http://www.mathematicsinindustry.com The latest research articles published by Journal of Mathematics in Industry 2012-01-03T00:00:00Z Purpose: Being able to predict the visual appearance of a painted steel sheet, given its topography before paint application, is of crucial importance for car makers. Accurate modeling of the industrial painting process is required. Results: The equations describing the leveling of the paint film are complex and their numerical simulation requires advanced mathematical tools, which are described in detail in this paper. Simulations are validated using a large experimental data base obtained with a wavefront sensor developed by PhasicsTM. Conclusions: The conducted simulations are complex and require the development of advanced numerical tools, like those presented in this paper.Keywords thin films, numerical simulation, industrial painting process, roughness, lubrication approximation http://www.mathematicsinindustry.com/content/2/1/1 Bruno Figliuzzi Dominique Jeulin Anael Lemaitre Gabriel Fricout Jean-Jacques Piezanowski Paul Manneville Journal of Mathematics in Industry 2012, null:1 2012-01-03T00:00:00Z doi:10.1186/2190-5983-2-1 /content/figures/2190-5983-2-1-toc.gif Journal of Mathematics in Industry 2190-5983 ${item.volume} 1 2012-01-03T00:00:00Z PDF In Airbus view, one major objective for the aircraft industry is the reduction of aircraft development lead-time and the provision of robust solutions with highly improved quality. In that context it is important to exploit all opportunities provided by enhanced or new classes of numerical simulation tools, e.g. high fidelity multi-disciplinary Computational Fluid Dynamics (CFD) and powerful High Performance Computing (HPC) capabilities.To help meet the challenge of superior product development it will finally be essential to numerically "flight-test" a virtual aircraft with all its multi-disciplinary interactions in a computer environment and to compile all of the data required for the development and certification with guaranteed accuracy in a reduced time frame. Numerical simulation is foreseen to provide a tremendous increase in aircraft design efficiency and quality over the next decades. This concept is considered by Airbus as one of the long term main objectives for aircraft development.Progress in HPC will essentially contribute to achieve this goal. Considerable changes of aircraft design processes and way of working will lead to significant reduction of development times while including more and more disciplines in the early phases of design activities in order to find an overall optimum aircraft design.Aerodynamic Design deals with the development of outer shapes of an aircraft, optimizing for its performance, handling qualities and loads. A major ingredient to the design process is the numerical simulation of the external airflow. The capabilities to predict the flow not only near the design point but also under other challenging conditions in a given flight envelope is a prerequisite for optimization towards market requirements.Since it began about 50 years ago, CFD has made important progress in terms of accuracy of the physical models, robustness and efficiency of the nonlinear solution algorithms and reliability of the overall prediction approach. This trend will continue over the next decades. In our view, along with the increasing capability to model and compute all major multi-disciplinary aspects of an aircraft, in the long term it will become possible to "fly" and investigate the complete aircraft in the computer.Currently numerical simulation provides good means to analyse the flow around the aircraft in detail, although the regime of flow separation onset up to maximum lift conditions is still not modelled accurately enough, nonlinearities and turbulence modelling for separated flows are still a major concern.It was not only the increase in HPC power that made more sophisticated Navier-Stokes solving enter the daily industrial design process. Better understanding and mathematical analysis of the system of Navier-Stokes equations led to more powerful algorithms, to more capable software and more comprehensive analysis of aircraft flows.However, a lot work remains to be done. Next decade's goal will be to better exploit more accurate and efficient numerical formulations, advanced turbulence models and to achieve a fully flexible and automatic CFD capability that works in a fully adaptive manner, providing the best quality solution at minimum cost and time. This will lead to a complete change in the way future aircraft will be designed. http://www.mathematicsinindustry.com/content/1/1/10 Adel Abbas-Bayoumi Klaus Becker Journal of Mathematics in Industry 2011, null:10 2011-12-12T00:00:00Z doi:10.1186/2190-5983-1-10 /content/figures/2190-5983-1-10-toc.gif Journal of Mathematics in Industry 2190-5983 ${item.volume} 10 2011-12-12T00:00:00Z PDF Purpose - Describe a high-throughput method for the analysis of uncertain models, e.g. in biological research. Methods: Generalized modeling for conceptual analysis of large classes of models. Results: Local dynamics of uncertain networks are revealed as a function of intuitive parameters. Conclusions: Generalized modeling easily scales to very large networks. http://www.mathematicsinindustry.com/content/1/1/9 Thilo Gross Stefan Siegmund Journal of Mathematics in Industry 2011, null:9 2011-12-12T00:00:00Z doi:10.1186/2190-5983-1-9 /content/figures/2190-5983-1-9-toc.gif Journal of Mathematics in Industry 2190-5983 ${item.volume} 9 2011-12-12T00:00:00Z PDF The use of porous ducts to deliver water to agricultural fields is an old technique which helps saving water and prevents ground erosion. Designing porous duct is not as a simple task as it looks and apparently has never been the subject of mathematical research. Here the problem is addressed making use of a double rescaling of space and velocity variables, which allows the derivation of the governing equations starting from the study of the classical Navier Stokes equations in a pipe. Such equations are then solved obtaining results of practical interest in design of irrigation pipes, both for low discharge pipes (small plants) and for high discharge pipes (large plants).AMS classification: 76S05, 76D05, 35C20 http://www.mathematicsinindustry.com/content/1/1/8 Antonio Fasano Angiolo Farina Journal of Mathematics in Industry 2011, null:8 2011-08-18T00:00:00Z doi:10.1186/2190-5983-1-8 /content/figures/2190-5983-1-8-toc.gif Journal of Mathematics in Industry 2190-5983 ${item.volume} 8 2011-08-18T00:00:00Z XML Background: We discuss the numerical solution of large scale nonlinear eigenvalue problems and frequency response problems that arise in the analysis, simulation and optimization of acoustic fields. We report about the cooperation with the company SFE in Berlin. We present the challenges in the current industrial problems and the state-of-the-art of current methods. Results: The difficulties that arise with current off-the-shelf methods are discussed and several industrial examples are presented. Conclusions: It is documented that industrial cooperation is by no means a one-way street of transfer from academia to industry but the challenges arising in industrial practice also lead to new mathematical questions which actually change the mathematical theory and methods.AMS classification: 65F18, 15A18. http://www.mathematicsinindustry.com/content/1/1/7 Volker Mehrmann Christian Schroder Journal of Mathematics in Industry 2011, null:7 2011-07-27T00:00:00Z doi:10.1186/2190-5983-1-7 /content/figures/2190-5983-1-7-toc.gif Journal of Mathematics in Industry 2190-5983 ${item.volume} 7 2011-07-27T00:00:00Z XML Despite the deluge of bioinformatics data, the extraction of information with respect to complex diseases remains an open challenge. The development of efficient tools allowing the re-engineering of functional biological networks will therefore be crucial for the future of the pharmaceutical and biotech industry. In this paper we present a method for efficient re-engineering of meso-scale network topologies for biomedical systems from stationary data. We show that the meso-scale topology is related to functional structures of the input-output data of the entire system, which can be unravelled from high throughput screening experiments, without information with respect to intermediate variables. Analysis of the functional structure of the data provides a complementary approach to established network reengineering methods based on combinatorial optimization. A combination of both approaches will help to overcome the drawbacks of the established network reengineering algorithms. http://www.mathematicsinindustry.com/content/1/1/6 Andreas Schuppert Journal of Mathematics in Industry 2011, null:6 2011-06-23T00:00:00Z doi:10.1186/2190-5983-1-6 /content/figures/2190-5983-1-6-toc.gif Journal of Mathematics in Industry 2190-5983 ${item.volume} 6 2011-06-23T00:00:00Z XML Geometric computing has recently found a new field of applications, namely the various geometric problems which lie at the heart of rationalization and construction-aware design processes of freeform architecture. We report on our work in this area, dealing with meshes with planar faces and meshes which allow multilayer constructions (which is related to discrete surfaces and their curvatures), triangles meshes with circle-packing properties (which is related to conformal uniformization), and with the paneling problem. We emphasize the combination of numerical optimization and geometric knowledge. http://www.mathematicsinindustry.com/content/1/1/4 Johannes Wallner Helmut Pottmann Journal of Mathematics in Industry 2011, null:4 2011-06-03T00:00:00Z doi:10.1186/2190-5983-1-4 /content/figures/2190-5983-1-4-toc.gif Journal of Mathematics in Industry 2190-5983 ${item.volume} 4 2011-06-03T00:00:00Z XML Reduction strategies, such as model order reduction (MOR) or reduced basis (RB) methods, in scientific computing may become crucial in applications of increasing complexity. In this paper we review the reduced basis method (built upon a high-fidelity "truth" finite element approximation) for a rapid and reliable approximation of parametrized partial differential equations, and comment on their potential impact on applications of industrial interest. The essential ingredients of RB methodology are: a Galerkin projection onto a low-dimensional space of basis functions properly selected, an affine parametric dependence enabling to perform a competitive Offline-Online splitting in the computational procedure, and a rigorous a posteriori error estimation used for both the basis selection and the certification of the solution. The combination of these three factors yields substantial computational savings which are at the basis of an efficient model order reduction, ideally suited for real-time simulation and many-query contexts (e.g. optimization, control or parameter identification). After a brief excursus on the methodology, we focus on linear elliptic and parabolic problems, discussing some extensions to more general classes of problems and several perspectives of the ongoing research. We present some results from applications dealing with heat and mass transfer, conduction-convection phenomena, and thermal treatments. http://www.mathematicsinindustry.com/content/1/1/3 Alfio Quarteroni Gianluigi Rozza Andrea Manzoni Journal of Mathematics in Industry 2011, null:3 2011-06-03T00:00:00Z doi:10.1186/2190-5983-1-3 /content/figures/2190-5983-1-3-toc.gif Journal of Mathematics in Industry 2190-5983 ${item.volume} 3 2011-06-03T00:00:00Z XML The optimal design of rotational production processes for glass wool manufacturing poses severe computational challenges to mathematicians, natural scientists and engineers. In this paper we focus exclusively on the spinning regime where thousands of viscous thermal glass jets are formed by fast air streams. Homogeneity and slenderness of the spun fibers are the quality features of the final fabric. Their prediction requires the computation of the fluid-fiber-interactions which involves the solving of a complex three-dimensional multiphase problem with appropriate interface conditions. But this is practically impossible due to the needed high resolution and adaptive grid refinement. Therefore, we propose an asymptotic coupling concept. Treating the glass jets as viscous thermal Cosserat rods, we tackle the multiscale problem by help of momentum (drag) and heat exchange models that are derived on basis of slender-body theory and homogenization. A weak iterative coupling algorithm that is based on the combination of commercial software and self-implemented code for flow and rod solvers, respectively, makes then the simulation of the industrial process possible. For the boundary value problem of the rod we particularly suggest an adapted collocation-continuation method. Consequently, this work establishes a promising basis for future optimization strategies.MSC-Classification. 76-xx, 34B08, 41A60, 65L10, 65Z05 http://www.mathematicsinindustry.com/content/1/1/2 Walter Arne Nicole Marheineke Johannes Schnebele Raimund Wegener Journal of Mathematics in Industry 2011, null:2 2011-06-03T00:00:00Z doi:10.1186/2190-5983-1-2 /content/figures/2190-5983-1-2-toc.gif Journal of Mathematics in Industry 2190-5983 ${item.volume} 2 2011-06-03T00:00:00Z XML PurposeThe polishing of cut lead glass crystal is effected through the dowsing of the glass in a mixture of two separate acids, which between them etch the surface and as a result cause it to be become smooth. In order to characterise the resultant polishing the rate of surface etching must be known, but when this involves multicomponent surface reactions it becomes unclear what this rate actually is. Methods: We develop a differential equation based discrete model to determine the effective etching rate by means of an atomic scale model of the etching process. Results: We calculate the etching rate numerically and provide an approximate asymptotic estimate. Conclusions: The natural extension of this work would be to develop a continuum advection-diffusion model. http://www.mathematicsinindustry.com/content/1/1/1 Jonathan Ward Andrew Fowler Stephen O'Brien Journal of Mathematics in Industry 2011, null:1 2011-06-03T00:00:00Z doi:10.1186/2190-5983-1-1 /content/figures/2190-5983-1-1-toc.gif Journal of Mathematics in Industry 2190-5983 ${item.volume} 1 2011-06-03T00:00:00Z XML