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“Liquid crystals” are a broad class of materials that sit between the solid/fluid dichotomy. To the naked eye they typically appear as fluids (“Liquid”), but are structured over molecular length scales (“Crystals”). Their obvious exposure comes from their use in LCD (Liquid Crystal Display) screens,…

The main goal of the lecture will be to give an overview of the problem studied in the field of kinetic equations. Those PDEs appear naturally in the modelling of systems composed by a large number of objects which are all subjected to the same…

Geometric modelling and computer-aided design (CAD) are fundamental disciplines to represent real-life objects in the digital world. In this course, we will discuss mathematical concepts of geometric modelling, particularly focusing on problems appearing in computer numerically controlled (CNC) machining. We introduce the basics of differential geometry…

In this course we present in detail the fundamentals of the theory of coarse-graining, explore different applications that range from thermodynamics of small systems to complex fluids (colloidal suspensions and other viscoelastic fluids), and describe particle-based simulation methodologies like DPD and SDPD for the simulation…

This course is devoted to the study of numerical techniques used for simulating dynamical systems, especially conservative systems such as those in celestial mechanics and molecular models. In a dynamical simulation, an integrator replaces a differential equation in continuous time by a difference equation defining…

This mini-course aims to provide an introduction to piecewise deterministic Markov processes (PDMP) applied to neuroscience. The PDMP formalism was introduced in the 1980s [2, 3], it is both simpler than the formalism of diffusion processes and, unlike the latter, PDMPs can directly be understood…