From turbulence to landscapes: Logarithmic mean profiles in bounded complex systems

Unambiguous Logarithmic Space Bounded Computations

On the logarithmic region in wall turbulence

Considerable discussion over the past few years has been devoted to the question of whether the logarithmic region in wall turbulence is indeed universal. Here, we analyse recent experimental data in the Reynolds number range of nominally 2 × 104 < Reτ < 6 × 105 for boundary layers, pipe flow and the atmospheric surface layer, and show that, within experimental uncertainty, the data support the...

Logarithmic Correlation Functions in Two Dimensional Turbulence

We consider the correlation functions of two-dimensional turbulence in the presence and absence of a three-dimensional perturbation, by means of conformal field theory. In the persence of three dimensional perturbation, we show that in the strong coupling limit of a small scale random force, there is some logarithmic factor in the correlation functions of velocity stream functions. We show that...

How to Obtain Transience from Bounded Radial Mean Curvature

We show that Brownian motion on any unbounded submanifold P in an ambient manifold N with a pole p is transient if the following conditions are satisfied: The p-radial mean curvatures of P are sufficiently small outside a compact set and the p-radial sectional curvatures of N are sufficiently negative. The ‘sufficiency’ conditions are obtained via comparison with explicit transience criteria fo...

Building Innovation Systems for Managing Complex Landscapes

T his chapter guides development practitioners in fostering communication and learning to shape innovation systems for managing agriculture and natural resources across landscape systems and to jointly achieve sustainable production, ecosystem/biodiversity, and rural livelihood goals. This ecoagriculture landscape perspective accounts for the physical and biological features of an area together...