Tidlegare gjesteforelesninger og seminarer - Side 21

C*-algebra seminar by Gaute Schwartz (University of Oslo)

A peculiarity of nonlinear hyperbolic problems is that they must be interpreted as limits of second-order equations with vanishing viscosity. Despite not explicitly being present in the hyperbolic case, diffusion is needed, e. g., at discontinuities or to avoid the occurrence of nonphysical states. In the case of gas dynamics, for instance, dissipation corresponds to the production of thermodynamic entropy. To solve hyperbolic problems numerically, one needs to adapt these ideas to the discrete setting. Standard high-order methods, however, do not incorporate the appropriate amounts of artificial viscosity because these need to be chosen adaptively based on the solution. Among the high-resolution schemes capable of doing so are the recently proposed monolithic convex limiting (MCL) techniques [1] to be discussed in this talk. They offer a way to enforce physical admissibility, entropy stability, and discrete maximum principles for conservation laws. These methods can also be generalized to systems of balance laws in a well-balanced manner [2]. In addition to second-order finite element methods, extensions to high-order discontinuous Galerkin (DG) schemes shall also be presented [3]. Numerical examples for the so-called KPP problem, the nonconservative shallow water system, and the compressible Euler equations will be shown. An overview of MCL and other property-preserving methods can be found in our recently published book [4].

Duncan Watts, Postdoctoral Fellow at Institute of Theoretical Astrophysics, University of Oslo.

We prove that (logarithmic, Nygaard completed) prismatic and (logarithmic) syntomic cohomology are representable in the category of logarithmic motives. As an application, we immediately obtain Gysin maps for prismatic and syntomic cohomology, and we precisely identify their cofibers. In the second part of the talk we develop a descent technique that we call saturated descent, inspired by the work of Niziol on log K-theory. Using this, we prove crystalline comparison theorems for log prismatic cohomology, log Segal conjectures and log analogues of the Breuil-Kisin prismatic cohomology, from which we get Gysin maps for the A_inf cohomology.

By Tamara Hiltunen (University of Oulu Finland) and Emmanuel Serrano (Autonomous University of Barcelona, Spain)

By Khuong Van Dinh, AQUA, IBV

Jonas Thoen Faber, PhD student of Rosseland Centre for Solar Physics, University of Oslo.

Prof. Natalia Korolkova, University of St. Andrews

We combine a pressure correction scheme with interior penalty discontinuous Galerkin (dG) discretisation to solve the time-dependent Navier–Stokes equations. We prove unconditional energy stability and a priori error estimates for the velocity. With duality arguments, optimal L2 error rates are obtained. Convergence of the discrete pressure is also established.  Further, we propose a splitting scheme,  integrating the pressure correction approach, for the Cahn–Hilliard–Navier–Stokes system  The numerical analysis of dG combined with this scheme is discussed. Namely, we show well--posedness, stability, and error estimates. Numerical results with manufactured solutions display our theoretical findings, and a spinodal decomposition example portrays the robustness of our approach.

Tim Zimmermann, PhD student at the Institute of Theoretical Astrophysics, University of Oslo.

Daniela Sueldo is an Associate Professor at the Department of Biology, NTNU. Daniela’s research focus is deciphering the molecular mechanisms that lead to the execution and control of cell death in photosynthetic organisms as part of the response to environmental stress

Dr. Joachim Mossige, Dept. of Physics, UiO.

Traditional quantile estimators are not well-suited for data streams because the memory and computational time increase with the volume of data received from the stream. Incremental quantile estimators refer to a class of methods designed to maintain quantile estimates for data streams. These methods operate by making small updates to the estimate every time a new observation is received from the stream. In this presentation, I will introduce some of the incremental quantile estimators we have developed.

Your brain has its own waterscape: whether you are reading, thinking or sleeping, fluid flows through or around the brain tissue, clearing waste in the process. These biophysical processes are crucial for the well-being and function of the brain. In spite of their importance we understand them but little, and mathematical and computational modelling could play a crucial role in gaining new insight. In this talk, I will give an overview of mathematical, mechanical and numerical approaches to understand mechanisms underlying pulsatility, fluid flow and solute transport in the human brain. Topics include fluid-structure interactions, generalized poroelasticity, mixed finite element discretizations and preconditioning, uncertainty quantification, and optimal control.

Håkon Dahle, Researcher at the Institute of Theoretical Astrophysics, University of Oslo.

By Daniel Vaulot, emeritus senior scientist at the Roscoff Biological Station (CNRS, France)

Blake D. Sherwin, Professor of Cosmology and Astrophysics, DAMTP, University of Cambridge.

Glenn Starkman, Distinguished University Professor at Case Western Reserve University (US).

C*-algebra seminar by Jordy Timo van Velthoven (University of Vienna)

This is a half-day online workshop on the numerics and theory of conservation laws and fluid equations. Abstracts and Zoom link can be found here.

The Section 4 seminar for the Autumn of 2023 will be held on Mondays at 10:15–12:00 (see the schedule)

Aditi Bhatnagar, PhD student at Rosseland Centre for Solar Physics, Institute of Theoretical Astrophysics, University of Oslo.