Progress in Industrial Mathematics at ECMI 2006

It has been a great honour for me to deliver the “Alan Tayler Lecture” in this ECMI Conference, to honour one of the leading founders and Presidents of ECMI. I have collaborated with Alan for many years, especially during my term as Chairman of the Educational Committee, and later during the first ECMI-HCM Project. While he was already very ill, he found the way to participate (even though only for a couple of days) in a workshop in Milan, opening ECMI to the Italian academic and industrial community, and highly supported the birth of MIRIAM (the Milan Research Centre for Industrial and Applied Mathematics).

The use of electrohydrodynamic (EHD) forces to generate highly charged coaxial jets of immiscible fluids, with diameters in the micro and nanoregime, has unravel itself as a quite interesting choice for producing complex nanostructures from a vast variety of precursors, provided they can solidify, polymerize or gel, in times comparable or shorter than the living time of the coaxial nanojet. For time ratios larger than one, the result of the process are micro or nanocapsules, while for time ratios smaller than one coaxial nanofibres are produced. We show examples of both situations, with organic and inorganic precursors. On the other hand, realization of the process in a liquid bath opens the door to production of controlled micro and nanosized complex emulsions.

This paper deals with mathematical modelling and numerical simulation of induction heating furnaces for axisymmetric geometries. The mathematical model presented consists in a coupled thermo-magneto-hydrodynamic problem with phase change. We propose a finite element method and an iterative algorithm to solve the equations. Some numerical results for an industrial furnace used for silicon purification are shown.

Epitaxy is the growth of a thin film by attachment to an existing substrate in which the crystalline properties of the film are determined by those of the substrate. In heteroepitaxy, the substrate and film are of different materials, and the resulting mismatch between lattice constants can introduce stress into the system. We have developed an island dynamics model for epitaxial growth that is solved using a level set method. This model uses both atomistic and continuum scaling, since it includes island boundaries that are of atomistic height, but describes these boundaries as smooth curves. The strain in the system is computed using an atomistic strain model that is solved using an algebraic multigrid method and an artificial boundary condition. Using the growth model together with the strain model, we simulate pattern formation on an epitaxial surface.

The subject of waves in fluids is addressed from three complementary points-of-view: (Sect. 2) 60 mathematical forms of the acoustic wave equation in fluids, applying to linear and non-linear, non-dissipative and dissipative, sound waves in homogeneous or inhomogeneous, steady or unsteady media, at rest or in motion, e.g. potential and vortical flows; (Sect. 3) the physical interactions between (i) sound waves due to pressure fluctuations in a compressible fluid, with (ii) magnetic waves in an ionized fluid under external magnetic fields, (iii) internal waves in a stratified fluid under gravity and (iv) inertial waves due to Coriolis forces on a rotating fluid, viz. magneto-acoustic-gravity-inertial waves; (Sect. 4) some engineering problems in the area of aerocoustics, which has applications to aircraft, helicopters, rockets and other aerospace vehicles, including acoustic fatigue, sonic boom, interior noise and airport noise, concentrating on the last aspect.

In this chapter, we review the recent theory of quantum diffusion models derived from the entropy minimization principle. These models are obtained by taking the moments of a collisional Wigner equation and closing the resulting system of equations by a quantum equilibrium. Such an equilibrium is defined as a minimizer of the quantum entropy subject to local constraints of given moments. We provide a framework to develop this minimization approach. The results of numerical simulations show that these models capture well the various features of quantum transport.

Here the theory of size functions is introduced and joined to some statistical techniques in order to build confidence regions for a family of random shapes. An algorithm for the computation of the discrete counterpart of the size functions is also introduced. The method is applied to the quality control of shapes impressed with a laser on a silicon wafer, in microelectronics. The robustness of the size functions in the description of random shapes has led to good experimental results, and thus to the possibility of enclosing this method into an automatic procedure for the quality control of electronic devices.

Delaying laminar-turbulent transition in boundary layers attached to commercial aircrafts has a significant impact in drag reduction, which in turn contributes to reducing both fuel consumption and environmental impact. This is a classical subtle problem in Fluid Mechanics that has received a continued attention during the last decades from both the experimental and the theoretical points of view, and involves some fascinating open problems in Applied Mathematics. The flavour of current European efforts in this direction can be appreciated in the various contributions below, which have been selected to illustrate the multidisciplinary character of this field.

This paper is concerned with a fascinating phenomenon in boundary layer transition, namely, three-dimensional disturbances undergo rapid amplification despite that they have smaller linear growth rates than two-dimensional ones. Physical mechanisms are sought by considering two types of nonlinear interactions between oblique and planar instability modes. The first is the well-known subharmonic resonance. The relevant mathematical theory and its main predictions are briefly summarised. This mechanism, however, operates only among a very restrictive set of modes, and hence is unable to explain the broadband nature of the amplifying disturbances observed in experiments. The second mechanism involves the interaction between a planar and a pair of oblique Tollmien—Schlichting (T—S) waves which are phase-locked in that they travel with (nearly) the same phase speed. It is a more general type of interaction than subharmonic resonance since no further restriction is imposed on the frequencies. Yet similar to subharmonic resonance, this interaction also leads to super-exponential growth of the oblique modes, while the planar mode remains to follow linear stability theory. The dominant planar mode therefore plays the role of a catalyst, the implications of which for the e

N

-method and for transition control are discussed.

Decreasing skin friction in boundary layers attached to aircraft wings can have an impact in both fuel consumption and pollutant production, which are becoming crucial to reduce operation costs and meet environmental regulations, respectively. Skin friction in turbulent boundary layers is about ten times that of laminar boundary layers. Thus, an obvious method to reduce friction drag is to delay transition to turbulence, which is a fairly involved process in real aircraft wings [J98]. Transition sis promoted either by

Tollmien—Schlichting

(TS) and

Klebanov

(K) modes [K94], with the former playing an essential role. Various methods (e.g., suction [SG00,ZLB04], wave cancellation [WAA01,LG06]) have been proposed to reduce TS modes in laminar boundary layers. Mode interaction methods have been successfully used in fluid systems to control related instabilities, such as the Rayleigh—Taylor instability [LMV01]. Here, we present some recent results on using these methods to control TS modes in a compressible, 2D boundary layer over a flat plate at zero incidence. A given unstable TS mode can be stabilized by coupling its spatial evolution with that of a second selected stable TS mode, in such a way that the stable mode takes energy from the unstable one and gives a stable coupled evolution of both modes. The coupling device is a wavetrain in the boundary layer, with appropriate wavenumber and frequency, which can be created by an array of oscillators on the wall, and promotes both (i) parametric coupling between the stable and unstable TS modes and (ii) a mean flow that is also stabilizing. Three differences with wave cancelation methods are relevant. Namely, (a) nonlinear terms play an essential role in the process; (b) the unstable TS mode is stabilized (its growth rate is decreased), not just canceled; and (c) stabilization does not depend on the phase of the incoming wave, which implies that active control is not necessary.

This contribution is about an unforeseen connection that arose while studying three seemingly unrelated research problems. For this reason I thought it appropriate to be presented at a meeting on the applications of mathematics to industry. I will follow the outline of the oral presentation and expose the three stories first, to later comment about their connection.

It has been known for some time that an appropriately designed compliant wall (artificial dolphin skin) is highly effective for laminar flow control in low-disturbance environments. Unfortunately, compliant walls are not really practical for aeronautical applications. Accordingly, we focus here on marine applications. The marine environment tends to have much higher levels of freestream turbulence than found in flight conditions typical of cruise. Herein, we explore the effects of freestream turbulence on laminar—turbulent transition. In particular, we investigate the velocity streaks generated in the boundary layer by freestream turbulence. Furthermore, we carry out a numerical-simulation study of the effects of wall compliance on the velocity streaks. We find that boundary layers over compliant walls are much less receptive to streaks than those over a rigid surface. This implies that compliant walls should be effective at laminar flow control even in environments with relatively high levels of freestream turbulence.

Linear stability theory is concerned with the evolution of small-amplitude disturbances superimposed upon a steady- or time-periodic so-called basic flow. The vast majority of investigations during the second half of the last century has dealt with the analysis of one-dimensional (“parallel”) basic flows. On the other hand,

Global flow instability

deals with essentially non-parallel (as well as with weakly non-parallel) flows [1] and is an emerging and highly active area of research, to which a Minisymposium has been dedicated. Four invited contributions from three countries were presented, one summarizing experimental work and the rest presenting alternative numerical methodologies to solve the large eigenvalue problem resulting in the context of BiGlobal instability analysis. Applications addressed ranged from laminar and turbulent separation control (Avi Seifert, Tel-Aviv University), vortex instabilities (Michael Broadhurst, Imperial College London), and cavity flow hydrodynamic (Leo González, School of Naval Engineering, UP Madrid) and aeroacoustic (Javier de Vicente, School of Aeronautics, UP Madrid) instabilities. With the exception of the first author, whose contribution is outlined below, papers were submitted describing in detail the contents of the talks delivered.

A particular feature of swirling flows with a strong core vorticity is the phenomenon of vortex breakdown. For vortices with an appreciable axial velocity component, [Hall (1972)] defines vortex breakdown as, “an abrupt change in the “vortex” structure with a very pronounced retardation of the flow along the axis”. One factor that is known to influence vortex breakdown, reviewed by [Leibovich (1984)], is the role of instability. This was also recognised by [Ash and Khorrami (1995)], who describe a possible mechanism of breakdown as, ‘a final outcome of vortex instability, with the caveat that vortex breakdown can also be produced by external means’. External influences might include pressure gradients. Consequently, the aim of the current research is to demonstrate the relationship between instability and spiral-type breakdown of a Batchelor vortex, and to assess the influence of pressure gradients on vortex stability using the parabolised stability equations.

Viscous linear three-dimensional BiGlobal instability analyses of incompressible flows have been performed using finite-element numerical methods, with a view to extend the scope of application of this analysis methodology to flows over complex geometries.

A novel approach for the solution of the viscous incompresible and/or compressible BiGlobal eigenvalue problems (EVP) in complex open cavity domains is discussed. The algorithm is based on spectral multidomain spatial discretization, decomposing space into rectangular subdomains which are resolved by spectral collocation based on Chebyshev polynomials. The eigenvalue problem is solved by Krylov subspace iteration. Here particular emphasis is placed on aspects of the parallel developments that have been necessary, on account of the high computing demands placed on the solver, as ever more complex “

T-store

” configurations are addressed.

The ordinary day to day operation of current aircraft turbomachines involves geometrically highly complex parts (bladed disks and vanes) working under extreme mechanical and thermal conditions. The mathematical modeling of these systems typically requires a compressible unsteady aerodynamic description of the fluid flow coupled to linear and nonlinear elastic models for the solid structure. The idea of this minisymposium is to give some insight into various interesting problems of industrial relevance associated with the modeling and analysis of the dynamics and vibration of Turbomachinery structures. The chapter by Berthillier et al. deals with a central problem in Turbomachinery vibration: the problem of blade mistuning. Bladed disks are cyclic structures in which a sector is repeated many times but, because of small unavoidable imperfections (mistuning), all sectors are not identical and these small sectorto-sector variations can give rise to very dangerous localized amplifications of the vibration response that result in a severe increase of blade fatigue. On the other hand, the chapter by Petrov presents some recent advances in the numerical study of structures with friction contact interfaces, which give rise to nonlinear elastic models for the vibration of the structure that can exhibit multiplicity of solutions, hysteresis, sub and superharmonic resonances, etc. And, finally, the last chapter by Corral and Gallardo describes a methodology for the estimation of the vibration levels for aerodynamically unstable Low-Pressure Rotor blades, where the saturation of the vibration amplitude results from the friction at the fir-tree attachment.

For cyclic structures with aeroelastic coupling, coriolis, and other rotational effects, the different eigen modes are traveling modes with constant interblade phase angle. However, because of small imperfections, as manufacturing tolerances, bladed discs are only quasi-cyclic structures. As a consequence, the dynamic behavior of actual bladed discs may be tremendously modified compared to their cyclic idealization. These small imperfections are called detuning or mistuning depending if they are or not deliberate. The eigen values are usually slightly affected, but the modes shapes could become localized. The vibrating energy is no more distributed along all the blades, but confined to a limited number of blades. From an industrial point of view, the effects of localization could be positive or negative. For example, in aeroelasticity, unstable rotors could be stabilized by the introduction of a judicious detuning pattern. In contrary, mistuning can greatly increase the forced response level, usually when localization occurs.

A methodology for the prediction of the vibration levels of welded-inpairs low-pressure-turbine rotors is presented. It combines three-dimensional viscous linear aerodynamic analyses with a simple friction model for the fir-tree attachment. Results are presented for an existing rotor and compared with experimental data.

Vast majority of machinery structures are assembled structures: they consist of two or, usually, more components assembled together and these joined components interact with each other at friction contact interfaces. The forces acting at friction contact interfaces are generally strongly nonlinear. Among many sources of the nonlinearity of the interaction are (1) unilateral contact of interaction along directions normal to contact surfaces, when compression normal stresses can act at these surfaces but tension stresses are not allowed; (2) variation of contact areas during loading, including closing and opening clearances and interferences resulting in contact—separation transitions over a whole interface surface or over its some parts; (3) friction forces with their magnitude and stick—slip transitions affected by contact—separation and normal stress variation. In this chapter recent developments in modeling and numerical analysis of nonlinear vibration of structures with friction interfaces are discussed.

In this minisymposium, Gabriella Puppo (Politecnico di Torino) and Giovanni Russo (U. Catania) present “Central Runge-Kutta schemes for stiff balance laws,” Susana Serna (UCLA) presents “Flow calculations using shock capturing schemes based on Power limiters,” and Fausto Cavalli, Giovanni Naldi, Matteo Semplice (U. Milano) and Gabriella Puppo (Politecnico di Torino) present “A comparison between relaxation and Kurganov—Tadmor schemes.”

In this work, we propose a new family of high order finite volume methods for stiff balance laws. These methods are characterized by an explicit integration of the nonlinear convective terms, while the possibly stiff source is computed implicitly with a novel approach that avoids cell coupling. For this reason, the methods enjoy a favorable stability restriction, without requiring the solution of large nonlinear systems of equations.

In this research work we address the issue of the use of slope limiters to design high order reconstruction procedures when combined with shock capturing schemes for the approximation of hyperbolic conservation laws.

In this work we compare two semidiscrete schemes for the solution of hyperbolic conservation laws, namely the relaxation [JX95] and the Kurganov Tadmor central scheme [KT00]. We are particularly interested in their behavior under small time steps, in view of future applications to convection diffusion problems. The schemes are tested on two benchmark problems, with one space variable.

In this minisymposium, Christoph Lunk, Bernd Simeon (TUMünchen) present “The Reverse Method of Lines in Flexible Multibody Dynamics,” J. Linn, T. Stephan (Fraunhofer ITWM, Kaiserslautern), J. Carlsson, and R. Bohlin (Fraunhofer—Chalmers Research Center FCC, Gö;teborg) present “Fast simulation of quasistatic rod deformations for VR applications,” and Michael Speckert and Klaus Dreßler (Fraunhofer ITWM, Kaiserslautern) present “Simulation and optimization of suspension testing systems.”

Adaptivity is a crucial prerequisite for efficient and reliable simulations. In multibody dynamics, adaptive time integration methods are standard today, but the treatment of elastic bodies is still based on an a priori fixed spatial discretization. This contribution introduces a basic algorithm in the fashion of the reverse method of lines that is able to adapt both the spatial grid and the time step size from step to step. The example of a catenary with a moving pantograph head illustrates the approach.

We present a model of flexible rods — based on

Kirchhoff's

geometrically exact theory — which is suitable for the fast simulation of quasistatic deformations within VR or functional DMU applications. Unlike simple models of

“mass & spring”

type typically used in VR applications, our model provides a proper

coupling of bending and torsion

. The computational approach comprises a

variational formulation

combined with a

finite difference discretization

of the continuum model. Approximate solutions of the equilibrium equations for sequentially varying boundary conditions are obtained by means of

energy minimization

using a nonlinear CG method. The computational performance of our model proves to be sufficient for the interactive manipulation of flexible cables in assembly simulation.

In automotive industry complex multi channel servo-hydraulic test rigs are used for physical testing of suspensions. Typically, wheel forces measured on a test track (target loads) are to be reproduced on the test rig. Most of the traditional rigs use one hydraulic actuator for one DOF, i.e. an actuator for the vertical force, one for the longitudinal force, etc. In [Wie02], a new concept for suspension test rigs based on the hexapod technology has been proposed. (see Fig. 2 in Sect. 3). Here six actuators are driving a platform (parallel kinematics) which is attached to the wheel hub.

The first presentation in this minisymposium

Optimal Station Keeping for Geostationary Satellites with Electric Propulsion Systems Under Eclipse Constraints

by P. Romero discusses the possible implementation of an optimal strategy to satisfy the constraints imposed by the occurrence of eclipses on the geostationary orbit. The second presentation by M. Folgueira and coworkers, the

International Reference Systems for Astrodynamics and Space Geodesy

, discusses different Earth rotation models in the proposal recently adopted by the IAU and IUGG. Finally, the new post-Newtonian covariant measurement formulations for SLR, SST and GPS and their possible implementation are discussed by J.M. Gambi and coworkers in the third presentation.

In order to keep geostationary satellites within the prescribed boundaries to satisfy mission requirements, orbital station keeping manoeuvres are performed periodically to compensate natural perturbations on the satellites.

The propulsion systems currently used to modify the orbit are of chemical nature (usually, hydrazine) but new trends in spatial propulsion point towards the use of electric systems. The use of these systems introduces new problems such as the impossibility to perform manoeuvres at eclipse epochs.

A procedure is proposed here to analyze the implementation of optimal strategies in terms of electric energy consumption to satisfy the additional constraints imposed by the use of these kind of systems.

The fields of Astrodynamics and Space Geodesy research are experiencing continuous growth. Advancements in science and technology are enabling missions with much more challenging goals. In response, many new techniques have been introduced to solve these demanding new mission design problems with a high precision.

Most spatial current high precision geodetic techniques, like those used in the Global Positioning System, have led to widely consider the assumption of a slightly curved space-time in the vicinity of the Earth (according to the general theory of relativity) as the essential basis to build geometric models for measurements formulations that allow correct interpretations of the results, at least up to the level of accuracy required at the present and near-future time. In this contribution, Synge's world function for the local geometric models associated to a global model of that space-time is used to give a flexible and structured set of covariant two-way local formulations for the four basic kind of measurements involved in Space Geodesy. Both local and global models are made compatible by using local and global Fermi coordinates, respectively. The measurements formulations are one-to-one general (weak) relativistic versions of the local classical formulations currently implemented in altimetry, satellite laser ranging and satellite-to-satellite tracking on the one hand, and on the other, of the classical version of the ballistic problem.

Among fossil fuels (coal, oil and gas), world proved reserves of coal are the largest and, at the current consumption rates, they would last for over two hundred years. Then, all along the current century, coal is expected to continue playing a key role, as a vital primary fuel for energy generation purposes. At present, coal combustion is a rather mature technology; nevertheless, advanced conversion processes are continuously being developed in order to reduce gaseous atmospheric emissions and other pollutants from coal power plants. Additional environmental concerns have recently emerged, as some health impacts are correlated to trace metal emissions and submicronic airborne particles. Moreover, the former indications of a potential global impact of emissions of greenhouse gases on climate change are becoming evidences. Scientific research and technological development on coal energy utilization are mainly focused on improving the understanding of the combustion and gasification underlying basic processes, as well as designing thermal cycles at higher pressures and temperatures. Efforts are aimed at increasing efficiency, reducing emissions and at separating the carbon dioxide from the flue gases for its possible subsequent storage.

The purpose of this paper is to contribute to the mathematical modelling of the combustion of coal particles in pulverised coal furnaces, and also to propose an algorithm for its numerical solution. The mathematical model includes two coupled phases: the solid phase, for the coal particles, where a Lagrangian description is used and an Eulerian description for the gas phase, where the effects of the combustion of coal particles are homogenised.

In coal combustion processes, a large amount of nonvolatile material is emitted as particular matter carried by the gas stream. Moreover, some condensable vapors (usually sulfates and nitrates) are formed by reaction in the flue gases. The control of these particles and vapors is a key factor in clean coal conversion technologies. Thus, the formation of soot and fly ash deposits and the condensation of vapors over heat exchanger tubes and exhaust lines reduce the heat transfer efficiency and promote corrosion problems, leading to shorter lifetimes of the equipment and increasing the production and maintenance costs. Also, the emission of submicron particles to the ambient air is an environmental issue of capital importance. Moreover, the bulk (porosity, hardness) and surface (roughness) properties of the formed deposit depend on the particle arrival dynamics. Therefore, the analysis of particle and vapor transport under controlled conditions and the study of deposit formation from particle laden gases are problems of wide practical implications in coal combustion. In particular, there is a need of theoretical analysis on the dynamics of particles in gases under strong temperature differences and intense radiative fluxes, as well as on the behavior of particles near obstacles to evaluate the deposition rates. Some model problems linked to the behavior of particles and vapors in gases and deposit formation will be discussed here.

When burned to produce energy, sulfur-containing fossil-fuels, such as coal or oil, often generate sulfur dioxide (SO

2

). SO

2

is known to be damaging to humans (at high concentration levels) and to the environment, being one of the main precursors of acid rain. Coal is the most abundant fossil fuel, with reserves estimated to be in excess of 150 years at current consumption rates. Thus, technologies aiming at minimising the environmental impact of coal utilization are subject of vigourous research worldwide. Among these, flue-gas cleanup, such as Flue-gas desulfurization (FGD), is perhaps the one offering at present the lowest technological risk, and the fastest route to implementation. FGD can be achieved using a number of technologies [3], but the vast majority of currently-installed capacity is for wet scrubbers. Wet scrubbers combine high SO

2

removal efficiency, high reagent utilization, and compact designs.

The correct simulation of industrial plants firing pulverized fuels (pf: coal, biomass, etc.) by means of commercial CFD codes relies on a number of submodels for the various processes, including, e.g. heat transfer (radiation, conduction through deposits, etc.) and particle combustion. The latter is of major importance in the design of the combustion chamber and the selection of the mills or, conversely, regarding the feasibility of burning a new fuel in an existing boiler. In the last decade, the introduction of new, internationally traded coals and alternative fuels into the power market has motivated renewed interest in the experimental and theoretical characterization of the combustion of these fuels. Regarding experimentation, it is generally accepted that the ‘reactivity’ of a fuel can not be determined in desktop analytical instruments; instead, drop tube furnaces or entrained flow reactors (EFR) must be used in order to reproduce the high temperature, high heating rate conditions found in a real pf combustion chamber [1]. Several alternative experimental procedures have been developed in the past and are still used (see, e.g. [2, 3]). On the other hand, two general approaches are used in the literature to model pulverized coal/biomass char combustion: one intends to characterize the evolution of the pores inside the burning particle, and considers both internal and external diffusion, whereas the kinetics for the basic homogeneous and heterogeneous reactions are taken from low temperature analysis or fundamental knowledge of the chemistry involved (e.g. [4]); the other one, followed here, makes use of an apparent kinetics based on the outer particle surface, and includes external diffusion [5]. In the latter case, two parameters governing an Arrhenius-like kinetics are the main unknowns to be determined from the experiments performed in an EFR. The aim of this paper is to discuss some aspects of the mathematical procedure for the determination of those parameters.

In recent years the need of exploiting reservoirs of oil of lesser quality has pushed the research of the chemical, physical and rheological behaviour of oils particularly rich in heavy hydrocarbons. The latter category includes a large class of n—alkanes, collectively termed “wax”, up to the so—called asphaltenes. Asphaltenes may develop a tendency to aggregate and to precipitate. Wax can segregate at sufficiently low temperatures and also give rise to the phenomenon of molecular diffusion induced by thermal gradients. The outcome of all such phenomena is the formation of deposits, which can reduce the lumen of pipelines, possibly leading to obstruction. Therefore it is quite obvious that the possibility of predicting the rate of precipitation of asphaltenes or the rate of wax deposition has a great economic impact.

Asphaltenes constitute the heaviest, most polar fraction of crude oil [1]; they form heavy organic deposits in oil production ducts, inducing flow rate reductions. The principle of economy (Ockham's razor) was employed to develop onset—constrained colloidal asphaltene model (OCCAM) [2]. It is a particularisation of the Flory—Huggins model [3]; a binary system is considered, constituted by the solvent mixture (pseudocomponent 1), grouping together components and solvents (possibly) added, and the asphaltene (pseudocomponent 2).

This work presents a model for the turbulent flow of a waxy crude oil in a pipeline, in which deposition is taken into account. Waxy crude oils (WCO's) are mineral oils with high content of heavy molecular weight compounds, usually called waxes. When a sufficiently low temperature is reached (

cloud point

,

T

cloud

) waxes begin to solidify, entrapping the oil in a gel—like structure.

The presence of solid waxes may lead to the formation of a deposit layer on the pipe walls during transportation at low temperatures. This phenomenon has important consequences, such as the increase of pressure requirements and, in the worst scenario, the blockage of the line. Deposition can be due to different mechanisms (see [1]), although there is a general agreement on considering that molecular diffusion is the dominant one. Diffusion refers to the radial mass flow of dissolved waxes towards the pipe wall due to a concentration gradient.

In the model presented herein, molecular diffusion is taken as the only deposition mechanism. The model is also based on the assumption that the deposit thickness is small compared to the pipe radius, as explained elsewhere [2]. Moreover, the effects of ablation, ageing and desaturation are also addressed in the model. Ablation refers to the removal of part of the deposit by the fluid shearing. On the other hand, ageing is a phenomenon that decreases the oil fraction in the deposit. Finally, desaturation takes into account the fact that the fluid is being depleted of waxes.

We simulate the Doi model for suspensions of rigid rod-like molecules. This model couples a microscopic Fokker—Planck type equation (the Smoluchowski equation) to a macroscopic Stokes equation. The Smoluchowski equation describes the evolution of the distribution of the rod orientation. It is a drift-diffusion equation on the sphere in every point of physical space. The drift term in the microscopic equation depends on the local macroscopic velocity gradient. Furthermore, the microscopic orientation of the rods leads to elastic effects which affect the rheological properties of the macroscopic flow.

For sufficiently high macroscopic shear rates the coupled problem shows the spurt phenomena, which describes a sudden increase in the volumetric flow rate. In this regime the drift term in the Smoluchowski equation is dominant and thus a numerical method appropriate for transport dominated PDEs is used.

In this minisymposium we consider computational and theoretical modeling of a variety of problems with complicated microstructure. As the title of this minisymposium says we present modeling of filtration problems in porous media. In his talk I. S. Pop derives upscaled Buckley—Leverett equations for two-phase flow in a porous medium with application to oil recovery. The upscaled equation is derived by the use of classical homogenization techniques. He also presents numerical results on the effective saturation. In the talk by N. Neuss he considers the Dirichlet problem for the Poisson equation with homogeneous boundary data in a domain Ωϵ with rapidly varying boundary ∂Ωϵ. He uses homogenization to derive an approximate solution

u

to the solution

u

ϵ. Here

u

solved an effective Dirichlet problem for the Poisson equation with homogeneous boundary data in a domain Ω with nonoscillatory boundary ∂Ω. He also presents numerical simulations of this very nice approximation technique. The third talk is by C. Timofte and concerns thermal diffusion with nonlinear lower order terms and nonlinear flux laws. The application in mind is the thermal transmission between two substances embedded in complicated microstructures. Using mathematical homogenization theory she derives effective laws for systems of nonlinear thermal diffusion equations. In particular she points out two cases of practical importance, the Langmuir and the Freundlich kinetics. In the fourth presentation N. Svanstedt considers a convection-diffusion model with possibly highly oscillatory random convection field and diffusion matrix. By combining tools from stochastic homogenization and reiterated homogenization he derives an effective convection enhanced diffusion model. He also presents some numerical simulations of the cell solutions for some two-dimensional convection-diffusion examples.

In physical problems, interesting phenomena often occur at boundaries or interfaces between different media. Often these phenomena are complicated due to the nature of the process or due to the intricate geometry of the interface. Therefore, they are usually described by effective boundary or interface laws.

In this contribution, we will discuss a model cases in a quasi-periodic setting, where the parameter function in an effective boundary condition can be calculated from the microscopic setting. Theoretically, this case was treated in [5]. Practical computations can be found in treatment of this case was done. First, we construct a suitable approximation and give a priori estimates for the error. Second, we consider the efficient numerical calculation of the effective law, and its use for approximating the solution to the original problem.

The general question which will make the object of this paper is the homogenization of some nonlinear problems arising in the modelling of thermal diffusion in a two-component composite. We shall consider, at the microscale, a periodic structure formed by two materials with different thermal properties. We shall deal with two situations: in the first one, we assume that we have some nonlinear sources acting in both components and that at the interface between our two materials the temperature and the flux are continuous, while in the second problem we shall address here, we assume that the flux is still continuous, but depends in a nonlinear way on the jump of the temperature field. In both cases, since the characteristic sizes of these two components are small compared with the macroscopic length-scale of the flow domain, we can apply an homogenization procedure.

We consider a two-phase flow model in a heterogeneous porous column. The medium consists of many homogeneous layers that are perpendicular to the flow direction and have a periodic structure resulting in a one-dimensional flow. Trapping may occur at the interface between a coarse and a fine layer. An effective (upscaled) model is derived by homogenization techniques.

In this minisymposium, C.E. Castro and E.F. Toro present “ADER DG and FV schemes for shallow water flows”, M. Castro Díaz, E.D. Fernández Nieto and A. Ferreiro Ferreiro present “Numerical simulation of bedload sediment transport using finite volume schemes”, L. Ferrer, Ad. Uriarte and M. González present “New Trends and Applications in Oceanographic Numerical Modelling”, M. J. Castro, A. M. Ferreiro, J. A. García, J. M. González and C. Parés present “Study and Development of Numerical Models for the simulation of geophysical flows: the DamFlow Project”, and I. Gejadze, M. Honnorat, F.X. Le Dimet and J. Monnier present “On variational data assimilation for 1D and 2D fluvial hydraulics”.

We are concern with ADER [3] high-order numerical methods for the timedependent two-dimensional non-linear shallow water equations [2] in the framework of finite volumes (FV) and discontinuous Galerkin (DG) finite elements methods using non-structured triangular meshes.

In this work we study high order finite volume methods by state reconstructions. We apply it to beload sediment transport problems. For the hydrodynamical component we consider Shallow Water Equations, for the morphodynamical component we consider a continuity equation

The development of numerical models for the simulation of marine hydrodynamics together with the increment in computational capacity of the new computers and the collaboration amongst interdisciplinary research groups, is slowly allowing to catch up with the delay of oceanic forecasting in comparison to other research areas like meteorology. Thanks to the knowledge gained in relation to oceanographic processes and the interaction between the ocean and atmosphere, new forecasting tools are being developed. These, comprise models of currents and waves, pollutant drift and aging, interaction between physical and biological processes with application to the management of fishing resources, or models for environmental impact assessment of coastal activities and uses (submarine outfalls, aquaculture cages, spill of dredged material, etc.). This chapter shows some examples of several applications of numerical models to regional and local scale areas.

The goal of this chapter is to describe briefly the DamFlow project whose goal is the efficient implementation of a numerical parallel solver to simulate geophysical flows. This chapter focuses on the numerical solution of shallow water systems by means of finite volume methods. A technique to develop a high level C++ small matrix library that takes advantage of SIMD registers of modern processors is introduced. A visualization toolkit specifically designed for the pre and post-process of the simulated problems is also presented. Finally, some numerical results are shown.

We address two problems related to variational data assimilation (VDA) [1] as applied to river hydraulics (1D and 2D shallow water models). In real cases, available observations are very sparse (especially during flood events). Generally, they are very few measures of elevation at gauging stations. The irst goal of the present study is to estimate accurately some parameters such as the inflow discharge, manning coefficients, the topography and/or the initial state. Since the elevations measures (eulerian observations) are very sparse, we develop a method which allow to assimilate extra lagrangian data (trajectory particles at the surface, e.g. extracted from video images). The second goal aims to develop a joint data assimilation - coupling method. We seek to couple accurately a 1D global net-model (rivers net) and a local 2D shallow water model (zoom into a flooded area), while we assimilate data. This “weak” coupling procedure is based on the optimal control process used for the VDA. Numerical twin experiments demonstrate that the present two methods makes it possible to improve on one hand the identification of river model parameters (e.g. topography and inflow discharge), on the other hand an accurate 1D–2D coupling combined with the identification of inflow boundary conditions.

Over the past years, Mathematical Materials Science has become an important discipline, with a significant impact both on mathematics and materials science. Modeling many properties of materials involves describing phenomena taking place in a wide range of scales, from the nanoscale up to the macroscale. One of the big challenges nowadays is to develop the tools to handle multiscale problems and understand how dynamics on one scale affect the others. Experimental, computational and theoretical advances provide a better understanding of materials, making it easier to design new materials with desired properties.

We present a model of aggregation, whereby clusters are created according to the Zeldovich nucleation rate and subsequently undergo diffusion limited growth as in the classic Lifshitz—Slyozov (LS) model. The mathematical formulation of this model as an advection PDE signaling problem is singular in the small super-saturation limit. Using singular perturbation methods, we find three successive eras: Nucleation, growth and coarsening. The long-term limit of the coarsening era solution converges to the discontinuous similarity solution of the LS PDE.

We know since decades that, to exploit and control mechanical properties of materials, a profound knowledge of the defects generated during deformation is required. The advent of nanotechnologies and the maturity of surface science have catalysed the development of nanoindentation techniques. Nanoindentation experiments, with both high spatial and load resolution, allow to determine defects emerging at the surface, and their relationship with discontinuities in the load vs. penetration curve. But sub-surface defect morphology generally remains hidden, and quite often only indirect conclusions can be inferred. Simulations are then a very valuable tool to unveil defect configurations. Among the present challenges regarding nanoindentation, one is the origin and correct interpretation of the piled-up material, i.e. the material displaced from the indentation point. Another problem is the role of the surface roughness on the mechanical properties at the nanoscale.

A two-dimensional discrete elasticity model is used to compute the critical thickness at which interfacial pure edge dislocations are energetically preferred to form in the InAs/GaAs(110) heteroepitaxial system. The calculated critical thickness of six monolayers, is fairly close to the measured value in experiments, five.

We present a study of 3D dislocation dynamics in BCC crystals based on discrete crystal elasticity. Ideas are borrowed from discrete differential calculus and algebraic geometry to construct a mechanics of discrete lattices. The notion of lattice complexes provides a convenient means of manipulating forms and fields defined over the crystal. Atomic interactions are accounted for via linearized embedded atom potentials thus allowing for the application of efficient fast Fourier transforms. Dislocations are treated within the theory as energy minimizing structures that lead to locally lattice-invariant but globally incompatible eigendeformations. The discrete nature of the theory automatically eliminates the need for core cutoffs. The quantization of slip to integer multiples of the Burgers vector along each slip system leads to a large integer optimization problem. We suggest a new method for solving this NP-hard optimization problem and the simulation of large 3D systems.

A new asymptotic approach for analysing pile-ups of large numbers of dislocations is described. As an example, the pile-up of

n

identical screw or edge dislocations on a single slip plane under the action of an external loading in the direction of a locked dislocation in that plane is considered. As

n

→ ∞ the continuum number density of the dislocations can be easily obtained whereas direct evaluation of the discrete dislocation positions from the set of force balance equations is not straightforward. However, in the framework of our method these positions can be revealed using the corresponding dislocation density.

In this chapter we examine the accuracy and efficiency of the simplified P

N

approximations of radiative transfer for natural convection problems in a square enclosure. A Boussinesq approximation of the Navier—Stokes equations is employed for the fluid subject to combined natural convection and radiation. Coupled with the simplified P

N

models, the system of equations results into a set of partial differential equations independent of the angle variable. Numerical results for different Rayleigh numbers are presented.

In this minisymposium the electronic and transport properties of different low-dimensional nanodevices have been discussed. In these devices, the interplay between charge, spin and vibrational degrees of freedom determines their main electronic and transport features. Moreover, the number of atoms in the system determines the more suitable theoretical framework and numerical techniques for each particular system.

Nanowires, i.e., systems with a diameter of the order of 1–10 nm, and length up to microns, form a subclass of modern nanoscale systems, which hold a great promise for future technologies. For example, they could be used as interconnects in future's nanoelectronics, or they could form the basis of extremely sensitive sensors. In addition to their possible practical applications, nanowires exhibit a wide range of physical properties, which are of their own intrinsic interest. The theoretical scientist attempting to model charge transport in these systems faces many challenges. The number of atoms or active charge carriers requiring a microscopic treatment may vary from a few to several millions. The transport may be coherent, or dominated by interaction effects. No single formalism can capture all the different facets, and in this article a review of a few selected modern techniques, operative at different length scales, is given. Specifically, we shall be considering four different physical systems: (1) semiconducting nanowires; (2) gold atomic wires; (3) molecular electronics, and (4) one-dimensional strongly correlated chains.

We investigate theoretically the transport properties of a closed Aharonov—Bohm interferometer containing two quantum dots in the Kondo limit. We find two distinct physical scenarios depending on the strength of the interdot Coulomb interaction. For negligible interdot interaction, transport is governed by the interference of two Kondo resonances, whereas for strong interdot interaction transport takes place via simultaneous correlations in both spin and orbital sectors.

Double quantum dot (DQD) structures provide a good system for studying the competition between the Kondo effect and the antiferromagnetic coupling of the electrons in the dots [2]. Such a system can be realized not only in semiconducting heterostructres but also in structures consisting of molecules and nanotubes attached to metallic electrodes [1, 4]. If the latter are superconducting then the interplay between the Josephson and the Kondo effects has to be taken into account. In the case of a single quantum dot placed between two superconductors, the energy gap in the density of the states may lead to a suppression of the Kondo effect and the appearance of an unscreened magnetic moment. This leads to the so-called π-phase with a reversal of the sign of the Josephson current [3]. In the case of a DQD the situation is more complicated since besides the Josephson and the Kondo effect one should also take into account the magnetic interaction between the dots. Here we provide a comprehensive analysis of the interplay between Josephson effect, Kondo and antiferromagnetic coupling in a S-DQD-S systems. We analyze the phase diagram and the appropriate correlation functions for a broad range of parameters. Like in the single S-QD-S system we identify phases in which the sign of the Josephson coupling is reversed.

Shuttle devices are a class of nanoelectromechanical systems generically described as movable single electron transistors. They exhibit an electromechanical instability from the standard tunnelling regime to the shuttling regime in which the quantum dot oscillates and transfer one electron per cycle. I present a theory for the device in which both the electrical and mechanical degrees of freedom are quantized. The different operating regimes are detected by analyzing current, noise and Wigner function distributions. The calculation of the stationary solution for the Generalized Master Equation which describes the system dynamics is the starting point for the evaluation of these quantities and represents a numerically challenging problem due to the size of the Hilbert space necessary to capture the tunnelling to shuttling transition.

Recent transport experiments in vertical double quantum dots (DQDs) show that Pauli exclusion principle plays an important role [1, 2] in current rectification. In particular, spin blockade (SB) is observed at certain regions of dc voltages, and the interplay between Coulomb and SB can be used to block the current in one direction of bias while allowing it to flow in the opposite one. Then DQDs could behave as externally controllable spin-Coulomb rectifiers with potential application in spintronics as spin memories and transistors. Spin de-coherence and relaxation processes [3, 4] induced by spin—orbit (SO) scattering [5] or hyperfine (HF) interaction [6], have shown to reduce SB producing a leakage current in the voltage region where the blockade occurs. We theoretically analyze recent experiments of transport through two weakly coupled vertical QDs [1]. In these experiments current flow is allowed when the electrons in each QD have antiparallel spins and a finite gate voltage allows one electron in the left dot to tunnel sequentially to the right one. However, there is a similar probability for the electron coming from the left lead to be parallel or antiparallel to the electron spin occupying the right dot. In the first case, the electron cannot tunnel to the right dot due to Pauli exclusion principle and SB takes place, presenting a plateau in the

I/V

dc

curve.

We study the dynamics of the reduced density matrix for coupled quantum dots systems under the influence of time-dependent ac potentials. By disregarding non-resonant processes, we find analytical expressions for the stationary charge current in different regimes.

We review the application of the quantum-transmitting-boundary algorithm to compute electronic currents in the presence of localized spin—orbit couplings. As specific physical realization we choose a semiconductor quantum wire containing a Rashba spin—orbit dot. The Rashba dot leads to the formation of quasibound states and to Fano profiles in the energy dependence of the wire conductance.

We investigate electron transport through resonant tunneling diodes doped with magnetic impurities. Due to exchange interaction between impurities and carriers, there arises a giant Zeeman splitting which dominates the

I–V

curves. We discuss a simple model which accounts for spin effects in these systems and examine its applicability in realistic samples.

We consider single electron transport through a II–VI semiconductor quantum dot doped with a single Mn atom. The spin dynamics of the Mn atom is controlled by the carriers electrically injected in the dot. We find that the chargevs.- gate curve can display hysteretic behaviour when the Mn-carrier interaction is anisotropic. We discuss the origin and implication of this result.

The discovery of nanostructured forms of molecular carbon has led to renewed interest in the varied properties of this element. Recent experiments and theoretical studies have suggested that electronic instabilities in pure graphite may give rise to superconducting and ferromagnetic properties, even at room temperature. Magnetic carbon could be used to make inexpensive, metalfree magnets for applications in medicine and biology, nanotechnology andtelecommunications. The following topics in the invited presentations to the minisymposium have been included in these proceedings: The state of the art of magnetism in nanographite is reviewed in two papers from the point of view of experimentalists (T. Makarowa and M.A. Ramos). The theoretical support is presented in the report by M.P. Lopez-Sancho, M.A.H. Vozmediano, F. Stauber, and F. Guinea. A. Cortijo discusses the electronic properties of topological defects in graphene, and F. Guinea presents a transistor effect in bilayer graphene. An additional presentation by L. Pisani on numerical studies of graphene nanoribbons could not be included in this volume.

Carbon nanostructures are regarded as all—carbon structures with the nanometer size. Building blocks of the future, building blocks of future information and energy technologies — here are the permanent epithets for carbon nanostructures. Scientific interest, sparked by the discovery of fullerenes [1], refocused on carbon nanotubes [2] and other exotic structures like nanofibers, nanoribbons, nanohoops, nanocones and nanohorns [3], toroids [4] and helicoidal tubes [5], onions and peapods [6], Schwarzites and Haeckelites [7]. More recently, it was discovered that the two—dimensional building block for creating the nanostructures of any other dimensionality, graphene, itself possesses unique electronic properties: ballistic electron transport, constant velocity for the electrons confined in the graphene sheets (massless particle behaviour), half—integer shift in the quantum Hall effect and quantized minimum conductivity [8–10]. The linear dependence of the energy on momentum in graphene leads to unusual features, not encountered in other materials [11].

Pure graphite, the stable crystalline allotrope of carbon at room temperature and ambient pressure, is known to exhibit a strong and anisotropic “textbook” diamagnetism, due to its delocalized π electrons. Nevertheless, in the last two decades several researchers have reported more or less clear evidences of ferromagnetic behavior in carbon at room temperature. We might mention the work by japanese groups [Mur91, Mur92], who observed it in amorphous carbon (relatively rich in hydrogen). The origin of this ferromagnetic behavior could be theoretically justified as arising from the mixture of sp

2

and sp

3

bonding in carbon structure [Ovc88]. More recently, new findings of this kind have appeared in the literature, as the presence of ferromagnetic signals in some polymerized fullerenes reported by Makarova et al. [Mak01], or that found in proton-irradiated highly-oriented pyrolitic graphite (HOPG) by the group led by Esquinazi [Esq02, Han03]. In the latter experimental work, the analysis of possible magnetic impurities has been much more rigorous as to overcome the natural skepticism arose by the former experiments. Moreover, several theoretical works seem to support the importance of disorder [Voz04] and/or of vacancy-hydrogen complexes [Leh04] for the appearance of magnetic moments in graphite.

Magnetic correlations in carbon-based materials have been reported for many years, but the lack of reproducibility have aroused scepticism about this topic. However, in recent years, the improvement of the characterization techniques has allowed the observation of ferromagnetism and the precise measurement of the impurity amounts in different samples of HOPG and Kish graphite [1]. Besides the ferromagnetic hysteresis loops [2] reported at room temperature, the enhancement of ferromagnetic behavior by proton bombardment of graphite has been observed in samples with an amount of impurities much lower than that needed to produce the saturation magnetization measured [3]. Irradiation induced magnetism in carbon nanostructures has been reported by N and C implantation [4]. A relation between the magnetic properties of pure bulk ferromagnetic graphite and the topographic defects introduced in the pristine material have been reported by comparison of atomic force microscopy (AFM) images and magnetic force microscopy (MFM) [5]. Soft X-ray dichroism spectromicroscopy has been used to analyze the magnetic order of metal free carbon films. A clear evidence of intrinsic ferromagnetic order at room temperature has been obtained in these carbon films that have been irradiated by a focused proton beam [6]. All these experiments suggest that there is a relation between topological defects in the lattice induced by irradiation and the ferromagnetic correlations [6]. We will study the ferromagnetism in a two-dimensional graphene plane by considering disorder, vacancies, and defects in the atomic network.

In this work we will focus on the effects produced by topological disorder on the electronic properties of a graphene plane. The presence of this type of disorder induces curvature in the samples of this material, making quite difficult the application of standard techniques of many-body quantum theory. Once we understand the nature of these defects, we can apply ideas belonging to quantum field theory in curved space-time and extract information on physical properties that can be measured experimentally.

Single layer graphene and stacks of graphene layers have recently attracted a great deal of attention, because of their unusual electronic properties and potential applications [1, 2].

Mathematical models of physical systems form the basis of numerical simulations used for industrial applications. The continuous advancement in technical design demands refined models, where more effects have to be included. Thus sophisticated analysis as well as efficient numerical methods have to be tailored to the arising complex systems. On the one hand, modelling dynamical systems by partial differential equations (PDEs) may involve singular matrices, which yield partial differential algebraic equations (PDAEs) in the sense of singular PDEs. On the other hand, a coupling of time-dependent systems of differential algebraic equations (DAEs) with PDEs describing spatial effects is called a system of PDAEs, too. Both cases represent concepts required in advanced simulation of technical processes. The systems often include a multirate behaviour with largely differing time scales. Hence, multiscale simulation using the underlying structure has to be performed for achieving an efficient technique. In particular, the design of electronic circuits is based on numerical simulation of DAE models resulting from a network approach, which specifies the evolution of node voltages and branch currents in time. Due to down-scaling, parasitic effects can not be neglected in the modelling any more. Thus, spatial physical phenomena like heat distribution, electromagnetic interaction or complex semiconductor behaviour are considered, where corresponding PDE models apply. The arising systems of PDAEs become more and more important in microelectronics to enable a realistic simulation. Furthermore, a specific signal model for oscillators yields singular PDEs in microelectronics. Nevertheless, PDAE models apply in other applications like chemical engineering, biology, mechanical engineering, hydrodynamics, etc., too. In the minisymposium, we have presented approaches based on PDAEs in the field of microelectronics and chemical engineering. Thereby, the emphasis has been on PDAEs in the sense of coupled systems of DAEs and PDEs. Mathematical modelling, analysis and numerical aspects have been addressed. Concerning the design of electronic circuits, the topics of PDAE modelling and multiscale simulation are present in the new Marie Curie Research Training Network COMSON (COupled Multiscale Simulation and Optimization in Nanoelectronics) supported by the European Commission.

This paper is meant to be the continuation of the previous work [1] where a coupled ODE/PDE method for the simulation of semiconductor devices was introduced. From a strictly mathematical viewpoint, analytical results on coupled PDE/ODE systems (as arising in integrated circuit simulation) can be found in [2]. In particular, in the present paper, we investigate numerically new algorithms of Domain Decomposition type for the simulation of circuits containing distributed devices (Sect. 2) as well as semiconductors in which some part is modeled with lumped parameters (Sect. 3). The results presented here have been investigated in the seminal work [3], while a more extended analysis is ongoing [4].

The design of electronic circuits is based on numerical simulation of corresponding mathematical models. Systems of differential algebraic equations (DAEs) reproduce the time behaviour of idealised electric networks. In nanoelectronics, miniaturisation causes parasitic effects, which can not be neglected any longer. These spatial phenomena yield models consisting of partial differential equations (PDEs). Thus the circuit's behaviour is given by partial differential algebraic equations (PDAEs), which couple DAEs in time and PDEs in time/space. We present a rough concept for classifying existing PDAE models in nanoelectronics. The categorisation rests primarily upon the physical background in each model.

Problems that exhibit multiple time scales arise naturally in many scientific and engineering fields. For transient, distributed process systems, the corresponding models consist of partial differential equations (PDEs), possibly coupled to ordinary differential equations (ODEs) or differential-algebraic equations (DAEs) that describe lumped processes or are used as boundary conditions.

In this paper we demonstrate model order reduction of a nonlinear academic model of a diode chain. Two reduction methods, which are suitable for nonlinear differential algebraic equation systems are used, the trajectory piecewise linear approach and the proper orthogonal decomposition with missing point estimation.

In this minisymposium, A. Majorana and V. Romano (U. Catania) present “Comparing kinetic and MEP model of charge transport in semiconductors”, and M. Galler and F. Schürrer (TU Graz) present “A Deterministic Solver to the Boltzmann-Poisson System Including Quantization Effects for Silicon- MOSFETs”.

The distribution function based on the maximum entropy principle (MEP) in the case of 8 moments is compared with the direct solution of the Boltzmann transport equation in typical one dimensional benchmark problems for semiconductor silicon devices. The energy bands are assumed to be described by the Kane dispersion relation.

We present a deterministic solver to the Boltzmann-Poisson system for simulating the electron transport in silicon MOSFETs. This system consists of the Boltzmann transport equations (BTEs) for free electrons and for the twodimensional electron gas (2DEG) formed at the Si/SiO2 interface. Moreover, the Poisson equation is coupled to the BTEs. Eigenenergies and wave functions of the 2DEG are dynamically calculated from the Schrödinger-Poisson system. Numerical studies prove the applicability and the efficiency of the proposed numerical technique for simulating ultrasmall semiconductor devices.

Thanks to the development of information technologies, the last decade has seen a considerable growth of interest in the statistical theory of shape and its application to many and diverse scientific areas.

Here the Theory of Size Functions is introduced and joined to some statistical techniques of discriminant analysis, to perform automatic classification of families of random shapes. The method is applied to the classification of normal and malignant tumor cell nuclei, described via their section profiles. The results here reported are compared with other techniques of shape analysis, already applied to the same data, showing some improvements.

Morphological analysis of cells (size, shape, texture, etc.) is fundamental in quantitative cytology. Anomalies and variations from the typical cell are associated with pathological situations, e.g. useful in cancer diagnosis, in cell-based screening of new active molecules, etc.

In order to ensure safety and optimal performance of medical ultrasound transducers it is necessary to measure the acoustic pressure fields of transducers. For the estimation of such pressure fields we use light intensity data that is obtained by a Schlieren system. Schlieren data corresponds mathematically to squared x-ray tomographic data. Acoustic pressure fields attain positive and negative values, but only the square of the line integrals are provided by the Schlieren system. Therefore the signs of the line integrals are not known, and Schlieren data cannot be reduced to data of classical x-ray CT. For the numerical estimation of pressure fields we used the loping Landweber—Kaczmarz method.

In this work, we use the results of plant developmental biology (such as molecular biology of pattern formation and cell cycle progression) and of plant physiology to develop a mathematical model of plant growth. Trying to describe the most essential features of growth mechanisms, we do not model some particular plant organs but the entire plant though with many simplifications, in particular, without taking into account root growth, leave and flower formation, or the biochemistry of photosynthesis.

In this minisymposium, R. Armañanzas, B. Calvo, I. Inza, P. Larrañaga, I. Bernales, A. Fullaondo and A.M. Zubiaga present “Bayesian Classifiers with Consensus Gene Selection: A Case Study in the Systemic Lupus Erythematosus”, A. Sánchez and J.L. Mosquera present “The Quest for Biological Significance,” M. Chagoyen, H. Fernandes, J.M. Carazo and Pascual-Montano present “Functional Classification of Genes Using Non-Negative Independent Component Analysis”, and D. Montaner, F. Al-Shahrour and J. Dopazo present “New Trends in the Analysis of Functional Genomic Data”.

Within the wide field of classification on the Machine Learning discipline, Bayesian classifiers are very well established paradigms. They allow the user to work with probabilistic processes, as well as, with graphical representations of the relationships among the variables of a problem.

With the advent of genomic technologies it has become possible to perform, in a routinely manner, new types of experiments to analyze simultaneously the behavior of thousands of genes or proteins in different conditions. A common trait in these type of studies is the fact that they generate huge quantities of data what has lead to using the term “high-throughput” to describe them. There are different types of high-throughput experiments, but we will refer from now on to the most well known ones: microarray experiments.

In the last few years, several analysis methods have been proposed to assist in the functional interpretation of genome-wide data. To this aim, we explore the use of non-negative Independent Component Analysis (nnICA) for the classifi- cation of genes based on their associated functional annotations.

Most analyses carried out using high throughput data consist of the repetition of the same statistical test for all genes in the dataset. As a result of such replicated analysis we get, for each gene, several estimates of statistical parameters: statistics,

p

-values or confidence intervals. Being aware that most statistical methods were developed to test for a single hypothesis, researchers will usually correct

p

-values for multiple testing before choosing a cut-off that will indicate the rejection of the null hypotheses, whichever it is. Once chosen the genes with alternative pattern (meaning different form the one stated in the null hypothesis) the next step is to biologically interpret such departure from hypothesis. Different repositories of functionally relevant biological information such as Gene Ontology [1], KEGG [2] or Interpro [3] are available and can be used for the functional annotation of genome-scale experiments. Thus the functional properties of the selected genes can be analysed.

The wide field of

Inverse Problems

plays an important role nowadays in industrial applications of applied mathematics. This minisymposium is intended to present some selected topics which have received much attention lately.

The accuracy and the robustness of the iterative multi-resolution strategy in dealing with inverse scattering problems involving multiple objects configurations has been enhanced by introducing a suitable morphological processing. In an iterative fashion, a set of scatterers are reconstructed by progressively increasing the resolution level in the Regions-of-Interest (RoIs), where the objects are localized, identified through suitable morphological operations. Selected numerical results are presented and discussed in order to assess the accuracy and effectiveness of the morphological-based processing.

Our goal is to develop an inversion algorithm for reconstructing the shape of 3D breast tumors using electromagnetic data. The method of moments (MoM) forward solver is used to calculate the electric and magnetic equivalent surface currents at the tumor interface and consequently the scattered electromagnetic fields. Using a so-called “adjoint scheme” for gradient calculation, the mismatch between calculated and measured fields at the receivers is used as new sources at all receiver locations and is back-propagated towards the tumor. The gradient is calculated then simultaneously for all nodes of the guessed tumor surface in order to obtain a correction displacement of each individual node of the surface which points into a descent direction of a least-squares cost functional. This process is repeated iteratively until the cost has decreased satisfactorily. Numerical results in 3D are presented based on the proposed technique using multiple transmitting sources/receivers at multiple microwave frequencies.

In this chapter we analyze the potential of a shape-based model based on a level-set technique for the early detection of breast cancer tumors from microwave data. A reconstruction using a shape-based model offers several advantages like well-defined boundaries and the incorporation of an intrinsic regularization that reduces the dimensionality of the inverse problem whereby at the same time stabilizing the reconstruction. In this chapter, we present a novel strategy that is able to detect very small tumors compared to the wavelength used for illuminating the breast.

In the chapter we discuss the use of sequential Gaussian simulations in order to create geostatistical initial guesses for an earlier introduced level set based shape reconstruction algorithm for the history matching problem in reservoir characterization. We present and discuss numerical results which compare the performance of the reconstruction algorithm for these different initial guesses.

In this paper we consider the recovery of ellipsoidal 3D shapes with piecewise constant coefficients in Diffuse Optical Tomography (DOT). We use an adjoint scheme for calculating gradients for the shape parameters defining the unknown ellipsoids, and a Newton-type optimisation process for the minimization of a least squares data misfit functional. A boundary integral formulation is used for the forward modelling. An advantage of the proposed method is the implicit regularisation effect arising from the reduced dimensionality of the inverse problem. Results of a numerical experiment in 3D are shown which demonstrate the performance of the method.

In Electrical Impedance Imaging (EII) a finite number of electrodes are positioned at the boundaries of closed conducting domains [LPB05]. Typically some of the electrodes are used to inject low-frequency current patterns into the domain, while others sample the induced voltage potential at the boundary. In the image reconstruction problem, the interior admittivity distribution must be recovered using the acquired noise-infused boundary measurements. This nonlinear problem is ill-posed and therefore a regularization scheme is necessitated in order to yield a stable and unique solution.

We present three articles in this minisymposium on three areas of mathematical finance. We open up with Klaus Schmitz on simulation-based valuation where a new scheme is presented that values exotic options that possesses better convergence properties than existing schemes and is therefore more efficient. This is then followed by Helen Haworth on structural default risk modelling. A credit contagion framework is presented that captures the interdependency of firms under the consideration of credit risk and economic reality. Finally, Eric Yu demonstrates the valuation of a selection of elementary exotics with strike price resets under the same framework that keeps the valuation problem two-dimensional and is therefore competitive over existing methods.

In finance, the strong convergence properties of discretisations of stochastic differential equations (SDEs) are very important for the hedging and valuation of exotic options. In this paper we show how the use of the Milstein scheme can improve the convergence of the multilevel Monte Carlo method, so that the computational cost to achieve an accuracy of

O

(

e

) is reduced to O(ϵ

−2

) for a Lipschitz payoff. The Milstein scheme gives first order strong convergence for all one-dimensional systems (one Wiener process). However, for processes with two or more Wiener processes, such as correlated portfolios and stochastic volatility models, there is no exact solution for the iterated integrals of second order (Lévy area) and the Milstein scheme neglecting the Lévy area gives the same order of convergence as the Euler-Maruyama scheme. The purpose of this paper is to show that if certain conditions are satisfied, we can avoid the calculation of the Lévy area and obtain first convergence order by applying an orthogonal transformation. We demonstrate when the conditions of the two-dimensional problem permit this and give an exact solution for the orthogonal transformation. We present examples of pricing exotic options to demonstrate that the use of both the orthogonal Milstein scheme and the multilevel Monte Carlo give a substantial reduction in the computation cost.

Credit risk, often thought of as the risk arising from a company default, is the risk that an obligor does not honour its obligations. It is the reason the multitrillion dollar credit derivatives market exists and its influence is pervasive across global financial markets. As multi-asset credit products have increased in popularity, the need for models incorporating a realistic dependence structure between companies has grown.

We demonstrate the valuation of a selection of elementary exotic options with strike price resets in this article using a simple change of variable that keeps the valuation problem two-dimensional.

American, and Passport Options. These options are modelled by free boundary equations and optimal stopping problems, and by HJB-equations and stochastic optimal control problems. A Bermudean Option contract allows early exercise only at discrete values of time prescribed in the contract. Bermudean Options are popular in high-dimensional fixed income markets and treated typically by Monte—Carlo simulations. At each possible date of expiration theholder of a Bermudean Option has to decide between the value of the product upon exercise and the value of the product upon non-exercise. The latter value is given in terms of conditional expectations. The approximation by conditional estimators involves Monte—Carlo errors. Christian Fries investigates the foresight bias of the Bermudean Option which he interpretes as an Option on the Monte—Carlo error of the conditional estimator. He shows how to apply an analytical correction on the foresight bias which allows for simplifications in coding and more efficient pricing. As the number of exercise dates increase and the maximal distance of two consecutive exercise times decreases, Bermudean Options approach American Options which can be exercised at any time up to expiration. The contribution of Etienne Chevalier provides a lower bound for the difference between the value function of a multivariate American Option and the payoff function. From this he obtains a convergence rate of the Bermudean exercies region to the American one. This result is important because up to now we have to rely on Monte—Carlo methods in order to price and exercise higher-dimensional American Options. A uniform approach for American options and some related early exercise problems is presented in the contribution of John Chadam. He summarizes a bunch of recent works concerning analytical and numerical treatment of American options, prepayment of mortgages, and shows that that the underlying approach can also be applied to the inverse first crossing problem of a default barrier. The approach is based on the representations of prices of early exercise options by fundamental solutions. The fundamental solution plays also a fundamental role in the contribution by Jörg Kampen. He determines the optimal strategy of a multivariate call option on a traded account where the option holder pays a premium upfront and is allowed to choose short and long positions of a portfolio within certain position limits. The so-called passport options is modelled by HJB-equations and optimal stochastic control problems.

We provide a definition and an analytic formula for the so called

foresight bias

that may appear in the Monte—Carlo pricing of Bermudan and compound options if the exercise criteria is calculated by the same Monte—Carlo simulation as the exercise values. The analytical correction for the foresight bias is then applied to the Monte—Carlo pricing of a Bermudan option (Bellman's principle), resulting in better prices, especially for very low number of paths.

American options valuation leads to solve an optimal stopping problem or a variational inequality. These two approaches involve the knowledge of a free boundary, boundary of the so-called exercise region. Numerical methods exist to solve this kind of problems but these methods are not very efficient in high dimension because some information on the free boundary is needed. To improve our knowledge of the value function near its exercise region, we give here a lower bound for the difference between the value function and the pay-off function near the free boundary. This result can be used, for instance, to get some estimation for the convergence rate of the Bermudean option exercise region to the American one.

We provide a unified approach to studying a wide variety of free boundary problems that arise in modern mathematical finance. For the most part, the main ideas will be presented in the simplest case of the early exercise boundary for the American put option on a geometric Brownian motion. In addition to discussing the existence and uniqueness of the solution to the problem, and the convexity of the free boundary, we will describe several fast and accurate numerical and analytical approximations for the location of these early exercise boundaries. The same approach can be used to treat similar problems with more general underliers such as jump diffusion processes. We will also show how the techniques can be carried over to treat other classes of free boundary problems such as the inverse first crossing problem of the default barrier of a credit process as well as the pricing of mortgage prepayment options. Various parts of this work are joint efforts with Xinfu Chen (Pittsburgh) and David Saunders (Pittsburgh and Waterloo) as well as our recent Ph.D. students Lan Cheng, Ge Han and Dejun Xie.

Passport options are options on traded accounts with payoff structure of a Call. Optimal strategies are naturally linked not only to hedging but also to evaluation of this type of options. We use recent results on mean stochastic comparison of [5, 6] in order to determine optimal strategies for multivariate passport options. Especially, we find that optimal strategies depend on the correlations of returns and are related to the Greeks.

During the last years, very intensive efforts have been devoted to develop meshfree methods that eliminate the need of element connectivity in the solution of PDEs. These methods are very flexible numerical tools and do not require the labor intensive step of mesh generation. At present, the fundamental theory of meshfree methods has been developed and considerable advances have been made in the implementation of the different methods which have been proposed. However, its use as a practical alternative to conventional finite element methods is still pending. In fact, many challenges still remain both in the mathematical analysis and in the practical implementation of the methods. The objective of this minisymposium is to review some of the most promising meshfree methods and analyze its application to relevant problems. In particular, the Finite Pointset Method (FPM) and the Radial Basis Function (RBF) method are reviewed and applied to relevant industrial modeling problems. Also, a new family of meshfree schemes based on local maximumentropy approximants is proposed.

A large number of important physical processes involve heat conduction and materials undergoing a change of phase. Examples include nuclear reactors, casting of metals, semiconductor manufacturing, geophysics, and industrial applications involving metals, oil, and plastics. These problems are often called Stefan's or moving boundary value problems.

In a previous chapter [F. Bernal and M. Kindelan An RBF Meshless Method for Injection Molding Modelling, Lecture Notes in Computational Science and Engineering, Springer (2006)], a novel meshless approach was proposed for solving the Hele-Shaw flow which models plastic injection molding, in the case of a Newtonian fluid. Here, we have extended this idea to non-Newtonian Hele-Shaw flow via a Newton algorithm for the resulting nonlinear PDE.

Nowadays artificial fibres made of polymers or glass are of increasing industrial importance. Worldwide a total amount of 37.9 million tons of chemical fibres was produced in 2004 and the production still increases by around 5% annually.

This work deals with the modeling and simulation of the dynamics of a curved inertial viscous Newtonian fiber. Neglecting surface tension and temperature dependence, the fiber flow is modeled as a 3D free boundary value problem (BVP) via instationary incompressible Navier—Stokes equations (NSE). From regular asymptotic expansions in powers of the slenderness parameter leading-order balance laws for mass and momentum are derived that combine the unrestricted motion of the fiber center-line with the inner viscous transport. The form of the 1D fiber model results from the introduction of the intrinsic velocity characterizing the convective terms. For the numerical simulations of the fiber evolution a finite volume approach is applied.

In our life-world non-woven products play an important role. Many products such as wipes, filters (air conditioning, cleaner, oil, …), hygiene products, floor-covering, etc., are made out of non-woven. New needs require improvement and development of new products which constitutes a permanent task. Modeling and numerical simulations can support the development.

We consider a model for the production of glass fibers in a rotating spinning device. The model depends on two small parameters, namely the Reynolds-number δ and the Rossby-number ε. For small Rossby-numbers, i.e., a fast rotating spinning drum, numerical difficulties arise. To overcome this problems, asymptotic expansions are carried out for the stationary, inviscid case δ = 0 as well as for the instationary, viscous case δ =

O

(1).

In knitted and woven fabrics, inter-yarn forces at the crossover regions tend to compress the yarns thus affecting their mechanical properties. Hence the need to relate lateral forces and yarn cross-sectional deformation. Some theoretical analysis [1, 2] assumed filaments are elasticas and forces are applied at discrete points [1, 2] or uniformly distributed [3] on the filaments. Harwood et al. [4] have proposed a model of yarn compressibility by extending the work of van Wyk [5] to oriented fibres. The present chapter is concerned with compression of continuous filament yarns. The filaments are assumed to be elasticas and follow helical paths in the yarn. The theory of three-dimensional elastica is developed from differential geometry of curves and is applied to lateral deformation of a single helix. Finally, a yarn geometrical model and the algorithm for yarn compression are described.

Nonwoven are technical textiles that may be described as random collections of straight fibers. Infinitely long fibers have the disadvantage that periodicity can not be ensured. We give a short fiber model with two anisotropy parameters that allows to account for periodicity and compute the nonwoven's permeability for some such models.

The two fields of computer aided design (CAD) and algebraic geometry deal with curves and surfaces defined by algebraic equations, but the objects are studied using different approaches. On the one hand, algebraic geometry has developed impressive results for understanding the theoretical nature of these objects. On the other hand, the CAD community focuses on practical applications of virtual shapes defined by algebraic equations, and the curves and surfaces are typically represented with limited precision, using floating point numbers.

A new seminumerical algorithm for computing the intersection curve between a plane and the offset of a parametric surface is presented. The corresponding implementation and the performed experimentation are also reported.

The support function (SF) representation of surfaces is useful for analyzing curvatures and for representing offset surfaces. After reviewing basic properties of the SF representation, we discuss several techniques for approximating the SF of a given surface.

Starting from the modelling requirements of the early design phase of the product development, the paper will show a possible strategy to overcome some limitations of current CAS/CAD systems. In fact, the styling stage involves both technical knowledge and fuzzy and dynamic aspects, which have to be taken into account for a proper management. The paper focuses on high-level modelling tools developed to deform surfaces with semantic (aesthetic) constraints, i.e. the crucial design elements for the stylist. Furthermore, the communication among the other actors of the design process is consequently facilitated.

Modeling and mathematical technologies are a vital resource for R&D and innovation in Europe. Ingenious exploitation of mathematics means opportunity to achieve competitive edge in effective design process, accelerate test cycles, support systems integration schemes, redesign production models.

In this paper we will show an industrial application of a new framework, called L

a

TEX2W

e

B, which translates L

a

TEX material into an interactive Web-based document. The more important characteristic of L

a

TEX2W

e

B is the possibility of integrating, in the Web-based document, external programs produced in every languages. We exploited L

a

TEX2W

e

B to create an interactive Web-based manual, which illustrates a new software for the multiobjective optimization applied to the parameter extraction in circuit design. Thanks to L

a

TEX2W

e

B it was possible to simulate the algorithms written in C, C++, and FORTRAN, used in the multiobjective optimization software.

The European project CoMSON (Coupled Multiscale Simulation and Optimization in Nanoelectronics) is an FP6 Marie Curie RTN (Research and Training Network) action. This project involves five universities (“Bergische” University of Wuppertal, “Politehnica” University of Bucharest, University of Calabria, University of Catania, TU Eindhoven) and three microelectronics companies, (NXP-Philips, Qimonda, STMicroelectronics).

The well known results of algorithm complexity show the limitations of exact analysis. That explains popularity of heuristic algorithms. It is well known that efficiency of heuristics depends on the parameters. Thus we need some automatic procedures for tuning the parameters of heuristics. That helps to compare results of different heuristics. This enhance their efficiency, too.

This paper introduces the principles of creating the web-tool on differential equations. It can be used to support European Master Program for Mathematics in Industry. Such a Program is working already on the leading partner universities of ECMI and now the use of e-study as an innovational step is being discussed.

The aim of this study is to test numerically the influence that incompressible flow pulsation has on heat transfer in configurations, such as the backward facing step, that appear in micro-electro mechanical systems (MEMS) and that are not very efficient from the thermal point of view. Two control parameters have been used to increase heat transfer: velocity pulsation frequency and pressure gradient amplitude at the inlet section. The working fluid is water with temperature dependent viscosity and thermal conductivity. The results obtained show that the time averaged Nusselt number grows when using appropriate flow pulsations.

The starting jet produced by the discharge of a submerged fluid stream through a circular orifice is investigated both numerically and experimentally for moderately large values of the jet Reynolds number,

Re

. Low-amplitude sinusoidal perturbations were superimposed to the jet exit velocity to reproduce the effect of flow perturbations on the trailing jet and leading vortex ring dynamics. while the trailing jet is strongly modified by flow perturbations, the evolution of the total circulation, as well as the leading vortex dynamics, remain relatively unaffected, and thus can be considered as more robust indicators of the dynamics of starting jets.

This chapter is concerned with the modelling and computer simulation of a dynamic failure development in the thin-walled automotive structural components made from the laminated polymer composite materials reinforced with fabric layers. The scope of the work includes geometrically non-linear numerical structural analysis coupled with the progressive damage material modelling and applicable to structures with complex geometries. Impact crash simulation of a scaled-down automotive composite spare-wheel compartment has been performed using the explicit finite element code (PAM-CRASH). Simulation results are compared to experimentally recorded data, and the predicted deformation states and failure patterns show good agreement with the experimental data.

The interaction between premixed flames and acoustic perturbations of the gas velocity leads to combustion noise. In order to design noise-free combustion devices, one needs to understand the detailed mechanism by which the combustion noise is produced. The conical Bunsen flame is an excellent model for theoretical studies of the combustion noise.

Thin-film flows occur in a variety of physical contexts including, for example, industry, biology and nature, and have been the subject of considerable theoretical research. (See, for example, the review by Oron, Davis and Bankoff [4].) In particular, there are several practically important situations in which an external airflow has a significant effect on the behaviour of a film of fluid, and consequently there has been considerable theoretical and numerical work done to try to understand better the various flows that can occur. (See, for example, the studies by King and Tuck [2] and Villegas-Díaz, Power and Riley [6].) The flow of a rivulet on a planar substrate subject to a shear stress at its free surface has been investigated by several authors, notably Myers, Liang and Wetton [3], Saber and El-Genk [5], and Wilson and Duffy [9]. All of these works concern a non-perfectly wetting fluid; the flow of a rivulet of a perfectly wetting fluid in the absence of a shear stress at its free surface has been treated by Alekseenko, Geshev and Kuibin [1], and by Wilson and Duffy [7,8]. In the present short paper we use the lubrication approximation to obtain a complete description of the steady unidirectional flow of a thin rivulet of a perfectly wetting fluid on an inclined substrate subject to a prescribed uniform longitudinal shear stress at its free surface.

The evaporation of liquid droplets is of fundamental importance to industry, with a vast number of applications including ink-jet printing, spray cooling and DNA mapping, and has been the subject of considerable theoretical and experimental research in recent years. Significant recent papers include those by Deegan [1], Deegan et al. [2], Hu and Larson [3], Poulard et al. [4], Sultan et al. [5], and Shahidzadeh-Bonn et al. [6].

Shallow flows are widespread in nature and engineering. Examples include shallow wakes (flows behind obstacles such as islands), shallow mixing layers (flows at river junctions) and shallow jets. Shallow flows, where the transverse length scale of the flow,

d

, is much larger than water depth,

h

, i.e.,

d/h

≫ 1, are very different from deep water flows. This difference is associated with the fact that bottom friction plays an important role in suppressing flow instability. In addition, limited water depth prevents the development of three-dimensional instabilities.

By the end of 2007, the “Lignitos de Meirama” open pit coal mine will cease its extraction activities definitively and a lake is expected to develop due to the hydrological conditions of the region. Its possible connection to a reservoir which supplies water to the city of A Coruña (NW Spain) enforces the mining company to fulfill the Spanish water quality standards. In this frame, a numerical model to predict the future lake water quality has been developed. The water quality of a lake generated by filling a former open pit coal mine depends on several factors, such as the presence of iron sulfides at the pit walls and the environmentally hazardous consequences of their oxidation (heavy metals release and water acidification), the establishment of a flow regime on the future lake as a result of the water discharges on the pit and the possible stratification of the water column due to seasonal changes of the solar radiation [2].

Coastal areas are continually exposed to land-based sources of pollution resulting from domestic and industrial activities including oil spills, discharge of sewage and industrial effluents, among others. These contaminants arrive in the sea through wastewater discharges from sewage farms where contaminant concentrations are reduced by means of biological or chemical processes.

State estimation is necessary in diagnosing anomalies inWater Demand Systems (WDS). In this paper we present a neural network performing such a task. State estimation is performed by using optimization, which tries to reconcile all the available information. Quantification of the uncertainty of the input data (telemetry measures and demand predictions) can be achieved by means of robust estate estimation. Using a mathematical model of the network, fuzzy estimated states for anomalous states of the network can be obtained. They are used to train a neural network capable of assessing WDS anomalies associated with particular sets of measurements.

We study the evolution of charged droplets of a conducting viscous liquid. The flow is driven by electrostatic repulsion and capillarity and may lead to the breakup of the droplets. These droplets are known to be linearly unstable when the electric charge is above the Rayleigh critical value. Here we investigate the nonlinear evolution that develops after the linear regime.

A model for charge transport in photoexcited undoped semiconductor superlattices is proposed and analyzed. Under dc voltage bias, self-sustained oscillations of the current due to repeated homogeneous nucleation of pairs of charge dipole waves inside the sample, followed by wave splitting and motion in opposite directions are among the numerical solutions of the model.

This paper deals with a coupled system of non-linear elliptic differential equations arising in electrodeposition modelling process. We show the existence and uniqueness of the solution. A numerical algorithm to compute an approximation of the weak solution is described. We introduce a domain decomposition method to take in account the anisotropy of the solution. We show the domain decomposition method convergence. A numerical example is presented and commented.

This chapter is concerned with the matter of mathematically modelling and computationally simulating the thermo and fluid dynamical phenomena occuring in the workpiece during a gas metal arc welding (GMAW) process, and does so by employing a continuum mechanical approach and a finite element formulation for approximating the solution of equations expressing the continuity of mass, the balance of linear momentum, the conservation of energy and the motion of the weld pool surface. GMAW is an electrode arc fusion welding process. The designation

arc fusion

signifies that an electric arc is struck between the welding electrode and the workpiece, and this causes the base material to melt on either side of the joint. During the subsequent solidification this will cause fusion between the workpiece parts. The electrode consist in a filler metal, and it is hence consumed during the process and molten droplets are, under the influence of electromagnetical and gravitational forces, transferred to the liquid weld pool. Mass is thus added to the workpiece and this causes a reinforcement of the joint.

The goal of this chapter is to analyze a finite element method to solve the magnetostatic problem in terms of scalar potentials. Several FEM have been developed to solve the magnetostatic problem in the last decades, because of its application in engineering; see, for instance, [BAL96,MSP98,PAL91,ST79, ST80]. The main difference in the numerical methods lies in the choice of the primary unknowns (vector potential, magnetic field or scalar potentials). The published numerical results ([MSP98,PAL91]) show that the combination of two different potentials, the so called

reduced scalar potential

and

total scalar potential

, seems to be the most effective in terms of accuracy and computer cost. This formulation, was introduced by Simkin and Trowbridge in [ST79] and is very well known in the engineering literature; however, to the best of the author's knowledge, the approximation of this formulation in bounded domains by standard finite elements has not been analyzed from a mathematical point of view. This is the aim of the present chapter in the context of three-dimensional domains.

Indoor location systems using 802.11 standard, based on the comparison of the received and predicted levels of the received signals from the Access Points, are a very interesting research area. The location information is computed by searching the nearest neighbour of the measured signal strength within the radio map. In this chapter, we apply a global optimization algorithm to obtain the Access Points location distribution that yields the best performance of these location systems.

Primary Open Angle Glaucoma (POAG) is a major cause of blindness, affecting 65–70 million sufferers worldwide ([ERC04]). The eye produces aqueous humour (AH: a water-like substance secreted by the ciliary body) which flows behind the iris, through the pupil aperture, out into the anterior chamber (AC) and drains from the eye via the drainage angle. From the drainage angle the AH passes through a biological filter (the trabecular meshwork or TM) into the canal of Schlemm (SC), the main drainage route from the eye, and finally exhausts into “collector channels”. POAG occurs when this drainage mechanism is somehow compromised [FW92]. Essentially the AH cannot be removed quickly enough and as a result the intraocular pressure (IOP) increases in the eye. Contrary to popular belief, glaucoma and elevated IOP are not synonymous. Though very often associated with elevated IOP, glaucoma is, in reality, an optic nerve neuropathy. Notwithstanding this, elevated IOP is always regarded as potentially harmful to the eye. In the current study we therefore seek to model the flow of AH from the AC through the TM and into the SC and to couple this flow to predictions of changes in IOP.

An isothermal single-phase 3D/1D model for liquid-feed direct methanol fuel cells (DMFC) is presented and validated against experimental results. 3D mass, momentum and species transport in the anode channel and gas diffusion layer is modelled using a commercial CFD code complemented with user supplied subroutines. The 3D model is locally coupled to a 1D model that imposes a physically sound boundary condition for the velocity and the methanol concentration field at the anode gas-diffusion-layer/catalyst-layer interface. The 1D model assumes non- Tafel kinetics to account for the complex kinetics of the (multi-step) methanol oxidation reaction at the anode, and includes the mixed potential induced by methanol crossover due to diffusion and electro-osmotic drag. Polarization curves obtained for various methanol feed concentrations, temperatures, and methanol feed velocities show good agreement with recent experimental results.

Two mathematical models for an electrochemical biosensor are proposed and compared with a view to determining the ratio of two immobilized enzymes which maximizes the amperometric signal amplitude.

This work presents a method for the segmentation of breast nodules in ultrasonography. Speckle noise is reduced using an anisotropic filter for which texture is described using Gabor filters. Afterwards, an initial segmentation is extracted using a front propagation scheme. Finally, the initial segmentation is refined using active contours. In order to delimit the nodules not only by means of image intensity, but also by texture pattern, we introduce certain terms in the classical active contours equations.

We consider a contrast invariant approach to motion estimation which uses the direction of the gradient fields. The approach is region-based and assumes an affine motion model for each region. We propose to check if the estimated motion parameters fit properly the apparent motion of the region by a motion significance analysis. Moreover, we propose a motion field improvement which consider those regions that are not properly estimated according to the significance analysis and reassign them a motion model of a properly estimated neighboring region.

Multiple sequential recurrences are one of the most important characteristics of superficial transitional cell carcinoma (TCC) of the bladder. Many investigations have been done to identify predictive factors for the first recurrence, but very few studies have investigated multiple recurrences of this cancer and its clinicopathologic factors associated. We consider counting process methods for analysing timeto-event data with recurrent outcomes using the models developed by Andersen and Gill and, Prentice, Williams, and Peterson. A postoperative nomogram is developed to predict recurrences based on those predictive factors.

Let the homogeneous of

L

degree function

g

(

x

) be defined in

N

dimensional space, and let the function

G

(

y

) be its Fourier transform in the distribution sense. The theorem that allows to present the function

G

(

y

) using only the values of function

g

(

x

) on the unit sphere is proved in the chapter for the case

L

> −

N

. The case

N

=3 and

L

= −1 corresponds to the properties of beam transform in 3D space. In the chapter it is shown how the theorem may be used for creation of numerical algorithms for cone-beam tomography.

Let the homogeneous of

L

degree function

g

(

x

) be defined in

N

-dimensional space, and let the function

G

(

y

) be its Fourier transform. In view of homogeneity, the function

g

(

x

) and its Fourier transform in sense of distributions are defined by their values on the unit sphere [GS00]. We will prove the theorem that allows to present the function

G

(

y

) using only the value of function

g

(

x

) on the unit sphere for the case

L

> −

N

.

The proportional rule has a long tradition in collective problems where some kind of utility (costs, profits, savings) is to be shared among the agents. However, while its (apparent) simplicity might be a reason for applying it in pure bargaining affairs, where only the whole and the individual utilities matter, it seems much more questionable in the case of general cooperative problems, where all marginal contributions should be taken into account. We will contrast the proportional rule with the Shapley value in this kind of problems.

Game Theory provides suitable tools to share the total utility among the economic agents or players when the possibilities of cooperation enable obtaining the utility of each group or coalition. The semivalues are solution concepts for situations of competence—cooperation that assign to each player a weighted sum of his/her marginal contributions to the coalitions, where the weights only depend on the coalition size. The Shapley value and the Banzhaf value are semivalues. The solutions introduced here are modifications of the semivalues when we consider a priori coalition blocks in the player set. A computation procedure is also offered.

In the context of offshore oil production, we are interested in accurate and fast computation of two-phase flows in pipelines. A one-dimensional model of hyperbolic equations is solved numerically by an explicit Lagrange-projection method. This chapter shows that adaptive multiresolution techniques can speed up the computation significantly. Even more so when local time-stepping enhancement is used.

The finite pointset method is a meshless Lagrangian particle method. In the application to incompressible viscous fluid flow the solution of Poisson problems on the cloud of particles is a fundamental subproblem. A valuable property of finite difference approximations to the Laplace operator is the positivity of stencils, i.e., all weights of neighboring points are positive. Classical least squares approaches do not guarantee positive stencils. We present a new approach, based on linear minimization, which enforces positivity of stencils and additionally yields a minimal number of nonzero stencil entries. The resulting system matrices are M-matrices, which is of particular interest with respect to multigrid solvers.

We combine the Lagrangian and Eulerian models of linear diffusion phenomena in a coherent differential-geometric framework. This approach is applied to the diffusion—advection equation and its implications are discussed.

A novel hierarchical approach based on decision diagrams (DD) to modelling digital systems is introduced. Two new contributions are proposed: a new classof structurally synthesized binary DDs for modelling structural aspects of digital circuits, and DDs for high-level modelling of systems. Combination of both types of graphs allows to implement uniform formal approach to low- and high-level diagnostic modelling with increased efficiency of fault simulation and test generation for digital systems.

Multidimensional integrals arise in the bayesian approach to positioning using measurements from satellites, mobile phone networks, wireless data networks, etc. Measurement geometries and nongaussian measurement errors produce distinctive features such as multiple peaks and curved ridges. In this chapter compare several subregion adaptive simplicial cubature methods and a Monte Carlo method for typical positioning situations. We find that subregion adaptive methods give the best accuracy for the same number of samples in many two- and three-dimensional problems but that in four dimensions the dimensionality effect favors the Monte Carlo method.

Recognition of control chart patterns (CCPs) is one of the most important technique for monitoring and achieving appropriate control of process environments to raise production quality. In the last 10 years several approaches have been proposed for precise and fast CCP recognition, including rule-based and expert systems, or artificial neural networks, and many efforts have been focused on comparative studies of approximate training algorithms.

This chapter presents a new approach for the identification of control chart patterns by using features dynamically extracted from raw data. Our strategy has the further advantage of avoiding the use of complex data structures and training processes.

We present in this communication an index-1 characterization for differential-algebraic circuit models without passivity assumptions. The use of treebased methods together with the Cauchy—Binet formula makes it possible to generalize previous results in the literature. The approach can be extended to modified node analysis (MNA) models and higher index configurations.

Fingerprints are currently the leading approach to biometric recognition [1]. The reasons are multiple — we mention on the one hand the more than centennial tradition of fingerprint use for forensic purposes and on the other hand the existence of some well-established experience — based rules derived along the line. Fingerprints have a specific flow dynamics, which comes in quite distinct flow patterns — these help define

classes

of fingerprints. The flow pattern carries various singularities, named

minutiae

— most important are line endings and bifurcations.

The second-order MUSCL schemes are considered in the present work. A new limitation procedure is detailed to enforce relevant robustness properties. The scheme is thus shown to preserve the invariant domain.

In this chapter an efficient conservation element—solution element (CE— SE)to construct numerical solutions of time-dependent advection-diffusion equation initial value problems is presented.Stability conditions of the method are established intermsofdata.

Industrial mathematical models often involve uncertainties in the data problem.In this chapter a vector random Euler method is proposed for constructing discrete mean square approximating processes of initial value problems for random differential equations with uncertainties.Convergence conditions and an illustrative example are included.

We discuss the direct use of cubic-matrix splines to obtain continuous approximations to the unique solution of matrix models of the type

Y

″(

x

) =

f

(

x

,

Y

(

x

)). For numerical illustration, an estimation of the approximation error, an algorithm for its implementation, and an example are given.