Advances in distributed parameter approach to the dynamics and control of activated sludge processes for wastewater treatment

This paper presents a review of modelling and control of biological nutrient removal (BNR)-activated sludge processes for wastewater treatment using distributed parameter models described by partial differential equations (PDE). Numerical methods for solution to the BNR-activated sludge process dynamics are reviewed and these include method of lines, global orthogonal collocation and orthogonal collocation on finite elements. Fundamental techniques and conceptual advances of the distributed parameter approach to the dynamics and control of activated sludge processes are briefly described. A critical analysis on the advantages of the distributed parameter approach over the conventional modelling strategy in this paper shows that the activated sludge process is more adequately described by the former and the method is recommended for application to the wastewater industry (c) 2006 Elsevier Ltd. All rights reserved.

Three-body recombination of ultracold Bose gases using the truncated Wigner method

We apply the truncated Wigner method to the process of three-body recombination in ultracold Bose gases. We find that within the validity regime of the Wigner truncation for two-body scattering, three-body recombination can be treated using a set of coupled stochastic differential equations that include diffusion terms, and can be simulated using known numerical methods. As an example we investigate the behavior of a simple homogeneous Bose gas, finding a very slight increase of the loss rate compared to that obtained by using the standard method.

Performance analysis using equivariant kernel density estimator in nonlinear mixture

This paper investigates the performance analysis of separation of mutually independent sources in nonlinear models. The nonlinear mapping constituted by an unsupervised linear mixture is followed by an unknown and invertible nonlinear distortion, are found in many signal processing cases. Generally, blind separation of sources from their nonlinear mixtures is rather difficult. We propose using a kernel density estimator incorporated with equivariant gradient analysis to separate the sources with nonlinear distortion. The kernel density estimator parameters of which are iteratively updated to minimize the output independence expressed as a mutual information criterion. The equivariant gradient algorithm has the form of nonlinear decorrelation to perform the convergence analysis. Experiments are proposed to illustrate these results.

Towards a Modeling Environment for Earth Systems Simulations

The developments of models in Earth Sciences, e.g. for earthquake prediction and for the simulation of mantel convection, are fare from being finalized. Therefore there is a need for a modelling environment that allows scientist to implement and test new models in an easy but flexible way. After been verified, the models should be easy to apply within its scope, typically by setting input parameters through a GUI or web services. It should be possible to link certain parameters to external data sources, such as databases and other simulation codes. Moreover, as typically large-scale meshes have to be used to achieve appropriate resolutions, the computational efficiency of the underlying numerical methods is important. Conceptional this leads to a software system with three major layers: the application layer, the mathematical layer, and the numerical algorithm layer. The latter is implemented as a C/C++ library to solve a basic, computational intensive linear problem, such as a linear partial differential equation. The mathematical layer allows the model developer to define his model and to implement high level solution algorithms (e.g. Newton-Raphson scheme, Crank-Nicholson scheme) or choose these algorithms form an algorithm library. The kernels of the model are generic, typically linear, solvers provided through the numerical algorithm layer. Finally, to provide an easy-to-use application environment, a web interface is (semi-automatically) built to edit the XML input file for the modelling code. In the talk, we will discuss the advantages and disadvantages of this concept in more details. We will also present the modelling environment escript which is a prototype implementation toward such a software system in Python (see www.python.org). Key components of escript are the Data class and the PDE class. Objects of the Data class allow generating, holding, accessing, and manipulating data, in such a way that the actual, in the particular context best, representation is transparent to the user. They are also the key to establish connections with external data sources. PDE class objects are describing (linear) partial differential equation objects to be solved by a numerical library. The current implementation of escript has been linked to the finite element code Finley to solve general linear partial differential equations. We will give a few simple examples which will illustrate the usage escript. Moreover, we show the usage of escript together with Finley for the modelling of interacting fault systems and for the simulation of mantel convection.

Modelling of transient heat transfer in annealing furnaces

This is a study of heat transfer in a lift-off furnace which is employed in the batch annealing of a stack of coils of steel strip. The objective of the project is to investigate the various factors which govern the furnace design and the heat transfer resistances, so as to reduce the time of the annealing cycle, and hence minimize the operating costs. The work involved mathematical modelling of patterns of gas flow and modes of heat transfer. These models are: Heat conduction and its conjectures in the steel coils;Convective heat transfer in the plates separating the coils in the stack and in other parts of the furnace; and Radiative and convective heat transfer in the furnace by using the long furnace model. An important part of the project is the development of numerical methods and computations to solve the transient models. A limited number of temperature measurements was available from experiments on a test coil in an industrial furnace. The mathematical model agreed well with these data. The model has been used to show the following characteristics of annealing furnaces, and to suggest further developments which would lead to significant savings: - The location of the limiting temperature in a coil is nearer to the hollow core than to the outer periphery. - Thermal expansion of the steel tends to open the coils, reduces their thermal conductivity in the radial direction, and hence prolongs the annealing cycle. Increasing the tension in the coils and/or heating from the core would overcome this heat transfer resistance. - The shape and dimensions of the convective channels in the plates have significant effect on heat convection in the stack. An optimal design of a channel is shown to be of a width-to-height ratio equal to 9. - Increasing the cooling rate, by using a fluidized bed instead of the normal shell and tube exchanger, would shorten the cooling time by about 15%, but increase the temperature differential in the stack. - For a specific charge weight, a stack of different-sized coils will have a shorter annealing cycle than one of equally-sized coils, provided that production constraints allow the stacking order to be optimal. - Recycle of hot flue gases to the firing zone of the furnace would produce a. decrease in the thermal efficiency up to 30% but decreases the heating time by about 26%.

Octane requirement increase arising from the use of lead free fuel

Lead in petrol has been identified as a health hazard and attempts are being made to create a lead-free atmosphere. Through an intensive study a review is made of the various options available to the automobile and petroleum industry. The economic and atmospheric penalties coupled with automobile fuel consumption trends are calculated and presented in both graphical and tabulated form. Experimental measurements of carbon monoxide and hydrocarbon emissions are also presented for certain selected fuels. Reduction in CO and HC's with the employment of a three-way catalyst is also discussed. All tests were carried out on a Fiat 127A engine at wide open throttle and standard timing setting. A Froude dynamometer was used to vary engine speed. With the introduction of lead-free petrol, interest in combustion chamber deposits in spark ignition engines has ben renewed. These deposits cause octane requirement increase or rise in engine knock and decreased volumetric efficiency. The detrimental effect of the deposits has been attributed to the physical volume of the deposit and to changes in heat transfer. This study attempts to assess why leaded deposits, though often greater in mass and volume, yield relatively lower ORI when compared to lead-free deposits under identical operating conditions. This has been carried out by identifying the differences in the physical nature of the deposit and then through measurement of the thermal conductivity and permeability of the deposits. The measured thermal conductivity results are later used in a mathematical model to determine heat transfer rates and temperature variation across the engine wall and deposit. For the model, the walls of the combustion cylinder and top are assumed to be free of engine deposit, the major deposit being on the piston head. Seven different heat transfer equations are formulated describing heat flow at each part of the four stroke cycle, and the variation of cylinder wall area exposed to gas mixture is accounted for. The heat transfer equations are solved using numerical methods and temperature variations across the wall identified. Though the calculations have been carried out for one particular moment in the cycle, similar calculations are possible for every degree of the crank angle, and thus further information regarding location of maximum temperatures at every degree of the crank angle may also be determined. In conclusion, thermal conductivity values of leaded and lead-free deposits have been found. The fundamental concepts of a mathematical model with great potential have been formulated and it is hoped that with future work it may be used in a simulation for different engine construction materials and motor fuels, leading to better design of future prototype engines.

A critical assessment of the finite element method for calculating electric and magnetic fields

The present dissertation is concerned with the determination of the magnetic field distribution in ma[.rnetic electron lenses by means of the finite element method. In the differential form of this method a Poisson type equation is solved by numerical methods over a finite boundary. Previous methods of adapting this procedure to the requirements of digital computers have restricted its use to computers of extremely large core size. It is shown that by reformulating the boundary conditions, a considerable reduction in core store can be achieved for a given accuracy of field distribution. The magnetic field distribution of a lens may also be calculated by the integral form of the finite element rnethod. This eliminates boundary problems mentioned but introduces other difficulties. After a careful analysis of both methods it has proved possible to combine the advantages of both in a .new approach to the problem which may be called the 'differential-integral' finite element method. The application of this method to the determination of the magnetic field distribution of some new types of magnetic lenses is described. In the course of the work considerable re-programming of standard programs was necessary in order to reduce the core store requirements to a minimum.

Design methodology for the servo control of high speed multi-axis machinery (BL): decoupling and synchronisation of a generic machine by blockwise decentralised MIMO control

Traditional machinery for manufacturing processes are characterised by actuators powered and co-ordinated by mechanical linkages driven from a central drive. Increasingly, these linkages are replaced by independent electrical drives, each performs a different task and follows a different motion profile, co-ordinated by computers. A design methodology for the servo control of high speed multi-axis machinery is proposed, based on the concept of a highly adaptable generic machine model. In addition to the dynamics of the drives and the loads, the model includes the inherent interactions between the motion axes and thus provides a Multi-Input Multi-Output (MIMO) description. In general, inherent interactions such as structural couplings between groups of motion axes are undesirable and needed to be compensated. On the other hand, imposed interactions such as the synchronisation of different groups of axes are often required. It is recognised that a suitable MIMO controller can simultaneously achieve these objectives and reconciles their potential conflicts. Both analytical and numerical methods for the design of MIMO controllers are investigated. At present, it is not possible to implement high order MIMO controllers for practical reasons. Based on simulations of the generic machine model under full MIMO control, however, it is possible to determine a suitable topology for a blockwise decentralised control scheme. The Block Relative Gain array (BRG) is used to compare the relative strength of closed loop interactions between sub-systems. A number of approaches to the design of the smaller decentralised MIMO controllers for these sub-systems has been investigated. For the purpose of illustration, a benchmark problem based on a 3 axes test rig has been carried through the design cycle to demonstrate the working of the design methodology.

Reconstruction of an unsteady flow from incomplete boundary data:Part I. Theory

Purpose – To propose and investigate a stable numerical procedure for the reconstruction of the velocity of a viscous incompressible fluid flow in linear hydrodynamics from knowledge of the velocity and fluid stress force given on a part of the boundary of a bounded domain. Design/methodology/approach – Earlier works have involved the similar problem but for stationary case (time-independent fluid flow). Extending these ideas a procedure is proposed and investigated also for the time-dependent case. Findings – The paper finds a novel variation method for the Cauchy problem. It proves convergence and also proposes a new boundary element method. Research limitations/implications – The fluid flow domain is limited to annular domains; this restriction can be removed undertaking analyses in appropriate weighted spaces to incorporate singularities that can occur on general bounded domains. Future work involves numerical investigations and also to consider Oseen type flow. A challenging problem is to consider non-linear Navier-Stokes equation. Practical implications – Fluid flow problems where data are known only on a part of the boundary occur in a range of engineering situations such as colloidal suspension and swimming of microorganisms. For example, the solution domain can be the region between to spheres where only the outer sphere is accessible for measurements. Originality/value – A novel variational method for the Cauchy problem is proposed which preserves the unsteady Stokes operator, convergence is proved and using recent for the fundamental solution for unsteady Stokes system, a new boundary element method for this system is also proposed.

An iterative method for the reconstruction of a stationary flow

In this article, an iterative algorithm based on the Landweber-Fridman method in combination with the boundary element method is developed for solving a Cauchy problem in linear hydrostatics Stokes flow of a slow viscous fluid. This is an iteration scheme where mixed well-posed problems for the stationary generalized Stokes system and its adjoint are solved in an alternating way. A convergence proof of this procedure is included and an efficient stopping criterion is employed. The numerical results confirm that the iterative method produces a convergent and stable numerical solution. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2007

Optimization of dispersion-managed optical fiber lines

We present various approaches to the optimization of optical fiber lines and discuss the ranges of validity of such methods. An effective scheme for upgrading of existing transmission lines using dispersion-management with optimization of the pre- and postcompensating fiber is examined. The theory and numerical methods are illustrated in application to the Upgrade of a specific installed Deutsche Telekom fiber line.

In memoriam: Dimitar Shishkov

Bulgarian and world computer science lost a prominent colleague: Dimitar Petrov Shishkov 22th January 1939, Varna – 8th March 2004, Sofia D. Shishkov graduated mathematics at Sofia University in 1962. In the last year of his studies he started a specialization as a programmer at the Joint Institute of Nuclear Research – Dubna which lasted three years. Then he worked at the Institute of Mathematics for two years. In 1966 D. Shishkov together with a group of experts transferred to the newly created Central Laboratory for Information Technologies. In 1976 he defended his PhD dissertation. He has been an associate professor in computer science at Sofia University since 1985 and a professor in computer science since 2000. His scientific interests and results were in the fields of computer architectures, computational linguistics, artificial intelligence, numerical methods, data structures, etc. He was remarkable with his teaching activities. D. Shishkov was the creator of high-quality software for the first Bulgarian electronic calculator “ELKA” – one of the first calculators in the world as well as for the series of next calculators and for specialized minicomputers. He was the initiator of the international project “Computerization of the natural languages”. He was a member of a range of international scientific organizations. Among his numerous activities was the organization of the I-st Programming competition in 1979. D. Shishkov was the initiator of sport dancing in Bulgaria (1967) and founder of the first sport-dancing high school education in the world. D. Shishkov was a highly accomplished person with a diversity of interests, with a developed social responsibility and accuracy in his work. In 1996 D. Shishkov was awarded with the International Prize ITHEA for outstanding achievements in the field of Information Theories and Applications. We are grateful to D. Shishkov for the chance to work together with him for establishment and development of IJ ITA.

Nonlinear Waves: An Introduction

This book deals with equations of mathematical physics as the different modifications of the KdV equation, the Camassa-Holm type equations, several modifications of Burger's equation, the Hunter-Saxton equation, conservation laws equations and others. The equations originate from physics but are proposed here for their investigation via purely mathematical methods in the frames of university courses. More precisely, we propose classification theorems for the traveling wave solutions for a sufficiently large class of third order nonlinear PDE when the corresponding profiles develop different kind of singularities (cusps, peaks), existence and uniqueness results, etc. The orbital stability of the periodic solutions of traveling type for mKdV equations are also studied. Of great interest too is the interaction of peakon type solutions of the Camassa-Holm equation and the solvability of the classical and generalized Cauchy problem for the Hunter-Saxton equation. The Riemann problem for special systems of conservation laws and the corresponding -shocks are also considered. As it concerns numerical methods we apply the CNN approach. The book is addressed to a broader audience including graduate students, Ph.D. students, mathematicians, physicist, engineers and specialists in the domain of PDE.

Елементи на обучение чрез синтаксис за студенти от професионално направление „Технически науки”

Доклад, поместен в сборника на Националната конференция "Образованието в информационното общество", Пловдив, май, 2011 г.