The Complex Materials and Industrial Mathematics research group holds lunchtime seminars, generally on the first Wednesday of each month, to review our past and current research.
In a broad range of industrial equipment and machinery, the presence of damage like holes, cracks or inclusions in the metallic parts can compromise their structural integrity, and even cause catastrophic failure. Among the wide variety of inspection methods available, we will focus on ultrasonic inspection, which consist of exciting the metallic pieces with elastic waves and measure their response. To process the acquired data we use the topological derivative, which is a scalar function that measures the sensitivity of a functional to infinitesimal domain perturbations. In this work we will address two industrial cases of interest: the inspection of welding joints using elastic waves, and the inspection of thin metallic plates using Lamb waves.
Abstract: For equilibrium hard spheres the stochastic geometry of the insertion space, the room to accommodate another sphere, relates exactly to the equation of state. We begin to extend this idea to active matter, analyzing insertion space for repulsive active particles in one and two dimensions using both on- and off-lattice models. In 1D we derive closed-form expressions for the mean insertion cavity size, cavity number, and total insertion volume, all in excellent agreement with simulations. Strikingly, activity increases the total insertion volume and tends to keep the insertion space more connected. These results provide the first quantitative foundation for the stochastic geometry of active matter, and opens up a new route to building a thermodynamics of active systems.
Partitioning of (bio)materials in polymeric mixtures is a fundamental process, relevant from the organization of cellular environments to industrial separation technologies. In cells, macromolecules often localize within coexisting biomolecular phases, while in industry, polymer–polymer aqueous systems are widely used for the extraction and purification of (bio)materials. Yet, the underlying physical and chemical factors that control this phase behavior remain poorly understood.
In this work [1], we develop a classical density functional theory (DFT) framework to describe phase coexistence and partitioning in mixtures containing multiple polymers and suspended components. As a model case, we study a binary polymer mixture undergoing phase separation with a third dispersed material, and explore how size ratios, concentrations, and interaction affinities determine its spatial distribution and coexisting densities.
Our DFT predictions are benchmarked against coarse-grained Brownian dynamics simulations, previously introduced to model the magnetic response of ferrofluidic aqueous two-phase systems [2]. Together, these approaches provide a coherent microscopic understanding of partitioning in complex soft-matter systems.
[1] V. A. Varma & A. Scacchi, "General approach for partitioning and phase separation in macromolecular coexisting phases", arXiv preprint arXiv:2509.14392, (2025).
[2] A. Scacchi, C. Rigoni, M. Haataja, J. V. I. Timonen, M. Sammalkorpi, "A corase-grained model for aqueous two-phase systems: Application to ferrofluids", Journal of Colloid and Interface Science 686, (2025).
An opportunity to meet and discuss research ideas. More detail to follow.
Abstract
In this study, the real-world application is concerned with the determination of a space-dependent index of refraction of an optical anti-reflection coating. The model is based on solving an inverse coefficient identification problem for the 1D Helmholtz equation. The additional data necessary for the inversion can be the full complex reflection coefficient or its absolute value only, measured for many wavenumbers. The numerical method is based on a FDM
direct solver combined with a nonlinear Tikhonov regularization. It is shown that, in general, the knowledge of the full complex reflection coefficient is necessary to determine uniquely a spacewise continuous index of refraction. When only the absolute value of the reflection coefficient is used as input data, constraints need to be imposed, e.g., the knowledge of the full integrated refraction index, additional smoothness assumptions on the index of refraction, or more reflectance data measured for many wavelengths. Apart from this insight into the uniqueness of solution of the inverse problem, the principal conclusion is that a better fit of the reflectance measured data is obtained by using a continuously varying index of refraction than when this coefficient is sought as a piecewise constant function.
An opportunity to meet and discuss research ideas. More detail to follow.
