Scope:
This is the first edition of the Workshop in Complex Fluids and Solid Mechanics, to be held at the Centre of Mathematics of the University of Minho in the 2nd of June 2023.

Complex Fluids and Solid Mechanics are of great interest and relevance to scientific research, experimental technologies, and industrial applications. The study of such materials is an interdisciplinary field, and Mathematics plays a crucial role in understanding and explaining the behavior and properties of these complex structures.

This workshop brings together several researchers from different mathematical fields to present their recent contributions to the study of complex fluids and solids, including theoretical analysis, mathematical modeling, and computational approaches, both at the macroscopic and microscopic scales. The main goal of this workshop is to foster discussion and collaboration among mathematicians with diverse backgrounds and a common interest in solving problems related to materials exhibiting complex behavior and properties.

Organizers:
Ana Jacinta Soares and Lisa Santos (Group ANAP of CMAT)

Registration:
Registration for the workshop is free of charge but, for logistical reasons, it is mandatory and should be done by email to:
lisa(at)math.uminho.pt until May 15.

Anyone wishing to have lunch at the University's restaurant (for approximately 12 euros) must mention this in the message, so that we can do the booking for all.

Program

June 2nd 2023

09:30-10:20

Eduardo Abreu (Universidade Estadual de Campinas, Brasil) Numerical approximation of nonlinear hyperbolic models in fluid mechanics Numerical approximation of nonlinear hyperbolic models in fluid mechanics Abstract: Nonlinear hyperbolic conservation (balance) laws are relevant to the mathematical modeling in fluid mechanics, nonequilibrium thermodynamics and complex fluids. We will discuss via numerical analysis how new insights on the improved concept of no-flow curves/surfaces, in a Lagragian-Eulerian framework, are the key ingredients for numerical approximation of nonlinear hyperbolic problems in classical fluid mechanics. Indeed, the approach is more general. We will also present recent advances in the design of a new class of positive Lagrangian-Eulerian semi-discrete schemes for solving multidimensional systems of hyperbolic-transport problems in a range of applications in fluid dynamics.

10:30-10:55

Eurica Henriques (UTAD e CMAT) Some results for fluids exhibiting an anisotropic diffusion Some results for fluids exhibiting an anisotropic diffusion Abstract: In this talk we'll focus on the study of fluids whose diffusion process takes a different form in each space direction - known as anisotropic diffusion. Namely, we'll discuss the ongoing joint works for the singular anisotropic evolutionary pdes related to the porous medium equation and to the p-Laplacean equation.

11:00-11:25

coffee-break

11:30-11:55

Ana Jacinta Soares (CMAT-Univ. Minho) Fluid-kinetic modelling and applications of chemically reactive mixtures Fluid-kinetic modelling and applications of chemically reactive mixtures Abstract: TBA

12:00-12:25

Luís Ferrás (FEUP e CMAT) Elasticity and Fluid Dynamics: mathematical modeling of complex fluids Elasticity and Fluid Dynamics: mathematical modeling of complex fluids Abstract: In this work, we give a brief introduction to constitutive modelling and provide a generalisation of the Maxwell integral model by developing a new relaxation modulus based on the Mittag-Leffler function. The new model provides a better fit to linear experimental data compared to a classical 2-mode Maxwell model. The model is improved to become frame invariant and several analytical solutions are derived to better understand the behaviour of the model.

12:30-14:30

lunch

14:30-14:55

Célio Fernandes (CEFT-FEUP e CMAT-Univ. Minho) Equilibrium properties and bi-dimensional linear stability of detonation solutions Equilibrium properties and bi-dimensional linear stability of detonation solutions Abstract: This work focuses on a comprehensive examination of the dynamics and linear stability of a detonation wave solution in a binary reacting gas mixture with a symmetric reversible explosive chemical reaction A+A?B+B. The study involves a detailed mathematical analysis of the detonation model, including the determination of the equilibrium Chapman-Jouguet point and the steady detonation wave solution. Furthermore, a numerical analysis is conducted to investigate the sensitivity of the detonation solution to small variations in some key parameters, such as the activation energy of the chemical reaction rate. The formulation of the two-dimensional linear stability problem for the wave detonation structure is also provided, utilizing a normal-mode approach. Finally, numerical results are presented to illustrate the structure of the detonation wave and its corresponding stability spectrum.

15:00-15:25

Lisa Santos (CMAT, Univ. Minho) Problems with the operator $\nabla\times(\alpha\nabla\times\cdot)$ Problems with the operator $\nabla\times(\alpha\nabla\times\cdot)$ Abstract: (Ver anexo)

15:30-16:20

Ángel Arós (Universidade da Coruña, Espanha) Asymptotic analysis of some contact problems for elastic and viscoelastic shells Asymptotic analysis of some contact problems for elastic and viscoelastic shells Abstract: During the last years, the research in our group has been focused in the derivation and mathematical justification of reduced models for elastic and viscoelastic shells under contact conditions. These problems have a wide range of applications (take for example, contact problems on the hull of a ship, the roof of a building or the wall of a human blood vessel). The method of asymptotic expansions, introduced by Lions in 1973, has been applied since then in the deduction of reduced models for numerous problems in solid mechanics. In this communication, we will review the most important results that we have obtained using these methods. Last, we will overview the future work.

16:30-17:00

coffee-break