Progress in Industrial Mathematics at ECMI 2000

This paper develops a subordinated stochastic process model for asset prices, where the directing process is identified as information. Motivated by recent empirical and theoretical work, we make use of the under-used market statistic of transaction count as a suitable proxy for the information flow. An option pricing formula is derived, and comparisons with stochastic volatility models are drawn.

This paper applies the uncertain nonlinear parameter approach, originally by Avellaneda et al. and Lyons, to model non-local changes in financial variables and the resulting impact on portfolios of derivatives and their underlying assets. It formulates the non-probabilistic uncertainty assumptions as a governing system of nonlinear PDEs about both the spatial and the time dimensions of the variables. The solution technique can be decomposed as a control problem for the former and a free-boundary problem for the latter. It is shown that, modelled in a non-probabilistic way any jump in a variable can be treated in the same manner as a dividend on equity.

In the last decade, offshore pipeline engineering extended its action field to very deep waters and continental slopes. This implies the necessity to deal with continental slopes instability and mass gravity flows. Even if a standard classification of mass gravity flows does not exist in literature, they can be divided in two main different classes having respectively laminar and turbulent regimes. The first class, namely debris flow, is a very dense laminar flow, up to 1800Kg/m3, with Bingham fluid characteristics. A debris flow could occur on steep slopes with velocity estimated to reach 30m/s. The main cause of debris flows occurrence is the seismicity. The second class, namely turbidity current, is a turbulent Newtonian flux with density up to 1200Kg/m3. They are usually associated to debris flows that generate a dense mixture of water and sediment that continues to flow down slope even after the debris flow has stopped. Maximum velocities reached by turbidity currents are of the order of 10 –15m/s; they generally last a long time and continue to flow down even on slopes of few degrees. Mass gravity flows are rare and have random occurrence and the direct measurement of the phenomena is practically impossible. This pushed toward the development of physical and numerical models apt to investigate the characteristics and intensity of the phenomena (Niedoroda et al., 2000a, Niedoroda et al., 2000b). In this paper two numerical models, one for debris flows and the other for turbidity currents, are presented. A further diffusion model has been implemented to couple these models, thus allowing the complete simulation of a mass gravity flow starting as a debris flow that flowing down generates a turbidity current.

A model for the dynamics of a liquid—liquid dispersion in a batch reactor with multiple breakage and volume scattering is presented. This model extends the one we proposed in [1,2] to show that it is possible to prevent the occurrence of too large droplets by a suitable modification of the evolution equation. The main feature is that each breakage mode appears explicitly in the balance equation through its own probability density.

It is well known that the presence of paraffin in a crude oil can create difficulties in storage, extraction, pumping and all classical operations in a pipeline system. Oils with high content of paraffin are usually called Waxy Crude Oils (WCO’s). One of the most important problem occurring in WCO’s, for low temperatures, is the formation of paraffin deposits on pipeline walls. This is a very complex mechanism for which many models have been proposed ([1], [2], [3] [4], [5], [6]). On the basis of available experimental results we propose here a physical-mathematical isothermal model for the deposition of paraffin on the walls of a cylindrical circular pipe of radius R,like the ones used in experimental laboratory, usually called loops.

The resolution of ground-based telescopes will be improved by means of Adaptive Optics (AO), a new technology which can compensate for the effects of atmospheric turbulence. As a consequence several large and innovative telescopes are in an advanced phase of design or construction. A very interesting example is provided by the Large Binocular Telescope (LBT) which will be available in a few years. In this paper we discuss a few restoration problems related to the processing of the images of LBT.

The Digital Still Camera is a very challenging application for Image Processing techniques.

This work contains a brief overview of the researches carried on by the authors on multiwavelet theory and applications. In particular, the effectiveness of multiwavelet techniques in image processing is shown and some evolutions of the theory are mentioned.

A lot of experiences have proved that multimedia and telematics offer new learning opportunities; methodologies for their use in education and training have been developed and tested with very interesting results in different contexts, from primary schools to university and post graduated training. But, even though the advantages of hypermedia and telematics for learning are acknowledged there is a need to bridge the gap between research and the concrete practice of educational technology. The aim of this paper is to analyse the factors making effective the use of ICT in concrete educational contexts.

In recent years, the label agent, used to specify from simple system process to highly expert software/hardware collections, denoting an entity created to perform either a specific task or set of tasks, has been included in the context of Artificial Intelligence. This trend takes place also in educational domain where agents are called Pedagogical Agents. By means of Pedagogical Agents teachers can create a new generation of learning environment: agents can display complex tasks, make use of locomotion and gesture to direct students’ attention on the most salient aspect of the task at hand, and convey emotional responses to the educational situation. The Visual Agent Scripting Helper (VASH) allows teachers to create multimedia projects in which it is possible to use pedagogical agents and to organise the agent’s behaviour in performing a specific educational task. Advanced educational contents will become commonplace only when the effort required to author them is reduced. Therefore authoring support is an essential component of VASH system which is an authoring tool and an interface for defining pedagogical agent behaviour. We should like to propose a conceptual framework in which the design and implementation of life-like pedagogical characters can be grounded. The system has been designed through a visual language interface that permits to script the agent behaviour, by dragging and dropping icons in the timeline of the multimedia sequence.

Is it possible to obtain pleasant evolved music by means of a fitness function, without human intervention? In this work a method based on a genetic algorithm to produce automatic music is presented. In particular we developed a fitness function based on consonance, which allows to evaluate the “pleasantness” of a sequence of notes generated by an algorithm. The fitness function has then been used within genetic algorithms to help the resulting melodies evolve. This function has been used with cellular automata. An initial sequence will allowed to evolve within a space-time pattern and then turned into music as is suitable. The use of the Fitness function permits the search for and the choosing of appropriate rules, which generate pleasant melodic sequences. The best results are obtained for CA whose state varies between 0 and 3 and for small lattice.

Some important features required for an effective use of the Internet in education are still missing from the Web. The main limits concern the lack of efficient support to navigation, the basic state-less http protocol, the author-centered approach to information content and structure. As a consequence, the Web does not support effective user interaction with information, which plays a key-role in learning process. However, it is still possible to develop Web-based architectures that can overcome these limits, thus increasing effective user interaction with the information. In this paper, the author reports on a specific web-based instruction system that provides for effective interaction mechanisms.

Document clustering based on semantics is a fundamental method of helping the users to search and browse in large repositories of documents. A lot of work has been done in this field and recently some papers have reported the applications of self organizing artificial neural networks in document clustering based on semantics. Using an opportune document representation these techniques can order the document space and generate useful tools to support browsing. In this paper an overview of the work in this field is presented and the obtained results are commented on.

We present results, for binary gas mixtures, for the construction of physically acceptable large size planar Discrete Velocity Models (DVMs) including a particle at rest and momenta different, filling all integer coordinates of the plane. We want, with binary collisions, 5 conservation laws (4 for the restriction along one axis): 1 for the light mass (m = 1) species, 1 for the heavy (M > 1), 2 for the momenta along the x, y axes and 1 for the energy. We start with a preliminary simple physical model and add, with geometrical tools, new momenta. We recall previous results and present a new one with M = 3/2.

In this paper we consider two models derived from the semiconductor Boltzmann equation by using the spherical harmonic expansion method. The first model contains only two terms of the expansion, the second also the third term. We look for space-homogeneous solutions to two Cauchy problems. Numerical results are found using a simple difference scheme and a comparison between the two models is shown.

Two models describing charge transport in semiconductors are considered. The first is the Boltzmann transport equation for an electron gas. The other is derived from the previous. It consists of a set of equations, which are equivalent to those obtained from the Boltzmann equation by using the spherical-harmonics expansion of the distribution function. Time-depending solutions of the both models are numerically found and compared.

In this paper we consider an extended hydrodynamical-like model describing the transport of electric charges in semiconductors. We start from the Boltzmann transport equation (BTE) and use the method of moments and the Maximum Entropy Principle (MEP) in the framework of Extended Thermodynamics. We apply this model to silicon semiconductors, for which we also test the accuracy of the closure relations by means of a comparison with Monte Carlo results.

Monte Carlo simulations are used to check the consistency of an Extended Hydrodynamic model describing charge transport in bulk silicon.

A quantum model for electron transport in split-gate devices is solved. The model consists in a quasi 3-dimensional Schrödinger system for electron motion coupled to a three dimensional Poisson equation accounting for space charge effects. The coupled system is discretized thanks to finite element method and the coupling between the Poisson solver and the Schrödinger solver is treated implicitly. We present numerical results in a stub configuration at zero applied bias. The numerical results exhibit tunneling effect which cannot be obtained with Thomas-Fermi simulation.

A first-order model of electron transport in silicon dioxide has been worked out in the frame of the spherical-harmonics expansion (SHE) method applied to the solution of the Boltzmann transport equation (BTE). The scattering rates for each collision process have been analyzed and a number of transport properties of electrons in bulk SiO₂ have been worked out. Moreover, a new model has been introduced into the SHE code to calculate the microscopic fluxes at the silicon interface, based on the thermionic emission theory. The information given by the high-energy tail of the distribution function above the energy barrier at the interface and within the SiO₂ allows to accurately analyze the electron injection into the gate oxide.

A numerical simulation of a horizontal Bridgman solidification process of a pure material in microgravity conditions is presented. The mathematical model here adopted describes the flow of the liquid phase, the heat transport phenomena within the whole sample and the evolution of the phase front. The stream-function/vorticity formulation of the liquid flow and the front-fixing treatment of the moving boundary are used. The numerical approximation is based upon a second order ENO (Essentially Non-Oscillatory) scheme combined with a second order time scheme. The validation of the mathematical and numerical model is provided in full gravity conditions versus physical experimental observations.

A computational model using finite volume approximations for studying phase change of a binary alloy is presented. Numerical results concern the prediction of the convective response to a small solutal perturbation localized near the solid/liquid interface in a rectangular domain.

This Paper presents numerical investigation of the 2-D and 3-D cylindrical convective flow developing in the liquid phase during upward Bridgman solidification of a binary alloy. The onset threshold of unsteadiness as function of confinement is identified. The striations induced in the crystal when the flow becomes unsteady are characterized. Calculations for Pb − 30%Tl alloy at various steady and unsteady regimes are compared to finite volume results.

The numerical features of the computer codes CrysVUn and STHAMAS which were developed at the Crystal Growth Laboratory in Erlangen/Germany, are presented. The results for the global simulation of a VCZ-GaAs furnace are shown. Special emphasis is put on optimization problems. Calculations for an optimized annealing process are briefly described.

A numerical procedure to optimize a thermo-electrical flange is proposed. These flanges are used in glass industry to heat pipes carrying hot glass melts. The objective is to reduce thermal gradients inside the flange and match a desired temperature. The optimization is based on an asymptotic analysis for dimension reduction and a variational approach for the solution of an inverse thickness identification. Using the results of such a two-dimensional optimization, numerical experiments for the real three-dimensional case are discussed.

A typical stage in the manufacturing of container glass, such as bottles and jars, is the pressing phase. At this stage a gob of hot glass (1000 C or higher) is pressed in a mechanical construction by a so called plunger. This paper describes an important part of the simulation, the motion of the plunger. The problem is to determine the velocity of the latter which appears as a (kinematic) boundary condition of the glass flow problem. We show how to effectively uncouple these and to solve the resulting stiff differential equation numerically.

The currently used TCAD transport modelling tools for semiconductor device simulation are reviewed, with particular emphasis on the performance and reliability issues relating to CMOS and non volatile memory devices. The different methods for approximating the solution of the Boltzmann transport equation (BTE) are compared, and their suitability for the high energy transport regime simulation is analyzed. Examples of the application of device simulations to the study the hot carrier reliability of CMOS transistors and charge carriers injection in non-volatile memory cell programming cycles are shown. The importance of proper definition and adaptation of the discretization grid is pointed out, and the implications of quantum effects in state-of-the-art deep submicron devices are discussed.

An energy-transport model for the charge carrier transport in a silicon semiconductor is presented. The model has been derived in [1] starting from the hydrodynamical one obtained by employing the maximum entropy principle upon the assumption that the energy bands are described by the Kane dispersion relation. An application to a benchmark problem is shown.

Neural Networks (NN) are potential alternative to semiconductor modeling for circuit simulation, in situations where physical modeling becomes critical. To cope with the complex behavior of a state-of-the-art bipolar device, a particular NN architecture has been developed, referred here as Higher-Level, where the main neurons are instances of differential equations, and other neurons are responsible for the coefficients of such equations. Unfortunately this type of neural architecture is difficult to train and even the most sophisticate methods often fail to converge to an acceptable error. The strategy here presented essentially reduces the problem of training the higher-level NN to model the bipolar device in all its working conditions, to the training of simpler auxiliary networks, each working at a single DC bias point.

Multirate methods in the simulation of coupled systems adapt the numerical effort to the activity level of the respective subsystems. Here, two different approaches will be presented: one based on operator splitting and a second using the concept of generalised multirated. For both the inverter-chain-benchmark serves as a test set, which will confirm the potential of multirate methods.

A novel time-domain method for finding the periodic steady-state of a free-running electrical oscillator is introduced. The method is based on the extrapolation technique MPE. This method is applied to the well-known Colpitt’s Oscillator, for which it turns out to have super-linear convergence.

An overview is given of iterative techniques for the solution of linear systems which occur during the simulation of electronic circuits. In developing a suitable method, several characteristics of electronic circuits have been used. The ordering of the unknowns is based on the observation that two types exist, namely currents and voltages. Furthermore, the linear systems are of a hierarchical structure which is quite different from what is found in discretized partial differential equations. Methods have been developed which make use of the aforementioned characteristics, and which are very suitable for the solution of large linear systems.

We investigate wave types which occur in the stable regime of a car-following model of road traffic based on a relaxation term. Numerical results show that several types of transitions from an upstream to a downstream headway exist, e.g. monotonic, oscillatory and dispersive. Moreover for specific upstream headways there is a travelling wave of maximum speed that is different from the theoretical maximum speed being deduced from the fundamental diagram. This wave occurs together with a second shock wave of different speed matching the downstream headway and a growing region of congested traffic in between. The different transitions are classified in a phase diagram whose structure depends on the sensitivity parameter of the model. It shows that the waves of maximum speed are analogous to jam fronts in the unstable regime. The qualitative behaviour of an autocade of different vehicles can be better understood with these phase diagrams.

A review of an empirical study of traffic phases and phase transitions in traffic flow is presented. A critical comparison of model results and results of traffic theories with of real features of traffic phase is given. A qualitative theory of congested traffic flow recently developed is discussed.

We consider the car-following model introduced by P.G. Gipps (1981). This model is of practical importance as it powers the UK Transport Research Laboratory highway simulation package SISTM. Firstly, a brief derivation of the model is given in simplified circumstances. Second, we show how uniform flow solutions and a speed-headway function may be derived. Finally, we consider the linear stability of uniform flow solutions. Conditions for stability and onset of instability are derived.

An asymptotic method to determine the air-flow around slender fibers in the case of low Reynolds numbers is presented. Based on the equations for linearized flow, the force acting on a fiber is approximated as the superposition of fundamental solutions. Matching asymptotic expansions valid in different regions of the flow field leads to an integral equation model for the force. The resulting non-standard, strongly singular Fredholm integral equation of the second kind is analyzed theoretically and solved numerically. The application of this model to an industrial melt-spinning process for artificial fibers is discussed.

Motivated by study of fibre dynamics in the carding machine, a textiles manufacturing process, we derive a continuum model for a medium composed of entangled fibres. Extensional and shearing simulations produce promising comparisons with experimental results.

A brief review is given of shock capturing central schemes for the numerical solution of hyperbolic systems of balance laws. It is shown how to construct high order schemes for conservation laws on a staggered mesh, by using Central Weighted Essentially Non-Oscillatory reconstruction, and how to construct second order central schemes for systems with stiff source which are accurate in the stiff limit. The development of higher order schemes for systems with stiff source is also discussed.

We suggest to augment second-order, nonoscillatory, central difference schemes with Harten’s artificial compression method (ACM) to sharpen the resolution of linear fields. ACM employs a partial characteristic decomposition to single out the linear fields, for which a steeper reconstruction is applied. The remarkable power of this technique is demonstrated for three test problems for the Euler equations from gas dynamics, and its dangers are pointed out.

In this note we describe a novel approach to the numerical solution of the Fokker-Planck-Landau equation in the non-homogeneous case. The method couples, through a time splitting algorithm, a finite volume scheme for the transport with a fast spectral solver for the efficient solution of the collision operator.

Various problems arising throughout engineering and applied sciences involve multiscale in space or time. Classical examples include the transport equations, such as the neutron transport and the radiative transfer, gas dynamics far from thermo or chemical equilibrium, fluid flows at different Reynolds number. Moreover, in many physical applications, the scaling parameter, i.e., the mean free path in kinetic theory, may differ in several order of magnitude from the rarefied regime to the hydrodynamic (or diffusive) regime within the same problem. In this work we are interested in numerical techniques for solving kinetic equations in the diffusive regimes (although the approach considered here is applicable to many physical problems of greater complexity). We will illustrate these basic techniques by means of a few simple models when the limit state is described by a general reaction-diffusion system. Some applications are presented including porous media equation, Fisher’s equation and ion diffusion.

In [SIAM Rev., 40 (1998) 616–635], we emphasized the relevance of a combination of similarity and numerical analysis for the numerical solution of moving boundary hyperbolic problems. Here we report on results obtained for one problem of the above class that is singular at the moving boundary.

We present some results regarding the propagation of an electron in a dynamical heat bath of phonons. Starting with the Landau—Von Neumann equation we derive in the weak coupling limit a quantum kinetic equation for the electronic Wigner function, and study stationary fixed points. An attempt is made to understand the regime where interference effects may set in, and provide a measurable footprint of quantum transport.

In this work a rigorous variational formulation of the time evolution of a quantum electron in an ionic crystal with dynamical classical ions (mean field polaron) is presented. Crystal polarization is described by a classical polarization field which may be reexpressed in terms of a self-consistent potential. We specifically study the mathematical consequences of non-locality in time (finite retardation effects) as well as non-locality in space (finite crystal lattice size), and in particular their existence, uniqueness and stability properties around a non-trivial solution.

Pinning and propagation phenomena in discrete drift-diffusion systems for photoexcited weakly coupled semiconductor superlattices under a constant current bias are studied. Depending on the parameters involved, different regimes arise in which either stationary wavefronts or waves moving to the right or the left are found.

Nonlinear electronic transport in weakly coupled superlattices results in formation of electric field domains, self-sustained current oscillations (periodic, quasiperiodic or chaotic), wave propagation and other interesting phenomena. These are explained here by means of a discrete self-consistent model including quantum mechanically calculated tunneling current, detailed electrostatics and appropiate boundary conditions. Simpler discrete drift-diffusion models (for which analytical results are known) are also derived from our model.

Certain equations with integral constraints have as solutions time-periodic recycling of pulses of a field-like unknown at boundaries while a current-like unknown oscillates periodically with time. A general asymptotic theory of this phenomenon, the generalized Gunn effect, has been recently found. Here we extend this theory to the case of nonlinearities having only one stable zero, which is the case for the usual Gunn effect in n-GaAs where the velocity-field characteristics has a local maximum after which the velocity decreases to a constant for large fields. The key of our theory is that we characterize the forefront and backfront of a given expanding or contracting pulse as certain trajectories in a phase plane and identify their velocities. Our ideas are presented in the context of a simple scalar model where the waves can be constructed analytically and explicit expressions for asymptotic approximations can be found.

This paper is devoted to the numerical simulation of nonisothermal crystallization of polymers, which may be modelled as a stochastic birth-and-growth process, coupled with the evolution equation of the temperature. One of the main aims for industrial applications is to develop efficient algorithms for the stochastic simulation of such processes.

This paper deals with to the modelling and simulation of the crystallization of polymers in an heterogeneous temperature field. Under realistic parameter ranges, of industrial interest, we face a multiple scale phenomenon since the temperature evolution occurs at a faster time scale with respect to the birth-and-growth process of crystallization. We propose a spatially structured stochastic bith-and-growth model for the crystallization process whose kinetics parameters depend locally upon the temperature field, and nonlocally upon the spatial distribution of the crystalline phase. For a large number of crystals the system can be shown to converge to a classical continuum deterministic model. We report here the results of the numerical simulation of the many particle system, and of the corresponding continuum model.

The problem of a single drop immersed in a flowing immiscible fluid is here investigated for second-order fluids, hence including the effects of constitutive elasticity. A perturbative approach is outlined, that leads to the complete analytic solution for small deformations of the drop, up to second order in the imposed flow rate. Validation of the theory through experiments determining the drop shape under flow is also discussed. Results in steady shear, obtained through video microscopy and image analysis, show marked deviations from the Newtonian case when an elastic suspending fluid is used, in agreement with the theoretical predictions.

Polymer melts usually have relaxation times in a broad frequency range. To capture the full rheological behaviour, multiple rheometers are used. Due to the different modes of operation, combination of the data into a single rheological function often involves solving one or more inverse, ill-posed problems. Here, as an alternative approach, a new approximate direct analytical method is presented that allows the broadening of oscillatory shear data obtained from dynamic mechanical spectrometers, to low frequencies by using converted constant stress compliance data. The accuracy of the broadened curves depends on the experimental accuracy and the specific time scales of the polymer and the rheometers. The method is most effective when used in combination with inverse problem solvers. By doing so, translucence, insight, and directness from the analytic method is added to the potential accuracy of the full inverse problem solver.

In this report a short overview is given of the instabilities that may occur during extrusion of a polymer. For the so—called spurt phenomenon a model is discussed that makes use of the JSO constitutive equation. It is shown that this model lead to a differential-algebraic-integral equation. The structure of the the equations is sketched in terms of time scales. For the stability analysis a new method is proposed that is based on discretization of the integral equation. This approximation reduces the model to a set of (singularly perturbed) ODEs, which can be analysed with standard methods.

The temperature distribution of a polymer melt, injected between two, cooled, plates is calculated. For this, the two-dimensional region occupied by the melt is divided into a part (G _I ) far behind the flow front and a part (G _II ) near the flow front. The melt is modelled as a Newtonian fluid. The temperature is governed by a diffusion-convection equation with appropriate boundary conditions. Asymptotic expansions, based on the small value of the dimensionless thermal conductivity are used. Both in G _I and G _II , boundary layers exist near the cooled walls.

The 3D-Navier-Stokes Equations (3D-NSE) describe the flow of fluids. Due to advanced numerical techniques and increased computer capacities, numerical solutions are available for many applications, but require expensive computations. In river hydraulics the Shallow Water Equations (SWE) are applied successfully to model the flow of water. They are derived from 3D-NSE via depth integration under the assumption that the vertical velocity components are negligible.Calculations for the flow of water in urban areas show differences between 3D-NSE and SWE. In particular when water is pressing out of a manhole or is flowing against or over a curb, vertical velocity components are not negligible.To give reliable forecasts for flood risks in urban areas with reduced computational efforts, SWE need to be modified appropriately.

For the simulation of water flow in rivers presently a network approach is applied. This approach is based on coupled ld models and should be extended to 2d submodel elements. Special difficulties arise due to the free boundaries caused by the wetting and drying and the source terms accounting for the sloping river bed and friction.A first order Roe scheme is adapted to these difficulties and is presented for a robust numerical solution method.

In the lattice Boltzmann method (LBM), macroscopic flow behavior is described by simulating a very simple, fully discrete, microscopic gas model instead of discretizing the flow equations directly. Based on the frequently used D2Q9 model (nine discrete velocities in two space dimensions), we show how surface tension effects can be combined with LBM. The applicability of the two-phase lattice Boltzmann method is demonstrated with simulations of filtration processes.

Mathematical modelling should be lectured with a strong emphasis on generic modelling principles and primary mathematical analysis of the models.

We are interested in effective methods to train a student of mathematics who is heading towards a job in industry. We first collect some key abilities a mathematician in industry should have from our point of view. Then we discuss how traditional education may cover these needs and describe the concept of Modelling Seminars as a suggestion of an additional part of the education which serves as a simulation of the whole process of problem solving. After presenting two actual examples from our Modelling Seminar we close with a short list of future plans.