相关论文: In--out intermittency in PDE and ODE models

We introduce a model for the turbulent energy cascade aimed at studying the effect of dynamical scaling on intermittency. In particular, we show that by slowing down the energy transfer mechanism for fixed energy flux, intermittency…

We study axisymmetric mean-field dynamo models containing differential rotation, the $\alpha$ effect and the additional turbulent induction effects. The additional effects result from the combined action of rotation and an inhomogeneity of…

The existence of non-continuous invariant graphs (or strange non-chaotic attractors) in quasiperiodically forced systems has generated great interest, but there are still very few rigorous results about the properties of these objects. In…

Invariant manifolds are important sets arising in the stability theory of dynamical systems. In this article, we take a brief review of invariant sets. We provide some results regarding the existence of invariant lines and parabolas in…

Using simple kinematics, we propose a general theory of linear wave interactions between the interfacial waves of a two dimensional (2D), inviscid, multi-layered fluid system. The strength of our formalism is that one does not have to…

In chemical reactions, trajectories typically turn from reactants to products when crossing a dividing surface close to the normally hyperbolic invariant manifold (NHIM) given by the intersection of the stable and unstable manifolds of a…

This paper addresses structures of state space in quasiperiodically forced dynamical systems. We develop a theory of ergodic partition of state space in a class of measure-preserving and dissipative flows, which is a natural extension of…

For system of two ordinary differential equations of the second order representing autonomous non-conservative holonomic mechanical system, in case of dynamics such as one-frequency periodical oscillations, is found integrated invariant of…

In this paper some piecewise smooth perturbations of a three-dimensional differential system are considered. The existence of invariant manifolds filled by periodic orbits is obtained after suitable small perturbations of the original…

This article deals with invariant manifolds for infinite dimensional random dynamical systems with different time scales. Such a random system is generated by a coupled system of fast-slow stochastic evolutionary equations. Under suitable…

The aim of this paper is to explore the relationship between invariant cones and nonlinear normal modes in piecewise linear mechanical systems. As a key result, we extend the invariant cone concept, originally established for homogeneous…

Previous results have shown that a large class of complex systems consisting of many interacting heterogeneous phase oscillators exhibit an attracting invariant manifold. This result has enabled reduced analytic system descriptions from…

We study the mean orbital pseudo-metric for Polish dynamical systems and its connections with properties of the space of invariant measures. We give equivalent conditions for when the set of invariant measures generated by periodic points…

It is known that scale invariance is broken in the developed hydrodynamic turbulence due to intermittency, substantiating complexity of turbulent flows. Here we challenge the concept of broken scale invariance by establishing a hidden…

The stratified inclined duct (SID) sustains an exchange flow in a long, gently sloping duct as a model for continuously-forced density-stratified flows such as those found in estuaries. Experiments have shown that the emergence of…

We find strong evidence for intermittency in forced two dimensional (2D) turbulence in a flowing soap film experiment. In the forward enstrophy cascade the structure function scaling exponents are nearly indistinguishable from 3D studies.…

While invariant measures are widely employed to analyze physical systems when a direct study of pointwise trajectories is intractable, e.g., due to chaos or noise, they cannot uniquely identify the underlying dynamics. Our first result…

$PSP$ and $SolO$ data are utilized to investigate magnetic field intermittency in the solar wind (SW). Small-scale intermittency $(20-100d_{i})$ is observed to radially strengthen when methods relying on higher-order moments are considered…

We analyze the field theory of fully developed Burgers turbulence. Its key elements are shock fields, which characterize the singularity statistics of the velocity field. The shock fields enter an operator product expansion describing…

In natural settings, intermittent dynamics are ubiquitous and often arise from a coupling between external driving and spatial heterogeneities. A well-known example is the generation of transient, turbulent puffs of fluid through a pipe…