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Thouless' quantization of adiabatic particle transport permits one to associate an integer topological charge with each atom of an electronically gapped material. If these charges are additive and independent of atomic positions, they provide a rigorous de ...
In this thesis we study stability from several viewpoints. After covering the practical importance, the rich history and the ever-growing list of manifestations of stability, we study the following. (i) (Statistical identification of stable dynamical syste ...
Recent theoretical advances, based on a combination of concepts from Thouless' topological theory of adiabatic charge transport and a newly introduced gauge-invariance principle for transport coefficients, have permitted to connect (and reconcile) Faraday' ...
Understanding the turbulent dynamics in the outermost region of the tokamak is essential to predict and control the heat and particle loads to the vessel wall, a crucial problem for the entire fusion program. In this thesis, the problem is approached via t ...
Dynamical systems are topologically equivalent when their orbits can be mapped onto each other via a homeomorphic change of coordinates. We will show that in general, closed-loop systems resulting from Linear Quadratic Optimal Control problems are all topo ...
Multiple mechanisms for extremely large magnetoresistance (XMR) found in many topologically nontrivial/trivial semimetals have been theoretically proposed, but experimentally it is unclear which mechanism is responsible in a particular sample. In this pape ...
Two dynamical systems are topologically equivalent when their phase-portraits can be morphed into each other by a homeomorphic coordinate transformation on the state space. The induced equivalence classes capture qualitative properties such as stability or ...
At the crossroads of the ethnography of scholarly practices and digital humanities, this study proposes to consider the exploratory aspect of the scientific activity as an intellectual path through a corpus made accessible by an online platform. My case st ...
Topological Weyl semimetals represent a novel class of nontrivial materials, where band crossings with linear dispersions take place at generic momenta across reciprocal space. These crossings give rise to low -energy properties akin to those of Weyl fermi ...
We define filter quotients of -categories and prove that filter quotients preserve the structure of an elementary -topos and in particular lift the filter quotient of the underlying elementary topos. We then specialize to the case of filter products of -ca ...
