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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 analysismechanics of materialsmicromagneticsmodelling 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.

Introduction to sub-Riemannian geometry

The lectures will start around mid/late october. The final schedule will be published here and announced via the SISSA mailing list by the end of september/first week of october 2022.

The aim of this course is to provide an introduction to the geometry of sub-Riemannian manifolds, and to illustrate some research directions in this domain. References:

Advanced Topics in CFD

The course deals with a list of advanced topics in computational fluid dynamics. In the first part, the governing equations governing fluid dynamics problems are reviewed and derived. Both compressible and incompressible flows are considered. The basics of the finite volume methods for the numerical discretization of fluid dynamics problems are reviewed and discussed starting from the basic example of an advection-diffusion equation.

Topics in Continuum Mechanics

  • Reminders on linear algebra and tensor calculus
  • Kinematics of deformable bodies
  • Eulerian and Lagrangian descriptions of motion
  • Balance laws of continuum mechanics: conservation of mass, balance of linear and angular momentum, energy balance and dissipation inequality
  • Constitutive equations
  • Fluid dynamics: the Navier Stokes equations
  • Solid mechanics: nonlinear and linearized elasticity
  • Selected topics from the mechanics of biological systems

 Books:

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