Narrow Results

We consider velocity structure functions in turbulence through an approach using cumulants, and for a fixed value of the distance ℓ. This allows to consider the cumulant generating function Φ_ℓ(q) = log〈|ΔV_ℓ|^q〉. Using an atmospheric turbulent database, we show that the cumulant generating function is nonanalytic, with a development compatible with a log-stable model of the form Φ_ℓ(q) = A_ℓq + B_ℓq^α and a parameter value of α = 1.5. The parameters A_ℓ, and B_ℓ are experimentally estimated: they are respectively increasing and decreasing functions of ℓ; their scaling ranges correspond to the scaling range of the velocity fluctuations. The dependence between these two functions is studied in relation to Extended Self Similarity and Generalized Extended Self Similarity properties.

Data from time lapse microscopy of live embryonic rat hippocampal neurons growing in cell culture are used to study the dynamics of axonal growth.¹ We analyze axonal trajectory data based on cells growing in a homogeneous medium. Due to the noisy nature of the data we develop filtering algorithms to smoothen out the paths while maintaining the underlying dynamics of the axon growth process. We analyze the new paths and propose a model for growth cone kinematics during axonogenesis without a gradient field. In this work we present a simple renewal process with the aim of reproducing certain path behaviors of the growth cone. Future development will include, renewal process simulation, and gradients effects.