Static and dynamic properties of arcs near plane surfaces

Abstract

Abstract. Discrete multiplicative turbulent cascades are described using a formalism involving infinitely divisible random measures. This permits to consider the continuous limit of a cascade developed on a continuum of scales, and to provide the stochastic equations defining such processes, involving infinitely divisible stochastic integrals. Causal evolution laws are also given. This gives the first general stochastic equations which generate continuous multifractal measures or processes.

Reexamining the framework for intermittency in Lagrangian stochastic models for turbulent flows: A way to an original and versatile numerical approach

“…Numerous studies on data analysis of intermittency in turbulence reveal the multifractal nature of the pseudodissipation. The seminal work of Frisch [11] to characterize intermittency based on Kolmogorov theories was followed among others by [19,21,22,[36][37][38]. Combining all the properties of intermittency mentioned in their work, we suggest the following list of criteria for the pseudodissipation to exhibit intermittency.…”

“…( 9). Several models [19][20][21][22] are based on this formalism which allows one to combine the continuous vision of a cascade and a causal structure of the process. Specific properties of the stochastic integrals must be defined to ensure intermittency of the dissipation and we present them in the following section.…”

“…In their work, Schmitt and Marsan [19,38] developed the following causal stochastic process, inspired by this regular-ized process:…”

“…Causal and sequential multifractal stochastic processes were developed in response (see Refs. [18][19][20][21][22]). However, most of them rely on long-term memory stochastic processes and can be computationally expensive.…”

Irregular dynamics of cellular blood flow in a model microvessel

“…For increasing time derivatives m, the n 50 correlation disappears. This is an indicator of stochastic-like features, which thus entails stochastic elements for reduced-order modeling [100].…”