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[PDE & Applications seminar] Sebastian Wieczorek: Rate-induced tipping in non-autonomous reaction-diffusion systems: An invariant manifold framework and shifting habitats

The mathematical modelling of tipping points - large and sudden changes in the state of a system that arise in response to small and slow changes in the external inputs - has mainly focused on ordinary differential equation (ODE) models. In this talk, I will begin with a brief overview of tipping points in ODEs. I will then consider reaction-diffusion equations (RDEs) with time-dependent (nonautonomous) and space-dependent (heterogenous) reaction terms that decay in space (asymptotically homogeneous). Such models are likely to exhibit new and interesting tipping mechanisms, but their analysis is more challenging and requires new techniques. As an illustrative example, we analyse a conceptual model of a habitat patch in one spatial dimension, that features an Allee effect in population growth and is geographically shrinking or shifting due to human activity and climate change. We identify two classes of tipping points to extinction: bifurcation-induced tipping (B-tipping) when the shrinking habitat falls below some critical length, and rate-induced tipping (R-tipping) when the shifting habitat exceeds some critical speed. To facilitate the analysis of tipping points in RDEs, such as the moving habitat model, we propose a new mathematical framework. This framework is underpinned by a special compactification of the moving-frame coordinate in conjunction with Lin’s method for constructing heteroclinic orbits along intersections of stable and unstable invariant manifolds of saddles. This allows us to (i) obtain multiple coexisting pulse and front solutions for the RDE by computing heteroclinic orbits connecting saddles from negative and positive infinity, (ii) detect tipping points as bifurcations of such heteroclinic orbits, and (iii) obtain two-parameter tipping diagrams by numerical continuation of such bifurcations.

[PDE&A] Anna Felden: : From the micro- to the km- scale: applications for every need with the AMR framework Chombo

This talk will be centered around applications developed with the LBNL’s Adaptive Mesh Refinement (AMR) framework Chombo. Chombo includes features that improve both scalability and accuracy that are not typically found in commercial software packages, e.g., parallel nonlinear implicit solvers and higher-order time integrators and discretizations. The AMR capability is particularly well suited to problems exhibiting a large range of spatial scales, such as the ones that will be discussed in this talk.

In a first part, I will discuss SUHMO, a 2D SUbglacial Hydrology MOdel.
Modeling subglacial hydrology is very challenging because of the large variety of subglacial elements which dynamically evolve over time -from channels to vast subglacial lakes. We handle the strong non-linearities present in the equations by resorting to an efficient non-linear Full Approximation Scheme (FAS-MG) algorithm. We accommodate the transition from unresolved to resolved elements with a novel diffusion-like term which enables to recover second-order convergence of all the variables of interest. After giving a brief overview of the context, I will outline the details of the algorithm and present convergence analysis results demonstrating its effectiveness.

I will then discuss HotChips, which is a Chombo-based solver for heat management in 3D stacked integrated circuit. 3D stacks consist of multiple layers of material with potentially large variations in thermal conductivity. Since Chombo is best suited for the Finite Volume (FV) method, flux reconstruction techniques that can handle material jumps and 2D heat sources are implemented. The efficiency of the solver is further increased by using anisotropic meshing, since material variations in the z-direction are predominant. The entire algorithm relies on the same efficient nonlinear FAS-MG scheme that could be easily extended to deal with temperature-dependent conductivities.
Examples of 3D simulation results of realistic chip layouts using HotChips are presented along with some comparisons with COMSOL Multiphysics.

Changing Publication Culture

Changing Publication Culture 08 oktober 2024 14:30 t/m 17:00 - Locatie: TU Delft, X | Zet in mijn agenda Register Publication is essential to the sharing of scientific knowledge. But the effectiveness of publishing is decreasing - scientists suffer under the ‘publish or perish’ culture; peer review becomes slower and more difficult; tenure committees still rely on outdated journal impact factors; and the costs of publishing are becoming unsustainable even for the wealthiest universities. Join this half-day event to discuss how we can develop a sustainable publication culture and policy at TU Delft and beyond. In this symposium, organised by the TU Delft Library together with representatives from different faculties, scholars and policymakers will share their perspectives on why a change of publication culture is needed, both from systemic as well as an individual perspective. All participants are invited to bring forward in an interactive session the publishing challenges they are currently facing. This symposium also marks the 5 years anniversary of TU Delft’s own open access publishing house: TU Delft Open Publishing - change maker in open access publishing. Experts will reflect on the national and international growing momentum for alternative publishing routes. Programme: 14:00 - 14:30 Doors open 14:30 - 14:35 Opening & welcome words 14:35 - 15:00 Keynote address 15:00 - 16:30 Panel discussion and interactive session 16:30 - 17:00 Panel discussion & closing 17:00 - 18:00 Drinks Confirmed speakers include: Prof. Dr. Martijn Warnier, full Professor of Complex System Design and head of the Multi-Actor Systems Department - Faculty of Technology, Policy and Management Prof.Dr.ir. Rinze Benedictus, Faculty of Aerospace Engineering, Department of Aerospace Structures and Materials Dr. Roberto Rocco de Campo, Associate Professor of Spatial Planning and Strategy, Department of Urbanism, Faculty of Architecture and the Built Environment Dr. Tahena Kuzniecow Bacchin, Associate Professor (tenured) of Urban Design and Critical Theory and Head of Research of the Section of Urban Design, Faculty of Architecture and the Built Environment Dr. Jason Moore, Assistant Professor, Faculty of Mechanical Engineering Dr. Claire Chassagne, Associate Professor in Environmental Fluid Mechanics, Faculty of Civil Engineering and Geosciences Just de Leeuwe, Publishing Advisor, TU Delft Library Margreet Nieborg, Director, University of Groningen Press Jeroen Sondervan, Programme Leader Open Scholarly Communication, Open Science NL Participation in this symposium is free of charge, but registration is mandatory.

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