We study the contact process on scale-free inhomogeneous random graphs evolving according to a stationary dynamics, where the neighbourhood of each vertex is updated with a rate depending on its strength. We identify the full phase diagram of metastability exponents in dependence on the tail exponent of the degree distribution and the rate of updating. […]

(Pseudo)spectral methods are popular for solving a wide variety of differential equations and generic optimization problems. Due to favourable approximation properties, such as rapid convergence for smooth functions, they are particularly popular and effective for solving time-independent Schrödinger equations. For example, in the domain of molecular quantum physics, spectral and pseudospectral methods are the building […]

Branching Brownian motion, branching random walks, and the F-KPP equation have been the subject of intensive research during the last couple of decades. By means of Feynman-Kac and McKean formulas, the understanding of the maximal particles of the former two Markov processes is related to insights into the position of the front of the solution […]

The dilute Curie-Weiss model is the Ising model on a (dense) Erdös-Rényi graph G(N,p). It was introduced by Bovier and Gayrard in 1990s. There the authors showed that on the level of laws of large numbers the magnetization as well as the free energy behave as they do in the usual Curie-Weiss model (i.e. mean-field […]

This talk will provide a partial overview of how to model molecular observables and spectral responses. We shall start with the essential quantum mechanical concepts and formalisms that are used in theoretical chemistry and molecular physics. This will be followed by an illustration of the tools that are involved in numerical simulations in this context.