Bielefeld University

The main goal of the present project is to make substantial contributions to the understanding of fundamental problems in the mathematical theory of fluid flows. This theory is formulated in terms of systems of nonlinear partial differential equations (PDEs). Major attention has been paid to the iconic example, the Navier-Stokes system for incompressible fluids, and the corresponding Millennium Problem. Despite joint efforts and a substantial progress for various models in fluid dynamics, fundamental questions concerning existence and uniqueness of solutions as well as long time behavior remain unsolved. This project is based on the conviction that a probabilistic description is indispensable in modeling of fluid flows to capture the chaotic behavior of deterministic systems after blow-up, and to describe model uncertainties due to high sensitivity to input data or parameter reduction. For a set of selected models, we investigate different aspects of the underlying deterministic and stochastic PDE dynamics. In particular, we are concerned with the question of solvability and well-posedness or alternatively ill-posedness. For some models including the incompressible stochastic Navier-Stokes system we investigate non-uniqueness in law. For the compressible counterpart we aim to prove existence of a unique ergodic invariant measure. The guiding theme of this research program is a core question in the field, namely, how to select physically relevant solutions to PDEs in fluid dynamics. The project lies at the challenging frontiers of PDE theory and probability theory and it will tackle several long standing open problems. The results will have an impact in the deterministic PDE theory, stochastic partial differential equations and from a wider perspective also in mathematical physics.

The transformation of China and Vietnam from centrally planned economies into today’s market economies has been fuelled by the labour of millions of migrant factory workers from rural areas. These countries started reforming at the turn of the 1980s, embracing marketisation while remaining under the Communist party’s political monopoly, a system now commonly termed market socialism. In what seems to be a reversal of the wider trends of austerity, there has been rapid expansion of social protection, much like what has been happening in other Global South contexts. While the shifts indicate state and societal responses to the social conflict and tension induced by marketization, they in turn have been foregrounded by the politics around how different groups of people should be cared for, politics that are part of wider moral struggles between actors in the new economy. Given their underclass status and their salience as a social force, the question of the migrant factory workers’ welfare is critical for the understanding of the on-going shifts in these countries’ welfare systems. WelfareStruggles is aimed at uncovering the politics of care underlying the provision of welfare for migrant factory workers in China and Vietnam. It does so through a comparative investigation that has two ground-breaking features: 1) the combination of ethnography with comparative social policy analysis, and 2) a translocal approach that takes into account the workers and their families’ negotiation for welfare across the city and the countryside. The comparison is expected to generate path-breaking knowledge about the variable moral dynamics of market socialist welfare. The knowledge will be essential for understanding the momentous yet little-known transformations of Global South welfare and has wider relevance to policy makers and organisations working with analysing and formulating solutions to the welfare needs of the migrant labour force in Vietnam, China and beyond.

Layered two-dimensional materials are novel quantum materials considered as the basis for future-generation electronics. The electronic and optical properties of such materials critically depend on so-called interlayer coupling – the interaction between the neighboring atomic layers within the material. What is of particular interest is that one can modulate this interlayer coupling, and thereby the material’s properties, by applying an electric field in the out-of-plane direction of the atomic layers. In this project, I focus on a typical semiconductor layered material called transition-metal dichalcogenides (TMDC). In TMDC, bandgap modulation with DC electric fields was recently achieved. However, the limitation of the modulation speed remains yet unclarified. In addition, the expected insulator-metal transition at the strong-field limit has not yet been realized because the required strong field causes a dielectric breakdown of the material. This project aims to (1) Realize ultrafast control of electronic properties of layered materials via direct ultrafast manipulation of interlayer coupling, (2) Identify the speed limitations to this controlling mechanism, and (3) Realize the insulator-metal transition in the layered material via the ultrafast control scheme. To investigate the ultrafast dynamics, I will utilize the terahertz technology, which enables us to apply a very short pulse of an electric field - a terahertz pulse - to the material and observe the change of its optical properties in an ultrafast timescale. A newly proposed micrometer-sized device, which converts an incident terahertz pulse to a strong out-of-plane electric field on TMDC, will enable ultrafast property control. The proposed scheme will be applicable for the ultrafast control of quantum phases in various layered-material systems. It is also expected to be applied as optoelectronic and all-optical ultrafast switches, which are important milestones for future ultrafast technologies.