相关论文: In--out intermittency in PDE and ODE models
Random metastability occurs when an externally forced or noisy system possesses more than one state of apparent equilibrium. This work investigates a class of random dynamical systems, arising from perturbing a one-dimensional piecewise…
The Sun's magnetic dynamo cycle features a distinct pattern: a propagating region of sunspot emergence appears around 30 degrees latitude and vanishes near the equator every 11 years. Moreover, longitudinal flows called "torsional…
A method for model reduction in nonlinear ODE systems is demonstrated through computational examples. The method does not require an implicit separation of time-scales in the fine dynamics to be effective. From the computational standpoint,…
A number of biological systems can be modeled by Markov chains. Recently, there has been an increasing concern about when biological systems modeled by Markov chains will perform a dynamic phenomenon called overshoot. In this article, we…
Intermittency (externally induced) in the two-dimensional (2D) enstrophy cascade is shown to be able to maintain a finite enstrophy along with a vorticity conservation anomaly. Intermittency mechanisms of three-dimensional (3D) energy…
A novel model of intermittency is presented in which the dynamics of the rates of energy transfer between successive steps in the energy cascade is described by a hierarchy of stochastic differential equations. The probability distribution…
We investigate the consequences of introducing non-uniform initial conditions in the dynamics of spin ensembles characterized by all-to-all interactions. Specifically, our study involves the preparation of a set of semi-classical spin…
Short abstract: We present fully 3-D simulations of supersonic, radiatively cooling intermittent jets with intermediate and long variability periods (that is, periods of the order of or longer than, the dynamical time scale of the jet).…
Modelling fluid turbulence using a `skeleton' of coherent structures has traditionally progressed by focusing on a few canonical laboratory experiments such as pipe flow and Taylor-Couette flow. We here consider the stratified inclined…
We study the long-term qualitative behavior of randomly perturbed dynamical systems. More specifically, we look at limit cycles of stochastic differential equations (SDE) with Markovian switching, in which the process switches at random…
The solar magnetic activity cycle has an amplitude that varies within a wide but limited range of values. This implies that there are nonlinear mechanisms that prevent runaway solutions. The purpose of this paper is to propose observable…
Non-interferometric experiments have been successfully employed to constrain models of spontaneous wave function collapse, which predict a violation of the quantum superposition principle for large systems. These experiments are grounded on…
We give a short introduction to the subject and review advances in understanding the basic ingredients of the mean-field dynamo theory. The discussion includes the recent analytic and numerical work in developments for the mean…
When complex systems are driven to extinction by some external factor, their non-stationary dynamics can present an intermittent behaviour between relative tranquility and burst of activity whose consequences are often catastrophic. To…
Helioseismology provides important constraints for the solar dynamo problem. However, the basic properties and even the depth of the dynamo process, which operates also in other stars, are unknown. Most of the dynamo models suggest that the…
Model order reduction in high-dimensional, nonlinear dynamical systems if often enabled through fast-slow timescale separation. One such approach involves identifying a low-dimensional slow manifold to which the state rapidly converges and…
The paper is concerned with the change of probability measures $\mu$ along non-random probability measure valued trajectories $\nu_t$, $t\in [-1,1]$. Typically solutions to non-linear PDEs, modeling spatial development as time progresses,…
We study intermittency as a departure from self-similarity of the solar wind magnetic turbulence and investigate the evolution with the heliocentric distance and latitude. We use data from the Ulysses spacecraft measured during two solar…
We present a general mechanism to establish the existence of diffusing orbits in a large class of nearly integrable Hamiltonian systems. Our approach relies on successive applications of the `outer dynamics' along homoclinic orbits to a…
Invariant manifolds are fundamental tools for describing and understanding nonlinear dynamics. In this paper, we present a theory of stable and unstable manifolds for infinite dimensional random dynamical systems generated by a class of…