Mathematical Analysis, Modelling, and Applications

The activity in mathematical analysis is mainly focussed on ordinary and partial differential equations, on dynamical systems, on the calculus of variations, and on control theory. Connections of these topics with differential geometry are also developed.The activity in mathematical modelling is oriented to subjects for which the main technical tools come from mathematical analysis. The present themes are multiscale analysis, mechanics of materials, micromagnetics, modelling of biological systems, and problems related to control theory.The applications of mathematics developed in this course are related to the numerical analysis of partial differential equations and of control problems. This activity is organized in collaboration with MathLab for the study of problems coming from the real world, from industrial applications, and from complex systems.

Beating of eukaryotic flagella via Hopf bifurcation of a system of stalled molecular motors

Anello I, Alouges F, De Simone A. Beating of eukaryotic flagella via Hopf bifurcation of a system of stalled molecular motors. European Journal of Mechanics - A/Solids [Internet]. 2025 ;114:105729. Available from: https://www.sciencedirect.com/science/article/pii/S0997753825001639

Water waves with vorticity

The water waves system was introduced by Euler in the 18th century to describe the motion of a fluid with a free surface under the action of gravity and surface tension, and it is still a very active research area in fluid dynamics. The unknowns of the problem are two time-dependent functions describing the velocity field of the fluid and the free-surface profile (giving the shape of the waves).

Read more about Water waves with vorticity

The Principle of Complementary Energy with a Spline-Based Stress Function

Read more about The Principle of Complementary Energy with a Spline-Based Stress Function

Models and applications in CFD

The course provides an introduction to the numerical simulation of incompressible flows at moderate values of the Reynolds number by using the open source C++ finite volume library OpenFOAM.

All lectures are at SISSA in room A-133 expect for Mon 16 June 2025 14:00 - 16:00 which is in room A-136.