This workshop was the third to be held under the EC program NETIAM (New and Emerging Technologies in Applied Mathematics), which emphasizes new and emerging applications of mathematics in the real world.
The aim of the workshop was to connect those mathematical methodologies that have greatest potential to predict the properties of complex porous materials, to understand how geometry influences these properties and ultimately how to design materials so that they have improved properties. As a specific example, the visualisation, simulation, analysis and design of filter materials with respect to filtration efficiency, pressure drop, and filter life time will be considered.
New production processes and new materials vastly increase the possibilities of making cheaper and better materials. Large numbers of production parameters and material choices as well as choices for material recombination together with shortened product cycles due to increased global competition as well as lack of experience with new materials and production processes make traditional trial and error approaches for material improvement obsolete. A particular challenge lies in the randomness of materials (for example, Nonwoven or foams) on small scales. Thus, many researchers in this field from material science, computer science and mechanical engineering have begun to use simulation and models to predict improvements under material variation.
Whereas there is a vast mathematical literature on individual aspects of virtual porous materials, the use of mathematical models and methods from a unified perspective is still at its dawn, and most works that treat all aspects of real world problems stem from mechanical engineers, computer scientists and material scientists.
The issues in the visualization of virtual porous materials as well as real materials include, but are not limited to the need for
- very large 3d data sets,
- complex and changing geometries as well as complex properties such as flow fields, displacement fields, electric fields, magnetic fields,
- representative, instructive agglomerate information and
- easily accessible detail information.
- extraction of 3d features from 2d images,
- 3d image acquisition and image processing,
- stochastic geometric models for random materials and
- bridging of scales from nanometres for geometric material features to meters for products assembled from these materials.
- computation of material properties,
- finding porous media material models with few parameters,
- continuous and discrete optimization methods,
- dealing with constraints on manufacturability and
- dealing with non-modelled side conditions, e.g. production cost.
According to the statements above, the mathematical works fall in three main categories:
- Visualization and Image analysis
- Stochastic geometry and Material Description
- Porous material design based on the simulation of material properties