Format (in-person or online) to be confirmed.
Registrations open 1st September 2021 via Eventbrite Annual student Colloquium – MAC-MIGS 2021 Tickets, Fri 24 Sep 2021 at 13:25 | Eventbrite
13:25 – 13:30 : Welcome and Introduction
13:30 – 14:15 : Dr. Olga Shishkina (University of Göttingen): “Scalings and structures in natural thermal convection”
Abstract:
Turbulent thermal convection which occurs due to the temperature differences imposed at the boundaries of the domain is omnipresent in nature in technology. In this talk, we will consider three classical setups, namely, Rayleigh-Benard convection, vertical convection, and horizontal convection. For these systems, we will discuss the scaling relations of the global heat and momentum transport, the proper boundary layer equations, and the large-scale flow organization. We will show that in some cases, the scaling of the global heat transport and the temperature profiles can be predicted by solving the proper boundary-layer equations that include turbulent fluctuations and correct boundary conditions. Further, we will discuss the global flow structures in turbulent Rayleigh-Benard convection in slender and wide containers. We will see that the self-organized turbulent flow takes the form of several convection rolls on top of each other if the container is slender or in a form of convection rolls that are attached to each other in a horizontal direction if the container is wide. The shape of these rolls strongly influences the global heat transport in the system. Finally, we will explain the reasons why the size of the self-organized rolls is quite restricted.
14:15 – 14:25 : Questions
14:25 – 14:30 : Break
14:30 – 15:15 : Prof. Philip K. Maini (University of Oxford): “Modelling collective cell movement in biology and medicine”
Abstract:
Collective cell movement is a common feature across biology. To give a few examples: in development, cells need to move to where they need to be; in wound healing, cells need to move into, and close, the wound; in cancer, cells move to invade normal tissue. In this lecture I will review our work in two of these areas – normal development and cancer – and present two different modelling approaches: coupled systems of partial differential equations, and hybrid agent-based modelling. We will use these approaches to show how cells of different phenotypes co-operate during collective movement and how simple mathematical models have led to new biological insights.
15:15 – 15:25 : Questions
15:25 – 15:30 : Break
15:30 – 16:15 : Prof. José A. Carrillo (University of Oxford): “The Landau equation as a Gradient flow”
Abstract:
The Landau equation introduced in the 1930’s is one of the most important partial differential equations in kinetic theory. It gives a description of colliding particles in plasma physics, and it can be formally derived as a limit of the Boltzmann equation when grazing collisions are dominant. The purpose of this talk is to propose a new perspective inspired from gradient flows for weak solutions of the spatially homogeneous Landau equation, which is in analogy with the relationship of the heat equation and the 2-Wasserstein metric gradient flow of the Boltzmann entropy. From the analytical viewpoint, we use the theory of metric measure spaces for the Landau equation by introducing a bespoke Landau distance. We show for a regularized version of the Landau equation that we can construct gradient flow solutions, curves of maximal slope, via the corresponding variational scheme. The main result obtained for the Landau equation shows that H-solutions with certain apriori estimates on moments and entropy dissipation are equivalent to gradient flow solutions of the Landau equation. Moreover, we can rigorously prove the grazing collision limit from Boltzmann to Landau via a Gamma-convergence approach using the gradient flow interpretation of the Boltzmann equation by Erbar. From the numerical viewpoint, we aim at using this interpretation to derive a deterministic particle method to solve efficiently the spatially homogeneous Landau equation. Our deterministic particle scheme preserves all the conserved quantities at the semidiscrete level for the spatially homogeneous Landau equation and is also entropy decreasing. We will illustrate the performance of these schemes with efficient computations using treecode and random-batch approaches for the 3D relevant Coulomb case.
This talk is based on a summary of works in collaboration with M. Delgadino, J. Hu, L. Wang, and J. Wu.
16:15 – 16:25 : Questions
16:25 – 16:30 : Closing remark
From 16:30 : Wine reception