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Über dieses Buch

This book contains the proceedings of the 17th European Conference on Mathematics for Industry, ECMI2012, held in Lund, Sweden, July 2012, at which ECMI celebrated its 25th anniversary. It covers mathematics in a wide range of applications and methods, from circuit and electromagnetic devices, environment, fibers, flow, medicine, robotics and automotive industry, further applications to methods and education.

The book includes contributions from leading figures in business, science and academia that promote the application of mathematics to industry and emphasize industrial sectors that offer the most exciting opportunities. The contributions reinforce the role of mathematics as being a catalyst for innovation as well as an overarching resource for industry and business.

The book features an accessible presentation of real-world problems in industry and finance, provides insight and tools for engineers and scientists who will help them to solve similar problems and offers modeling and simulation techniques that will provide mathematicians with a source of fresh ideas and inspiration.

Inhaltsverzeichnis

Frontmatter

Circuits and Electromagnetic Devices

Frontmatter

Normal Hyperbolicity of Manifolds of Equilibria in Nonlinear Circuits with Mem-Devices

The memristor

Nano-electronics

Circuits with mem-devices

Circuits

Riaza, R.

and other mem-devices are displaying a great impact on modern electronics. We examine in this communication certain dynamical features of circuits with memristors, memcapacitors and meminductors, related to the systematic presence of non-isolated equilibria in these nonlinear circuits.

Ricardo Riaza

Index Analysis of Branch-Oriented and Hybrid Models of Non-passive Circuits

We extend

Circuits

DAE index analysis

DAE index

Riaza, R.

García de la Vega, I.

in this communication previous index analyses of branch-oriented and hybrid circuit models to a non-passive context. Specifically, in the absence of coupling effects, we present a complete characterization of index one and index two branch-oriented models, and index zero and index one hybrid models. The results are based on the structure of the forests of certain circuit minors.

Ignacio García de la Vega, Ricardo Riaza

Multiscale Modeling of Heterojunction Organic Photovoltaic Devices

In this

Porro, M.

de Falco, C.

Sacco, R.

Verri, M.

Organic solar cell

Nonlinear reaction-diffusion system with electrostatic convection

Scale transition

Multiscale analysis

communication, we present a computational model for heterojunction Organic Photovoltaic (OPV) devices consisting of a system of semilinear PDEs and ODEs. The mathematical model is discussed, focusing on the transmission conditions at material interfaces, together with the numerical method used for its solution. Steady-state and transient simulations are performed on realistic devices with various interface morphologies.

Matteo Porro, Carlo de Falco, Riccardo Sacco, Maurizio Verri

Simulation of Nanoscale Double-Gate MOSFETs

A nanoscale

Camiola, V.D.

Mascali, G.

Romano, V.

Nanoscale double-gate MOSFET

Subband model

Maximum entropy principle

double-gate MOSFET is simulated by using a subband model based on the maximum entropy principle (MEP).

V. Dario Camiola, Giovanni Mascali, Vittorio Romano

Coupled Heat-Electromagnetic Simulation of Inductive Charging Stations for Electric Vehicles

Coupled

Kaufmann, C.

Günther, M.

Klagges, D.

Richwin, M.

Schöps, S.

ter Maten, E.J.W.

Coupled simulation

Cot

Electromagnetic

Heat

Time integration

electromagnetic-heat problems have been studied for induction or inductive heating, for dielectric heating, for testing of corrosion, for detection of cracks, for hardening of steel, and more recently for inductive charging of electric vehicles. In nearly all cases a simple co-simulation is made where the electromagnetics problem is solved in the frequency domain (and which thus is assumed to be linear) and the heat equation in the time domain. One exchanges data after each time step (or after some change in the heat profile). However, the coupled problem is non-linear in the heat variable. In this paper we propose to split the time domain in windows in which we solve the electromagnetics problem in frequency domain. We strengthen the coupling by iterations, for which we prove convergence. By this we obtain a higher accuracy, which will allow for larger time steps and also for higher order time integration. This fully exploits the multirate behavior of the coupled system. An industrial example illustrates the analysis.

Christof Kaufmann, Michael Günther, Daniel Klagges, Matthias Richwin, Sebastian Schöps, E. Jan W. ter Maten

Environment

Frontmatter

Optimal Location of River Sampling Stations: A Case Study

Usual

Water pollution monitoring station

Pollution

Optimal location

Optimization

Alvarez-Vázquez, L.J.

Martínez, A.

Vázquez-Méndez, M.E.

Pollak, A.W.

Peirce, J.J

methods for monitoring and controlling river pollution include the establishment of water pollution monitoring stations located along the length of the river. The point where each station is located (known as sampling point) is of crucial importance if we want to obtain representative information about industrial and domestic pollution in the whole river, not only in the sampling points. In this work, the optimal location of sampling points is studied combining numerical simulation and optimization techniques. Based on a one dimensional system of partial differential equations, a mathematical formulation of the optimization problem is proposed, and it is solved for a real case on Neuse River (North Caroline, USA), where interesting conclusions are derived for the number of water quality sensors and their respective locations.

Lino J. Alvarez-Vázquez, Aurea Martínez, Miguel E. Vázquez-Méndez, A. W. Pollak, J. Jeffrey Peirce

Global Analysis of a Nonlinear Model for Biodegradation of Toxic Compounds in a Wastewater Treatment Process

The

Dimitrova, N.

Wastewater treatment

Bazb

Stability analysis

Numerical simulation

paper presents rigorous mathematical stability analysis of a dynamic model, describing biodegradation of toxic substances in a wastewater treatment plant. Numerical simulations support the theoretical results.

Neli Dimitrova

Pollutant Transport and Its Alleviation in Groundwater Aquifers

Dissolved

Pollution

transport

Pollution

Aquifer flow

Pollution

remediation

Ali, A.

Sweatman, W.L.

McKibbin, R.

chemicals are transported through groundwater aquifers by a mixture of advection with the underlying fluid flow and dispersion within that fluid. The aquifers can be modelled using a layered structure which simplifies the calculation of vertical transport. This simplified model still allows for the natural stratification which occurs in such systems and the changes in physical properties of the aquifer that occur between different geological layers. Equations are presented to calculate the subsequent concentration of the releases of chemicals into this system. A particular example is considered where an instantaneous release of pollutant occurs and it is subsequently remediated by the downstream release of a suitable pollutant removal agent.

Amjad Ali, Winston L. Sweatman, Robert McKibbin

Optimal Shape Design of Wastewater Canals in a Thermal Power Station

Inside

Alvarez-Vázquez, L.J.

Martínez, A.

Vázquez-Méndez, M.E.

Rodríguez, C.

Vilar, M.A.

Optimal design

Wastewater canal

Power plant

the canals of wastewater treatment plants of thermal power stations usually produces in a natural way a deposition of particles in suspension, which causes a change in geometry of the bottom of channel, with the consequent appearance of accumulated sludge and growth of algae and vegetation. This fact may lead to a misfunction of the purification process in the plant. Our main aim focuses on the optimal design of the geometry of such canals to avoid the difficulties derived from these processes. The problem can be formulated as a control-constrained optimal control problem of partial differential equations, and discretized via a characteristics/finite element method. For a simplified case study (canals of rectangular section), theoretical and applicable results are presented.

Aurea Martínez, Lino J. Alvarez-Vázquez, Carmen Rodríguez, Miguel E. Vázquez-Méndez, Miguel A. Vilar

Mathematical Treatment of Environmental Models

Large-scale

Enviromental model

Air pollution

Pollution

Zlatev, Z.

Faragó, I.

Havasi, A.

environmental models can successfully be used in different important for the modern society studies as, for example, in the investigation of the influence of the future climatic changes on pollution levels in different countries. Such models are normally described mathematically by non-linear systems of partial differential equations, which are defined on very large spatial domains and have to be solved numerically on very long time intervals. Moreover, very often many different scenarios have also to be developed and used in the investigations. Therefore, both the storage requirements and the computational work are enormous. The great difficulties can be overcome only if the following four tasks are successfully resolved: (a) fast and sufficiently accurate numerical methods are to be selected, (b) reliable and efficient splitting procedures are to be applied, (c) the cache memories of the available computers are to be efficiently exploited and (d) the codes are to be parallelized.

Zahari Zlatev, István Faragó, Ágnes Havasi

Model-Based Assessment of Geophysical Observations: From Numerical Simulations Towards Volcano Hazard Forecasting

Geodetic,

Currenti, G.

Del Negro, C.

FEM simulations

Volcano hazard forecasting

Finite element method

Numerical simulation

gravity and magnetic field changes, produced by mass and stress redistributions accompanying magma migration and accumulation within the volcano edifice, are numerically computed by an integrated elastic 3-D model based on Finite Element Method (FEM). Firstly, comparisons are made between analytical and numerical solutions to validate the numerical model and to estimate the perturbations caused by medium heterogeneity and topographic features. Successively, the integrated numerical procedure was applied to interpret geophysical observations collected at Etna volcano during unrest periods. The obtained results highlight that heterogeneity and topography engender deviations from analytical results in the geophysical changes and, hence, the disregard of these complexities could lead to an inaccurate estimate of source parameters in inversion procedure. The FEM approach allows for considering a picture of a fully 3D model of Etna volcano, which advance the reliability of model-based assessments of geophysical observations. This approach, based on observable data and complemented by physical modeling techniques, makes the step ahead in the volcano hazard assessment and in the understanding of the underlying physics and poses the basis for future developments of scenario forecasting.

Gilda Currenti, Ciro Del Negro

Thermal and Rheological Aspects in a Channeled Lava Flow

We

Filippucci, M..

Tallarico, A.

Dragoni, M.

Lava flow

Cooling

Pseudoplastic

Heat

equation

investigated the cooling of a lava flow in the steady state considering that lava rheology is pseudoplastic and dependent on temperature. We consider that cooling of the lava is caused by thermal radiation at the surface into the atmosphere and thermal conduction at the channel walls and at the ground. The heat equation is solved numerically in a 3D computational domain. The fraction of crust coverage is calculated under the assumption that the solid lava is a plastic body with temperature dependent yield strength. We applied the results to the Mauna Loa (1984) lava flow. Results indicate that the advective heat transport significantly modifies the cooling rate of lava slowing down the cooling process also for gentle slope.

Marilena Filippucci, Andrea Tallarico, Michele Dragoni

Fibers

Frontmatter

On Viscoelastic Fiber Spinning: Die Swell Effect in the 1D Uniaxial UCM Model

This

Jet spinning

Die swell

UCM model

Lorenz, M.

Marheineke, N.

Wegener, R.

work deals with a stationary viscoelastic jet under gravitational forces described by an upper convected Maxwell (UCM) model. For spinning processes we demonstrate that a die swell-like behavior of the solution is in general possible for the asymptotically derived one-dimensional model equations. Nevertheless, to use the model for the prediction of a die swell appropriate boundary conditions or the inclusion of further effects such as surface tension have to be considered. Moreover, the regime of existence of solutions for drawing processes is determined numerically.

Nicole Marheineke, Raimund Wegener

Numerical Treatment of Non-stationary Viscous Cosserat Rod in a Two-Dimensional Eulerian Framework

This

Viscous jet

Jet spinning

Arne, W.

Marheineke, N.

Meister, A.

Wegener, R.

work deals with the modeling and simulation of the dynamics of a slender viscous jet as it arises in spinning processes. There exist two classes of asymptotic one-dimensional models for such a jet, string and more complex rod models, that are given by systems of partial and ordinary differential equations. In this paper, we present non-stationary simulations of a rod in an Eulerian framework for arbitrary parameter ranges of 2d spinning where the string models failed so far. The numerical treatment is based on a finite volume approach with mixed central, up- and downwinded differences, the time integration is performed by a Radau method.

Walter Arne, Nicole Marheineke, Andreas Meister, Raimund Wegener

Asymptotic Modeling Framework for Fiber-Flow Interactions in a Two-Way Coupling

In

Cibis, T.M.

Marheineke, N.

Wegener, R.

Fiber f

Slender-body theory

Two-way coupling

Asymptotics

this work we describe fiber-flow interactions by help of a two-way coupling approach that is based on slender-body theory and the modeling of exchange functions in terms of drag forces and heat sources. The exchange functions are incorporated in the conservation equations for linear momentum and energy with respect to flow and fibers and satisfy a generalized action-reaction principle.

Thomas Martin Cibis, Nicole Marheineke, Raimund Wegener

Efficient Simulation of Random Fields for Fiber-Fluid Interactions in Isotropic Turbulence

In

Hübsch, F.

Marheineke, N.

Wegener, R.

Turbulent flow

Fiber f

Jet spinning

Random field

One-way coupling

Isotropy

Turbulence

Turbulence

models

some processes for spinning synthetic fibers the filaments are exposed to highly turbulent flows to achieve a high degree of stretching. The quality of the resulting fabric is thus determined essentially by the turbulent fiber-fluid interactions. Due to the required fine resolution, direct numerical simulations fail. Therefore we model the flow fluctuations as random field in

$${\mathbb{R}}^{4}$$

on top of a k-

ε

turbulence description and describe the interactions in the context of slender-body theory as one-way-coupling with a corresponding stochastic aerodynamic drag force on the fibers. Hereby we exploit the special covariance structure of the random field, namely isotropy, homogeneity and decoupling of space and time. In this work we will focus on the construction and efficient simulation of the turbulent fluctuations assuming constant flow parameters and give an outlook on applications.

Florian Hübsch, Nicole Marheineke, Raimund Wegener

On Stability of a Concentrated Fiber Suspension Flow

Linear

Stability analysis

Fiber suspension

Modified Folgar-Tucker model

Instability

Orr-Sommerfeld eigenvalues

Strautins, U.

stability analysis of a fiber suspension flow in a channel domain is performed using a modified Folgar-Tucker equation. Two kinds of potential instability are identified: one is associated with overcritical Reynolds number and another is associated with certain perturbations in fiber orientation field and is present for any Reynolds numbers. The second type of instability leads to initially growing transient perturbations in the microstructure. It is shown that both types of instability lead to instability of the bulk velocity field. As for the perturbed Orr-Sommerfeld eigenvalues, the presence of fibers increases the stability region; the stability region increases with growing

C

i

and decreases with growing

S

0

in the modified Folgar-Tucker model.

Uldis Strautins

Microstructure Simulation of Paper Forming

This

Svenning, E.

Mark, A.

Martinsson, L.

Lai, R.

Fredlund, M.

Nyman, U.

Edelvik, F.

Fiber suspension

Fluid structure interaction

Immersed boundary methods

Microstructure

work presents a numerical framework designed to simulate the early paper forming process. This process is complex and includes strong fluid-structure interaction and complex geometries. The fluid flow solver IBOFlow, employs immersed boundary methods to simulate the flow around the fibers without the necessity of a boundary conforming grid. The fibers are approximated as slender beams with an elliptic cross section and modeled with the Euler-Bernoulli beam equation. A penalty based contact model is implemented. Finally, the potential of the framework is illustrated with an example.

Erik Svenning, Andreas Mark, Lars Martinsson, Ron Lai, Mats Fredlund, Ulf Nyman, Fredrik Edelvik

Three-Dimensional Fiber Lay-Down in an Industrial Application

In

Klar, A.

Maringer, J.

Wegener, R.

Fiber lay-down

Stochastic differential equations

Parameter identification

this work we present fiber lay-down models that enable an efficient simulation of nonwoven structures. The models describe the form of deposited fibers with help of stochastic differential equations. The model parameters have to be estimated from more complex models in combination with measurements of the resulting nonwoven. We discuss the adaptation of a three-dimensional model on the basis of a typical industrial problem.

Johannes Maringer, Axel Klar, Raimund Wegener

3d Modeling of Dense Packings of Bended Fibers

For the

Altendorf, H.

Jeulin, D.

Mathematical morphology

Multivariate von Mises-Fisher distribution

Random walk

Stochastic modeling

Force-biased fiber packing

simulation of fiber systems, there exist several stochastic models: systems of straight non overlapping fibers, systems of overlapping bending fibers, or fiber systems created by sedimentation. However, there is a lack of models providing dense, non overlapping fiber systems with a given random orientation distribution and a controllable level of bending. We present in this paper the recently developed stochastic model that generalizes the force-biased packing approach to fibers represented as chains of balls. The starting configuration is a boolean system of fibers modeled by random walks, where two parameters in the multivariate von Mises-Fisher orientation distribution control the bending. The points of the random walk are associated with a radius and the current orientation. The resulting chains of balls are interpreted as fibers. The final fiber configuration is obtained as an equilibrium between repulsion forces avoiding crossing fibers and recover forces ensuring the fiber structure. This approach can provide high volume fractions up to 72 %. Furthermore, we study the efficiency of replacing the boolean system by a more intelligent placing strategy, before starting the packing process. Experiments show that a placing strategy is highly efficient for intermediate volume fraction.

Hellen Altendorf, Dominique Jeulin

Flow

Frontmatter

Simulation of a Rubber Beam Interacting with a Two-Phase Flow in a Rolling Tank

The

Svenning, E.

Mark, A.

Edelvik, F.

Fluid structure interaction

Immersed boundary methods

Sloshing tank

FSI benchmark

aim of this paper is to present and validate a modeling framework that can be used for simulation of industrial applications involving fluid structure interaction with large deformations. Fluid structure interaction phenomena involving elastic structures frequently occur in industrial applications such as rubber bushings filled with oil, the filling of liquid in a paperboard package or a fiber suspension flowing through a paper machine. Simulations of such phenomena are challenging due to the strong coupling between the fluid and the elastic structure. In the literature, this coupling is often achieved with an Arbitrary Lagrangian Eulerian framework or with smooth particle hydrodynamics methods. In the present work, an immersed boundary method is used to couple a finite volume based Navier-Stokes solver with a finite element based structural mechanics solver for large deformations. The benchmark of an elastic rubber beam in a rolling tank partially filled with oil is simulated. The simulations are compared to experimental data as well as numerical simulations published in the literature. 2D simulations performed in the present work agree well with previously published data. Our 3D simulations capture effects neglected in the 2D case, showing excellent agreement with previously published experiments. The good agreement with experimental data shows that the developed framework is suitable for simulation of industrial applications involving fluid structure interaction. If the structure is made of a highly elastic material, e.g. rubber, the simulation framework must be able to handle the large deformations that may occur. Immersed boundary methods are well suited for such applications, since they can efficiently handle moving objects without the need of a body-fitted mesh. Combining them with a structural mechanics solver for large deformations allows complex fluid structure interaction problems to be studied.

Erik Svenning, Andreas Mark, Fredrik Edelvik

Modelling of a Simplified Fluid-Structure Interaction Formulation

A

Fluid structure interaction

Differential algebraic equations

Niemeyer, J.

Simeon, B.

simplified formulation of the fluid-structure interaction problem is presented in order to analyze the coupling conditions and the effect of a moving fluid domain on the numerical solution. The resulting one-dimensional model equations are discretized by the finite element method in space and then solved by implicit timestepping schemes, with the coupling conditions explicitly enforced by means of corresponding constraint equations in a differential-algebraic formulation. First numerical results indicate an influence of the moving fluid mesh on the stability properties of commonly used time integrators.

Julia Niemeyer, Bernd Simeon

Sinking Bubbles in Stout Beers

Anyone

Cummins, C.P.

Benilov, E.S.

Lee, W.T.

Guinness beer

Fluid bubbles

who has ever tried Guinness or another stout beer knows that the bubbles in the glass appear to sink. This suggests that they are driven by a downward flow, the velocity of which exceeds the upward velocity of the bubble due to the Archimedean force. The existence of such a flow near the wall of the glass implies that there must be an upward flow somewhere in the interior. The mechanism of such a circulation is, however, unclear. In this work, we demonstrate that the circulation in a glass of stout—or any other container with a bubbly liquid—is determined by the container’s shape. If it narrows downwards (as the stout glass does), the circulation is directed downwards near the wall and upwards in the interior. If the container widens downwards, the circulation is opposite to that described above.

Cathal P. Cummins, Eugene S. Benilov, William T. Lee

Analysis of Two-Phase Flow in the Gas Diffusion Layer of a Polymer Electrolyte Fuel Cell

The

Gordon, A.

Vynnycky, M.

Polymer electrolyte fuel cell (PEFC)

Two-phase (gas/liquid) flow

Porous gas diffusion layer (GDL)

Darcy’s law

Porous material

last decade has seen a proliferation of modelling activity on the polymer electrolyte fuel cell (PEFC); an important subset of this activity is the modelling of the two-phase (gas/liquid) flow that occurs in the porous gas diffusion layer (GDL) on the cathode (Djilali, Energy 32:269–280, 2007; Gurau and Mann, SIAM J. Appl. Maths 70:410–454, 2009). The prevailing approach employs a generalized form of Darcy’s law, which has been widely used over the last several decades to analyze the movement of oil and water in soils and porous rock (Bear, Dynamics of Fluids in Porous Media, American Elsevier, New York, 1972). Applied to water transport in fuel cells, the Darcy model characterizes the response of the porous material by the capillary pressure, the gas and liquid phase relative permeabilities, and the effective gas diffusion coefficient, all of which depend on the fraction of the local pore volume occupied by liquid water; an additional feature is that the porous medium can be either hydrophobic or hydrophilic. The majority of approaches have, however, been primarily numerical, which has obscured some of the properties of the model. Here, using asymptotic methods, we extend earlier work (Vynnycky, Appl. Math. Comp. 189:1560–1575, 2007) to demonstrate how the degree of water saturation depends on the liquid phase relative permeability, as well as how the model behaves when the GDL is only just hydrophilic.

Andrew Gordon, Michael Vynnycky

A Criterion for Air-Gap Formation in Vertical Continuous Casting: The Effect of Superheat

The

Vynnycky, M.

Continuous casting

Air pola

Asymptotics

formation of an air gap at the mould-metal interface in continuous casting has long been known to have a detrimental effect on the efficiency of the process, and has therefore attracted many attempts at mathematical modelling. While many efforts consist of complex three-dimensional numerical simulations of the phenomenon, a sequence of recent papers by the present author has used asymptotic techniques to derive a quasi-analytical model that captures the essential characteristics. The model allows for full two-way coupling between the thermal and mechanical problems: the formation of the air gap affects the heat transfer, whilst the heat transfer affects the stresses that lead to the formation and evolution of the air gap. In this contribution, earlier numerical results for the case of superheat—when the molten metal temperature is greater than the melting temperature—are complemented by an analysis of the criterion that predicts how the onset of air-gap formation depends on process parameters: the mould temperature, the casting speed and the superheat itself.

Michael Vynnycky

Moulding Contact Lenses

The

Murphy, E.

Lee, W.T.

Monomer flow

Polar coordinates

moulding process in the manufacture of a certain monomer-based product, is modelled using the thin film approximation with the aim of reducing defects in which the mould is partially filled. A simple model neglecting curvature of the moulds is considered first. This assumption is verified by a polar coordinate model that investigates the effects of curvature of the dynamics of the fluid. We investigate the role of surface tension and horizontal motion of the lower mould in the formation of defects.

Ellen Murphy, William T. Lee

Enhanced Water Flow in Carbon Nanotubes and the Navier Slip Condition

A

Carbon nanotubes

Nanotubes

Enhanced flow

Slip length

Navier slip

Myers, T.G.

possible explanation for the enhanced flow in carbon nanotubes is given using a mathematical model that includes a depletion layer with reduced viscosity near the wall. In the limit of large tubes the model predicts no noticeable enhancement. For smaller tubes the model predicts enhancement that increases as the radius decreases. An analogy between the reduced viscosity and slip-length models shows that the term slip-length is misleading and that on surfaces which are smooth at the nanoscale it may be thought of as a length-scale associated with the size of the depletion region and viscosity ratio. The model therefore provides a physical interpretation of the classical Navier slip condition and explains why “slip-lengths” may be greater than the tube radius.

Tim G. Myers

Flow Field Numerical Research in a Low-Pressure Centrifugal Compressor with Vaneless Diffuser

This

Frolov, A.

Izmaylov, R.

Voroshnin, D.

Centrifugal compressor

Vaneless diffuser

Precursor stall

Rotating stall

Turbulence

models

Numerical simulation

work demonstrates the results of the first phase of the problem that is aimed at the numerical investigation of such unsteady effects as the precursor stall and the rotating stall in the stage with a vaneless diffuser of a centrifugal compressor. This paper is focused on the capabilities and constraints of the steady-state numerical simulations for an accurate prediction of the flow through the compressor stage. Numerical simulations were carried out in NUMECA FINE/TURBO 8.9.1 for a single blade passage. The results were validated through a comparison with the experimental data at the diffuser inlet and outlet. The results of numerical simulations using different discretization schemes and turbulence models predicted different flow structure. The results obtained with the second order discretization agree with the experiments for the steady-state case in the region of high flows rates. In the area of low flow rates the unsteady effects significantly influence the flow leading to poor predictions. An analysis of an influence of the geometry model and the grid resolution on the convergence is required to predict the satisfactory agreement with experiment.

Alexey Frolov, Rudolf Izmaylov, Denis Voroshnin

Large Eddy Simulation of Boundary-Layer Flows over Two-Dimensional Hills

Large

Chaudhari, A.

Hellsten, A.

Agafonova, O.

Hämäläinen, J.

Boundary layer

Large eddy simulation

Hill

Hill

slope

Separation

Turbulence

Turbulence

models

Eddy Simulations (LES) are performed for turbulent boundary-layer flows over two-dimensional (2D) hills or ridges of two different slopes at Reynolds number equal to 3,120 based on the hill height and the free stream velocity. The surface of the hill is assumed to be aerodynamically smooth. The hill height is considerably smaller than the boundary-layer depth. The hill models used in this study are the same as those used in the RUSHIL wind tunnel experiment carried out by Khurshudyan et al. (United States Environmental Protection Agency Report, EPA-600/4-81-067, 1981) and LES results are compared with the wind tunnel measurements. This study focuses on the overall flow behaviour changes as a function of the hill slope. The results of the mean velocity, the flow separation, and the turbulence quantities are discussed in the paper. It is shown that LES produces overall satisfactory results on the turbulent flow over the 2D hills. Especially for less steep hill, the flow behaviour is well predicted by LES.

Ashvinkumar Chaudhari, Antti Hellsten, Oxana Agafonova, Jari Hämäläinen

Medicine

Frontmatter

A Visual Representation of the Drug Input and Disposition Based on a Bayesian Approach

Compliance

Drug input and deposition

Bayesian approach

Barrière, O.

Li, J.

Nekka, F.

to a drug prescription describes the degree to which a patient correctly follows medical advice. Poor compliance significantly impacts on the efficacy and safety of a planned therapy, which can be summed up by the dictum: “a drug only works if it’s taken”. However, the relationship between drug intake and pharmacokinetics (PK) is only partially known, especially the so-called inverse problem, concerned with the issue of retracing the patient compliance scenario using limited clinical knowledge. Based on the Bayesian theory, we develop a decision rule to solve this problem. Given an observed concentration, we determine, among all possible compliance scenarios, which is the most probable one. Using a simulation approach, we are able to judge the quality of this retracing process by measuring its global performance. Since the sampling concentration is the result of both patient compliance (drug input) and patient PK characteristics (drug disposition), two natural questions arise here: first, given two different sampling concentration values, can we expect the same performance of the retracing process? Second, how is this performance affected by the PK variability between individuals? For this, we here design an heatmap-style image, called Compliance Spectrum, that provides an intuitive and interactive way to evaluate the relationship between drug input and drug disposition along with their consequences on PK profile. The current work provides a solution to this inverse problem of compliance determination from a probability viewpoint and uses it as a base to build a visual representation of drug input and disposition.

Olivier Barrière, Jun Li, Fahima Nekka

Modelling a Competitive Antibody/Antigen Chemical Reaction that Occurs in the Fluorescence Capillary-Fill Device

A

Rebelo, M.

Diogo, T.

McKee, S.

Fluorescence capillary-fill device

Competitive antibody/antigen chemical reaction

Diffusion equation

Integro-differential equation

mathematical model in the form of two coupled diffusion equations is provided for a competitive chemical reaction between an antigen and a labelled antigen for antibody sites on a cell wall; boundary conditions are such that the problem is both nonlinear and nonlocal. This is then re-characterized as a pair of coupled singular integro-differential equations which is solved by a product integration method. Some numerical results based on real data are presented.

Magda Rebelo, Teresa Diogo, Sean McKee

Model-Based Medical Decision Support for Glucose Balance in ICU Patients: Optimization and Analysis

Model-based medical decision support in terms of computer simulations and predictions gains increasing importance in health care systems worldwide. This work deals with the control of the glucose balance in ICU patients using an insulin therapy. The basis of our investigations is the simulation model GlucoSafe by Pielmeier et al. that describes the temporal evolution of the blood glucose and insulin concentrations in the human body by help of a nonlinear dynamic system of first-order ordinary differential equations. We aim at the theoretical analysis and numerical treatment of the arising optimal control problem.

Thomas Martin Cibis, Nicole Marheineke

Epileptic Seizures Diagnose Using Kunchenko’s Polynomials Template Matching

The paper related to epilepsy’s diagnosis as EEG analysis problem. Template matching method based on a Kunchenko’s polynomials for EEG processing introduced. To demonstrate efficiency of method numeric experiment is given.

Oleg Chertov, Taras Slipets

Robotics and Automotive Industry

Frontmatter

Collision-Free Path Planning of Welding Robots

In a competitive industry, production lines must be efficient. In practice, this means an optimal task assignment between the robots and an optimal motion of the robots between their tasks. To be optimal, this motion must be collision-free and as fast as possible. It is obtained by solving an optimal control problem where the objective function is the time to reach the final position and the ordinary differential equations are the dynamics of the robot. The collision avoidance criterion is a consequence of Farkas’s lemma. The criterion is included in the optimal control problem as state constraints and allows us to initialize most of the control variables efficiently. The resulting model is solved by a sequential quadratic programming method where an active set strategy based on backface culling is added.

Chantal Landry, Matthias Gerdts, René Henrion, Dietmar Hömberg, Wolfgang Welz

Motion Planning for Mechanical Systems with Hybrid Dynamics

Planning and optimal control of mechanical systems are challenging tasks in robotics as well as in many other application areas, e.g. in automotive systems or in space mission design. This holds in particular for hybrid, i.e. mixed discrete and continuous dynamical models. In this contribution, we present an approach to solve control problems for hybrid dynamical systems by motion planning with motion primitives. These canonical motions either origin from inherent symmetry properties of the systems or they are controlled maneuvers that allow sequencing of several primitives. The motion primitives are collected in a motion planning library. A solution to a specific optimal control problem can then be found by searching for the optimal sequence of concatenated primitives. Energy efficiency often forms an important objective in control applications. We therefore extend the motion planning framework by primitives that are motions along invariant manifolds of the uncontrolled dynamics, e.g. trajectories on (un)stable manifolds of equilibria. The approach is illustrated by an academic example motivated by an operating scenario of an open-chain jointed robot.

Kathrin Flaßkamp, Sina Ober-Blöbaum

Performance of Sensitivity Based NMPC Updates in Automotive Applications

In this work we consider a half car model which is subject to unknown but measurable disturbances. To control this system, we impose a combination of model predictive control without stabilizing terminal constraints or cost to generate a nominal solution and sensitivity updates to handle the disturbances. For this approach, stability of the resulting closed loop can be guaranteed using a relaxed Lyapunov argument on the nominal system and Lipschitz conditions on the open loop change of the optimal value function and the stage costs. For the considered example, the proposed approach is realtime applicable and corresponding results show significant performance improvements of the updated solution with respect to comfort and handling properties.

Jürgen Pannek, Matthias Gerdts

Optimal Control in Proactive Chassis Dynamics: A Fixed Step Size Time-Stepping Scheme for Complementarity Problems

This paper is about a fixed step size time-stepping scheme for the computation of solutions of complementarity problems. As we want to optimise chassis dynamics by solving optimal control problems, we took a closer look at modeling contact conditions. The latter are important, as the contact force is directly related to handling caracteristics of the automobile. This plays an important role particularly in certain driving situations, e.g. driving over a pothole. Hereafter the motivation for the development is carried out and the components of the scheme are explained. At the end we compare the calculation of a quartercar with a spring-damper road to wheel interaction to those resulting from the complementarity problem.

Johannes Michael, Matthias Gerdts

Model Reduction of Contact Problems in Elasticity: Proper Orthogonal Decomposition for Variational Inequalities

In this contribution a model order reduction method is applied to a Signorini contact problem. Due to the contact constraints classical linear reduction methods such as Craig–Bampton are not applicable. The Signorini contact problem is formulated as a variational inequality and Proper Orthogonal Decomposition (POD) is used to calculate an optimal projection subspace. Numerical results of the reduced model’s quality and efficiency for an Encastre beam with contact are presented.

Joachim Krenciszek, René Pinnau

Novel Updating Mechanisms for Stochastic Lattice-Free Traffic Dynamics

We present a novel lattice-free microscopic stochastic process in order to model vehicular traffic. Vehicles advance freely in a multi-lane environment without lattice cells limitations. As a result vehicles perform their moves based on a modified stochastic spin-flip and spin-exchange Arrhenius dynamic potential. Furthermore we put forward a modified kinetic Monte Carlo algorithm which produces the solution for these dynamics in real-time even for the case of a large traffic streams. An up to now unknown discrepancy is revealed between models using classical lattice-based methods versus those implementing this new lattice-free approach. The solution proposed by Renyi as well as the Palasti conjecture help in clarifying this discrepancy by showing that indeed the new proposed lattice-free process is correct in predicting traffic densities while avoiding the overestimates produced by classic Cellular Automata type, lattice-based, approaches.

Alexandros Sopasakis

Further Applications

Frontmatter

Modelling Some Recrystallization Processes with Random Growth Velocity of the Grains

Heterogeneous transformations (or reactions) may be defined as those transformations in which there is a sharp moving boundary between the transformed and untransformed region. Such transformations may be modelled by the so-called birth-and-growth processes. We focus here on the effect that a random velocity of the moving boundaries of the grains has in the overall kinetics. One example of a practical situation in which such a model may be useful is that of recrystallization; a recent review of 3-D experimental results on recrystallization kinetics concluded that there is compelling evidence that every grain has its own distinct growth rate. Motivated by this practical application we present general kinetics expressions for various situations of practical interest, in which a random distribution of growth velocities is assumed. Previously known results follow here as particular cases. Although the motivation was recrystallization, the expressions presented here may be applied to nucleation and growth reactions in general.

Elena Villa, Paulo R. Rios

A Mathematical Model for the Melting of Spherical Nanoparticles

This paper will specifically deal with the melting process of gold nanoparticles. Based on scale analysis we first show that retaining previously neglected terms in the Gibbs–Thomson equation (describing the melt temperature as a function of size) can have a significant effect on results. Asymptotic and numerical results for the position of the melting front are presented for spherical nanoparticles. They appear to match well down to the final stages of melting.

Francesc Font, Tim G. Myers, Michelle MacDevette

Local Quantum-Like Updates in Classical Molecular Simulation Realized Within an Uncoupling-Coupling Approach

In this article a method to improve the precision of the classical molecular dynamics force field by solving an approximation problem with scattered quantum mechanical data is presented. This novel technique is based on two steps. In the first step a partition of unity scheme is used for partitioning the state space by meshfree basis functions. As a consequence the potential can be localized for each basis function. In a second step, for one state in each meshfree basis function, the precise QM-based charges are computed. These local QM-based charges are then used, to optimize the local potential function. The performance of this method is shown for the alanine tripeptide.

Konstantin Fackeldey, Alexander Bujotzek

Design of Automatic Eye Protective Welding Devices

LCD light shutters used as eye protective devices in welding environments have different requirements from LCD display devices typically used in consumer electronics. Their contrast must be many scales greater, while in the open state the shutter should be brighter. The light scattering should almost vanish and the switching time should be much shorter. This implies a different approach as typical solutions used in LCD displays don’t meet the required criteria. Although there are many solutions and concepts that are shared between both types of devices, the light shutters have a much different design. In order to find an optimal configuration many cells should be built and tested. However, this is a very time consuming task as there are many parameters that should be taken in consideration and each cell may take few days to build and test. This is where the computer simulation steps into. It takes only a few minutes to build an appropriate setup for a particular cell and to simulate it, leaving to the experimental tests only some fine tuning. Furthermore, the simulations give a deeper insight in what is really happening with the light polarization within the cell. Such a way a better understanding can be achieved. The simulator works with two different approaches. In the first approach it tries to give the best possible and exact numerical solution. It does so by minimizing the Frank elastic energy of a particular LC layer and by solving the Maxwell equations for the complete stack of optical elements. For the latter the Berreman method is used reducing a system of partial differential equations to 4 × 4 matrices manipulation (multiplication, inversion and eigenvalue problem). Although such an approach is very accurate and mimics the reality quite well it doesn’t give a deeper insight in the cell functionality. In such cases it is better to reduce the LC layer to a few simple uniaxial layers and follow the light polarization change by means of the transformations on the Poincar sphere. This makes it a very efficient tool in shutter design.

Matej Bazec, Bernarda Urankar, Janez Pirs

A Three-Segment Inverse Method for the Design of CoA Correcting TIR Collimators

Color-over-Angle (CoA) variation in the light output of white phosphor-converted LEDs is a common and unsolved problem. Recently, the same authors introduced a new inverse method to reduce CoA variation using a special collimator. This short paper introduces a variant of the method with two important advantages compared to the original method.

Corien Prins, Jan ten Thije Boonkkamp, Teus Tukker, Wilbert IJzerman

Mathematical Modelling of Haptic Touchscreens

Haptic keyboards for touchscreen mobile devices would increase the accuracy of users typing, allow touchtyping and increase the satisfaction of users interacting with the devices. We report the results of a feasibility study of one method of implementing such haptic keyboards: driving transverse waves of the touchscreen using piezoelectric transducers mounted at the edges. Our results, while very preliminary, do suggest that this approach is feasible, and that a more detailed investigation is worthwhile.

William T. Lee, Eoin English, Mark Murphy

A Covariant Spacetime Approach to Transformation Acoustics

Transformation acoustics focuses on the design of advanced acoustic devices by employing sophisticated mathematical transformation techniques for engineering acoustic metamaterials—materials artificially fabricated with extraordinary acoustic properties beyond those encountered in nature. We present differential-geometric methods together with a variational principle and show how they form the basis for a powerful framework to control acoustic waves in industrial applications. We conclude with a practical example and implement the acoustic wave equation within a uniform accelerating rigid frame (UAF). As expected, an acoustic event horizon emerges, i.e., a boundary in spacetime beyond which events cannot acoustically affect any outside observer.

Michael M. Tung, Jesús Peinado

Location and Management of a New Industrial Plant

Within the framework of numerical simulation and multi-objective control of partial differential equations (PDE), in this work we deal with the problem of determining the optimal location of a new industrial plant. We begin presenting a mathematical model (a system of nonlinear parabolic PDE) for the numerical simulation of air pollution. Based on this model, and taking into account economic and ecological objectives, we formulate the problem in the field of multi-objective optimal control. We analyze the problem from a cooperative viewpoint, recalling the standard concept of Pareto-optimal solution, and pointing out the Pareto-frontier as a very useful tool in the decision-making process. Finally, some preliminary results for a hypothetical situation in the region of Galicia (NW Spain) are also presented.

Miguel E. Vázquez-Méndez, Lino J. Alvarez-Vázquez, Néstor García-Chan, Aurea Martínez

A Satellite-to-Satellite Laser Tracking Solution Within the Post-Newtonian Model of the Earth Outer Space

Two second order post-Newtonian formulae, one for the two-way frequency shift and the other for the two-way Laser ranging, are derived by means of Synge’s world-function. The formulae can be used to increase the Classical accuracy in tracking passive targets by means of APT systems on board Earth satellites.

Jose M. Gambi, Maria Luisa Garcia del Pino

Methods

Frontmatter

Polynomial-Chaos Based Methods for Differential Algebraic Equations with Random Parameters

Mathematical modelling of technical applications often yields systems of differential algebraic equations (DAEs), for example, in the simulation of electric circuits or mechanical multibody problems. Imperfections of a manufacturing procedure cause undesired variations in the produced devices. These variations can be taken as uncertainties of physical parameters in a DAE model. We replace the varying parameters by random variables to achieve an uncertainty quantification. The time-dependent solution of the DAEs becomes a random process, which is expanded into a series of the polynomial chaos. We can use either a stochastic Galerkin method or a stochastic collocation technique to determine the unknown coefficient functions. The Galerkin method yields a larger coupled system to be solved once, whereas the collocation approach requires to solve the original systems many times. We present numerical simulations of an illustrative example from electrical engineering.

Roland Pulch

Efficient Calculation of Uncertainty Quantification

We consider Uncertainty Quantification (UQ) by expanding the solution in so-called generalized Polynomial Chaos expansions. In these expansions the solution is decomposed into a series with orthogonal polynomials in which the parameter dependency becomes an argument of the orthogonal polynomial basis functions. The time and space dependency remains in the coefficients. In UQ two main approaches are in use: Stochastic Collocation (SC) and Stochastic Galerkin (SG). Practice shows that in many cases SC is more efficient for similar accuracy as obtained by SG. In SC the coefficients in the expansion are approximated by quadrature and thus lead to a large series of deterministic simulations for several parameters. We consider strategies to efficiently perform this sequence of deterministic simulations within SC.

E. Jan W. ter Maten, Roland Pulch, Wil H. A. Schilders, H. H. J. M. Janssen

A Stochastic Geometric Framework for Dynamical Birth-and-Growth Processes: Related Statistical Analysis

A birth-and-growth model is rigorously defined as a suitable combination, involving the Minkowski sum and the Aumann integral, of two very general set-valued processes representing nucleation and growth respectively. The simplicity of the proposed geometrical approach let us avoid problems arising from an analytical definition of the front growth such as boundary regularities. In this framework, growth is generally anisotropic and, according to a mesoscale point of view, is not local, i.e. for a fixed time instant, growth is the same at each point space. The proposed setting allows us to investigate nucleation and growth processes also from a statistical point of view. Different consistent set-valued estimators for growth processes and for the nucleation hitting function are derived.

Giacomo Aletti, Enea G. Bongiorno, Vincenzo Capasso

MATLAB Implementation of Functional Type A Posteriori Error Estimates with Raviart-Thomas Approximation

Work is devoted to comparison of adaptive algorithms based on the functional approach to a posteriori error estimation. Classical elliptic boundary value problems with discontinuities of the first kind in coefficients are considered. Adaptive algorithms are implemented in MATLAB. Both, a standard finite element with continuous piecewise linear approximations and the simplest Raviart-Thomas finite element are used. For mesh adaptations different error indicators are applied. Sequences of finite-element meshes, effectivity indexes for estimates, relative errors of approximate solutions are compared for different error indicators. The results demonstrate that the usage of the Raviart-Thomas approximation considerably improves the efficiency of the corresponding adaptive algorithm.

Maria A. Churilova, Maxim E. Frolov

Finite Element Concepts and Bezier Extraction in Hierarchical Isogeometric Analysis

Isogeometric analysis is an emerging approach combining computer aided geometric design and numerical analysis. Still local refinement techniques for isogeometric analysis are a major issue. One solution is proposed in Vuong et al. (Comput. Methods Appl. Mech. Eng. 200:3554–3567, 2011) and employs a hierarchical concept. This paper is an extension of this work and will discuss the corresponding element concept and apply the Bézier extraction to illustrate the connection to standard finite elements.

Anh-Vu Vuong

A Second Order Finite-Difference Ghost-Cell Method for the Steady-State Solution of Elasticity Problems

This work presents a second order finite-difference ghost cell method for the steady-state solution of elasticity problems. Numerical results are shown for the application of underground volcano activities.

Armando Coco, Gilda Currenti, Giovanni Russo

Time-Exact Solution of Large Linear ODE Systems by Block Krylov Subspace Projections

We propose a time-exact Krylov-subspace-based method for solving large linear inhomogeneous systems of ODE (ordinary differential equations). The method consists of two stages. The first stage is an accurate piecewise polynomial approximation of the inhomogeneous source term, constructed with the help of the truncated SVD (singular value decomposition). The second stage is a special residual-based block Krylov subspace method for the matrix exponential. The accuracy of the method is only restricted by the accuracy of the piecewise polynomial approximation and by the error of the block Krylov process. Since both errors can, in principle, be made arbitrarily small, this yields, at some costs, a time-exact method. Numerical experiments are presented to demonstrate efficiency of the new method, as compared to an exponential time integrator with Krylov subspace matrix function evaluations. This conference paper is based on the preprint (Botchev, A block Krylov subspace time-exact solution method for linear ODE systems, Memorandum 1973, Department of Applied Mathematics, University of Twente, Enschede, 2012,

http://eprints.eemcs.utwente.nl/21277/

).

Mike A. Botchev

Computing Hyperbolic Matrix Functions Using Orthogonal Matrix Polynomials

Hyperbolic matrix functions play a fundamental role in the exact solution of coupled partial differential systems of hyperbolic type. For the numerical solution of these problems, analytic-numerical approximations are most suitable obtained by using the hyperbolic matrix functions sinh(

A

) and cosh(

A

). It is well known that the computation of both functions can be reduced to the cosine of a matrix cos(

A

), which can be effectively calculated, with the disadvantage, however, to require complex arithmetic even though the matrix

A

is real. In this work we focus on approximate calculation of the hyperbolic matrix cosine cosh(

A

) using the truncation of a Hermite matrix polynomials series for cosh(

A

). The proposed approximation allows the efficient computation of this matrix function. An illustrative example is given.

Emilio Defez, Jorge Sastre, Javier Ibáñez, Pedro A. Ruiz

Counter-Harmonic Mean of Symmetric Positive Definite Matrices: Application to Filtering Tensor-Valued Images

Mathematical morphology is a nonlinear image processing methodology based on the computation of supremum (dilation operator) and infimum (erosion operator) in local neighborhoods called structuring elements. This paper deals with computation of supremum and infimum operators for symmetric positive definite (SPD) matrices, which are the basic ingredients for the extension mathematical morphology to SPD matrices-valued images. Approximation to the supremum and infimum associated to the Löwner ellipsoids are computed as the asymptotic cases of nonlinear averaging using the original notion of counter-harmonic mean for SPD matrices. Properties of this approach are explored, including also image examples.

Jesús Angulo

Heat Conduction Problem for Double-Layered Ball

Heat conduction models for double layered spherical sample are developed. Parabolic (classic, based on Fourier’s Law) and hyperbolic (based on Modified Fourier’s Law) heat conduction equations are used to describe processes in the sample during Intensive Quenching. Solution and numerical results are obtained for 1D model using Conservative Averaging method and transforming the original problem for a sphere to a new problem for a slab, with non classic boundary condition. Models include boundary conditions of third kind and non-linear BC case. Numerical results are presented for several relaxation time and initial heat flux values.

Sanda Blomkalna, Andris Buikis

Education

Frontmatter

The ECMI Educational Programme in Mathematics for Industry: A Long Term Success Story

Here a description of the history and the main characteristics of the ECMI Educational Programme in Mathematics for Industry is provided. The Programme started in 1987 and evolved in time, according to the increasing new requirments coming both from the industrial and academic world. It is now running since 25 years and the success and brilliant career, both in Industry and Academy, of many students who followed the Programme in these years are the best recognition of the long term success of this educational activity.

Matti Heilio, Alessandra Micheletti

Recent Evolution Enhancing the Interface Between Mathematics and Industry in French Higher Education

The paper focuses on some recent initiatives in the French higher education system, in particular the creation of an Agency for the interactions of Mathematics with the Industry and the Society, AMIES, and its possible impact on already existing MSc programmes in industrial mathematics in the French university.

Edwige Godlewski

Two Examples of Collaboration Between Industry and University in Spain

Modelling of industrial processes is one of the ground lines of the research group Ingeniería Matemática (mat+i), from the University of Santiago de Compostela. Different activities have been developed in order to be in contact with the industry needs. Two examples of this close collaboration are presented here: the first one was proposed by the company FerroAtlántica to simulate the magnetic field and the temperature evolution of an electrode for electric-arc furnaces. The second one was proposed by company Gamelsa to simulate the energy efficiency of a newly designed solar collector. The difficulties arisen in the numerical simulation are summarized, as well as the benefits for both, the industry and the academic community.

Francisco Pena

ECMI Master Programmes at the Faculty of Mathematics and Informatics, Sofia University

The Faculty of Mathematics and Informatics, Sofia University, has been an ECMI member since 2011. The ECMI Educational Committee approved Sofia University as a provisional ECMI Teaching Centre at a meeting held on July 29th, 2011 in Milan, Italy. Here we present two of the Master programmes of the Faculty of Mathematics and Informatics, which correspond to the two branches—Techno-Mathematics and Econo-Mathematics—of the ECMI Model Master in Industrial Mathematics (ECMIMIM). These two programmes are “Computational Mathematics and Mathematical Modelling” and “Mathematical Modelling in Economics”. We show that they satisfy all the requirements of the ECMI Model Master in Industrial Mathematics.

Stefka Dimova

Backmatter

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