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 …

In the design of practical combustion systems, ensuring safety and reliability is an important
requirement. For instance, reliably avoiding lean blowout, flame flashback or inlet unstart is …

We analyze the decay and instant regularization properties of the evolution semigroups
generated by two-dimensional drift-diffusion equations in which the scalar is advected by a …

We study diffusion and mixing in different linear fluid dynamics models, mainly related to
incompressible flows. In this setting, mixing is a purely advective effect that causes a transfer …

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 …

Chemotaxis plays a crucial role in a variety of processes in biology and ecology. In many
instances, processes involving chemical attraction take place in fluids. One of the most …

We study the problem of the optimal mixing of a passive scalar under the action of an
incompressible flow in two space dimensions. The scalar solves the continuity equation with …

We study the mixing and dissipation properties of the advection–diffusion equation with
diffusivity 0< κ ≪ 1 0< κ≪ 1 and advection by a class of random velocity fields on T^ d T d …

The chaotic dynamics of low-dimensional systems, such as Lorenz or Rössler flows, is
guided by the infinity of periodic orbits embedded in their strange attractors. Whether this is …

In 1959 Batchelor predicted that the stationary statistics of passive scalars advected in fluids
with small diffusivity k should display a power spectrum along an inertial range contained in …