The programming language python in earth system simulations

-scale vary from a planetary scale and million years for convection problems to 100km and 10 years for fault systems simulations. Various techniques are in use to deal with the time dependency (e.g. Crank-Nicholson), with the non-linearity (e.g. Newton-Raphson) and weakly coupled equations (e.g. non-linear Gauss-Seidel). Besides these high-level solution algorithms discretization methods (e.g. finite element method (FEM), boundary element method (BEM)) are used to deal with spatial derivatives. Typically, large-scale, three dimensional meshes are required to resolve geometrical complexity (e.g. in the case of fault systems) or features in the solution (e.g. in mantel convection simulations). The modelling environment escript allows the rapid implementation of new physics as required for the development of simulation codes in earth sciences. Its main object is to provide a programming language, where the user can define new models and rapidly develop high-level solution algorithms. The current implementation is linked with the finite element package finley as a PDE solver. However, the design is open and other discretization technologies such as finite differences and boundary element methods could be included. escript is implemented as an extension of the interactive programming environment python (see www.python.org). Key concepts introduced are Data objects, which are holding values on nodes or elements of the finite element mesh, and linearPDE objects, which are defining linear partial differential equations to be solved by the underlying discretization technology. In this paper we will show the basic concepts of escript and will show how escript is used to implement a simulation code for interacting fault systems. We will show some results of large-scale, parallel simulations on an SGI Altix system. Acknowledgements: Project work is supported by Australian Commonwealth Government through the Australian Computational Earth Systems Simulator Major National Research Facility, Queensland State Government Smart State Research Facility Fund, The University of Queensland and SGI.

Modelling financial time series with switching state space models

The deficiencies of stationary models applied to financial time series are well documented. A special form of non-stationarity, where the underlying generator switches between (approximately) stationary regimes, seems particularly appropriate for financial markets. We use a dynamic switching (modelled by a hidden Markov model) combined with a linear dynamical system in a hybrid switching state space model (SSSM) and discuss the practical details of training such models with a variational EM algorithm due to [Ghahramani and Hilton,1998]. The performance of the SSSM is evaluated on several financial data sets and it is shown to improve on a number of existing benchmark methods.

Motion sharpening and contrast:Gain control precedes compressive non-linearity?

Blurred edges appear sharper in motion than when they are stationary. We (Vision Research 38 (1998) 2108) have previously shown how such distortions in perceived edge blur may be accounted for by a model which assumes that luminance contrast is encoded by a local contrast transducer whose response becomes progressively more compressive as speed increases. If the form of the transducer is fixed (independent of contrast) for a given speed, then a strong prediction of the model is that motion sharpening should increase with increasing contrast. We measured the sharpening of periodic patterns over a large range of contrasts, blur widths and speeds. The results indicate that whilst sharpening increases with speed it is practically invariant with contrast. The contrast invariance of motion sharpening is not explained by an early, static compressive non-linearity alone. However, several alternative explanations are also inconsistent with these results. We show that if a dynamic contrast gain control precedes the static non-linear transducer then motion sharpening, its speed dependence, and its invariance with contrast, can be predicted with reasonable accuracy. © 2003 Elsevier Science Ltd. All rights reserved.

Fast response static var generator for improving the power system performance of an electric arc furnace (EAF)

Cascaded multilevel inverters-based Static Var Generators (SVGs) are FACTS equipment introduced for active and reactive power flow control. They eliminate the need for zigzag transformers and give a fast response. However, with regard to their application for flicker reduction in using Electric Arc Furnace (EAF), the existing multilevel inverter-based SVGs suffer from the following disadvantages. (1) To control the reactive power, an off-line calculation of Modulation Index (MI) is required to adjust the SVG output voltage. This slows down the transient response to the changes of reactive power; and (2) Random active power exchange may cause unbalance to the voltage of the d.c. link (HBI) capacitor when the reactive power control is done by adjusting the power angle d alone. To resolve these problems, a mathematical model of 11-level cascaded SVG, was developed. A new control strategy involving both MI (modulation index) and power angle (d) is proposed. A selected harmonics elimination method (SHEM) is taken for switching pattern calculations. To shorten the response time and simplify the controls system, feed forward neural networks are used for on-line computation of the switching patterns instead of using look-up tables. The proposed controller updates the MI and switching patterns once each line-cycle according to the sampled reactive power Qs. Meanwhile, the remainder reactive power (compensated by the MI) and the reactive power variations during the line-cycle will be continuously compensated by adjusting the power angles, d. The scheme senses both variables MI and d, and takes action through the inverter switching angle, qi. As a result, the proposed SVG is expected to give a faster and more accurate response than present designs allow. In support of the proposal there is a mathematical model for reactive powered distribution and a sensitivity matrix for voltage regulation assessment, MATLAB simulation results are provided to validate the proposed schemes. The performance with non-linear time varying loads is analysed and refers to a general review of flicker, of methods for measuring flickers due to arc furnace and means for mitigation.

Unequal OTDM channels in a 2R regenerated, dispersion managed transmission system

The dynamics of switching and transmission of an optical signal comprising individual OTDM channels of unequal amplitudes in a dispersion-managed link with in-line non-linear fibre loop mirrors is investigated for the first time.

A type system with usage aspects

Linear typing schemes can be used to guarantee non-interference and so the soundness of in-place update with respect to a functional semantics. But linear schemes are restrictive in practice, and more restrictive than necessary to guarantee soundness of in-place update. This limitation has prompted research into static analysis and more sophisticated typing disciplines to determine when in-place update may be safely used, or to combine linear and non-linear schemes. Here we contribute to this direction by defining a new typing scheme that better approximates the semantic property of soundness of in-place update for a functional semantics. We begin from the observation that some data are used only in a read-only context, after which it may be safely re-used before being destroyed. Formalising the in-place update interpretation in a machine model semantics allows us to refine this observation, motivating three usage aspects apparent from the semantics that are used to annotate function argument types. The aspects are (1) used destructively, (2), used read-only but shared with result, and (3) used read-only and not shared with the result. The main novelty is aspect (2), which allows a linear value to be safely read and even aliased with a result of a function without being consumed. This novelty makes our type system more expressive than previous systems for functional languages in the literature. The system remains simple and intuitive, but it enjoys a strong soundness property whose proof is non-trivial. Moreover, our analysis features principal types and feasible type reconstruction, as shown in M. Konen'y (In TYPES 2002 workshop, Nijmegen, Proceedings, Springer-Verlag, 2003).

A study of the effect of harmonics in the system on the performance of residual current-operated circuit-breakers and electromechanical overcurrent relays

Residual current-operated circuit-breakers (RCCBs) have proved useful devices for the protection of both human beings against ventricular fibrillation and installations against fire. Although they work well with sinusoidal waveforms, there is little published information on their characteristics. Due to shunt connected non-linear devices, not the least of which is the use of power electronic equipment, the supply is distorted. Consequently, RCCBs as well as other protection relays are subject to non-sinusoidal current waveforms. Recent studies showed that RCCBs are greatly affected by harmonics, however the reasons for this are not clear. A literature search has also shown that there are inconsistencies in the analysis of the effect of harmonics on protection relays. In this work, the way RCCBs operate is examined, then a model is built with the aim of assessing the effect of non-sinusoidal current on RCCBs. Tests are then carried out on a number of RCCBs and these, when compared with the results from the model showed good correlation. In addition, the model also enables us to explain the RCCBs characteristics for pure sinusoidal current. In the model developed, various parameters are evaluated but special attention is paid to the instantaneous value of the current and the tripping mechanism movement. A similar assessment method is then used to assess the effect of harmonics on two types of protection relay, the electromechanical instantaneous relay and time overcurrent relay. A model is built for each of them which is then simulated on the computer. Tests results compare well with the simulation results, and thus the model developed can be used to explain the relays behaviour in a harmonics environment. The author's models, analysis and tests show that RCCBs and protection relays are affected by harmonics in a way determined by the waveform and the relay constants. The method developed provides a useful tool and the basic methodology to analyse the behaviour of RCCBs and protection relays in a harmonics environment. These results have many implications, especially the way RCCBs and relays should be tested if harmonics are taken into account.

Mathematical modelling and control of agitated extraction columns

Liquid-liquid extraction has long been known as a unit operation that plays an important role in industry. This process is well known for its complexity and sensitivity to operation conditions. This thesis presents an attempt to explore the dynamics and control of this process using a systematic approach and state of the art control system design techniques. The process was studied first experimentally under carefully selected. operation conditions, which resembles the ranges employed practically under stable and efficient conditions. Data were collected at steady state conditions using adequate sampling techniques for the dispersed and continuous phases as well as during the transients of the column with the aid of a computer-based online data logging system and online concentration analysis. A stagewise single stage backflow model was improved to mimic the dynamic operation of the column. The developed model accounts for the variation in hydrodynamics, mass transfer, and physical properties throughout the length of the column. End effects were treated by addition of stages at the column entrances. Two parameters were incorporated in the model namely; mass transfer weight factor to correct for the assumption of no mass transfer in the. settling zones at each stage and the backmixing coefficients to handle the axial dispersion phenomena encountered in the course of column operation. The parameters were estimated by minimizing the differences between the experimental and the model predicted concentration profiles at steady state conditions using non-linear optimisation technique. The estimated values were then correlated as functions of operating parameters and were incorporated in·the model equations. The model equations comprise a stiff differential~algebraic system. This system was solved using the GEAR ODE solver. The calculated concentration profiles were compared to those experimentally measured. A very good agreement of the two profiles was achieved within a percent relative error of ±2.S%. The developed rigorous dynamic model of the extraction column was used to derive linear time-invariant reduced-order models that relate the input variables (agitator speed, solvent feed flowrate and concentration, feed concentration and flowrate) to the output variables (raffinate concentration and extract concentration) using the asymptotic method of system identification. The reduced-order models were shown to be accurate in capturing the dynamic behaviour of the process with a maximum modelling prediction error of I %. The simplicity and accuracy of the derived reduced-order models allow for control system design and analysis of such complicated processes. The extraction column is a typical multivariable process with agitator speed and solvent feed flowrate considered as manipulative variables; raffinate concentration and extract concentration as controlled variables and the feeds concentration and feed flowrate as disturbance variables. The control system design of the extraction process was tackled as multi-loop decentralised SISO (Single Input Single Output) as well as centralised MIMO (Multi-Input Multi-Output) system using both conventional and model-based control techniques such as IMC (Internal Model Control) and MPC (Model Predictive Control). Control performance of each control scheme was. studied in terms of stability, speed of response, sensitivity to modelling errors (robustness), setpoint tracking capabilities and load rejection. For decentralised control, multiple loops were assigned to pair.each manipulated variable with each controlled variable according to the interaction analysis and other pairing criteria such as relative gain array (RGA), singular value analysis (SVD). Loops namely Rotor speed-Raffinate concentration and Solvent flowrate Extract concentration showed weak interaction. Multivariable MPC has shown more effective performance compared to other conventional techniques since it accounts for loops interaction, time delays, and input-output variables constraints.

Dynamic simulation of chemical processes

This thesis describes the design and implementation of an interactive dynamic simulator called DASPRII. The starting point of this research has been an existing dynamic simulation package, DASP. DASPII is written in standard FORTRAN 77 and is implemented on universally available IBM-PC or compatible machines. It provides a means for the analysis and design of chemical processes. Industrial interest in dynamic simulation has increased due to the recent increase in concern over plant operability, resiliency and safety. DASPII is an equation oriented simulation package which allows solution of dynamic and steady state equations. The steady state can be used to initialise the dynamic simulation. A robust non linear algebraic equation solver has been implemented for steady state solution. This has increased the general robustness of DASPII, compared to DASP. A graphical front end is used to generate the process flowsheet topology from a user constructed diagram of the process. A conversational interface is used to interrogate the user with the aid of a database, to complete the topological information. An original modelling strategy implemented in DASPII provides a simple mechanism for parameter switching which creates a more flexible simulation environment. The problem description generated is by a further conversational procedure using a data-base. The model format used allows the same model equations to be used for dynamic and steady state solution. All the useful features of DASPI are retained in DASPII. The program has been demonstrated and verified using a number of example problems, Significant improvements using the new NLAE solver have been shown. Topics requiring further research are described. The benefits of variable switching in models has been demonstrated with a literature problem.

Bayesian data assimilation

This thesis addresses data assimilation, which typically refers to the estimation of the state of a physical system given a model and observations, and its application to short-term precipitation forecasting. A general introduction to data assimilation is given, both from a deterministic and' stochastic point of view. Data assimilation algorithms are reviewed, in the static case (when no dynamics are involved), then in the dynamic case. A double experiment on two non-linear models, the Lorenz 63 and the Lorenz 96 models, is run and the comparative performance of the methods is discussed in terms of quality of the assimilation, robustness "in the non-linear regime and computational time. Following the general review and analysis, data assimilation is discussed in the particular context of very short-term rainfall forecasting (nowcasting) using radar images. An extended Bayesian precipitation nowcasting model is introduced. The model is stochastic in nature and relies on the spatial decomposition of the rainfall field into rain "cells". Radar observations are assimilated using a Variational Bayesian method in which the true posterior distribution of the parameters is approximated by a more tractable distribution. The motion of the cells is captured by a 20 Gaussian process. The model is tested on two precipitation events, the first dominated by convective showers, the second by precipitation fronts. Several deterministic and probabilistic validation methods are applied and the model is shown to retain reasonable prediction skill at up to 3 hours lead time. Extensions to the model are discussed.

Practical methods of tracking of nonstationary time series applied to real-world data

In this paper, we discuss some practical implications for implementing adaptable network algorithms applied to non-stationary time series problems. Two real world data sets, containing electricity load demands and foreign exchange market prices, are used to test several different methods, ranging from linear models with fixed parameters, to non-linear models which adapt both parameters and model order on-line. Training with the extended Kalman filter, we demonstrate that the dynamic model-order increment procedure of the resource allocating RBF network (RAN) is highly sensitive to the parameters of the novelty criterion. We investigate the use of system noise for increasing the plasticity of the Kalman filter training algorithm, and discuss the consequences for on-line model order selection. The results of our experiments show that there are advantages to be gained in tracking real world non-stationary data through the use of more complex adaptive models.

Basic principles of design and functioning of multifunctional laser diagnostic system for non-invasive medical spectrophotometry

The devising of a general engineering theory of multifunctional diagnostic systems for non-invasive medical spectrophotometry is an important and promising direction of modern biomedical engineering. We aim in this study to formalize in scientific engineering terms objectives for multifunctional laser non-invasive diagnostic system (MLNDS). The structure-functional model as well as a task-function of generalized MLNDS was formulated and developed. The key role of the system software for MLNDS general architecture at steps of ideological-technical designing has been proved. The basic principles of block-modules composition of MLNDS hardware are suggested as well. © 2011 Copyright Society of Photo-Optical Instrumentation Engineers (SPIE).

A Differential Game Described by a Hyperbolic System

An antagonistic differential game of hyperbolic type with a separable linear vector pay-off function is considered. The main result is the description of all ε-Slater saddle points consisting of program strategies, program ε-Slater maximins and minimaxes for each ε ∈ R^N > for this game. To this purpose, the considered differential game is reduced to find the optimal program strategies of two multicriterial problems of hyperbolic type. The application of approximation enables us to relate these problems to a problem of optimal program control, described by a system of ordinary differential equations, with a scalar pay-off function. It is found that the result of this problem is not changed, if the players use positional or program strategies. For the considered differential game, it is interesting that the ε-Slater saddle points are not equivalent and there exist two ε-Slater saddle points for which the values of all components of the vector pay-off function at one of them are greater than the respective components of the other ε-saddle point.

Facilitating intuitive-guided learning in a serious game through integration with a learning content management system

Increased global uptake of entertainment gaming has the potential to lead to high expectations of engagement and interactivity from users of technology-enhanced learning environments. Blended approaches to implementing game-based learning as part of distance or technology-enhanced education have led to demonstrations of the benefits they might bring, allowing learners to interact with immersive technologies as part of a broader, structured learning experience. In this article, we explore how the integration of a serious game can be extended to a learning content management system (LCMS) to support a blended and holistic approach, described as an 'intuitive-guided' method. Through a case study within the EU-Funded Adaptive Learning via Intuitive/Interactive, Collaborative and Emotional Systems (ALICE) project, a technical integration of a gaming engine with a proprietary LCMS is demonstrated, building upon earlier work and demonstrating how this approach might be realized. In particular, how this method can support an intuitive-guided approach to learning is considered, whereby the learner is given the potential to explore a non-linear environment whilst scaffolding and blending provide guidance ensuring targeted learning objectives are met. Through an evaluation of the developed prototype with 32 students aged 14-16 across two Italian schools, a varied response from learners is observed, coupled with a positive reception from tutors. The study demonstrates that challenges remain in providing high-fidelity content in a classroom environment, particularly as an increasing gap in technology availability between leisure and school times emerges.

Complete Integrability of a Nonlinear Elliptic System, Generating Bi-umbilical Foliated Semi-symmetric Hypersurfaces in R^4

Николай Кутев, Величка Милушева - Намираме експлицитно всичките би-омбилични фолирани полусиметрични повърхнини в четиримерното евклидово пространство R^4