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 …

This work reviews the present position of and surveys future perspectives in the physics of
chaotic advection: the field that emerged three decades ago at the intersection of fluid …

Mixing of initially distinct substances plays an important role in our daily lives as well as in
ecological and technological worlds. From the continuum point of view, which we adopt …

Chaotic advection has served as the paradigm for mixing in fluid flows with simple time
dependence. Its skeletal structure is based on analysis of invariant attracting and repelling …

Mixing is relevant to many areas of science and engineering, including the pharmaceutical
and food industries, oceanography, atmospheric sciences and civil engineering. In all these …

We address the challenge of optimal incompressible stirring to mix an initially
inhomogeneous distribution of passive tracers. As a quantitative measure of mixing we …

We construct universal mixers, incompressible flows that mix arbitrarily well general
solutions to the corresponding transport equation, in all dimensions. This mixing is …

Mixing and un-mixing by incompressible flows Page 1 DOI 10.4171/JEMS/709 J. Eur. Math.
Soc. 19, 1911–1948 c European Mathematical Society 2017 Yao Yao · Andrej Zlatoš Mixing …

We quantitatively study the interaction between diffusion and mixing in both the continuous,
and discrete time setting. In discrete time, we consider a mixing dynamical system …

Consider a diffusion-free passive scalar θ being mixed by an incompressible flow u on the
torus ${\mathbb T}^ d $. Our aim is to study how well this scalar can be mixed under an …