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This book addresses mathematics in a wide variety of applications, ranging from problems in electronics, energy and the environment, to mechanics and mechatronics. Using the classification system defined in the EU Framework Programme for Research and Innovation H2020, several of the topics covered belong to the challenge climate action, environment, resource efficiency and raw materials; and some to health, demographic change and wellbeing; while others belong to Europe in a changing world – inclusive, innovative and reflective societies.

The 19th European Conference on Mathematics for Industry, ECMI2016, was held in Santiago de Compostela, Spain in June 2016. The proceedings of this conference include the plenary lectures, ECMI awards and special lectures, mini-symposia (including the description of each mini-symposium) and contributed talks.

The ECMI conferences are organized by the European Consortium for Mathematics in Industry with the aim of promoting interaction between academy and industry, leading to innovation in both fields and providing unique opportunities to discuss the latest ideas, problems and methodologies, and contributing to the advancement of science and technology. They also encourage industrial sectors to propose challenging problems where mathematicians can provide insights and fresh perspectives. Lastly, the ECMI conferences are one of the main forums in which significant advances in industrial mathematics are presented, bringing together prominent figures from business, science and academia to promote the use of innovative mathematics in industry.

Inhaltsverzeichnis

Frontmatter

Plenary Lectures

Frontmatter

Semiparametric Prediction Models for Variables Related with Energy Production

In this paper a review of semiparametric models developed throughout the years thanks to extensive collaboration between the Department of Statistics and Operations Research of the University of Santiago de Compostela and a power station located in As Pontes (A Coruña, Spain) property of Endesa Generation, SA, is shown. In particular these models were used to predict the levels of sulfur dioxide in the environment of this power station with half an hour in advance. In this paper also a new multidimensional semiparametric model is considered. This model is a generalization of the previous models and takes into account the correlation structure of errors. Its behaviour is illustrated in the prediction of the levels of two important pollution indicators in the environment of the power station: sulfur dioxide and nitrogen oxides.

Wenceslao González-Manteiga, Manuel Febrero-Bande, María Piñeiro-Lamas

Emergent Behaviour in T Cell Immune Response

The ability of our immune system to fight off challenges posed by pathogenic agents (external or internal) is amazing. Indeed, many times during a normal lifespan immune cells have to identify and destroy incoming threats while leaving harmless cell trafficking undisturbed. Most remarkably, this careful regulation of body function is achieved in the absence of any organ in charge of controlling immune response. The latter is just an emergent property resulting from a very limited number of individual actions taken by immune cells, using only local information from their immediate neighbourhood. We shortly review here some striking aspects of this emergent behaviour. In particular, we will focus our attention on two issues, namely the way immune system regulates the number of effector T cells required to wipe out an acute infection and the mechanisms to distinguish friends from foes upon inspection of circulating antigens.

Clemente F. Arias, Miguel A. Herrero

Ray Mappings and the Weighted Least Action Principle

Two basic problems in optics are presented. The solutions to both problems are formulated in terms of the associated ray mappings. An alternative formulation based on a weighted sum of the actions along the rays is derived. Existence of solutions is established via the Weighted Least Action Principle. Numerical methods for computing the ray mappings are discussed. Finally, we demonstrate the theoretical considerations by presenting a complete solution to a specific beam shaping lens design.

Jacob Rubinstein, Yifat Weinberg, Gershon Wolansky

Hansjörg Wacker Memorial Prize

Frontmatter

Numerical Methods for Optimization Problems Arising in Energetic Districts

This paper deals with the optimization of energy resources management of industrial districts, with the aim of minimizing the customer energy bill. Taking into account real time information on energy needs and production and on energy market prices, a cost function is built that should be minimized. Here we focus on the solution of the arising nonlinear constrained optimization problem. We describe the two solvers that have been employed for its solution: a Sequential Linear Programming and a Particle Swarm Optimization.

Elisa Riccietti, Stefania Bellavia, Stefano Sello

Minisymposia

Frontmatter

Minisymposium: Advanced Numerical Methods for Hyperbolic Problems

The purpose of the minisymposium was to gather researchers interested in industrial application of numerical methods for hyperbolic problems. Hyperbolic systems are involved in the description of many physical problems, ranging from classical applications in aerodynamics to shallow water models for the simulation of waves in lakes and rivers, from combustion problems to hydrodynamical models of semiconductors, to mention just a few examples. Because of the actuality and impact of the subject, a recent European Marie Curie ITN project, called ModCompShock (Modelization and computation of shocks and interfaces) has been approved and has just started. The project involves eight main European Universities and several partner research centers. Several participants to the project were invited to contribute to the minisymposium, which became a unique opportunity of scientific exchange between this community and ECMI.

Giovanni Russo, Sebastiano Boscarino

High Order Extrapolation Techniques for WENO Finite-Difference Schemes Applied to NACA Airfoil Profiles

Finite-difference WENO schemes are capable of approximating accurately and efficiently weak solutions of hyperbolic conservation laws. In this context high order numerical boundary conditions have been proven to increase significantly the resolution of the numerical solutions. In this paper a finite-difference WENO scheme is combined with a high order boundary extrapolation technique at ghost cells to solve problems involving NACA airfoil profiles. The results obtained are comparable with those obtained through other techniques involving unstructured meshes.

Antonio Baeza, Pep Mulet, David Zorío

The Influence of the Asymptotic Regime on the RS-IMEX

In this work, we investigate the performance and explore the limits of a novel implicit-explicit splitting (Kaiser and Schütz, A high-order method for weakly compressible flows. Commun. Comput. Phys. 22(4): 1150–1174, 2017) for the efficient treatment of singularly perturbed ODEs. We consider a singularly perturbed ODE where, based on the choice of initial conditions, the unperturbed equation does not necessarily describe the behavior of the perturbed one accurately. For the splitting presented in Kaiser and Schütz, (A high-order method for weakly compressible flows. Commun. Comput. Phys. 22(4): 1150–1174, 2017), this has a tremendous influence as it explicitly depends on the solution to the unperturbed equation. That this indeed poses a problem is shown numerically; but also the remedy of using the ‘correct’ asymptotics is presented. Comparisons with a fully implicit and a standard implicit-explicit splitting are shown.

Klaus Kaiser, Jochen Schütz

Minisymposium: Aeroacoustics

Aeroacoustics can be seen as a branch of fluid mechanics that deals with the propagation of acoustic waves in moving fluids (flows). There are obviously many industrial applications of aeroacoustics to begin with aeronautics and car industry (controlling the noise emitted by airplanes and cars is definitely a major issue) but also the control of noise in domestic ducts like air-conditioning for instance.

Patrick Joly, Jean-François Mercier

Simulation of Reflection and Transmission Properties of Multiperforated Acoustic Liners

In this paper we study the fundamental and higher-order modes propagation in a cylindrical acoustic duct with a multi-perforated liner section. This study relies on an established approximate model that is mathematically verified by a multiscale analysis and that takes the presence of the liner into account through transmission conditions. We simulate the reflection and transmission behaviour by an hp-adaptive finite element method that effectively resolves the solution in presence of strong singularities at the rim of the duct. Moreover, we introduce a new mode matching method based on the complete mode decomposition that depends in the liner section on the Rayleigh conductivity. It turns out that the mode matching method achieves similar accuracies with all propagating and just a number of evanescent modes.

Adrien Semin, Anastasia Thöns-Zueva, Kersten Schmidt

Minisymposium: Applied Mathematics in Stent Development

Coronary artery disease is a global problem and devising effective treatments is the subject of intense research activity throughout the world. Over the past decade, stents have emerged as one of the most popular treatments. Acting as a supporting scaffold, these small mesh devices are now routinely inserted into arteries where the blood flow has become dangerously restricted. Stents have evolved from bare metal scaffolds to polymer coated drug-delivery vehicles and, more recently, sophisticated fully biodegradable drug delivery configurations. Despite these advances, significant opportunities to improve on arterial stent design remain. The relative success of coronary artery stenting has led to the emergence of stenting technology for the carotid, neural and peripheral vasculature. In addition, the adaptability of the stent concept has opened horizons beyond the vasculature, with stent technology now being developed for, amongst others, pulmonary, gastro-intestinal and structural heart applications.

Tuoi T. N. Vo, Sean McGinty

Mathematical Modelling of Drug Elution from Drug-Filled Stents

In this paper, we outline the first model to describe drug elution from a drug-filled stent. This novel polymer-free drug-eluting stent stores the therapeutic drug in the inner layer of a tri-layer wire. This inner layer acts a reservoir releasing the drug through laser-drilled holes on the outer surface of the stent struts. We simplify the general model using the assumption of low drug solubility and consider a special case where the dissolution occurs in a uniform downward direction. The main advantage of our simplified model is the ability to achieve analytical solutions. These solutions allow for calculating the drug release profile rapidly and for identifying the dependence of the various parameters of the system. We find that the duration of drug elution is prolonged when the solubility or diffusivity of the drug decreases.

Tuoi T. N. Vo, Amy M. M. Collins, William T. Lee

Minisymposium: Charge Transport in Semiconductor Materials: Emerging and Established Mathematical Topics

Modern electronic devices would be unthinkable without semiconductor materials. Few inventions have shaped our modern society like they have. There are emerging fields such as organic semiconductors, where there is still the demand to develop models and new theory, and there are many well-established fields, e.g. particle detector simulations, where it is mostly required to develop advanced numerical methods.

Patricio Farrell, Dirk Peschka, Nella Rotundo

Comparison of Scharfetter-Gummel Flux Discretizations Under Blakemore Statistics

We discretize the semiconductor device equations assuming a Blakemore distribution function using a finite volume scheme and compare three thermodynamically consistent Scharfetter-Gummel type flux discretizations, namely the exact solution to a two-point boundary value probem and two fluxes incorporating certain averages. In order to do this, we simulate an n-i-n semiconductor device and study the electron densities as well as the total current. While the diffusion-enhanced flux approximation using logarithmic averaging of the nonlinear diffusion enhancement behaves somewhat similarly to the exact solution of the two-point boundary value problem (the generalized Scharfetter-Gummel scheme), the scheme based on averaging the inverse activity coefficients scheme exhibits a noticeably different behavior.

Patricio Farrell, Thomas Koprucki, Jürgen Fuhrmann

A PDE Model for Electrothermal Feedback in Organic Semiconductor Devices

Large-area organic light-emitting diodes are thin-film multilayer devices that show pronounced self-heating and brightness inhomogeneities at high currents. As these high currents are typical for lighting applications, a deeper understanding of the mechanisms causing these inhomogeneities is necessary. We discuss the modeling of the interplay between current flow, self-heating, and heat transfer in such devices using a system of partial differential equations of thermistor type, that is capable of explaining the development of luminance inhomogeneities. The system is based on the heat equation for the temperature coupled to a p(x)-Laplace-type equation for the electrostatic potential with mixed boundary conditions. The p(x)-Laplacian allows to take into account non-Ohmic electrical behavior of the different organic layers. Moreover, we present analytical results on the existence, boundedness, and regularity of solutions to the system. A numerical scheme based on the finite-volume method allows for efficient simulations of device structures.

Matthias Liero, Axel Fischer, Jürgen Fuhrmann, Thomas Koprucki, Annegret Glitzky

Minisymposium: Computational Electromagnetism

Electromagnetic phenomena is one of the fundations of modern technology and developing models, approximation methods and software tools for electromagnetics computations have a direct impact and great relevance in industry. In the past thirty years computational electromagnetism has became also a prolific and strengthened research field on applied mathematics. The aim of this minysimposium was to bring together a small group of engineers and mathematicians working on common interests to present advanced topics on modeling and discretization of electromagnetic fields and to discuss the effective impact on industrial applications and software design of these advanced techniques.

Ana Alonso Rodríguez, Ruben Specogna

FEMs on Composite Meshes for Plasma Equilibrium Simulations in Tokamaks

We rely on a combination of different finite element methods on composite meshes, for the simulation of axisymmetric plasma equilibria in tokamaks. One mesh with Cartesian quadrilaterals covers the vacuum chamber and one mesh with triangles discretizes the region outside the chamber. The two meshes overlap in a narrow region around the chamber. This approach gives the flexibility to achieve easily and at low cost higher order regularity for the approximation of the flux function in the area that is covered by the plasma, while preserving accurate meshing of the geometric details in the exterior. The continuity of the numerical solution across the boundary of each subdomain is enforced by a new mortar-like projection.

Holger Heumann, Francesca Rapetti, Minh Duy Truong

Eddy Current Testing Models for the Analysis of Corrosion Effects in Metal Plates

Direct method for the solution of eddy current testing problem for the case where an air core coil is located above a conducting two-layer plate with a flaw in the form of a cylindrical inclusion with reduced electrical conductivity is presented in the paper. Semi-analytical approach (the TREE method) is used to construct the solution of the system of equations for the components of the vector potential. The flaw is assumed to be symmetric with respect to the coil. Numerical calculations are performed using the proposed model and Comsol Multiphysics software. The obtained values of the change in impedance of the coil for both methods are found to be in a good agreement. The proposed model can be used for the assessment of the effect of corrosion in metal plates.

Valentina Koliskina, Andrei Kolyshkin, Rauno Gordon, Olev Märtens

Convergence of a Leap-Frog Discontinuous Galerkin Method for Time-Domain Maxwell’s Equations in Anisotropic Materials

We present an explicit leap-frog discontinuous Galerkin method for time-domain Maxwell’s equations in anisotropic materials and establish its convergence properties. We illustrate the convergence results of the fully discrete scheme with numerical tests. This work was developed in the framework of a more general project that aims to develop a computational model to simulate the electromagnetic wave’s propagation through the eye’s structures in order to create a virtual optical coherence tomography scan (Santos et al., 37th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), pp. 8147–8150, 2015).

Adérito Araújo, Sílvia Barbeiro, Maryam Khaksar Ghalati

Topics in Magnetic Force Theory: Some Avatars of the Helmholtz Formula

There is a great variety of formulas purporting to describe the force field inside magnetized matter. They don’t always agree, which is puzzling. Starting from the Korteweg–Helmholtz formula, obtained thanks to the highly reliable Virtual Power Principle (VPP), we show how variant expressions can result from algebraic manipulations that assume, without making this explicit, extra physical hypotheses. Those we discuss here, assuming a B = μH magnetic law, are (1) Dependence of μ on density, (2) Incompressibility of the magnetic medium in which the magnetic forces develop.

Alain Bossavit

Minisymposium: Computational Methods for Finance and Energy Markets

This minisymposium was an activity of the ECMI Special Interest Group on Computational Finance [2]. The SIG was launched at ECMI-2014 in Taormina (June 9–13, 2014) and (together with the ITN STRIKE network [3]) organized several sessions of a minisymposium in Computational Finance. The corresponding reporting can be found in [1]. At ECMI-2016 we brought together again twelve speakers.

E. Jan W. ter Maten, Matthias Ehrhardt

Efficient Multiple Time-Step Simulation of the SABR Model

In this work, we present a multiple time-step Monte Carlo simulation technique for pricing options under the Stochastic Alpha Beta Rho (SABR) model. The proposed method is an extension of the one time-step Monte Carlo method that we proposed in Leitao et al. (Appl. Math. Comput. 293: 461–479, 2017). We call it the mSABR method. A highly efficient method results, with many interesting and nontrivial components, like Fourier inversion for the sum of log-normals, stochastic collocation, Gumbel copula, correlation approximation, that are not yet seen in combination within a Monte Carlo simulation. The present multiple time-step Monte Carlo method is especially useful for long-term or for exotic options. This paper is a short version of an already published paper (Leitao et al. On an efficient multiple time-step Monte Carlo simulation of the SABR model. Quantitative Finance.

Álvaro Leitao, Lech A. Grzelak, Cornelis W. Oosterlee

Uncertainty Quantification and Heston Model

In this paper, we study the impact of the parameters involved in Heston model by means of Uncertainty Quantification. The Stochastic Collocation Method already used for example in computational fluid dynamics, has been applied throughout this work in order to compute the propagation of the uncertainty from the parameters of the model to the output. The well-known Heston model is considered introduced and parameters involved in the Feller condition are taken as uncertain due to their important influence on the output. Numerical results where the Feller condition is satisfied or not are shown as well as a numerical example with real market data.

María Suárez-Taboada, Jeroen A. S. Witteveen, Lech A. Grzelak, Cornelis W. Oosterlee

Reduced Models in Option Pricing

We consider the computational efficiency of the backward vs. forward approaches and compare these with the respective ones resulting from a parametric reduced order model, whose speed-up can be put to good use in the calibration of the underlying dynamics. We apply a global Proper Orthogonal Decomposition in the time domain to obtain the reduced basis and the Modified Craig-Sneyd ADI and Chang-Cooper schemes to numerically solve the partial differential equations. The numerical results are presented for the Black-Scholes and Heston models.

José P. Silva, E. Jan W. ter Maten, Michael Günther, Matthias Ehrhardt

Minisymposium: Differential Equation Models of Propagation Processes

The aim of this mini symposium was to present results about modeling different propagation processes by using ODEs and PDEs. Epidemic propagation on networks was considered with focusing on the relation between the structure of the network and the qualitative behavior of the solutions of the corresponding differential equations. Old and new product formulas for evolution equations were surveyed. Applications to numerical analysis and operator theoretic properties of the evolution equation were given.

András Bátkai, Peter L. Simon

Variance of Infectious Periods and Reproduction Numbers for Network Epidemics with Non-Markovian Recovery

For a recently derived pairwise model of network epidemics with non-Markovian recovery, we prove that under some mild technical conditions on the distribution of the infectious periods, smaller variance in the recovery time leads to higher reproduction number when the mean infectious period is fixed.

Gergely Röst, István Z. Kiss, Zsolt Vizi

Minisymposium: Effective Solutions for Industry Using Mathematical Technology

The main aim of this symposium was to present five of the most successful projects of ITMATI (Technological Institute of Industrial Mathematics) oriented to industrial customers, as a result of an intense relationship with our environment since our formal origin in February 2013, focusing in win-win engagements with all our stakeholders. We focused in projects developed from specific needs of companies, reason of our conviction to promote the Transference of Applied Knowledge to the Industry. Specifically,

José Durany, Wenceslao González, Peregrina Quintela, Jacobo de Uña, Carlos Vázquez

Practical Industrial Mathematics: Between Industry and Academia

Teknova is a small research institute located in the southern part of Norway. We collaborate closely with several metallurgical companies, among others, within industrial mathematics. Two cases from challenging, interdisciplinary projects are presented: One case where the proper non-dimensionalized equation is applied to derive the electrical regimes relevant for smelting furnaces, and one showing how a mathematical point of view largely can enhance simulations based on metallurgical background.We have experienced that many factors are required to succeed in our projects within industrial mathematics: Trust, technical/industrial competence, broad mathematical competence, translator skills, and proper network. Our role is between industry and academia. We will not succeed without proper and extensive cooperation with ‘both worlds’.

Svenn Anton Halvorsen

Minisymposium: EU-MATHS-IN: Success Stories of Mathematical Technologies in Societal Challenges and Industry

The development of new products, production processes or improvements in the society today is dominated by the use of simulation and optimization methods that, based on a detailed mathematical modeling, support or even replace the costly production of prototypes and classical trial-and-error methods. To address this development and following the Recommendations of the Forward Look ‘Mathematics and Industry’ published by the European Science Foundation, several European research networks have established a new organization to increase the impact of mathematics on innovations in key technologies and to foster the development of new modeling, simulation and optimization tools.

Peregrina Quintela, Antonino Sgalambro

Modeling Oxygen Consumption in Germinating Seeds

The consumption of oxygen by a germinating seed is assumed to be a good indicator of seed vitality and can potentially be used to predict the germination time. With the current availability of relatively simple single-seed respiration measurement methods and more oxygen consumption data opportunities emerge for detailed analysis of the underlying mechanisms relating respiration to germination processes. Due to the complex (structural and physiological) nature of seeds experimental analysis alone is very difficult. Mathematical modeling may provide an insight into the relationship between the germination of seeds and respiration. We have approached this problem by considering the population dynamics of mitochondria in seeds subject to limited oxygen supply and present a simple but rigorous and easily testable mathematical model that can handle large amounts of data and is interpretable in terms of the effective biological parameters of the seeds.

Neil Budko, Bert van Duijn, Sander Hille, Fred Vermolen

Mathematical Modelling of a Wave-Energy Converter

We report progress towards developing a mathematical model that can be used to optimise the design of a novel power take off unit for a wave energy generator. We show that the power take off unit can be considered as a non-smooth, dissipative dynamical system. We derive equations of motion using the Lagrangian framework, incorporating a Rayleigh dissipation function and discuss a procedure for generating approximate analytical solutions.

William Lee, Michael Castle, Patrick Walsh, Patrick Kelly, Cian Murtagh

Aerodynamic Web Forming: Pareto-Optimized Mass Distribution

In the technical textile industry an objective of the airlay process is the production of high quality nonwoven fabrics with the minimal use of fiber raw material. Since a process simulation of the multi-scale two-phase problem is very computationally expensive, we deduce an efficiently evaluable surrogate model to handle the multi-criteria optimization task.

Nicole Marheineke, Sergey Antonov, Simone Gramsch, Raimund Wegener

Minisymposium: Finite Volume Schemes for Degenerate Problems

This minisymposium was a response to the growing use of finite volume schemes combined with finite element schemes in degenerate problems and was intended to bring together developers and researchers from academia and industry.

Mazen Saad

Convergence of a Nonlinear Control Volume Finite Element Scheme for Simulating Degenerate Breast Cancer Equations

In this paper, a positive nonlinear CVFE scheme is considered for the simulation of an anisotropic degenerate breast cancer model. This scheme includes the use of the finite element method combined with the Godunov scheme to approximate the diffusion terms over a primal mesh, and it uses a nonclassical upwind finite volume scheme to approximate the other terms over a barycentric dual mesh. This scheme ensures the discrete maximum principle and it converges to a weak solution without any restriction on the transmissibility coefficients. Numerical experiment is supplied in order to show the efficiency of the scheme to simulate an anisotropic breast cancer model over a general mesh.

Françoise Foucher, Moustafa Ibrahim, Mazen Saad

Minisymposium: Fluid Instabilities and Transport Phenomena in Industrial Processes

This minisymposium focused on the mathematical modeling and analysis of processes occurring in industry (for example, food and drink, pharmaceutical, and oil sector). These were some of the challenging industrial

Ricardo Barros

Mathematical Modelling of Waves in Guinness

We provide a simple two-dimensional model of bubbly two-phase flow which can be used to investigate why waves form and propagate downward while a pint of Guinness is settling. We start out with the basic equations of the two-phase flow and use the large timescale difference of beer convection and rising bubbles in order to treat the convection flow as quasistatic. Using this argument we further simplify the two-phase mixture equations to that of a single liquid whose density varies with bubble concentration. A stability analysis shows that waves can occur through an instability analogous to the Kelvin-Helmholtz instability which forms in parallel shear flow. We provide a description of the form of these waves, and compare them to observations. Our theory provides a platform for the description of waves in more general bubbly two-phase shear flows.

Simon Kaar, William Lee, Stephen O’Brien

Viscoelastic Cosserat Rod Model for Spinning Processes

Embedded in the special Cosserat theory (slender-body theory) we propose an incompressible viscoelastic rod model that covers viscous and elastic behavior in the asymptotic limits. Its applicability is demonstrated in an industrial fiber spinning process.

Walter Arne, Nicole Marheineke, Raimund Wegener

Minisymposium: Masters in Industrial Mathematics. Overview and Analysis of Graduates and Business Collaborators

To educate in Industrial Mathematics is one of the main objectives of ECMI. In the past editions of the ECMI conferences the different training opportunities offered by institutions have been analyzed.

Elena Vázquez-Cendón, Carlos Vázquez, José Durany, Manuel Carretero, Fernando Varas

The Master Degree on Applied Mathematics to Engineering and Finance, School of Engineering, Polytechnic of Porto

The Master on Applied Mathematics to Engineering and Finance of the School of Engineering of the Polytechnic of Porto, Portugal, started its first edition in the scholar year of 2012/2013. This course is divided into four semesters (two scholar years). It emerged in an engineering school that has a strong tradition of dialog and collaboration with industry and business partners. In the second year, students must attend the subject of Dissertation/Project/Internship. This subject may be developed in a business or industrial environment. We will present some successful stories on applying this methodology in the above-mentioned master course, showing the benefits and the difficulties that arise from the collaboration with industry and business partners.

Stella Abreu, José Matos, Manuel Cruz, Sandra Ramos, Jorge Santos

Minisymposium: Mathematical Modeling and Simulation for Nanoelectronic Coupled Problems (nanoCOPS)

In this minisymposium recent advances in mathematical modeling, uncertainty quantification (UQ) and model order reduction (MOR) for electronic devices were presented. They are the research results from the cooperation between the academic and industrial partners in the framework of nanoCOPS (‘Nanoelectronic Coupled Problems Solutions’). It is a collaborative research project within the research program ‘Information and communication technologies’ of the Seventh Framework Programme for Research and Technological Development (FP7) funded by the European Union.

Sebastian Schöps, Lihong Feng

Identification of Probabilistic Input Data for a Glue-Die-Package Problem

In mathematical models, physical or geometrical parameters often involve uncertainties due to measurement errors, estimations or imperfections of an industrial production. An uncertainty quantification can be performed by a stochastic description, where parameters are substituted by random variables or random processes. The probability distributions of the parameters have to be predetermined as an input to the stochastic model. However, the variability of input parameters often cannot be measured directly, whereas the output quantities are available. We consider a test problem from nanoelectronics, where a piece of glue connects a die and a package. The geometrical parameters as well as the material parameters are uncertain for the piece of glue. We fit the input probability distributions of the random parameters to measurements of the output, which represents a kind of inverse problem. For this purpose, a minimization problem is defined including a piecewise linear approximation of the cumulative distribution functions. We present numerical results for this test problem.

Roland Pulch, Piotr Putek, Herbert De Gersem, Renaud Gillon

Parametric Model Order Reduction for Electro-Thermal Coupled Problems with Many Inputs

The modified BDSM-ET method is a model order reduction (MOR) technique which was developed to reduce non-parametric electro-thermal (ET) coupled problems with many inputs. The method leads to block-wise sparse reduced-order models (ROMs) which are accurate and computationally cheaper compared to the existing MOR methods. In this work, we extend the modified BDSM-ET method to parametrized ET coupled problems with many inputs.

Nicodemus Banagaaya, Peter Benner, Lihong Feng

Nanoelectronic Coupled Problem Solutions: Uncertainty Quantification of RFIC Interference

Due to the key trends on the market of RF products, modern electronics systems involved in communication and identification sensing technology impose requiring constraints on both reliability and robustness of components. The increasing integration of various systems on a single die yields various on-chip coupling effects, which need to be investigated in the early design phases of Radio Frequency Integrated Circuit (RFIC) products. Influence of manufacturing tolerances within the continuous down-scaling process affects the output characteristics of electronic devices. Consequently, this results in a random formulation of a direct problem, whose solution leads to robust and reliable simulations of electronics products. Therein, the statistical information can be included by a response surface model, obtained by the Stochastic Collocation Method (SCM) with Polynomial Chaos (PC). In particular, special emphasis is given to both the means of the gradient of the output characteristics with respect to parameter variations and to the variance-based sensitivity, which allows for quantifying impact of particular parameters to the variance. We present results for the Uncertainty Quantification of an integrated RFCMOS transceiver design.

Piotr Putek, Rick Janssen, Jan Niehof, E. Jan W. ter Maten, Roland Pulch, Bratislav Tasić, Michael Günther

Minisymposium: Mathematical Modeling of Charge Transport in Graphene and Low Dimensional Structure

The minisymposium was concerned with the mathematical modeling and simulation of charge transport in graphene and other 2D materials and in structures, like double gate MOSFETs, nano-ribbons and nano-wires, where the presence of confinement effects allows for the formal description of the carrier flow as that of a two dimensional or one dimensional electron gas.

Antonino La Magna, Giovanni Mascali, Vittorio Romano

Low-Field Electron Mobility in Silicon Nanowires

Silicon nanowires (SiNWs) are quasi-one-dimensional structures in which electrons are spatially confined in two directions and they are free to move in the orthogonal direction. The subband decomposition and the electrostatic force field are obtained by solving the Schrödinger—Poisson coupled system. The electron transport along the free direction can be tackled using a hydrodynamic model, formulated by taking the moments of the multisubband Boltzmann equation. We shall introduce an extended hydrodynamic model where closure relations for the fluxes and production terms have been obtained by means of the Maximum Entropy Principle of Extended Thermodynamics, and in which the main scattering mechanisms such as those with phonons and surface roughness have been considered. By using this model, the low field mobility for a Gate-All-Around (GAA) SiNW transistor has been evaluated.

Orazio Muscato, Tina Castiglione, Armando Coco

On Some Extension of Energy-Drift-Diffusion Models: Gradient Structure for Optoelectronic Models of Semiconductors

We derive an optoelectronic model based on a gradient formulation for the relaxation of electron-, hole- and photon-densities to their equilibrium state. This leads to a coupled system of partial and ordinary differential equations, for which we discuss the isothermal and the non-isothermal scenario separately.

Alexander Mielke, Dirk Peschka, Nella Rotundo, Marita Thomas

Minisymposium: Mathematics in Nanotechnology

Nanotechnology is one of the key modern research directions, with billions being invested by governments throughout the world, and in particular by the US, Europe and Japan. Nanotechnology is relevant to a vast range of practical applications, such as in medicine, electronics, biomaterials and energy production. To date the vast majority of research has focussed on the experimental side, with the theory often lagging behind. However, there are a number of mathematical groups now working on topics relevant to the nano industry. In this minisymposium we intended to bring together a selection of speakers who discussed a broad range of topics relevant to nanoscience and who were able to demonstrate the relevance of mathematics to this research field.

Timothy G. Myers

A Model for Nanoparticle Melting with a Newton Cooling Condition and Size-Dependent Latent Heat

In this paper we study the melting of a spherical nanoparticle. To match with experimental data, the model includes several new features such as size-dependent latent heat and a cooling boundary condition at the boundary. Melt temperature variation and density change are also included. A novel form of Stefan condition is used to determine the position of the melt front. Results show that melting times can be significantly faster than those predicted by previous theoretical models, primarily due to the latent heat variation.

Helena Ribera, Timothy G. Myers

The Stochastic Drift-Diffusion-Poisson System for Modeling Nanowire and Nanopore Sensors

We use the stochastic drift-diffusion-Poisson system to model charge transport in nanoscale devices. This stochastic transport equation makes it possible to describe device variability, noise, and fluctuations. We present—as theoretical results—an existence and local uniqueness theorem for the weak solution of the stochastic drift-diffusion-Poisson system based on a fixed-point argument in appropriate function spaces. We also show how to quantify random-dopant effects in this formulation. Additionally, we have developed an optimal multi-level Monte-Carlo method for the approximation of the solution. The method is optimal in the sense that the computational work is minimal for a given error tolerance.

Leila Taghizadeh, Amirreza Khodadadian, Clemens Heitzinger

A Mathematical Proof in Nanocatalysis: Better Homogenized Results in the Diffusion of a Chemical Reactant Through Critically Small Reactive Particles

We consider a reaction-diffusion in which the reaction takes place on the boundary of the reactive particles. In this sense the particles can be thought of as a catalysts that produce a change in the ambient concentration w ε of a reactive element. It is known that depending on the size of the particles with respect to their periodic repetition there are different homogeneous behaviors. In particular, there is a case in which the kind of nonlinear reaction kinetics changes and becomes more smooth. This case can be linked with the strange behaviors that arise with the use of nanoparticles. In this paper we show that concentrations of a catalyst are always higher when nanoparticles are applied.

Jesús Ildefonso Díaz, David Gómez-Castro

The Effect of Depth-Dependent Velocity on the Performance of a Nanofluid-Based Direct Absorption Solar Collector

In this paper we present a two-dimensional model for the efficiency of an inclined nanofluid-based direct absorption solar collector. The model consists of a system of two differential equations; a radiative transport equation describing the propagation of solar radiation through the nanofluid and an energy equation. The Navier-Stokes equations are solved by applying no-slip boundary conditions to give a depth-dependent velocity profile. The heat source term is approximated via a power law approximation. The energy equation is solved numerically and the resulting solution is then used to calculate the efficiency. We investigate the effect of depth-dependent velocity and show how it affects the temperature, and thus the efficiency.

Gary J. O’Keeffe, Sarah L. Mitchell, Tim G. Myers, Vincent Cregan

Minisymposium: Maths for the Digital Factory

Around one in ten of all enterprises in the EU-27s non-financial business economy were classified to manufacturing in 2009, a total of 2.0 million enterprises. The manufacturing sector employed 31 million persons in 2009, generated 5.812 billion Euro of turnover and 1.400 billion Euro of value added. (source: Eurostat). In the last five or ten years all industrialised countries have launched initiatives related to digital manufacturing, sometimes also referred to as Industry 4.0 (in Europe) or Smart Manufacturing (US).

Dietmar Hömberg

Modelling, Simulation, and Optimization of Thermal Deformations from Milling Processes

During a machining process, the produced heat results in thermomechanical deformation of the workpiece and thus an incorrect material removal by the cutting tool, which may exceed given tolerances.We present a numerical model including a finite element simulation for thermomechanics, a dexel model for material removal, and a process model for forces and heating produced by the machining tool.For minimization of the final shape deviation, this forward model defines the constraints for an optimal control problem. Main control variables are the process parameters and the path of the machining tool. These are varied according to a compensation and optimization approach.

Alfred Schmidt, Carsten Niebuhr, Daniel Niederwestberg, Jost Vehmeyer

Minisymposium: MODCLIM: Erasmus+ Project

MODCLIM is an integrated research training course and problem solving workshop for challenging mathematical and computational problems from industry and applied sciences. During each of the years of the project, a group of 20–30 PhD and advanced undergraduate (MSc) level students are trained, and 4–6 industrial problems from leading edge technological development are worked through. The project unites a number of ECMI partners (all of whom have experience in running a Masters programme in industrial mathematics and have contacts with industry in their region) but is also the first one of this kind in the Sub-Mediterranean area and an important step towards cross-mediterranean collaboration in industrial mathematics.

Matylda Jabłońska-Sabuka

Modeling Clinic for Industrial Mathematics: A Collaborative Project Under Erasmus+ Program

Modeling Clinic for Industrial Mathematics (MODCLIM) is a Strategic Partnership for the Development of Training Workshops and Modeling Clinic for Industrial Mathematics, funded through the European Commission under the Erasmus Plus Program, Key Action 2: Cooperation for innovation and the exchange of good practices.MODCLIM develops a project focused on mathematical technologies needed for the progress of industry and novel engineering solutions. The project pretends to contribute in addressing the challenges that industrial mathematics, as a part of the next generation of methodologies in research and development (R&D) and knowledge management, represents for university education, curriculum development, training practices and research collaboration.MODCLIM project introduces into European higher education a novel concept in academic research training and education of industrial mathematics by combining elements from earlier successful ideas tested worldwide. It is organized in cycles, each consisting of three interconnected steps: (1) Training school, (2) Intermediate online-project, and (3) Modeling Clinic. The project’s aim is to provide an integrated learning experience for the students, thus ensuring a proper connection between these three steps.In this paper we expose an overall idea about MODCLIM project, and a brief description of two MODCLIM cycles organized in 2015 and 2016.

Agnieszka Jurlewicz, Claudia Nunes, Giovanni Russo, Juan Rocha, Matti Heilio, Matylda Jablonska-Sabuka, Nada Khoury, Poul Hjorth, Susana Serna, Thomas Goetz

Minisymposium: Moving Boundary Problems in Industrial Applications

Moving boundary problems appear in the modelling of a variety of physical processes including phase-change (melting and solidification) and the dissolution of a solid in a solvent and fluid dynamics. Due to this broad scope, we see moving boundary problems in many industrial applications including (but not limited to) metal-casting, nanotechnology and pharmacology. Here we presented a collection of studies from these diverse fields and we highlight various analytical and numerical techniques.

Brendan J. Florio

Nanoparticle Growth via the Precipitation Method

We consider a model for the evolution of a system of nanoparticles in solution via the processes of size focusing and Ostwald ripening. The model consists of a diffusion equation for the concentration of the solution, a Stefan-type condition to track the particle-liquid interfaces and a time-dependent expression for the bulk concentration obtained via mass conservation. Based on a small dimensionless parameter we propose a pseudo-steady state model, which is solved numerically to obtain the average particle radius and standard deviation. The results are shown to be in good agreement with experimental data for cadmium selenide nanoparticles.

V. Cregan, T. G. Myers, S. L. Mitchell, H. Ribera, M. C. Schwarzwälder

Minisymposium: New Developments in Models of Traffic and Crowds

Modern society is increasingly faced with problems arising from overcrowded and congested motorways, and control of large crowds (sometimes failing, resulting in casualties, even loss of life). Over-engineering or oversizing available space is not always an option, and there is a need for mathematically sophisticated solutions arising from dynamical systems modelling.

Poul G. Hjorth, Mads Peter Sørensen

Numerical Simulation for Evaluating the Effect of Traffic Restrictions on Urban Air Pollution

Traffic flow is the main pollution source in many urban areas, so when the pollutant concentration is above the permitted level, a common public policy consists of restricting the vehicular traffic. However, this restriction presents a negative impact on the economic activities and the inhabitants mobility. For these reasons different sectors question its efficiency arguing that the pollution reduction is due to wind changes and not to a lower vehicular traffic. In this work we estimate the pollution emission rate and pollutant concentration with a novel methodology that consists of combining the 1D Lighthill-Whitham-Richards (LWR) traffic model for road networks with a 2D advection-diffusion-reaction model for air pollution. This allows us to verify the efficiency of restrictions on vehicular traffic in the framework of numerical simulations in a real urban domain: the Guadalajara Metropolitan Area in Mexico.

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

A General Microscopic Traffic Model Yielding Dissipative Shocks

We consider a general microscopic traffic model with a delay. An algebraic traffic function reduces the equation to the Aw-Rascle microscopic model while a sigmoid function gives the standard “follow the leader”. For zero delay we prove that the homogeneous solution is globally stable. For a positive delay, it becomes unstable and develops dispersive and dissipative shocks. These are followed by a finite time singularity for the algebraic traffic function and by kinks for the sigmoid function.

Yuri Borissovich Gaididei, Jean-Guy Caputo, Peter Leth Christiansen, Jens Juul Rasmussen, Mads Peter Sørensen

Minisymposium: Nonlinear Diffusion Processes: Cross Diffusion, Complex Diffusion and Related Topics

Nonlinear diffusion equations have attracted a lot of attention over the last few years in many practical applications. After the pioneering work of Keler and Segel in the 1970s, cross-diffusion models became very popular in biology, chemistry and physics to emulate systems with multiple species. The range of application is even wider and, in particular, complex-diffusion models are of special relevance for example in the field of image processing. Meanwhile the underlying mathematical theory has been developed in a synergetic way with applications, in recent years, this topic became the focus of an intensive research within the mathematics community. In spite of the relevance of cross-diffusion models in numerous fields of application and all the mathematical activity around them, important questions remain unanswered and meaningful challenging problems still need to be addressed.

Adérito Araújo, Sílvia Barbeiro, Ángel Durán, Eduardo Cuesta

Cross-Diffusion in Reaction-Diffusion Models: Analysis, Numerics, and Applications

Cross-diffusion terms are nowadays widely used in reaction-diffusion equations encountered in models from mathematical biology and in various engineering applications. In this contribution we review the basic model equations of such systems, give an overview of their mathematical analysis, with an emphasis on pattern formation and positivity preservation, and finally we present numerical simulations that highlight special features of reaction-cross-diffusion models.

Anotida Madzvamuse, Raquel Barreira, Alf Gerisch

On a Splitting-Differentiation Process Leading to Cross-Diffusion

We generalize the dynamical system model proposed by Sánchez-Palencia for the splitting-differentiation process of populations to include spatial dependence. This gives rise to a family of cross-diffusion partial differential equations problems, among which we consider the segregation model proposed by Busenberg and Travis. For the one-dimensional case, we make a direct parabolic regularization of the problem to show the existence of solutions in the space of BV functions. Moreover, we introduce a Finite Element discretization of both our parabolic regularization and an alternative regularization previously proposed in the literature. Our numerical results suggest that our approach is more stable in the tricky regions where the solutions exhibit discontinuities.

Gonzalo Galiano, Virginia Selgas

A Discrete Cross-Diffusion Model for Image Restoration

In this paper a fully discrete cross-diffusion model for image restoration is introduced. The image is represented by a two-component vector field, and the restoration process is governed by a nonlinear cross-diffusion difference system. We explore numerically the potentialities of using the nonlinear cross-diffusion approach as an image filter, in particular as a preprocessing step for image segmentation.

Adérito Araújo, Silvia Barbeiro, Eduardo Cuesta, Ángel Durán

Consensus-Based Global Optimization

We discuss some algorithms for global optimization and opinion formation and their relation to consensus-based optimization (CBO). The proposed CBO algorithm allows to pass to the mean-field limit, resulting in a Fokker-Plank type equation with non-linear, non-local and degenerate drift and diffusion term. We shed some light on the prospects of justifying the efficacy of the CBO algorithm on the PDE level.

Claudia Totzeck

Minisymposium: Return of Experience from Study Groups

Study Groups with Industry are now a well established tool throughout Europe (and beyond) to promote industrial mathematics. This minisymposium gave the opportunity to PhD students who had recently participated in such Study Groups to report on their experience, present results obtained during the Study Group, and indicate the follow up of their work. This minisymposium also showed the diversity of topics and applications addressed in Study Groups. It gave visibility to the PhD students and advertised about Study Groups towards all public (students, faculty and industrialists) attending the ECMI conference.

Georges-Henri Cottet, Agnieszka Jurlewicz

Packing and Shipping Cardboard Tubes

Spiralpack - Manipulados de Papel, S.A. is one of the main Iberian peninsula players in the production of standard and high performance cardboard tubes. This company attended at 101st European Study Groups with Industry (ESGI) to address the following questions concerning their packing and shipping processes: Given an order for a certain tube specification, possibly with a grouping request, what is the maximum number of tubes that can be packed inside a given container (usually the truck space) and how should they be positioned? Given several pallets of tubes, what is the most efficient way to arrange them in a container? In this work we show an industrial mathematics approach to these challenges, as well as some insight on the software developed to help Spiralpack addressing those questions.

Isabel Cristina Lopes, Manuel Bravo Cruz

Minisymposium: Simulation and Optimization of Water and Gas Networks

The minisymposium dealt with topics regarding aspects of modelling, simulating and optimizing flow behaviour within water and gas networks. These networks can consist of rivers or channels, gas and water supply or sewer systems. The flow in every single network element is usually modelled by hyperbolic conservation laws or some simplifications. In addition, single flow reaches given must be coupled by appropriate coupling and boundary conditions. This approach finally leads to PDAEs (partial differential algebraic equations) and requires very robust and efficient numerical methods for their solution. Moreover, the optimization of the network operation with respect to the security of supply or energy consumption is of importance. Suitable optimization methods for these requirements are an active field of research.

Gerd Steinebach, Tim Jax, Lisa Wagner

Stability-Preserving Interpolation Strategy for Parametric MOR of Gas Pipeline-Networks

Optimization and control of large transient gas networks require the fast simulation of the underlying parametric partial differential algebraic systems. Surrogate modeling techniques based on linearization around specific stationary states, spatial semi-discretization and model order reduction allow for the set-up of parametric reduced order models that can act as basis sample to cover a wide parameter range by means of matrix interpolations. However, the interpolated models are often not stable. In this paper, we develop a stability-preserving interpolation method.

Yi Lu, Nicole Marheineke, Jan Mohring

A Structure-Preserving Model Order Reduction Approach for Space-Discrete Gas Networks with Active Elements

Aiming for an efficient simulation of gas networks with active elements a structure-preserving model order reduction (MOR) approach is presented. Gas networks can be modeled by partial differential algebraic equations. We identify connected pipe subnetworks that we discretize in space and explore with index and decoupling concepts for differential algebraic equations. For the arising input-output system we derive explicit decoupled representations of the strictly proper part and the polynomial part, only depending on the topology. The proper part is characterized by a port-Hamiltonian form that allows for the development of reduced models that preserve passivity, stability and locally mass. The approach is exemplarily used for an open-loop MOR on a network with a nonlinear active element.

Björn Liljegren-Sailer, Nicole Marheineke

Generalized ROW-Type Methods for Simulating Water Supply Networks

In order to help water suppliers estimating and improving effectiveness of their facilities with respect to economy and ecology, simulating real pipe networks is of increasing importance. Corresponding models take into account relevant processes such as procurement and preparation of drinking water as well as its subsequent distribution. Resulting mathematical systems prove to be demanding and require research in advanced efficient and robust numerical methods that in particular allow for fast computation. In this context, generalized Rosenbrock-Wanner type methods introduced by Jax and Steinebach (J Comput Appl Math 316:213–228, 2017) seem to be an useful tool to solve arising differential-algebraic equations.In this article, we investigate pros and cons when exploiting properties of these methods for computing problems that represent typical characteristics of pressurized flows given in water supply networks. Results are promising for tests with proper Jacobian structures. But they also motivate research in enhanced schemes.

Tim Jax, Gerd Steinebach

Minisymposium: Spacetime Models of Gravity in Space Geolocation and Acoustics

The geometrization of gravity has become one of the cornerstones of modern science having an impact on the industrial progress connected to many activities of daily life. In fact, in the last decades substantial research has been invested into post-Newtonian corrections for high-precision space geodesy and navigation [1–3, 12], as well as into the design of analogue models of gravity by making use of advanced optical and acoustic metamaterials (see e.g. [4, 5, 13]). Other present industrial procedures requiring very accurate timing show the need of innovative development of computationally efficient space-time models for use in space. In particular, these models become important in geolocation of passive radiotransmitters in space and to improve active space debris removal [8, 14, 15]. Moreover, acoustic metamaterials—artificially produced materials with exceptional properties not found in nature—provide the engineer with tools to fabricate acoustic devices with highly unusual features.

Jose M. Gambi, Michael M. Tung, Emilio Defez, Manuel Carretero

FDOA Determination of Velocities and Emission Frequencies of Passive Radiotransmitters in Space

Two systems of FDOA equations are introduced to determine in real time the velocities of passive, i.e. non-cooperative, radiotransmitters at the emission instants of the signals, together with the frequencies of emission. The systems correspond to the Newtonian and post-Newtonian frameworks of the Earth surrounding space. The transmitters may be located on the Earth surface or in space. Each system yields accurate unique solutions at the corresponding level of approximation, provided that the locations are determined by appropriated TDOA measurements. The systems are derived by means of Synge’s world functions for the vicinity of the Earth, since it allows to clearly identify the post-Newtonian corrections due to the Earth tidal potential and to the gravitational signals’ time delays.

Jose M. Gambi, Michael M. Tung, Maria L. García del Pino, Javier Clares

Non-linear Post-Newtonian Equations for the Motion of Designated Targets with Respect to Space Based APT Laser Systems

The equations introduced in this paper are aimed to gain accuracy in the determination of the motion of middle size space objects with respect to space based APT laser systems; therefore, they can be used for these systems to engage cataloged space debris objects whose size ranges between 1 and 10 cm. The equations are derived under the assumption that the framework of the Earth surrounding space is post-Newtonian and, unlike the standard p-N equations, they are valid for distant targets. Further, their time validity is also substantially larger than that of the standard equations. The reason is that they include non-linear terms that model the Earth tidal potential along the lines joining the systems and the targets. The equations are derived in local Cartesian orbital coordinates; therefore, they are primarily adapted for use with inertial-guided systems.

Jose M. Gambi, Maria L. García del Pino, Maria C. Rodríguez-Teijeiro

Post-Newtonian Corrections to the Newtonian Predictions for the Motion of Designated Targets with Respect to Space Based APT Laser Systems

Numerical experiments are carried out to validate the short/long term differences between the solutions of the Newtonian equations for the relative motion of middle size targets in space with respect to space based APT systems and the respective solutions of a system of non-linear post-Newtonian equations. This system has been introduced in the ECMI 2016 contribution Non-linear post-Newtonian equations for the motion of designated targets with respect to space based APT laser systems. Two auxiliary systems of post-Newtonian equations are used to carry out the validation. The simulations are made under the following assumptions: (i) the structures of the Earth surrounding space are respectively the Euclidean and that of the post-Newtonian approximation to the exterior Schwarzschild field; (ii) the targets are on equatorial circular orbits, and (iii) the APT systems are ECI oriented inertial-guided systems placed onboard HEO, MEO and LEO satellites in equatorial orbits about the Earth. The APT systems have initially been placed at short and successively increasing distances from the targets.

Jose M. Gambi, Maria L. García del Pino, Jürgen Gschwindl, Ewa B. Weinmüller

Acoustics in 2D Spaces of Constant Curvature

Maximally symmetric spaces play a vital role in modelling various physical phenomena. The simplest representative is the 2-sphere ??2 $${\mathbb S}^2$$ , having constant positive curvature. By embedding it into (2 + 1)D spacetime with Lorentzian signature it becomes the prototype of homogeneous and isotropic spacetime of constant curvature with constant scale factor: the Einstein cylinder ℝ×??2 $${\mathbb R}\times {\mathbb S}^2$$ . This work outlines a variational approach on how to model acoustic wave propagation on this particular curved spacetime. On the Einstein cylinder, the analytical solutions of the wave equation for the acoustic potential are shown to reduce to solutions of a differential equation of Sturm-Liouville type and simple harmonic time and angular dependence. Moreover, we discuss the implementation of such an underlying curved spacetime within an acoustic metamaterial—an artificially engineered material with remarkable properties exceeding the possibilities found in nature.

Michael M. Tung, José M. Gambi, María L. García del Pino

Minisymposium: Stochastic PDEs and Uncertainty Quantification with Applications in Engineering

Stochastic partial differential equations are becoming more and more important to model uncertainties, noise, fluctuations, process variations, material properties etc. in various applications.

Clemens Heitzinger, Hermann Matthies

Uncertainty Quantification for a Permanent Magnet Synchronous Machine with Dynamic Rotor Eccentricity

The influence of dynamic eccentricity on the harmonic spectrum of the torque of a permanent magnet synchronous machine is studied. The spectrum is calculated by an energy balance method. Uncertainty quantification is applied by using generalized Polynomial Chaos and Monte Carlo. It is found that the displacement of the rotor impacts the spectrum of the torque the most.

Zeger Bontinck, Oliver Lass, Herbert De Gersem, Sebastian Schöps

Minisymposium: The Treatment of Singularities and Defects in Industrial Applications

Very often industries are interested in removing, and therefore understanding, defects and singularities arising in materials and fluids. In other instances, it is the focusing inherent to singularities and their potential use to manufacture small things what makes them interesting for industrial purposes. This minisymposium gathered researchers who deal with singularities and defects that appear in industrial applications like, for instance, in problems of electro-wetting, superconductivity or dislocations. Such defects are usually undesirable and it becomes crucial to control its origin and evolution. In this sense, many of the topics that were covered in these sessions were at the latest cutting edge. Also, the topic itself was transversal since its industrial motivation ranges from so different fields like fluid dynamics to the allocation of dislocations or superconductivity. Finally, the mathematics involved are usually far from trivial, involving strong nonlinear effects and multiple length and time scales.

María Aguareles, Marco Antonio Fontelos

Computing Through Singularities in Potential Flow with Applications to Electrohydrodynamic Problems

Many interesting fluid interface problems, such as wave propagation and breaking, droplet and bubble break-up, electro-jetting, rain drops, etc. can be modeled using the assumption of potential flow. The main challenge, both theoretically and computationally, is due to the presence of singularities in the mathematical models. In all the above mentioned problems, an interface needs to be advanced by a velocity determined by the solution of a surface partial differential equation posed on this moving boundary. By using a level set framework, the two surface equations of the Lagrangian formulation can be implicitly embedded in PDEs posed on one higher dimension fixed domain. The advantage of this approach is that it seamlessly allows breakup or merging of the fluid domain and therefore provide a robust algorithm to compute through these singular events. Numerical results of a solitary wave breaking, the Rayleigh-Taylor instability of a fluid column, droplets and bubbles breaking-up and the electrical droplet distortion and subsequent jet emission can be obtained using this levelset/extended potential model.

Maria Garzon, James A. Sethian, Len J. Gray, August Johansson

Minisymposium: 8 Years of East African Technomathematics

Lappeenranta University of Technology, with the help of funding from the Finnish Ministry of Foreign Affairs, has now for eight consecutive years supported the development of applied and industrial mathematics in the East African region. The collaboration started from North-South-South exchange projects where students from the South would get the chance to visit LUT for study periods from 5 to 9 months. Over the last three years our activities have also extended into revision of the Applied Mathematics curricula in the East African universities, as well as establishment of contact between local industries and academia to enhance research collaboration and applicability. Several staff visits of 1–5 weeks and intensive courses have been organised.

Matti Heiliö, Matylda Jabłońska-Sabuka

Building Applied Mathematics Knowledge Base in East Africa

There is vast demand in Africa for technological development including modernization of higher education. Reforms in industrial processes through engineering skills are pivotal for the environmental concern and goals of sustainable development. Lappeenranta University of Technology has actively contributed to the spread of Industrial Mathematics in East African region over the past decade through development projects financed by the Finnish Ministry of Foreign Affairs. In this article, we summarize these projects and present their achievements. The story of European Consortium for Mathematics in Industry (ECMI) and the accumulated experience over 25 years have been the encouragement and inspiration for our initiatives. They were focused on Applied Mathematics curriculum development in Partner countries, and on organization of ECMI-style practical workshops like modeling weeks. There is obvious demand to broaden the cooperation between Africa and the European applied mathematics community.

Matti Heiliö, Matylda Jabłońska-Sabuka, Godwin Kakuba

Minisymposium: 10 Years of Portuguese Study Groups with Industry

This minisymposium provided an overview of the implementation and evolution of European Study Groups (ESGI) in Portugal, describing our experience and some industrial problems dealt with, the challenges that had to be overcome and examples of successful and less successful stories.

Manuel Cruz, Pedro Freitas, João Nuno Tavares

A Scheduling Application to a Molding Injection Machine: A Challenge Addressed on the 109th European Study Group with Industry

This paper addresses a scheduling optimization problem applied to a molding injection machine. This optimization problem was posed as a challenge to the mathematical community present at the 109th European Study Group with Industry (ESGI), held in Portugal in 2015. We propose a mathematical model for the scheduling optimization problem, which was coded in a widely known modeling language. The model is validated through a set of numerical results obtained with a state-of-the-art solver.

Isabel Cristina Lopes, Sofia O. Lopes, Rui M. S. Pereira, Senhorinha Teixeira, A. Ismael F. Vaz

Contributed Talks

Frontmatter

Numerical Simulation of a Li-Ion Cell Using a Thermoelectrochemical Model Including Degradation

A thermoelectrochemical model for the simulation of Li-ion cells is presented and numerically solved herein. The model, based on Newman’s (Newman and Thomas-Alyea, Electrochemical Systems, Wiley, New York, 2004) concentrated solution theory, covers electrochemical, thermal and aging effects. The degradation mechanism considered is the growth, due to a solvent decomposition reaction, of the Solid Electrolyte Interface layer (SEI) in the graphite electrode. Model homogenization is phenomenological but detailed particle-scale models are considered for the diffusion of species within active particles and SEI. The one dimensional thermal model incorporates reversible, irreversible, and ohmic heat generation, as well as the temperature dependence of the various transport, kinetic and mass transfer parameters. The governing equations are semi-discretized in space using finite elements (with FEniCS software package (Alnæs et al., Arch Numer Softw 3(100), 2015)) and integrated in time with implicit Euler method. For each time step, this leads to a set of nonlinear equations that is solved fully coupled through Newton’s iterations. This implementation is used to numerically simulate several charge-discharge cycles of a cell at 1C regime with an execution time around 50 times faster than real-time in a standard PC.

David Aller Giráldez, M. Teresa Cao-Rial, Pedro Fontán Muiños, Jerónimo Rodríguez

Numerical Simulation of a Network of Li-Ion Cells Using an Electrochemical Model

The battery system of an electric vehicle comprises hundreds of battery packs connected in both parallel and series, plus many other electric components required for the correct charge, power and thermal management of the system. Furthermore, each battery pack is a stack of several individual electrochemical cells connected in both parallel and series and thermally coupled. The aim of the present work is the numerical simulation of a pack of Li-ion cells. To this end, the device is modeled as an electrical network where the edges that contain electrochemical cells are handled by means of a Steklov-Poincaré operator associated to a model that covers electrochemical, thermal and aging effects. The full differential-algebraic system issued from the space discretization of the cells and the coupling between edges through Kirchhoff’s laws is integrated in time by means of implicit Euler method and Newton’s iterations. This procedure allows to decouple the resolution of the electrochemical cells leading to a highly parallelizable and computationally efficient algorithm. This approach is used to numerically simulate a pack of cells.

David Aller Giráldez, M. Teresa Cao-Rial, Manuel Cremades Buján, Pedro Fontán Muiños, Jerónimo Rodríguez

Symplectic Lanczos and Arnoldi Method for Solving Linear Hamiltonian Systems: Preservation of Energy and Other Invariants

Krylov subspace methods have become popular for the numerical approximation of matrix functions as for example for the numerical solution of large and sparse linear systems of ordinary differential equations. One well known technique is based on the method of Arnoldi which computes an orthonormal basis of the Krylov subspace. However, when applied to Hamiltonian linear systems of ODEs, this method fails to preserve the symplecticity of the solution under numerical discretization, or to preserve energy. In this work we apply the Symplectic Lanczos Method to construct a J-orthogonal basis of the Krylov subspace. This basis is then used to construct a numerical approximation which is energy preserving. The symplectic Lanczos method is widely used to approximate eigenvalues of large and sparse Hamiltonian matrices, but the approach for solving linear Hamiltonian systems is not well known in the literature. We also show that under appropriate additional assumptions on the structure of the linear Hamiltonian system, the Arnoldi method can preserve certain invariants of the system. We finally investigate numerically the energy and global error behaviour for the methods.

Elena Celledoni, Lu Li

A Self-adapting LPS Solver for Laminar and Turbulent Fluids in Industry and Hydrodynamic Flows

In this work we address the solution of the Navier–Stokes equations (NSE) in turbulent regime. On one side we focus is on the high-order term-by-term stabilization method that has one level, in the sense that it is defined on a single mesh, and in which the projection-stabilized structure of standard LPS methods is replaced by an interpolation-stabilized structure. The interest of LPS methods is that it ensures a self-adapting high accuracy in laminar regions of a turbulent flow, that turns to be of overall optimal high accuracy if the flow is fully laminar. On another side we present a reduced basis Smargorinsky turbulence model, based upon an empirical interpolation of the eddy viscosity term. This method yields dramatical improvements of the computing time, over 1000, for benchmark flows.

Tomás Chacón Rebollo, Enrique Delgado Ávila, Macarena Gómez Mármol, Samuele Rubino

Classification of Codimension-One Bifurcations in a Symmetric Laser System

We consider a class symmetric laser system, particularly rings of n identical semiconductor lasers coupled bidirectionally. The model is described using the Lang-Kobayashi rate equations where the finite propagation time of the light from one laser to another is reflected by a constant delay time parameter in the laser optical fields. Due to the network structure, the resulting system of delay differential equations has symmetry group ??n×S1 $$\mathbb {D}_n\times \textbf {S}^1$$ . We follow the discussions in Buono and Collera (SIAM J Appl Dyn Syst 14:1868–1898, 2015) for the general case, then give the important example where n = 4 to explicitly illustrate the general method which is a classification of codimension-one bifurcations into regular and symmetry-breaking. This particular example complements the recent works on rings with unidirectional coupling (Domogo and Collera, AIP Conf Proc 1787:080002, 2016), and on laser networks with all-to-all coupling (Collera, Mathematical and computational approaches in advancing modern science and engineering. Springer, Cham, 2016). Numerical continuation using DDE-Biftool are carried out to corroborate our classification results.

Juancho A. Collera

Approximating a Special Class of Linear Fourth-Order Ordinary Differential Problems

Differential matrix models are an essential ingredient of many important scientific and engineering applications. In this work, we propose a procedure to approximate the solutions of special linear fourth-order matrix differential problems of the type Y(4)(x) = A(x)Y (x) + B(x) with higher-order matrix splines. An example is included.

Emilio Defez, Michael M. Tung, J. Javier Ibáñez, Jorge Sastre

Evaluation of Steel Buildings by Means of Non-destructive Testing Methods

Non-destructive testing methods became popular within the last few years. For steel beams incorporated in buildings there are currently only destructive ways for testing the yield limit as well as for determination of the current stress level. Rise of ultrasonic and micro-magnetic tools for (non-destructive) measurements allows the characterization of the inbuild material especially of old steel bridges as economical maintenance of the infrastructure. It is possible to determine the reserve of residuence of bridges or of any other existing steel buildings in order to upgrade them competitively for future usage by the possibility of a simple way of strengthening by welding or using bolds.

Markus Doktor, Christian Fox, Wolfgang Kurz, Christina Thein

A Novel Multi-Scale Strategy for Multi-Parametric Optimization

The motion of a sailing yacht is the result of an equilibrium between the aerodynamic forces, generated by the sails, and the hydrodynamic forces, generated by the hull(s) and the appendages (such as the keels, the rudders, the foils, etc.), which may be fixed or movable and not only compensate the aero-forces, but are also used to drive the boat. In most of the design, the 3D shape of an appendage is the combination of a plan form (2D side shape) and a planar section(s) perpendicular to it, whose design depends on the function of the appendage. We often need a section which generates a certain quantity of lift to fulfill its function, but the lift comes with a penalty which is the drag. The efficiency, equilibrium and speed of a sailing boat depend on the appendage hence on the planar section. We describe a multi-scale strategy to optimize the shape of a section in a multi-parametric setting by embedding the problem within a discrete multiresolution framework. We show that our strategy can be easily implemented and, combined with appropriate optimization techniques, provides a fast algorithm to obtain an ‘optimal’ perturbation of the original shape.

Rosa Donat, Sergio López-Ureña, Marc Menec

Optimal Shape Design for Polymer Spin Packs

A shape optimization approach for the design of cavities with a specified wall shear stress profile is presented. Applications are in the design of spin pack geometries with low and homogeneous residence times and without dead spaces to prevent polymer degradation for sensitive materials. Furthermore, a related operator is studied which suggests that the set of attainable wall shear stresses is rather large.

Robert Feßler, Christian Leithäuser, René Pinnau

A Fast Ray Tracing Method in Phase Space

Ray tracing is a widely used method in geometric optics to simulate the propagation of light through a non-imaging optical system. We present a new ray tracing approach based on the source and the target phase space (PS) representation of two-dimensional optical systems. The new PS method allows tracing far fewer rays through the system compared to the classical ray tracing approach. The efficiency of the PS method is demonstrated by numerical simulations that compare the new approach with Monte Carlo (MC) ray tracing. The results show that the PS method is very accurate and much faster than MC.

Carmela Filosa, Jan ten Thije Boonkkamp, Wilbert IJzerman

Homogenization of a Hyperbolic-Parabolic Problem with Three Spatial Scales

We study the homogenization of a certain linear hyperbolic-parabolic problem exhibiting two rapid spatial scales {ε, ε2}. The homogenization is performed by means of evolution multiscale convergence, a generalization of the concept of two-scale convergence to include any number of scales in both space and time. In particular we apply a compactness result for gradients. The outcome of the homogenization procedure is that we obtain a homogenized problem of hyperbolic-parabolic type together with two elliptic local problems, one for each rapid scale.

Liselott Flodén, Anders Holmbom, Pernilla Jonasson, Marianne Olsson Lindberg, Tatiana Lobkova, Jens Persson

A Heuristic Method to Optimize High-Dimensional Expensive Problems: Application to the Dynamic Optimization of a Waste Water Treatment Plant

The mathematical description of industrial processes usually requires the use of models consisting of large systems of differential and algebraic equations. The numerical simulations of such models may lead to high computation times, therefore, making optimization unaffordable using classical optimization methods.This contribution describes an evolutionary approach for the optimization of computationally expensive, highly dimensional problems. The performance of the algorithm has been compared against well known surrogate based optimization methods using classical benchmark functions. The results show that our method outperforms the reference methods, specially for the high dimensional case.The proposed algorithm has been applied to the optimization of the operation parameters of a waste water treatment plant, using dynamic profiles. The algorithm has been able to produce better solutions than those obtained previously using static profiles.

Alberto Garre, Pablo S. Fernandez, Julio R. Banga, Jose A. Egea

Reduced Basis Method Applied to a Convective Instability Problem

Numerical reduced basis methods are instrumental to solve parameter dependent partial differential equations problems in case of many queries. Bifurcation and instability problems have these characteristics as different solutions emerge by varying a bifurcation parameter. Rayleigh-Bénard convection is an instability problem with multiple steady solutions and bifurcations by varying the Rayleigh number. In this paper the eigenvalue problem of the corresponding linear stability analysis has been solved with this method. The resulting matrices are small, the eigenvalues are easily calculated and the bifurcation points are correctly captured. Nine branches of stable and unstable solutions are obtained with this method in an interval of values of the Rayleigh number. Different basis sets are considered in each branch. The reduced basis method permits one to obtain the bifurcation diagrams with much lower computational cost.

Henar Herrero, Yvon Maday, Francisco Pla

Independent Loops Search in Flow Networks Aiming for Well-Conditioned System of Equations

We approach the problem of choosing linearly independent loops in a pipeflow network as choosing the best-conditioned submatrix of a given larger matrix. We present some existing results of graph theory and submatrix selection problems, based on which we construct three heuristic algorithms for choosing the loops. The heuristics are tested on two pipeflow networks that differ significantly on the distribution of pipes and nodes in the network.

Jukka-Pekka Humaloja, Simo Ali-Löytty, Timo Hämäläinen, Seppo Pohjolainen

Modeling and Optimization Applied to the Design of Fast Hydrodynamic Focusing Microfluidic Mixer for Protein Folding

In this paper, we are interested in the design of a microfluidic mixer based on hydrodynamic focusing which is used to initiate the folding process (i.e., changes of the molecular structure) of a protein by diluting a protein solution to decrease its denaturant concentration to a given value in a short time interval we refer to as mixing time. Our objective is to optimize this mixer by choosing suitable shape and flow conditions in order to minimize its mixing time. To this end, we first introduce a numerical model that enables computation of the mixing time of a considered mixer. Then, we define a mixer optimization problem and solve it using a hybrid global optimization algorithm.

Benjamin Ivorra, María Crespo, Juana L. Redondo, Ángel M. Ramos, Pilar M. Ortigosa, Juan G. Santiago

A Second Order Fixed Domain Approach to a Shape Optimization Problem

A fixed second order domain approach for solving optimal shape design problems is presented. The original optimal shape design problem is converted to an optimal control problem defined on a fixed domain. First and second order optimality conditions are derived. Numerical results are presented which demonstrate the robustness of the second order optimality conditions.

Henry Kasumba, Godwin Kakuba, John Mango Magero

Semi-Discretized Stochastic Fiber Dynamics: Non-Linear Drag Force

We analyze a spatially discretized model for the dynamics of a thin, long, elastic, inextensible fiber in a turbulent flow as occurring, e.g., in the spunbond production process of non-woven textiles. It consists of a high-dimensional stochastic differential equation with a non-linear algebraic constraint and an associated Lagrange multiplier term. We prove existence and uniqueness of a global strong solution for the case of a non-linear underlying drag force model. Our result generalizes previous findings which are based on a simplified linear drag force model.

Felix Lindner, Holger Stroot, Raimund Wegener

Simulating Heat and Mass Transfer with Limited Amount of Sensor Data

We consider the problem of dynamically modeling the distribution of temperature and concentration of water vapor inside a building. It is assumed that the building is equipped with a network of sparsely located sensors and a data management system recording measurements of temperature, relative humidity, and air flow. The measurements serve as input data for a time-dependent boundary value problem proposed to simulate heat and mass transfer inside a building.

Vanessa López

Prototype Model of Autonomous Offshore Drilling Complex

The prototype model of autonomous offshore drilling complex consists of several sub models corresponding to different considered phenomena: vibrations of drilling string; circulation of drilling mud; mud filtration; deformation of the liquid filled soil and so on. All sub models are combined into unified prototype model and exchange data during simulations.The project of prototype model development is launched jointly by St. Petersburg Polytechnic University and Rubin ship design bureau. Specialized in software code is developed and used for simulation by applying methods from different branches of computational mechanics.

Sergey Lupuleac, Evgeny Toropov, Andrey Shabalin, Mikhail Kirillov

A Competitive Random Sequential Adsorption Model for Immunoassay Activity

Immunoassays rely on highly specific reactions between antibodies and antigens and are used in biomedical diagnostics applications to detect biomarkers for a variety of diseases. Antibody immobilization to solid interfaces through random adsorption is a widely used technique but has the disadvantage of severely reducing the antigen binding activity and, consequently, the assay performance. This paper proposes a simple mathematical framework, based on the theory known as competitive random sequential adsorption (CRSA), for describing how the activity of immobilized antibodies depends on their orientation and packing density and generalizes a previous model by introducing the antibody aspect ratio as an additional parameter which could influence the assay behaviour.

Dana Mackey, Eilis Kelly, Robert Nooney

A Finite Volume Scheme for Darcy-Brinkman’s Model of Two-Phase Flows in Porous Media

In this paper, we are interested in the displacement of two incompressible phases in a Darcy-Brinkman flow in a porous media. The equations are obtained by the conservation of the mass and by considering the Brinkman regularization velocity of each phase. This model is treated in its general form with the whole nonlinear terms. This paper deals with construction and convergence analysis of a finite volume scheme together with a phase-by-phase upstream according to the total velocity. Finally, numerical tests illustrate the behavior of the solutions of this proposed scheme.

Houssein Nasser El Dine, Mazen Saad, Raafat Talhouk

Optimization and Sensitivity Analysis of Trajectories for Autonomous Small Celestial Body Operations

Within this paper, a method for on-board trajectory calculation in the vicinity of a small celestial body is introduced. Therefore, high precision methods of nonlinear optimization and optimal control are used. Additionally, a parametric sensitivity analysis is implemented. This tool allows to approximate a perturbed optimal solution in case of model parameter deviations from nominal values without noticeable computational effort. Parametric sensitivity analysis is a recent research area of great interest. Parameter perturbations that occur in the dynamic of the system as well as in boundary conditions or in state and control constraints can be analyzed. Thus, additional stability information is provided. Furthermore, the fast and reliable approximation of perturbed controls can be used for real-time control in time critical navigation phases.

Anne Schattel, Andreas Cobus, Mitja Echim, Christof Büskens

A Finite Volume Method with Staggered Grid on Time-Dependent Domains for Viscous Fiber Spinning

The spinning of slender viscous fibers can be described by the special Cosserat theory with one-dimensional models consisting of partial differential and algebraic equations on time-dependent spatial domains. We propose a first-order finite volume method on a staggered grid with flux approximation suitable for the underlying differential-algebraic characteristics and a proper geometric handling of the space-time domain. The numerical results confirm the theoretical convergence orders. As exemplary application a rotational spinning scenario is studied.

Stefan Schiessl, Nicole Marheineke, Walter Arne, Raimund Wegener

A Variational Approach to the Homogenization of Double Phase p h (x)-Curl Systems in Magnetism

We introduce a variational approach to study the homogenization of a class of p h (x)-curl systems arising in Magnetism based on the study of the Γ-convergence of the sequence of associated energies. The explicit characterization of the effective coefficients is obtained by means of a three dimensional minimization problem when p h (x) is a double phase exponent.

Hélia Serrano

Modelling of Combustion and Diverse Blow-Up Regimes in a Spherical Shell

Physical phenomena with critical blow-up regimes simulated by the 3D nonlinear diffusion equation in a spherical shell are studied. For solving the model numerically, the original differential operator is split along the radial coordinate, as well as an original technique of using two coordinate maps for solving the 2D subproblem on the sphere is involved. This results in 1D finite difference subproblems with simple periodic boundary conditions in the latitudinal and longitudinal directions that lead to unconditionally stable implicit second-order finite difference schemes. A band structure of the resulting matrices allows applying fast direct (non-iterative) linear solvers using the Sherman-Morrison formula and Thomas algorithm. The developed method is tested in several numerical experiments. Our tests demonstrate that the model allows simulating different regimes of blow-up in a 3D complex domain. In particular, heat localisation is shown to lead to the breakup of the medium into individual fragments followed by the formation and development of self-organising patterns, which may have promising applications in thermonuclear fusion, nonlinear inelastic deformation and fracture of loaded solids and media and other areas.

Yuri N. Skiba, Denis M. Filatov

Parameterized Model Order Reduction by Superposition of Locally Reduced Bases

We present an approach for model order reduction of parameterized linear dynamical systems which combines local reduced bases using singular value decompositions. The local reduced bases are computed for a fixed set of sample points in the parameter domain by moment matching techniques. Covering the parameter domain with sample points may yield a very large set of samples. We investigate a superposition approach that takes only a few of the local models into account to keep the resulting reduced dimension small. Our approach will be compared to one existing approach which directly interpolates local bases in some illustrating numerical experiments.

Tino Soll, Roland Pulch

A Preliminary Statistical Evaluation of GPS Static Relative Positioning

The objective of this work is to evaluate GPS static relative positioning (Hofmann-Wellenhof et al, GNSS-Global Navigation Satellite Systems GPS, GLONASS, Galileo, and more. Springer Verlag-Wien, New York, 2008; Kaplan and Hegarty, Understanding GPS: Principles and Applications. Artech House, Norwood, 2006; Leick, GPS Satellite Surveying. John Wiley & Sons, New Jersey, 2004), regarding accuracy, as the equivalent of a Real Time Kinematic (RTK) network and to address the practicality of using either a continuously operating reference stations (CORS) or a passive control point for providing accurate positioning control. The precision of an observed 3D relative position between two global navigation satellite systems (GNSS) antennas, and how it depends on the distance between these antennas and on the duration of the observing session, was studied. We analyze the performance of the software for each of the six chosen ranges of length in each of the four scenarios created, considering different intervals of observation time. The relation between observing time and baseline length is established. In this work are applied different statistical techniques, such as data analysis and elementary/intermediate inference level techniques (Tamhane and Dunlop, Statistics and Data Analysis: From Elementary to Intermediate. Prentice Hall, New Jersey, 2000) or multivariate analysis (Turkman and Silva, Modelos Lineares Generalizados da teoria a prática. Sociedade Portuguesa de Estatística, Lisboa, 2000; Anderson, An Introduction to Multivariate Analysis. Jonh Wiley & Sons, New York, 2003).

M. Filomena Teodoro, Fernando M. Gonçalves

Numerical Simulation of Flow Induced Vocal Folds Vibration by Stabilized Finite Element Method

This paper is interested in the numerical simulation of human vocal folds vibration induced by fluid flow. A two-dimensional problem of fluid-structure interaction is mathematically formulated. An attention is paid to the description of a robust method based on finite element approximation. In order to capture the typical flow velocities involved in the physical model resulting in high Reynolds numbers, the modified Streamline-Upwind/Petrov-Galerkin stabilization is applied. The mathematical description of the considered problem is presented, where the arbitrary Lagrangian-Euler method is used to describe the fluid flow in time dependent domain. The viscous incompressible fluid flow and linear elasticity models are considered. Further, the numerical scheme is described for the fluid flow and the elastic body motion. The implemented coupling procedure is explained. The numerical results are shown.

Jan Valášek, Petr Sváček, Jaromír Horáček

Wiener Chaos Expansion for an Inextensible Kirchhoff Beam Driven by Stochastic Forces

In this work we study the feasibility of the Wiener Chaos Expansion for the simulation of an inextensible elastic slender fiber driven by stochastic forces. The fiber is described as Kirchhoff beam with a 1d-parameterized, time-dependent curve, whose dynamics is given by a constrained stochastic partial differential equation. The stochastic forces due to a surrounding turbulent flow field are modeled by a space-time white noise with flow-dependent amplitude. Using the techniques of polynomial chaos, we derive a deterministic system which approximates the original stochastic equation. We explore the numerical performance of the approximation and compare the results with those obtained by Monte-Carlo simulations.

Alexander Vibe, Nicole Marheineke

A Methodology for Fasteners Placement to Reduce Gap Between the Parts of a Wing

We concerned with the methodology of automatic fastener placement that reduces the gap between the parts of the wing. The gap is assumed to be of stochastic nature, therefore, it is modeled as a random field. The major issue we ran into is lack of sufficient amount of data, thus, a special small sample statistical estimator for the random field parameters is used. As a final result, the procedure is proposed to successively install the fasteners in such a way that their placement suits multiple wings at once, reducing the gap to a certain level.

Nadezhda Zaitseva, Sergey Berezin

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