The topological properties of an object, associated with an integer called the topological
invariant, are global features that cannot change continuously but only through abrupt …

Turbulent flows are characterized by the non-linear cascades of energy and other inviscid
invariants across a huge range of scales, from where they are injected to where they are …

A variety of observations impose upper limits at the nano Gauss level on magnetic fields that
are coherent on inter-galactic scales while blazar observations indicate a lower bound∼ …

The universe is magnetized on all scales probed so far. On the largest scales, galaxies and
galaxy clusters host magnetic fields at the micro Gauss level coherent on scales up to ten …

We introduce a measure of the local density of chirality of the electromagnetic field. This
optical chirality determines the asymmetry in the rates of excitation between a small chiral …

This textbook presents a modern account of turbulence, one of the greatest challenges in
physics. The state-of-the-art is put into historical perspective five centuries after the first …

The first-order phase transition between two tetrahedral networks of different density—
introduced as a hypothesis to account for the anomalous behaviour of certain …

The discovery of coherent structures in turbulence has fostered the hope that the study of
vortices will lead to models and an understanding of turbulent flow, thereby solving or at …

The study of the dynamics of fluids is a central theme of modern applied mathematics. It is
used to model a vast range of physical phenomena and plays a vital role in science and …

In spite of its universality, mixing is poorly understood and generally speaking, mixing
problems are attacked on a case-by-case basis. This is the first book to present a unified …