The recent publications in the field of computational and applied mathematics reveal a strong trend towards the development and application of advanced numerical methods and model reduction techniques to solve complex inverse problems and transport-dominated phenomena. A significant focus is on enhancing computational efficiency and accuracy through innovative approaches such as reduced-order modeling, low-rank structure exploitation, and mimetic finite difference schemes. These methodologies are being tailored to address specific challenges in various applications, including food engineering, turbulence modeling, plasma physics, and acoustic scattering, demonstrating a clear push towards interdisciplinary research and practical problem-solving.

Particularly noteworthy is the emphasis on optimizing sensor placement and data assimilation techniques for accurate temperature estimation in food freezing, the exploration of low-rank structures for solving inverse scattering problems with far-field data, and the development of energy-preserving mimetic finite difference schemes for transport operators in plasma physics. These advancements not only contribute to the theoretical understanding of the underlying phenomena but also offer promising tools for real-world applications.

Highlighted Papers

• A reduced-order framework for temperature estimation in food freezing from optimally located sensors, including turbulent conjugate flow scenarios: Introduces a novel framework for efficient temperature field estimation in food freezing, leveraging a reduced-order model and optimized sensor placement.
• Exploring low-rank structure for an inverse scattering problem with far-field data: Presents a groundbreaking low-rank structure approach for the inverse scattering problem, enhancing stability and accuracy in reconstructions.
• Mimetic finite difference schemes for transport operators with divergence-free advective field and applications to plasma physics: Develops a mimetic finite difference method that preserves energy in wave problems, with applications to plasma physics demonstrating its effectiveness.