A group theoretical approach to hydrodynamics considers hydrodynamics to be the
differential geometry of diffeomorphism groups. The principle of least action implies that the …

A review of classical percolation theory is presented, with an emphasis on novel
applications to statistical topography, turbulent diffusion, and heterogeneous media …

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 most widely used definitions of a vortex are not objective: they identify different
structures as vortices in frames that rotate relative to each other. Yet a frame-independent …

The dynamics of realistic Hamiltonian systems has unusual microscopic features that are
direct consequences of its fractional space-time structure and its phase space topology. The …

This book is a comprehensive and intensive monograph for scientists, engineers and
applied mathematicians, as well as graduate students in fluid dynamics. It starts with a brief …

We prove analytic criteria for the existence of finite-time attracting and repelling material
surfaces and lines in three-dimensional unsteady flows. The longest lived such structures …

Up-to-Date Coverage of the Navier–Stokes Equation from an Expert in Harmonic Analysis
The complete resolution of the Navier–Stokes equation—one of the Clay Millennium Prize …

On one level, this text can be viewed as suitable for a traditional course on ordinary
differential equations (ODEs). Since differential equations are the basis for models of any …

Chaos: from simple models to complex systems aims to guide science and engineering
students through chaos and nonlinear dynamics from classical examples to the most recent …