing complex marine systems in the context of industry based disturbances. This paper presents Dynamic Bayesian Networks (DBNs) for predicting the temporal response of a marine ecosystem to anthropogenic disturbances. The DBN provides a visual representation of the problem domain in terms of factors (parts of the ecosystem) and their relationships. These relationships are quantified via Conditional Probability Tables (CPTs), which estimate the variability and uncertainty in the distribution of each factor. The combination of qualitative visual and quantitative elements in a DBN facilitates the integration of a wide array of data, published and expert knowledge and other models. Such multiple sources are often essential as one single source of information is rarely sufficient to cover the diverse range of factors relevant to a management task. Here, a DBN model is developed for tropical, annual Halophila and temperate, persistent Amphibolis seagrass meadows to inform dredging management and help meet environmental guidelines. Specifically, the impacts of capital (e.g. new port development) and maintenance (e.g. maintaining channel depths in established ports) dredging is evaluated with respect to the risk of permanent loss, defined as no recovery within 5 years (Environmental Protection Agency guidelines). The model is developed using expert knowledge, existing literature, statistical models of environmental light, and experimental data. The model is then demonstrated in a case study through the analysis of a variety of dredging, environmental and seagrass ecosystem recovery scenarios. In spatial zones significantly affected by dredging, such as the zone of moderate impact, shoot density has a very high probability of being driven to zero by capital dredging due to the duration of such dredging. Here, fast growing Halophila species can recover, however, the probability of recovery depends on the presence of seed banks. On the other hand, slow growing Amphibolis meadows have a high probability of suffering permanent loss. However, in the maintenance dredging scenario, due to the shorter duration of dredging, Amphibolis is better able to resist the impacts of dredging. For both types of seagrass meadows, the probability of loss was strongly dependent on the biological and ecological status of the meadow, as well as environmental conditions post-dredging. The ability to predict the ecosystem response under cumulative, non-linear interactions across a complex ecosystem highlights the utility of DBNs for decision support and environmental management.

Nano-meter scale plasticity in KBr studied by nanoindenter and force microscopy

The early stages of plasticity in KBr single crystals have been studied by means of nano-meter-scale indentation in complementary experiments using both a nanoindenter and an atomic force microscope. Nanoindentafion experiments precisely correlate indentation depth and forces, while force microscopy provides high-resolution force measurements and images of the surface revealing dislocation activity. The two methods provide very similar results for the onset of plasticity in KBr. Upon loading we observe yield of the surface in atomic layer units which we attribute to the nucleation of single dislocations. Unloading is accompanied by plastic recovery as evident from a non-linear force distance unloading curve and delayed discrete plasticity events.

Bond graph model of doubly fed three phase induction motor using the Axis Rotator element for frame transformation

Induction motor is a typical member of a multi-domain, non-linear, high order dynamic system. For speed control a three phase induction motor is modelled as a d–q model where linearity is assumed and non-idealities are ignored. Approximation of the physical characteristic gives a simulated behaviour away from the natural behaviour. This paper proposes a bond graph model of an induction motor that can incorporate the non-linearities and non-idealities thereby resembling the physical system more closely. The model is validated by applying the linearity and idealities constraints which shows that the conventional ‘abc’ model is a special case of the proposed generalised model.

Thrombophilia and direct thrombin inhibitor lepirudin clinical and monitoring aspects

Thrombophilia (TF) predisposes both to venous and arterial thrombosis at a young age. TF may also impact the thrombosis or stenosis of hemodialysis (HD) vascular access in patients with end-stage renal disease (ESRD). When involved in severe thrombosis TF may associate with inappropriate response to anticoagulation. Lepirudin, a potent direct thrombin inhibitor (DTI), indicated for heparin-induced thrombocytopenia-related thrombosis, could offer a treatment alternative in TF. Monitoring of narrow-ranged lepirudin demands new insights also in laboratory. The above issues constitute the targets in this thesis. We evaluated the prevalence of TF in patients with ESRD and its impact upon thrombosis- or stenosis-free survival of the vascular access. Altogether 237 ESRD patients were prospectively screened for TF and thrombogenic risk factors prior to HD access surgery in 2002-2004 (mean follow-up of 3.6 years). TF was evident in 43 (18%) of the ESRD patients, more often in males (23 vs. 9%, p=0.009). Known gene mutations of FV Leiden and FII G20210A occurred in 4%. Vascular access sufficiently matured in 226 (95%). The 1-year thrombosis- and stenosis-free access survival was 72%. Female gender (hazards ratio, HR, 2.5; 95% CI 1.6-3.9) and TF (HR 1.9, 95% CI 1.1-3.3) were independent risk factors for the shortened thrombosis- and stenosis-free survival. Additionally, TF or thrombogenic background was found in relatively young patients having severe thrombosis either in hepatic veins (Budd-Chiari syndrome, BCS, one patient) or inoperable critical limb ischemia (CLI, six patients). Lepirudin was evaluated in an off-label setting in the severe thrombosis after inefficacious traditional anticoagulation without other treatment options except severe invasive procedures, such as lower extremity amputation. Lepirudin treatments were repeatedly monitored clinically and with laboratory assessments (e.g. activated partial thromboplastin time, APTT). Our preliminary studies with lepirudin in thrombotic calamities appeared safe, and no bleeds occurred. An effective DTI lepirudin calmed thrombosis as all patients gradually recovered. Only one limb amputation was performed 3 years later during the follow-up (mean 4 years). Furthermore, we aimed to overcome the limitations of APTT and confounding effects of warfarin (INR of 1.5-3.9) and lupus anticoagulant (LA). Lepirudin responses were assessed in vitro by five specific laboratory methods. Ecarin chromogenic assay (ECA) or anti-Factor IIa (anti-FIIa) correlated precisely (r=0.99) with each other and with spiked lepirudin in all plasma pools: normal, warfarin, and LA-containing plasma. In contrast, in the presence of warfarin and LA both APTT and prothrombinase-induced clotting time (PiCT®) were limited by non-linear and imprecise dose responses. As a global coagulation test APTT is useful in parallel to the precise chromogenic methods ECA or Anti-FIIa in challenging clinical situations. Lepirudin treatment requires multidisciplinary approach to ensure appropriate patient selection, interpretation of laboratory monitoring, and treatment safety. TF seemed to be associated with complicated thrombotic events, in venous (BCS), arterial (CLI), and vascular access systems. TF screening should be aimed to patients with repeated access complications or prior unprovoked thromboembolic events. Lepirudin inhibits free and clot-bound thrombin which heparin fails to inhibit. Lepirudin seems to offer a potent and safe option for treatment of severe thrombosis. Multi-centered randomized trials are necessary to assess the possible management of complicated thrombotic events with DTIs like lepirudin and seek prevention options against access complications.

Seismic damage estimation through measurable dynamic characteristics

Ductility based design of reinforced concrete structures implicitly assumes certain damage under the action of a design basis earthquake. The damage undergone by a structure needs to be quantified, so as to assess the post-seismic reparability and functionality of the structure. The paper presents an analytical method of quantification and location of seismic damage, through system identification methods. It may be noted that soft ground storied buildings are the major casualties in any earthquake and hence the example structure is a soft or weak first storied one, whose seismic response and temporal variation of damage are computed using a non-linear dynamic analysis program (IDARC) and compared with a normal structure. Time period based damage identification model is used and suitably calibrated with classic damage models. Regenerated stiffness of the three degrees of freedom model (for the three storied frame) is used to locate the damage, both on-line as well as after the seismic event. Multi resolution analysis using wavelets is also used for localized damage identification for soft storey columns.