**NOVA Math – UNIDEMI Talks**

3rd Edition

**Date | Time:** May 31, 2023 | 14h00 – 15h00

**Location:** Building VII, Seminar room (2nd floor)

**14:00 – 14:15 **

**Duarte Albuquerque, **Department of Mechanical and Industrial Engineering, UNIDEMI

**High-order Numerical Methods for Fluid Mechanics and “Marriage” with Machine-learning **

**Abstract:** This talk will show the results with high-order finite volume methods obtained in the HIBforMBP national project. These advances are presented from a numerical analysis point of view. Additionally, works that connect numerical methods and machine-learning will be presented. The talk intends to provide possible collaborations between the mathematical department and the professor’s research.

**14:15 – 14:30 **

**Magda Rebelo, **Department of Mathematics, NOVA MATH

**Fractional Calculus and Applications**

**Abstract:** Fractional calculus, a branch of mathematics dealing with derivatives and integrals of non-integer orders, has emerged as a powerful tool for modeling complex physical phenomena. This presentation focuses on two specific phenomena: anomalous diffusion and viscoelasticity. Anomalous diffusion, characterized by non-Gaussian and non-Fickian behaviors, challenges the conventional understanding of diffusion processes. On the other hand, viscoelasticity describes the time-dependent response of materials to external forces, encompassing both viscous and elastic properties.

The objective of this presentation is to explore the intricate relationship between these three fields and their applications in various scientific and engineering disciplines. We will delve into recent advancements in fractional calculus techniques that are specifically tailored for modeling anomalous diffusion processes, which classical diffusion equations fail to effectively capture. Furthermore, we will examine the integration of viscoelasticity into fractional calculus models, enabling a more precise representation of real-world systems with time-dependent responses.

Through the exploration of theoretical developments, numerical methods, and experimental investigations, we aim to shed light on the synergy between fractional calculus, anomalous diffusion, and viscoelasticity. This presentation welcomes researchers from diverse backgrounds, including mathematics, physics, mechanics, engineering, materials science, and biophysics, to explore the immense potential of these intertwined fields.

**14:30 – 15:00 **

**Discussion**