A comprehensive review of spatiotemporal pattern formation in systems driven away from
equilibrium is presented, with emphasis on comparisons between theory and quantitative …

Investigating the dynamics of a network of oscillatory systems is a timely and urgent topic.
Phase synchronization has proven paradigmatic to study emergent collective behavior …

Scaling (power-type) laws reveal the fundamental property of the phenomena--self similarity.
Self-similar (scaling) phenomena repeat themselves in time and/or space. The property of …

Many phenomena in nature, engineering or society when seen at an intermediate distance,
in space or time, exhibit the remarkable property of self-similarity: they reproduce …

Perturbative renormalization group theory is developed as a unified tool for global
asymptotic analysis. With numerous examples, we illustrate its application to ordinary …

These introductory notes are about functional renormalization group equations and some of
their applications. It is emphasised that the applicability of this method extends well beyond …

We show with several examples that renormalization group (RG) theory can be used to
understand singular and reductive perturbation methods in a unified fashion. Amplitude …

We present a general method for studying long‐time asymptotics of nonlinear parabolic
partial differential equations. The method does not rely on a priori estimates such as the …

We propose a computationally efficient approach to multiscale simulation of polycrystalline
materials, based on the phase field crystal model. The order parameter describing the …

A bstract In this work we aim to gain qualitative insight on the far-from-equilibrium behavior
of the gluon plasma produced in the early stages of a heavy-ion collision. It was recently …